Insight Editions · No. 250
Time’s Arrow and Archimedes’ Point
New Directions for the Physics of Time
Huw Price
Price adopts the view from nowhen and argues that the arrows of time trace to one low-entropy boundary, that causal direction is a projection of agency, and that the future may constrain the past.
A study guide to Time’s Arrow and Archimedes’ Point by Huw Price. Shared free for personal reading; not for sale and not endorsed by the authors or publishers. Please read and buy the original.
Most errors about time's arrow come from failing to separate the world from our temporal viewpoint. From an atemporal "view from nowhen", the real puzzle is the low-entropy past, causal direction is perspectival, and microscopic time symmetry favours advanced action, which makes quantum mechanics local and Einsteinian.
Thermodynamics and Boltzmann, the radiative arrow and Wheeler–Feynman, big bang cosmology and Gold universes, μInnocence, the philosophy of causation and counterfactuals, Bell, GHZ and the interpretation of quantum mechanics; updated to 2026.
Boltzmann, Loschmidt, Burbury, Wheeler and Feynman, Gold, Penrose, Hawking, Davies, Reichenbach, Lewis, Dummett, Einstein, Bohr, Schrödinger, Bell, Bohm, Putnam, Cramer.
Readers who want the sharpest philosophical audit of how physics handles time, and the original case for retrocausal quantum mechanics.
The Book on One Page
Huw Price, a philosopher, argues that physics has not yet completed the oldest move in science: separating how the world is from how it looks from where we stand. Applied to time, that move shows that the physical arrows all trace to one unexplained low-entropy boundary, that causal direction is a projection of our nature as agents, and that once those are set aside, symmetry favours a world in which the future constrains the microscopic past.
- The method. Adopt the view from nowhen: assume the block universe (no objective present or flow), and test every argument about time's arrow by imagining time reversed. If you would reject the reversed argument, the original commits the double standard fallacy: it gets out exactly the asymmetry it put in.
- Thermodynamics (ch 2). Boltzmann's H-theorem smuggles in asymmetry via molecular chaos (PI3, independence of incoming influences). The deeper lesson, which Boltzmann half saw, is that high entropy is normal; what needs explaining is why entropy was low in the past. The "why does entropy increase?" project is largely a pseudo-problem.
- Radiation (ch 3). Outgoing waves look like a separate arrow, but reinterpreted Wheeler–Feynman mathematics shows emitters and absorbers are both centred on coherent waves. The asymmetry is that coherent sources clump (stars, galaxies) and sinks do not: the same low-entropy past again.
- Cosmology (ch 4). The arrows reduce to the smooth early universe. Explaining it with time-symmetric physics seems to demand a smooth big crunch too (Gold's universe): the basic dilemma. Inflation, Hawking's no-boundary proposal and the standard objections to Gold all slip in double standards.
- The hinge (ch 5). Physics assumes μInnocence, that micro-systems are uncorrelated before they interact. Unlike its macroscopic cousin it has no observational support, so it conflicts with T-symmetry. Quantum nonlocality and indeterminacy follow only from QM plus μInnocence.
- Causation (chs 6–7). No physical "third arrow" grounds causal direction: the fork asymmetry vanishes at the micro level. Causal and counterfactual asymmetry are perspectival, fixed by our orientation as agents. But conventionalism leaves an objective remainder: worlds where the inaccessible past depends on the future, advanced action, which bilking cannot refute when observation disturbs.
- Quantum mechanics (chs 8–9). Einstein's incompleteness view is underrated: Bell rules out only local hidden variables, and rivals are nonlocal too. Dropping Bell's independence assumption via a common future (not a conspiratorial common past) gives a local, realist, relativity-friendly account of Bell, GHZ and superposition, with free will intact.
| Ch | Title | One-line payload |
|---|---|---|
| 1 | The View from Nowhen | Separate the asymmetry of time from asymmetry in time; assume the block universe; beware the double standard. |
| 2 | "More Apt to Be Lost than Got" | The H-theorem shifts the problem; the real puzzle is the low-entropy past; high entropy needs no explanation. |
| 3 | New Light on the Arrow of Radiation | Radiation is micro-symmetric; the arrow is that sources clump and sinks do not. |
| 4 | Arrows and Errors in Contemporary Cosmology | The basic dilemma: explain a smooth bang without a smooth crunch, or accept Gold. |
| 5 | Innocence and Symmetry in Microphysics | μInnocence is unobserved and anti-symmetric; dropping it defuses quantum strangeness. |
| 6 | In Search of the Third Arrow | No physical arrow grounds causation; it is a projection of agency. |
| 7 | Convention Objectified and the Past Unlocked | Counterfactual asymmetry is conventional but forced; advanced action is its objective remainder. |
| 8 | Einstein's Issue | Survey of interpretations: Einstein's incompleteness view is underrated. |
| 9 | The Case for Advanced Action | A common future explains Bell and GHZ locally, with free will intact. |
| 10 | Overview | Conclusions, an agenda, and why the view from nowhen is worth having. |
The View from Nowhen
Price sets out the method of the whole book: the main errors in the physics of time come from failing to separate how the world is from how it looks to creatures who live inside time. To understand time's arrow we must imagine standing outside time, at an Archimedean point: the view from nowhen. From there, most of what we call the asymmetry of time turns out to be an asymmetry of things in time, and some of what physicists take for granted about causation turns out to be a projection of our own temporal standpoint.
Augustine (354–430) noticed that time is both utterly familiar and deeply mysterious: he knew what it was until somebody asked him. Price's questions are of the same everyday kind. What is the difference between past and future? Could the future affect the past? What gives time its direction or "arrow"? Could a universe be symmetric in time, and is ours? He writes as a philosopher, not as a physicist popularising his own field, and his stated goal is to remove the philosophical confusions that physicists commonly bring to these questions.
The diagnosis is single and sweeping. Physicists and philosophers alike pay too little attention to the temporal character of our own viewpoint. We are creatures in time, and that shapes how we think about time. The old scientific project of reaching the "view from nowhere" (Thomas Nagel's phrase for the untainted, Archimedean perspective) has never been properly extended to the temporal dimension. Price proposes to do that: to identify and quarantine the ways our thought reflects our temporal location, so that we can see how much of temporal asymmetry is objective and therefore needs a physical explanation.
The book works at two levels at once. It tries to get the physics of time asymmetry right, and it tries to characterise philosophically the view from nowhen: which features of the ordinary world survive when the temporal standpoint is removed and which were artefacts of it all along. The two tasks are one task, because the source of the physical errors is the asymmetry of our own perspective.
Perspective shifts in science
Price places his proposal in a long line of perspective shifts in which a familiar view is unmasked as local and self-centred. The great examples are the Copernican revolution (no privileged Earth), Darwinism (no privileged humanity) and the discovery of cosmological time (human history as a speck). His own shift is not in that league; it is hard to dehumanise further a world in which humanity is already so insignificant. But it has the same horizon-extending effect: our view of temporal structure is still distorted by the contingencies of our standpoint. In Wilfrid Sellars's terms, we have not yet separated the scientific image of time from the manifest image.
As in earlier cases, the constraint is largely self-imposed. "To notice the new standpoint is to be free to take it up", at least for physics. We cannot actually stand outside time, but we can imagine the physics of a creature who could.
Outline of the book
The book has a preliminary chapter and two main parts.
The plan of the book
- Chapter 1: preliminaries. Set aside the stock debates about time (the present, flow) by assuming the block universe; distinguish the asymmetry of time from asymmetry of things in time.
- Chapter 2: thermodynamics. The asymmetry of the second law and the first examples of the double standard fallacy; Boltzmann as an early exponent of the atemporal view; the real question is why entropy was low in the past.
- Chapter 3: radiation. Why waves spread outwards; critique of the Wheeler–Feynman absorber theory, whose mathematics is right but whose use is wrong; radiation's apparent asymmetry traces to the same source as thermodynamics.
- Chapter 4: cosmology. Cosmologists explain a low-entropy big bang with arguments that, applied consistently, would equally demand a low-entropy big crunch; the same mistakes as a century earlier.
- Chapter 5: microphysics. The intuition that interacting systems are uncorrelated before they meet (μInnocence) clashes with the symmetry of physics; dropping it would help quantum theory.
- Chapter 6: causation. Causal asymmetry cannot be reduced to any physical asymmetry; it is perspectival, a reflection of our position as agents who deliberate about the future from information about the past.
- Chapter 7: convention objectified. The perspectival view adds no new objective arrow, yet it leaves room for limited backward causation (advanced action).
- Chapter 8: quantum theory. Einstein's question, is quantum mechanics complete?, is still live; Bell's work did not settle it against him.
- Chapter 9: advanced action. Admitting backward influence removes the main obstacles to a classical, observer-free, local hidden-variable view.
- Chapter 10: overview.
The first part (chapters 2–4) treats the three places where temporal asymmetry appears in physics: thermodynamics, radiation and cosmology. In each the puzzle is why the world is asymmetric at all when the laws are very largely symmetric. The characteristic error is a double standard: an argument that would work equally in either temporal direction is applied in one direction only, and an asymmetric conclusion results. The asymmetry the theorist gets out is just the asymmetry he put in.
The second part turns to physics more generally, and to its most puzzling puzzle, the meaning of quantum theory. Price's bold claim is that the most promising interpretation has been almost entirely overlooked because physicists did not notice how far their picture of the world is a product of our asymmetric standpoint. Think about what microphysics we should expect, given what we know about the origins of time asymmetry, and quantum theory begins to look like exactly the kind of theory we should have expected. This path offers a far more classical view of quantum mechanics: it seems to dissolve nonlocality and to permit the interpretation Einstein wanted, with an objective world and no mysterious role for observers.
He anticipates the obvious objection: if such a solution existed, how could it have gone unnoticed? His answer is that the presuppositions it challenges, about causation and physical dependence, are so deeply embedded that we do not notice them, and when we do notice them, giving them up seems crazier than the bizarre alternatives quantum theory already offers. Only by approaching them from an angle unrelated to quantum theory, the physics of time asymmetry, do we find independent reason to give them up. Physicists often call the asymmetry of dependence "subjective" or "merely metaphysical", yet it keeps shaping which models they find intuitively acceptable.
The attack on that intuition has two prongs. Chapter 5 shows that it sits badly with the picture of time asymmetry developed in chapters 2–4. Chapters 6 and 7 investigate its origins: it cannot be reduced to the second law, because the physical asymmetries are macroscopic while our causal intuitions are just as firm about microphysics. Causal asymmetry is instead anthropocentric, rooted in our nature as deliberating agents. This has two satisfying consequences: causal asymmetry is not a further ingredient of reality, so it does not multiply the objective arrows; and it leaves room for a world in which, from our own standpoint, some present actions would properly be said to cause earlier effects. Physics, having rightly concluded that causal asymmetry is not physical, has failed to practise what it preaches by continuing to let that asymmetry constrain its models.
| Einstein's question | Usual verdict | Price's verdict |
|---|---|---|
| Is quantum mechanics a complete description? | Einstein lost to Bohr; Bell (1960s) drove in the last nail | Einstein's view is far less implausible than thought, even before advanced action |
| Can a local, objective reality underlie it? | No: Bell rules it out | Yes, if we admit limited backward causation, which symmetry actually favours |
On style, Price aims for clarity over rigour, warns that physicists will find his physics simplistic and philosophers his philosophy obscure, quarantines technical passages, and gives impatient readers a shortcut: start at chapter 5 and follow the arrows.
The stock philosophical debates about time
Much of Augustine would pass for twentieth-century philosophy of time. His two concerns remain the two standard debates:
- The status of the past–present–future distinction, and with it the reality of past and future (the past has ceased to exist, the future does not yet exist).
- The flow or passage of time.
Philosophers divide into two camps.
| Dynamic ("moving present") view | Block universe view |
|---|---|
| Passage is objective; the present is its leading edge | The present is perspectival, like "here" |
| Some (Augustine): only the present is real; others: past real, future not, so the present is reality coming into being | No ontological difference between past, present and future |
| Reality is a changing entity set in time | Reality is a single four-dimensional entity with time as an ingredient |
Price locates himself in the block tradition of D. C. Williams, J. J. C. Smart, Adolf Grünbaum and D. H. Mellor, and takes its conclusions as given. He warns against calling the block "static": that suggests a time frame in which the block stays the same. There is none; time is inside the block, so the block is neither static nor dynamic. It is not an entity in time at all.
The case against objective flow and an objective present
Price summarises the main arguments, which are philosophical rather than physical except for one.
Four arguments against objective passage
- The rate argument. If time flows, it makes sense to ask how fast. "One second per second" is not a rate: it is a dimensionless ratio. (One might as well say π flows at 3.14 seconds per second.)
- The direction argument (rarer, stronger). Any flow has a direction only relative to a choice of which way counts as positive. Saying the sun moves east to west or clock hands move clockwise already assumes the convention that the positive time axis points toward what we call the future. Without an objective ground for that convention there is no objective fact about which way time flows, nor whether reality is "growing" or "shrinking" at the edge of the present.
- The relativity argument. Combine Augustine's view that only the present is real with Einstein's special relativity, which denies objective simultaneity between distant events. Then what is real becomes observer-relative, and the distinctive claim that the content of the present is an objective feature of the world is lost.
- The linguistic diagnosis. Augustine's reasons were partly linguistic ("there are no dinosaurs"). But "dinosaurs do not exist" means "do not exist now". The basic notion is existence somewhen, just as "icebergs do not exist here in Sydney" presupposes the unqualified notion of existence somewhere. Tensed grammar builds a temporal qualifier into the simplest form and misleads us.
The most influential argument for objective flow is psychological: it seems to us that time flows, and the best explanation is that it does. Price replies with a mapping argument.
The block-universe twin. Suppose time really flows. Now imagine a world just like ours except that it is a four-dimensional block rather than a three-dimensional dynamic world. Map each event-at-a-time in the dynamic world onto an event-at-a-location in the block, including each of our mental states moment by moment. Our copies in the block would surely have exactly the experiences we have. So the experience of flow is not distinctive of a dynamic universe: things would seem this way even if we were elements of a block.
The moral is to explain the appearance without assuming it corresponds to reality, by finding a feature of the standpoint that accounts for it: rose-tinted spectacles explain why the world looks warm to those who wear them. Price will extend this kind of explanation from flow to causal and other temporal asymmetries.
Price explicitly assumes the block universe rather than defending it; he calls the case "very powerful, by philosophical standards" but not conclusive. Readers sympathetic to the A-theory (growing block, presentism, moving spotlight) may see the book's later results as a reductio of the block view rather than as support for it, and Price concedes that some will "take the point in reverse". The relativity argument in particular has well-known replies (privileged foliations, for example in Bohmian or some quantum-gravity frameworks).
The assumptions work mainly negatively: since there is no flow, Price will not explore the idea that flow gives time its direction.
The arrows of time
The phrase "asymmetry of time" suggests that time itself is asymmetric, but the interesting issues mostly concern the asymmetry of things in time.
The long dinner table. A long narrow table is set for a meal. Its contents might vary from end to end: meat at one end, vegetarian food at the other, steak knives only at one end, every fork pointing the same way. That is asymmetry on the table. Or the table itself might vary: wider at one end, or bounded at one end and infinite at the other (a Judgment Day feast with limited seating at the meat end). That is asymmetry of the table. Time is the table; the physical world is the setting. The arrows that puzzle physicists are almost all asymmetries of the setting.
Time itself could be asymmetric, for instance with an earliest moment but no latest, or (if flow made sense) in its flow. But the core questions concern the arrangement of the contents of the block along the time axis. Many processes show a marked temporal preference: buildings collapse into rubble, rubble never "uncollapses", which is why reversed films look absurd, even though the reverse process is equally consistent with the laws of mechanics.
Taxonomy and genealogy
The two problems of temporal asymmetry
- The taxonomy problem. Catalogue the distinct arrows (thermodynamic, radiative, cosmological, causal, psychological, and so on) and sort out their family relationships, including whether one "master arrow" underlies the rest. The leading candidate has long been the thermodynamic arrow.
- The genealogy problem. Explain why there is any significant asymmetry of things in time, given that the fundamental laws are (almost) time-symmetric: if a process is permitted, so is its reverse.
A first exercise in the atemporal style: the second law is usually stated as "the entropy of an isolated system never decreases". That statement presupposes that the positive time direction points toward what we call the future. Choose the opposite orientation and the law reads "entropy never increases". The objective fact is only that all isolated systems show an entropy gradient and that all the gradients slope the same way; whether they slope up or down is a matter of convention. From nowhen they go neither way.
Entropy curves of separate isolated systems: the objective fact is that the gradients are aligned; calling them "increases" depends on which way we point the time axis.
The kaon exception
There is one known exception to the time symmetry of fundamental laws: the decay of the neutral kaon, discovered in 1964 (by Christenson, Cronin, Fitch and Turlay), distinguishes past from future to a very tiny extent. Price sets it aside as a strategy: study the familiar arrows as if the laws were exactly symmetric, find where the puzzles lie, and only then ask whether the kaon could help. It is hard to see how so tiny and specialised an effect could explain buildings collapsing.
T-violation is now measured directly. CP violation (which, given CPT symmetry, implies T-violation) has since been found in B mesons (BaBar and Belle, 2001), and BaBar reported a direct observation of time-reversal violation in B-meson transitions in 2012. In 2025 the LHCb collaboration announced the first observation of CP violation in baryons (Λb decays). Neutrino experiments (T2K, NOvA) hint at CP violation in the lepton sector. None of this changes Price's point: these effects are tiny, microscopic and nowhere near large enough to explain the thermodynamic arrow, and the standard view remains that the macroscopic arrows come from boundary conditions, not from T-violating laws.
The puzzle of origins: the double standard
The most famous attempt at the genealogy problem is Ludwig Boltzmann's claim, in the second half of the nineteenth century, to derive the second law for gases from a statistical treatment of time-symmetric Newtonian mechanics. Critics soon noticed that he relied on a time-asymmetric assumption, the Stosszahlansatz or "assumption of molecular chaos". This is the prototype of a fallacy that will recur throughout the book.
The double standard fallacy (first statement)
- We want to explain an observed difference between past and future.
- We reason about the world using some principle P.
- Without noticing, we apply P in one temporal direction and not in the other.
- We derive an asymmetric conclusion.
- But the asymmetry of the conclusion is exactly the asymmetry built into the selective use of P. Unless that selective use is independently justified, nothing has been explained; the lump in the carpet has merely moved.
The fallacy is common not because physicists are dim but because temporal asymmetry is ingrained in our ways of thinking, so asymmetric presuppositions are hard to see. The cure is to stand in thought outside time and describe the world in atemporal terms. Price calls the book "a kind of self-help manual" for that Archimedean journey.
Two routes of anthropocentrism
History offers a template. Galileo's insight behind Newton's first law was that the friction-dominated world of everyday mechanics is not the universal natural condition: left alone, a moving body moves forever. In the same period came the distinction between primary and secondary qualities. Galileo wrote in 1623 that tastes, odours and colours "hold their residence solely in the sensitive body", so that if the animal were removed they would be annihilated. Physics concerns itself with the primary qualities, those not produced by our perceptual peculiarities, and the boundary moves as physics changes.
| Locational anthropocentrism | Constitutional anthropocentrism |
|---|---|
| We live in an exceptional region and mistake a local speciality for the norm | We project our own makeup onto the world |
| Geocentric gravity; ubiquitous friction | Colours, tastes, odours (secondary qualities) |
| Physicists readily accept that more such cases may come (our universe may be an unusual patch of something bigger) | Harder to swallow, since it challenges physics' image of itself as objective |
The two routes are not sharply separate, since our constitution is adapted to our region. Price's charge is that in its treatment of time asymmetry, physics still suffers from a constitutional distortion, rooted in one of the most basic facts about what kind of entities we are. If the history of science is a sequence of progressively more detached standpoints, physics has not yet reached the one needed here: an atemporal standpoint, a point outside time.
Both kinds of anthropocentrism will appear. The low-entropy past is plausibly locational (we live in an unusual region of the universe's history). The asymmetry of causation and dependence is constitutional (it reflects our nature as agents). Price's distinctive claim is that the second has gone unnoticed in physics and has quietly ruled out the best interpretation of quantum mechanics.
How to use the method. Whenever an explanation produces an asymmetry, ask: would the same reasoning, run in the other temporal direction, yield the mirror conclusion? If yes, and the reasoner accepts it in only one direction, look for the hidden double standard. The same audit works for any model trained or reasoned only "forwards": it may simply be recording the direction it was given.
"More Apt to Be Lost than Got": The Lessons of the Second Law
The second law is the most famous arrow in physics, and the nineteenth-century attempt to ground it in symmetric mechanics produced the first examples of the double standard. Price argues that the debate has always looked at the wrong end of the entropy gradient. What needs explaining is not why entropy goes up toward the future but why it was so low in the past; high entropy is the natural condition of matter and needs no explanation. Boltzmann nearly saw this; his successors mostly did not.
Irreversibility discovered: Newton to Boltzmann
Science is selective about what it explains. Phenomena can go unnoticed until a theory makes them problematic, and the reverse can also happen: science can decide that something once thought to need explanation does not. Irreversibility seems too obvious to be "discovered" (historian Stephen Brush: it is hard to conceive of a time when people did not know heat flows from hot to cold), but irreversibility is a contrast notion. Science could not notice it as a problem until it had a picture of reversibility, and that came with Newtonian mechanics.
Newton himself was interested in dissipation, in connection with whether a mechanical universe needs divine top-ups: motion, he wrote, "is much more apt to be lost than got, and is always upon the decay" (the chapter's title). By the late eighteenth century science knew many processes that never run backwards: diffusion of gases, frictional dissipation, heat flow from warm to cold. A general principle was slow to come, perhaps because irreversibility is so familiar.
- 1788 John Hunter: heat tends to diffuse itself equally until bodies reach the same temperature (earliest general statement Brush records).
- 1852 William Thomson (Lord Kelvin): "a universal tendency in nature to the dissipation of mechanical energy".
- 1865 Rudolf Clausius: "the universal tendency of entropy to increase", the first modern statement of the second law.
- 1867 James Clerk Maxwell, "On the Dynamical Theory of Gases": derives the equilibrium velocity distribution.
- late 1860s Maxwell's demon; Maxwell, Thomson and P. G. Tait see that every approach to equilibrium has a reversed twin.
- 1872 Boltzmann's H-theorem (quantity first called E).
- 1876–77 Loschmidt's reversibility objection; Boltzmann's statistical reply and his "peculiar consequence" note.
- 1889 Poincaré's recurrence theorem.
- 1894–95 Debate in Nature, opened by Edward Culverwell (Trinity College Dublin); S. H. Burbury's contributions.
- 1895–96 Zermelo's recurrence objection; Boltzmann's symmetric, anthropic view.
Thermodynamics introduced the notion of equilibrium, the state a system tends toward when left alone. Price notes that this is an asymmetric notion at first sight: it concerns what will happen to a system, not what happened to it. After a brief mid-century calm in which thermodynamics could be treated as an autonomous science, the kinetic theory of heat (heat as molecular motion) and its statistical extensions made it impossible to deny that thermodynamic phenomena are the mechanical behaviour of microscopic constituents. The conflict became unavoidable: irreversible phenomena from reversible laws.
Maxwell's independence assumption
Maxwell argued that a gas with his velocity distribution will not depart from it (and informally that no other distribution has this property); since equilibrium is by definition stable, equilibrium is the Maxwell distribution. The argument assumed that the number of collisions between molecules of velocities v₁ and v₂ is proportional to the product of the numbers having each velocity. If 1 in 1,000 molecules has v₁ and 1 in 1,000 has v₂, then 1 in 1,000,000 collisions involves that pair: the velocities of colliding molecules are independent. It looks harmless; it carries the whole asymmetry.
Boltzmann's H-theorem
Ludwig Boltzmann (1844–1906) divided velocities into tiny intervals and tracked how collisions shift molecules among them. He defined a quantity, later called H, and argued:
- H takes its minimum when the gas has the Maxwell distribution.
- If the gas is not in the Maxwell distribution, collisions make H always decrease with time.
Together these say the gas will not leave the Maxwell distribution and will tend to it if not there: exactly the definition of equilibrium. For a gas in equilibrium, H equals minus Clausius's entropy, so H generalises entropy, and the theorem amounts to a proof of the second law for gases: entropy always increases.
But the underlying mechanics is time-symmetric. The asymmetric conclusion comes from an asymmetric input: the Stosszahlansatz, or assumption of molecular chaos, which is Maxwell's independence assumption. Colliding particles are no more or less likely to have a given pair of velocities because they are about to collide.
PI3: the Principle of the Independence of Incoming Influences
- Statement. Systems (particles, influences) that come together to interact are uncorrelated before the interaction, unless they have interacted in the past.
- Its mirror. We expect the outgoing products of an interaction to be correlated with one another, even if they never meet again.
- Why it is asymmetric. Read in reverse, outgoing products become incoming ones, and they are correlated. We apply independence to one temporal side of interactions only.
- Its role. It is the main form in which asymmetry slips unnoticed into explanations of the arrows. Price flags it for later: its microphysical cousin, μInnocence, will be challenged in chapter 5.
So the H-theorem does not explain the second law's asymmetry; it shifts the problem to the asymmetry of the Stosszahlansatz. Shifting is not useless: tracing asymmetry from less basic to more basic manifestations is exactly the job. The danger is overlooking the problem in its new form.
The atemporal reformulation makes the shift visible. The question is not "why does entropy increase?" (from the reverse perspective it would be "why does it always decrease?") but the common factor: why is entropy uniformly higher in one direction than the other? Boltzmann's answer then reads "because there is molecular chaos in one direction and not the other", and the lump in the carpet has plainly just moved.
The reversibility objection I
Statistical treatments implied that the second law cannot be exceptionless: violations are improbable, not impossible. Maxwell's demon, a creature that sorts fast from slow molecules to make one side hot and the other cold, makes the point that what it does might happen by accident. And for any gas approaching equilibrium there is another departing from it: the same gas with every molecular velocity exactly reversed, which by Newtonian determinism retraces its path. Maxwell, Thomson and Tait, and independently Franz Loschmidt in Vienna, saw this.
Tradition credits Boltzmann with the ironic retort "Go ahead and reverse them!" Price offers an irony-proof version: given no objective direction of time, nothing need be reversed. Every actual case of entropy increase is equally a case of entropy decrease; it is objectively just an entropy difference over time. Counterexamples are not merely possible (like winning the lottery ten times running); they are all around us.
Historically, Maxwell, Thomson and Loschmidt read the objection as an attack on the law's universality, not on the claim to have derived asymmetry. Boltzmann partly saw the deeper point. In replying to Loschmidt (1877) he noted a "peculiar consequence": following the world into the infinitely distant past, it is just as probable that we would reach a state with no temperature differences as it is in the distant future.
Entropy as probability
Boltzmann's new conception: a macrostate (a description in ordinary, macroscopic terms) can be realised by many microstates (arrangements of molecules), and macrostates differ enormously in how many.
Two chambers and a thousand coins. Gas fills two connected, equal chambers: 52% in A, 48% in B is realised by an astronomical number of molecular arrangements; 99% in A by comparatively few. It is the same as tossing a coin 1,000 times: there are vastly more ways to get 500 heads than 5 heads. If all microstates are equally likely, the gas spends almost all its time in the macrostates with most realisations. These are the equilibrium states, and entropy measures a macrostate's probability in microstate-counting terms. Entropy tends to increase because from any starting point there are far more microstates leading to higher-entropy macrostates.
This builds in the statistical character of the law and seems to bypass the H-theorem and molecular chaos. Where, then, does the asymmetry come from? Nowhere: as Boltzmann saw, the counting argument is symmetric. At any moment there are far more possible histories in which entropy was higher in the past, just as there are far more futures in which it is higher. Find the gas unevenly distributed, and the statistics predict it was more even a moment ago as well as more even a moment hence. The argument counts combinations and knows nothing of time's direction.
Boltzmann's decisive advance was to see that the statistical treatment makes it deeply puzzling why entropy is not higher in the past, and in fact why it was even lower than now.
The reversibility objection II
About a decade later Edward Culverwell revived the objection in its deeper form: how can an asymmetric conclusion, even a statistical one, come from symmetric classical mechanics? (His own fix was an asymmetric effect of the aether on matter.) The resulting correspondence in Nature in 1894–95 (alongside, Price notes, a series of letters on cannibalism in snakes) shows how hard it is to keep one's eye on the ball.
S. H. Burbury, one of the sharpest contributors, saw the role of the independence assumption, but framed the problem as whether independence continues to hold once molecules have begun colliding, since previous collisions might correlate future collision partners. That worry accepts that molecules are uncorrelated before they first interact; it does not question PI3 itself. Burbury's positive suggestion: real systems receive disturbances from without, "coming at haphazard", which produce the distribution needed for H to fall.
The environment move, and why it fails. Appeals to external perturbation remain popular a century later. But the assumption that incoming disturbances "come at haphazard" is itself an instance of PI3. Nobody applies it in reverse: we assume the minute influences a system exerts on its environment are correlated, reflecting their common origin. View the same events in reverse and those correlated influences are the incoming ones. By what right do we assume Burbury's disturbances "go at haphazard" in the other direction? Price notes that the point was missed in the 1890s, rarely made since, and missed even by Boltzmann.
Boltzmann's own reply to Burbury was that gas molecules travel far between collisions compared to their mean spacing, so they rarely collide with recent partners and prior correlations are negligible. That also ignores the basic asymmetry of the independence assumption. And, ironically, Boltzmann's own symmetric statistical view meant he did not need to defend the H-theorem at all.
Boltzmann's symmetric view
The statistical approach brings two unwelcome consequences:
- To the extent it explains entropy increase toward the future, it predicts increase toward the past too.
- Since all microstates are equally probable, the present low-entropy state is itself highly improbable, and the even lower past state more so.
In 1889 Henri Poincaré proved the recurrence theorem: under general conditions a bounded system will eventually return arbitrarily close to any state it has occupied, including very low-entropy states. In 1896 Ernst Zermelo argued that this is incompatible with a mechanical account of thermodynamic asymmetry. Price notes that this merely confirmed what Boltzmann had conceded in the 1870s: improbable outcomes become likely given enough time. But it spurred Boltzmann's most audacious proposal.
Boltzmann's fluctuation hypothesis (1895–96)
- The universe as a whole is in, or near, thermal equilibrium almost all the time, and is vast in space and time.
- Fluctuations to lower entropy occur at random; the deeper the dip, the far rarer it is.
- In a large enough universe, regions as ordered as ours are inevitable. What needs explaining is only that we find ourselves in one.
- Anthropic step: life needs a low-entropy environment (life on Earth depends on the Sun as a low-entropy hot spot), so observers can only exist in such regions. Compare: it is unsurprising that we live on a planet's surface, though such places are rare.
- Direction step: our sense of past and future depends on the entropy gradient, so creatures on a slope will always call the direction of increase "the future".
- On the other slope of a fluctuation, or elsewhere, creatures would have the opposite orientation, and there would be no fact about who is right.
Boltzmann's picture: an eternal equilibrium with rare fluctuations. Observers on either slope of a dip take the uphill direction as their future.
Price praises the proposal as a great advance: it explains apparent asymmetry by a hypothesis symmetric on the large scale, and it treats the direction of time as an appearance, a product of our orientation in time, not an objective matter. Few successors matched it.
Why the fluctuation picture fails
Three objections to Boltzmann's hypothesis
- The cheapest-fluctuation problem. The most probable way to reach a given entropy below the maximum is at or near a minimum of the curve. If our region evolved naturally from a still lower-entropy past, it is far more improbable than it needs to be. Compare (1) a fluctuation down to the very low-entropy state from which our world supposedly evolved, with (2) a fluctuation that produces the world from scratch in its present condition. Option (2) is overwhelmingly more probable, by definition of entropy. So our records and memories are almost certainly misleading, products of the fluctuation itself; our real past is a mirror image of our future, a rise from equilibrium. It is no use protesting that (2) needs "miraculous" correlations; (1) needs far more.
- The spatial version. By the same logic we should expect the low-entropy region to be no larger than we already know. It would be cheaper to produce pictures of galaxies than galaxies. Yet astronomy now sees vastly more than in Boltzmann's day, and order extends as far as we can see.
- Cosmology. Twentieth-century cosmology suggests the universe is not old enough for fluctuations of the required size, and offers an alternative account of the low-entropy past (chapter 4), making the hypothesis both implausible and unnecessary.
Boltzmann brains and the Past Hypothesis. Objection 1 is now called the Boltzmann brain problem: in a universe dominated by fluctuations, lone observers with false memories vastly outnumber evolved ones. It became a live constraint on cosmology after dark energy (1998): a universe that approaches eternal de Sitter space could generate such fluctuations forever (Albrecht and Sorbo 2004; Dyson, Kleban and Susskind 2002; Page; Carroll's "cognitive instability" argument). The positive lesson Price draws, that an extra low-entropy boundary condition is needed, was named the Past Hypothesis by David Albert (Time and Chance, 2000) and built into the "Mentaculus" of Albert and Barry Loewer: dynamical laws plus the Past Hypothesis plus a statistical postulate (uniform probability over compatible microstates). Live debates since: whether the Past Hypothesis is a law (Loewer, Callender) or a brute fact; Eddy Keming Chen's "Wentaculus" (2020s), which takes the initial state as a low-entropy density matrix and makes the Past Hypothesis part of quantum law; and Carroll–Chen (2004) style models in which baby universes spawn from a high-entropy background, giving entropy gradients in both directions with no special initial moment.
The lesson for the modern debate: the main task is to explain why the universe is so far from equilibrium, and was further still in the past. Boltzmann's anthropic point, that our calling that direction "the past" is explained by its low entropy, has not been refuted. The difference from Boltzmann is that his account needed nothing beyond the statistical premise (all microstates equally likely). Its failure means a satisfactory explanation needs an extra ingredient: some additional constraint that makes the universe start this way, not just a lucky accident. That extra ingredient, Price warns, makes a big difference to whether we can still apply the statistical argument toward the future.
Do we need to explain why entropy increases?
Price's most provocative thesis. Suppose we had explained why entropy is low in the past, why the curve slopes down in that direction. Is there a separate question why it slopes up in the other? Almost everyone, from Boltzmann and his critics to modern writers, has assumed so; that is what a sound H-theorem was supposed to supply.
Watching the universe in reverse. From the reverse perspective, entropy is high in the past and always decreases. That decrease would be adequately explained if a law imposed a low-entropy boundary condition at some point in the future: each local decrease is a contribution to the required general decrease. Would we need to explain why entropy is high in the (reversed) past? No: by the statistics, that is the unexceptional way for things to be. But if this is a satisfactory account of the reversed view, it is a satisfactory account of the view we actually have, because the two differ only in perspective, not in the facts.
The conclusion applies to individual processes as well as to the law.
The beer bottle. Open a bottle of beer and pressurised gas escapes. Tradition says this needs explaining. The gas escapes because its microstate is one in which, when the bottle is opened, that is what happens. One then asks why the microstate is like that; Price answers that it needs no explanation: such microstates are overwhelmingly the natural ones. What is unusual is that the microstate is such that, viewed in reverse, the gas enters the bottle; in the ordinary time sense, that is just the question of how the gas got into the bottle in the first place.
Our ordinary notion of explanation runs past to future, earlier conditions "giving rise to" later ones, and there is no reason to expect that asymmetry to survive the atemporal standpoint. Two features of explanation plausibly do survive:
- Explanatory priority. Some things explain others because they are more basic in theory.
- Normalcy. Things need explaining the more they depart from their natural condition; science can revise what counts as natural, as Galileo and Newton did for motion.
The nineteenth century revealed that thermodynamic equilibrium is the natural condition of matter. Departures from it need explanation, and our world shows a huge, apparently monotonic departure toward what we call the past. A high-entropy future is the natural condition and calls for no explanation in that sense. Together with the low-entropy past it accounts for the whole gradient. The puzzle is the starting point of the journey, not its destination.
If it's Galway you're after, why the devil are you leaving from here?The Irishman of comic fame, asked for directions
The role of the H-theorem
This is controversial because it rejects a century-old project. Even critics who complain that the Stosszahlansatz is asymmetric see that as a difficulty for a worthwhile project: almost everyone wants a dynamical explanation of why entropy always goes up. Price's verdict: "the H-theorem has its eyes set to the future, while all the interesting action is actually in the past." It tries to explain what needs no explanation and leaves the real puzzle untouched.
The attention lavished on the theorem's asymmetric assumptions (the Stosszahlansatz, PI3) treats them as the source of the arrow. What is puzzling is not that they hold toward the future but that they fail in reverse; if they held in reverse, the theorem would "prove" that entropy increases toward the past too. A statistically natural world would be one where the assumptions held in both directions, not one where they held in neither.
A legitimate, descriptive role
Price keeps a role for the theorem. Characterising the endpoints of a gradient is one task; describing how systems get from one end to the other is another. The second, local project is legitimately asymmetric: it concerns systems constrained in one direction but not the other. On this reading the H-theorem and its descendants describe behaviour on the gradient given that there is one, not why there is one.
- Compatible with the atemporal view. It describes the most probable path between A and B, not "from A to B".
- PI3 becomes harmless. It is a default assumption, held other things being equal; if it fails in some case, we ask why.
Why PI3 cannot be an explanation
Can the needed asymmetric assumption be stated non-circularly? Price doubts it. We want a condition on the constituents of matter that is necessary and sufficient for entropy to increase: if not sufficient, the explanation is incomplete; if not necessary, it is not the condition whose failure in reverse lets entropy go down. That seems to collapse into the trivial condition that matter is arranged so that entropy increases.
Horwich's initial randomness. In Asymmetries in Time (1987), Paul Horwich proposes that the second law is explained by the randomness of the universe's initial microstate, while the final microstate must be highly correlated, being the deterministic product of a low-entropy start. Price's reply:
- Nobody would say the universe has an ordered initial state because its final microstate is highly correlated.
- If there is an explanation either way here, it runs from the early ordered macrostate to the late correlated microstate; more accurately, these are two descriptions of one fact.
- But then by what right does an initial microstate explain a final macrostate? Only by the habit that the past explains the future, which cannot be assumed when temporal asymmetry is what we are explaining.
- So there is no substantial explanation in either direction. The requirement that initial conditions satisfy for entropy to rise is just the requirement that final conditions fail to satisfy given that entropy falls toward the past: initial conditions are not correlated so as to make entropy decrease. That is a redescription, not an explanation.
Does chaos theory make a difference?
The Brussels School of Ilya Prigogine (Nobel chemistry, 1977, for non-equilibrium thermodynamics) claims that nonlinear dynamics and chaos resolve the conflict between thermodynamics and mechanics through "symmetry-breaking". Price's answer has two parts: such methods may describe systems on the gradient, but they do not explain how the gradient arose; and they fall to a sharp version of the reversibility objection.
The t + 1 challenge. Describe a system to which the new method applies, giving its state at time t. Ask its proponents for the state at t + 1, without saying whether t + 1 is earlier or later than t in the real world.
- If they can answer without that information, the theory is time-symmetric: it gives the same result in both directions, so no asymmetry emerges.
- If they need the information, the theory treats the directions differently somewhere, slipping asymmetry in at the start, like the original H-theorem.
Either way there is no "symmetry-breaking": no theory of a system's evolution can give different results for the two temporal directions unless it treats them differently in the first place.
Prigogine's programme. Price's dismissal is shared by most philosophers of physics (Sklar, Bricmont, Lebowitz), who see Prigogine's "intrinsic irreversibility" as importing asymmetry through the choice of forward-in-time semigroup evolution or initial-condition restrictions. Prigogine's defenders argued that the restriction is to physically realisable states, not an arbitrary choice; on Price's analysis, that restriction is precisely where the asymmetry enters. The programme has had little influence on mainstream foundations since Prigogine's death in 2003.
Branch systems
The second law governs the universe and also countless subsystems, many isolated for long periods. Why are their entropy changes all aligned? (Hans Reichenbach called these "branch systems".)
- Burbury-style answer: no branch system is truly isolated, so random external influences drive it. Against this: the coffee and milk would still mix if perfectly isolated; and the needed notion of randomness is either an instance of PI3 or vacuous.
- Direct appeal to randomness: assume initial conditions in branch systems are such that entropy increases. Lawrence Sklar objects that this merely posits the parallelism; he adds that the low-entropy Big Bang does not explain it either.
Price disagrees with Sklar's second claim, provided we pose the question in reverse.
Why does entropy in branch systems always decrease toward the past? Because almost all the low-entropy systems we meet owe their condition, ultimately, to the state of the universe very early in its history. "They have all escaped from the same bottle", which explains why they all approach it as we trace them back. That they all move away from the bottle toward the future is the same fact redescribed. There is no separate problem of why branch-system entropy rises; only the big problem of why everything was in the bottle.
Branch systems inherit their low entropy from one early boundary condition; their aligned gradients need no separate explanation.
A real follow-up question remains: why is there no corresponding constraint in the future, which would produce entropy-reducing systems? That is a question about cosmological constraints on the universe at large, not about dynamical behaviour of individual systems, and it does not threaten the lesson that high-entropy states are normal.
Could entropy eventually decrease?
Would a future low-entropy constraint require an immensely unlikely future? Yes, but the significance of that depends on how we explain the low-entropy past.
- On Boltzmann's view, the low-entropy past is explained by the statistical hypothesis; our region is the kind of rare fluctuation the hypothesis predicts. Future decrease is then also bound to happen eventually, but on timescales so vast that no region relevant to us will see it.
- If Boltzmann is rejected and some additional principle explains the low-entropy past, that principle conflicts with the equiprobability of microstates. The statistical argument, a weapon that can be pointed either way, has met a genuine counterexample in the past direction and been trumped.
Keen and Able, the used-car twins. Identical twins Keen and Able sell similar cars. Each says, "Trust me, this car is completely reliable." Keen's car loses its wheels before you leave the yard. Should you trust Able? Not without an independent reason to think the cases differ. The statistical argument failed in the past direction; trusting it about the future, with no independent check, is a double standard.
What could justify trusting it toward the future? Only a reason to think the future is not subject to the kind of constraint that makes entropy low in the past. Absent that, the honest conclusion is weak: entropy will increase unless it is constrained to do otherwise. That is not quite "entropy will go up unless it goes down", because high entropy stays the default needing no explanation. But it is absolutely powerless to rule out a universe that is symmetric, in which whatever requires low entropy in the past also requires it in the future. Chapter 4 shows how cosmology has stumbled over exactly this.
Summary: five lessons of the second law
- Beware unrecognised asymmetric assumptions. Recognised ones are fine if we see that they only shift the burden. The tendency has been noticed; its significance, a misunderstanding of what needs explaining, has not. The project of explaining why entropy increases is misconceived.
- The real puzzle is the low-entropy past. The debate has concentrated on the wrong end of the gradient.
- Think atemporally. It is not objective that entropy increases rather than decreases; what is objective is an entropy gradient, not motion along it in one direction.
- Guard against temporal double standards. A justification for treating past and future differently must itself rely on some further temporal asymmetry, so lesson 1 applies again.
- PI3 has surprisingly little role. The project needing it is misconceived, and it is hard to state non-vacuously. But as a powerful intuitive asymmetry it is flagged: a close relative plays a large role elsewhere in physics, with dubious credentials.
Explain the anomaly, not the default. Price's reorientation is a general lesson about explanation: identify the natural condition of a system and explain departures from it. In incident analysis, for example, the question is rarely "why did the system degrade?" (entropy is the default) but "what kept it ordered until then, and what was that order borrowed from?"
New Light on the Arrow of Radiation
Ripples spread out from an otter slipping into a loch; they never converge to throw an otter out. Price argues that this arrow of radiation is neither a cause nor a consequence of the second law but a junior sibling of it, with the same cosmological source. Radiation is symmetric at the micro level: emitters and absorbers are both centred on coherent wave fronts, and the only asymmetry is that emitters clump into huge coherent sources while absorbers do not. He gets there by reinterpreting the Wheeler–Feynman absorber theory, whose mathematics is right but whose original use commits the double standard.
Gavin Maxwell's Ring of Bright Water (life with the otter Mijbil in north-west Scotland) supplies the image. Circular ripples always spread outwards; inward-converging ripples, which are just the film run backwards, are never seen (whether the otter is entering or leaving the water). The same holds for sound, light and every other wave phenomenon. Dieter Zeh: after a stone drops into a pond we see outgoing waves; the time-reversal-invariant laws are equally compatible with focusing waves that eject a stone, but such reversed processes are never observed.
James Clerk Maxwell's electromagnetism made the puzzle sharp, because its equations visibly admit two families of solutions:
- Retarded solutions: outgoing concentric waves, what we observe.
- Advanced solutions: incoming concentric waves, the temporal inverse, apparently never found.
Ritz versus Einstein (1909). The Swiss physicist Walther Ritz proposed that the retarded character of radiation is a fundamental law, and that it might explain the thermodynamic arrow. Einstein replied that the asymmetry is "exclusively due to reasons of probability", of the same origin as thermodynamics, and that neither is a fundamental law: both rest on the initial conditions in our region of the universe. Zeh notes a weakness in Ritz's view: an electromagnetic law would not explain the asymmetry of sound and water waves.
Karl Popper's 1956 letter to Nature attacked the belief that all irreversibility is entropic. His "trivial counterexample": film a stone dropped into still water; the reversed film shows contracting circular waves of increasing amplitude, with a circle of undisturbed water closing in behind the highest crest. That would need a vast number of distant coherent wave generators whose coordination, to be explicable, would have to originate from one centre, which reproduces the problem. So classical irreversibility exists, independent of thermodynamics.
| Position | Relation of radiative to thermodynamic arrow |
|---|---|
| Ritz | Radiation is fundamental and explains thermodynamics |
| Popular view (Davies, Zeh, Wheeler–Feynman) | Radiation is explained by thermodynamics |
| Middle view (Einstein, Popper, Price) | Neither explains the other; common origin in initial conditions or cosmology |
Price defends the middle view but distinguishes two versions of it, using a chemical analogy.
Left-handed sugar. A compound comes in left- and right-handed forms (ordinary sugar is one). Every molecule we examine in a sample is left-handed. Two explanations: (1) the sample really contains only left-handed molecules; (2) it contains both, but our technique sees only the left-handed ones, for instance because the right-handed form is very soluble and we examine only crystals. Applied to radiation: (1) there is no incoming radiation in nature; (2) incoming radiation exists but is arranged so that we do not notice it. Price defends version (2): radiative processes are symmetric in themselves, but other factors make the retarded solutions far more noticeable.
His route is unconventional: a complete reinterpretation of the Absorber Theory of Radiation of John Wheeler and Richard Feynman, developed in the early 1940s when Feynman was Wheeler's graduate student at Princeton. They too held that radiation "just looks" asymmetric, but explained the look by thermodynamics. Price argues their argument is fallacious, both in its appeal to thermodynamics and in its picture of symmetric radiation, while its mathematical core survives reinterpretation. He also warns that the double standard here comes closer to logical circularity than in chapter 2.
The circular wave argument
The common argument that thermodynamics explains retarded radiation is simple. For converging waves to appear in a still pond (arriving just in time to help a stone that has been "miraculously expelled" from the bottom), the random motions of the material at the pond's edge would all have to cooperate, giving precisely coordinated nudges at every point around the rim: simultaneously for a circular pond, at suitable intervals otherwise.
The circular wave argument and its two failures
- Converging waves require precisely coordinated motions in the boundary material.
- Such coordination is "impossible" (Popper) or "overwhelmingly improbable on thermodynamic grounds" (Paul Davies: waves are damped at the edges by friction, and the reverse is improbable "though not impossible"; Zeh: "the radiation arrow may thus very easily be derived from the thermodynamical one").
- So there are no converging waves.
Failure if "impossible" is weak: if it just means "never happens around here", it is true but explains nothing. Failure if "impossible" is strong: look at the ordinary world in reverse and you see exactly this cooperative behaviour: a reversed film of outgoing waves shows the rim conspiring to produce a converging wave. Toward what we call the past such behaviour is exceedingly common. Anyone claiming it is impossible toward the future must say what distinguishes the cases.
With the second law treated as exceptionless, Price grants, the argument would work: converging radiation in a finite system would violate a universal law. But the statistical second law kills it. Zeh himself saw this: advanced solutions require improbable initial conditions, but "the phenomena observed in nature are precisely as improbable." Both normal retarded waves and abnormal advanced ones require statistically outrageous events in surrounding matter.
The coordinated events at the edge of an ordinary pond happen despite their improbability, because they are explained by what appear, in reverse, to be later circumstances at the centre (the stone). Advanced waves would occur, despite their improbability, if the centre were as it is in the reversed ordinary case: wave crests converging, stones being expelled. So the improbability argument, to exclude advanced waves, must already assume that we have diverging and not converging radiation. That is assuming what was to be proved.
The double standard hides the real lesson. Treat outgoing waves as natural and you miss the real question: why are conditions so exceptional in what we call the past? Why does the universe contain the sources of coherent outgoing radiation: stars, radio transmitters, otters slipping into ponds? Radiative sources are a special kind of concentration of energy whose dissipation takes a special form, so the radiation question is plausibly a subclass of the entropy question. That already sketches Einstein's view: the asymmetry of radiation is neither cause nor consequence of the second law but has its origin in the same puzzling features of the distant past.
The two solution families of the wave equation. Each is the time reverse of the other; nature seems to show only the left-hand kind at macroscopic scale.
Radiation and banking
To clarify what the asymmetry actually is, Price compares radiation with banking. Why does money deposited on Wednesday appear in my balance on Thursday but not Tuesday? Nothing puzzling: a deposit just is a transaction that adds to the prior balance, increasing the subsequent one. The terms presuppose a temporal orientation. On a film of a bank run in unknown direction, we cannot tell whether a masked figure is a thief or an eccentric depositor.
The banking analogy
- Deposit ↔ transmitter (energy into the field); withdrawal ↔ receiver (energy out of the field).
- Symmetry: with orientation fixed, the sum appears in the balance after a deposit and before a withdrawal; a withdrawal is the temporal inverse of a deposit. Likewise, for the energy balance, reception is the inverse of transmission.
- Apparent asymmetry: the effects of both deposits and withdrawals show up afterwards; likewise the effects of transmitters and receivers on the field both appear after the event. It is tempting to say banking is "retarded, not advanced".
- Diagnosis: that asymmetry is not in the mechanisms of banking, which are as reversible as addition and subtraction plus a means of holding the balance constant. It comes from how we apply cause and effect (chapters 6–7). There is no alternative structure banking "could have had".
So whatever the asymmetry of radiation is, it does not lie in the fact that receivers as well as transmitters have retarded effects. Here Price disagrees with Zeh, who takes the delayed effects of receivers to refute the idea that reception is simply the inverse of transmission.
Nonfrictionless banking
Zeh's refinement: there are no pure receivers in nature, since all reradiate some incoming energy. Price builds a bank to match.
The 25 percent bank. No overdrafts are allowed, and the bank insists on redepositing 25 percent of every withdrawal. Complete withdrawal of funds becomes possible only asymptotically, after an endless sequence of transactions. Is banking now asymmetric? Only superficially: describe it with the mirror-image notions of pure deposit and pure withdrawal, and add that every real withdrawal is impure, a pure withdrawal mixed with a proportional pure deposit. For radiation: advanced solutions do describe radiation arriving at absorbers, but real absorbers retransmit a fraction, so their full interaction mixes advanced and retarded solutions. And as the fraction shrinks to zero, the system approaches the frictionless case, so impurity cannot account for the all-or-nothing asymmetry radiation supposedly shows. (Quantisation makes the same point: at the micro level an absorber must be able to take energy without immediately reradiating.)
What would time-symmetric radiation look like?
So any real asymmetry must lie in the dissipative character of radiation, the only feature that distinguishes it from banking. The obvious candidate: only transmitters are centred on coherent wave fronts; waves arriving at receivers are centred on transmitters elsewhere. On a film showing the waves themselves we could tell transmission from reception, and forward from backward projection.
Here Price finds a confusion that, he suspects, has hidden the simple solution. Two formulations are treated as equivalent:
Six formulations (Price's numbering)
- (3-1) Organised waves get emitted, but only disorganised waves get absorbed (Davies). The asymmetry, correctly stated.
- (3-2) All emitters produce retarded rather than advanced wave fronts. Looks equivalent, but is not.
What symmetry would be, read through 3-1 (remove the emitter/absorber contrast):
- (3-3) Both emitters and absorbers are centred on coherent wave fronts, outgoing for emitters, incoming for absorbers. Price's answer.
- (3-4) Neither emitters nor absorbers are centred on coherent fronts.
- (3-5) Both are centred on coherent fronts that are half outgoing and half incoming in both cases.
What symmetry would be, read through 3-2:
- (3-6) Emitters themselves (the entities we normally call emitters) are associated equally with advanced and retarded fronts, either statistically (half the emitters advanced) or individually (each emitter half and half).
The difference matters because explaining an asymmetry requires knowing the contrast class, what would count as not needing explanation. On 3-3, symmetry requires no change to our transmitters; they need not "transmit into the past". It only requires that receivers be centred on incoming coherent radiation. On 3-6, the transmitters themselves must change character.
The working men. In some community, men work and women do not; we describe this as "all workers are male". Two ways to restore symmetry: (a) the women become workers, or are recognised as already working (this is 3-3); (b) half the male workers become female, or each becomes half male and half female (this is 3-6). The Wheeler–Feynman theory, at first sight, addresses version (b): it tells us that each of what we thought were male workers is "really" half male and half female.
If successful, Wheeler–Feynman establishes 3-6 and also 3-5, so it does not disappoint those who understand that 3-1 is the real mystery. But it "panders" to the misunderstanding that the mystery is the absence of 3-6. And Price thinks it is not successful as it stands.
The Wheeler–Feynman theory in brief
Accelerating a charged particle takes extra energy compared with a neutral one of the same mass; the extra flows away as radiation. The resistance is radiative damping or radiation resistance. Early accounts struggled with the mathematics of a charge acting on its own field. Wheeler and Feynman assumed instead that a charge does not interact with its own field, and that radiative reaction comes from distant charges. The approach could not be extended to quantum electrodynamics, so its interest now lies in the arrow of radiation. The original motivation perhaps explains why they took symmetry to mean 3-6: each accelerated charge radiates equally into past and future.
The Wheeler–Feynman argument
- A source charge i is accelerated; it is surrounded by an absorber of charged particles.
- Assume symmetry (3-6): every charge's field is ½ retarded + ½ advanced.
- The (full) retarded wave from i accelerates the absorber particles, whose own fields are ½ retarded + ½ advanced.
- Add the advanced waves of all absorber particles. Between i and the absorber, after the acceleration, they sum to what looks exactly like a half-strength outgoing wave from i.
- Before the acceleration, the absorber's advanced response is in such phase that it cancels the half-strength advanced wave from i.
- So: source ½ ret + ½ adv; absorber ½ ret − ½ adv; net full retarded wave, no advanced wave.
- Conclusion: radiation that is really symmetric appears fully retarded, thanks to the thermodynamic properties of the universe's absorbers.
The Wheeler–Feynman setup: the source's wave drives absorber charges, whose advanced responses converge back on the source and, summed, supply half the observed outgoing wave.
Why doesn't the argument work in reverse?
Wheeler and Feynman saw that the reasoning could be run with reversed orientation: a past absorber of the half-advanced wave might cancel the retarded wave and build the advanced wave up to full strength. Then the net field in an absorbing enclosure would be both fully retarded and fully advanced. Their answer, in Davies's words: absorption is an irreversible, entropy-increasing damping effect; the advanced solution would require cooperative "anti-damping" of every particle in the cavity wall, ions excited and radiating at the precise moment to collapse a coherent wave onto the centre. In their own words, "small a priori probability of the given initial conditions provides our only basis on which to exclude" the advanced case.
The blatant double standard. This is Popper's pond argument again. On statistics alone, the arrangement of absorber particles needed for incoming radiation is exactly as improbable as that needed for outgoing radiation. One might reply that in the retarded case a boundary condition (a retarded wave from the source) makes the otherwise unlikely absorber correlations highly probable. True, but Wheeler and Feynman's own premise is that the source really emits a half-advanced wave too. Given that wave, the anti-damping correlation in the wall is equally guaranteed. So statistics gives no grounds whatever for preferring the retarded self-consistent solution. Replying that the advanced wave is cancelled by the future absorber does not help: Wheeler and Feynman do not deny the advanced wave exists, and saying it is cancelled assumes the retarded solution whose priority is in question. If valid, the argument would actually refute the symmetry assumption, by deriving a field that is both fully retarded and fully advanced.
Are the components distinct?
A second, overlooked flaw. The argument represents the observed retarded wave as a sum of two equal components: the half-retarded wave from i and the summed half-advanced waves from the absorber. Adding them requires that they be distinct.
Double interest. I deposit money, withdraw it a month later, and claim interest both on the sum put in and on the sum taken out. My bank manager points out that there are not two sums but two descriptions of one sum. If the Wheeler–Feynman "components" are just two descriptions of one wave, there is nothing to interfere constructively.
- No measurable difference. The two waves are qualitatively identical.
- Different sources? To get an absorber response of the right size, the argument needs a full retarded wave from i, treated as sourced at i (start with only half and the response halves, leaving the total 25 percent short even if summing is allowed). By the end, half of that full wave is reassigned to the absorber. That is consistent only if sources are non-unique and perspective-dependent; but then sources cannot be used to distinguish the components.
Ad hoc assumptions can earn their keep by success, but this theory is already in trouble, and the assumption can be dropped entirely.
The new interpretation
Take 3-1 and 3-3 as the target: the puzzle is that transmitters are centred on organised outgoing fronts while receivers do not seem to be centred on organised incoming ones. The fact that transmitters go with outgoing radiation is no more puzzling than deposits showing up afterwards.
Price's reinterpretation
- A transmitter i radiates a fully retarded wave.
- The surrounding shell of particles are receivers, transferring field energy into non-electromagnetic forms; from their point of view the field is fully advanced (incoming).
- Assume, contrary to appearances, that this incoming radiation is coherently centred on each absorber particle: each is the focus of a converging coherent front.
- Wheeler and Feynman's mathematics then shows that between i and the receivers, after the acceleration, this field equals the original wave from i (no factor of one half, because the response is now fully advanced).
- Why equal? Because they are one and the same wave (rejecting the distinctness assumption).
- Conclusion (3-3): the same field can be described either as a coherent front diverging from i or as a sum of coherent fronts converging on the absorber particles. Both transmitters and receivers are centred on coherent wave fronts, without inconsistency. A free charge that absorbs and reradiates has coherent incoming and outgoing fronts.
Why the apparent asymmetry?
The radiative asymmetry is simply an imbalance between transmitters and receivers: large-scale sources of coherent radiation are common, but large coherent sinks are unknown. Every individual absorber is a coherent sink; at the micro level things are symmetric. At the macro level only sources are noticed, because only they combine in organised ways in huge numbers.
Big deposits, tiny withdrawals. A bank account gains its funds from a few very large deposits and loses them to a great many very small withdrawals. There is a temporal imbalance, but not in banking itself: micro-withdrawals are inverses of micro-deposits. The macro difference arises because micro-deposits clump into macro-transactions and micro-withdrawals do not. To explain it, look at the bank's connections with the outside world.
What needs explaining, then, is why there are large coherent sources (huge numbers of tiny transmitters acting in unison) and no large coherent sinks. The former is the real puzzle, since it is the abundance of sources that is statistically improbable and tied to the universe being far from equilibrium. In thermal equilibrium, sources and sinks would be equally rare, and the field would be like a pond in a heavy rainstorm: an incoherent mess of tiny interactions with no pattern in either direction. Stars and galaxies are the electromagnetic equivalent of giant rocks (or otters) that impose pattern on that disorder.
The reinterpreted theory does not depend on the absorber's thermodynamic properties, or even on its presence. The radiative arrow is "not so much a child of the second law as a junior sibling". Both lead to the same cosmological question: why does the universe have a history that produces stars and galaxies rather than a more likely one, and why so asymmetrically? Why are there no "sink stars" on which radiation converges?
No need for a future absorber
In the orthodox theory the absorber is essential. Without it the reasoning predicts a half-strength outgoing wave and an uncancelled half-strength incoming field. Wheeler and Feynman's escape requires explicit advanced effects. So orthodoxy offers a choice: either the future universe is an (almost) perfect absorber, a very strong cosmological constraint, or, to the extent that the future is transparent, source-free radiation must be postulated in the early universe. Some physicists (Hogarth, Hoyle and Narlikar) treated this as evidence for particular cosmologies; most saw the tight link between electromagnetism and cosmology as a defect.
Price's version has no such consequence. Where no absorber exists, the retarded wave simply propagates to future infinity. Where there is an absorber, its interaction can be consistently redescribed as converging coherent waves. The usual wave no longer needs two finite sources, one past and one future; if it has both, their contributions are consistent. Time-symmetric electromagnetism is freed from cosmology.
Related issues in physics
| Spin-off | Price's assessment |
|---|---|
| Absorber theories for other particles (e.g. Paul Csonka: all particles "emitted, and absorbed, in a time-symmetric manner") | Address a nonexistent problem. Within the kaon limits, particle physics is already T-symmetric: absorption is the inverse of emission, and symmetry does not require rolling the two into one. |
| Feynman's talk of particles "travelling backwards in time" | Misleading if literal. Particles, like waves, are retarded relative to their emission and advanced relative to their absorption by the meaning of the words, not as a physical fact. |
| John Cramer's transactional interpretation of quantum mechanics | Attractive and unjustly neglected; the most developed advanced-action approach. The state between emitter and detector depends on the retarded "offer wave" and an advanced "confirmation wave" from the future apparatus (like a standing wave in a cavity). It need not rely on the Wheeler–Feynman picture of symmetry and can be reinterpreted the same way, though chapters 8–9 argue it misses the most appealing route. |
Absorber theory and transactions since 1996. Wheeler–Feynman electrodynamics remains a minority framework, but it has had technical revivals: work on direct-interaction (action-at-a-distance) electrodynamics, the existence of solutions for Wheeler–Feynman's delay equations, and Hoyle–Narlikar style quantum extensions. Cramer's interpretation was developed by Ruth Kastner into the "possibilist transactional interpretation" (books 2012, 2022), which addresses Tim Maudlin's 1994 objection that contingent absorber placement makes transactions inconsistent. Cramer's popular book The Quantum Handshake appeared in 2016. Price's preferred advanced-action route has also flourished independently (chapters 8–9 updates). His micro-symmetric reading of radiation is now commonly cited alongside the view that the radiative arrow is a boundary-condition effect sharing a source with the thermodynamic arrow, the view associated with Zeh's The Physical Basis of the Direction of Time (fifth edition 2007).
Check the contrast class. Price's 3-1 versus 3-2 distinction is a general tool: before explaining an asymmetry, specify exactly what the symmetric alternative would look like. Two descriptions that seem equivalent may imply different contrast classes, and one of them may set you a problem that does not exist (making each emitter "half advanced") while hiding the real one (why sources clump).
Summary
- State the asymmetry correctly. The puzzle is not that transmitters fail to transmit into the past; it is that waves leaving transmitters are organised while waves arriving at receivers seem disorganised.
- Micro-symmetry is consistent. Reinterpreted, Wheeler–Feynman shows that micro-emitters and micro-absorbers can both be centred on organised fronts. The apparent asymmetry arises because micro-emitters clump into macroscopic sources and absorbers do not. This version escapes both objections to the original (the double standard and the distinctness assumption).
- Explain the clumping of sources, not the lack of clumping of sinks. A statistically natural world would have neither. Resist (a) thinking the question is why there is no incoming coherent radiation and (b) answering with statistics: (b) is the double standard and (a) ignores the real puzzle, that we do see incoming coherent radiation when we look the other way in time. Question (a) becomes important in cosmology (chapter 4).
- Coordinated behaviour toward the past. Radiation joins thermodynamics in showing remarkable coordination in the direction we call future-to-past; cosmology must explain the sources, stars and galaxies.
- PI3 may be only macroscopic. Incoming concentric waves seemed a paradigm violation of PI3 (distant segments of the front are correlated), and outgoing waves a paradigm of correlated outgoing influences. But here macroscopic asymmetry rests on microscopic symmetry. This suggests PI3 holds only at the macroscopic level: a clue to the nature of causality, and perhaps "the missing secret of quantum mechanics itself".
Arrows and Errors in Contemporary Cosmology
Modern cosmology replaced Boltzmann's desperate fluctuation story with a better one: the arrows of time trace to the extraordinarily smooth, low-entropy state of the universe just after the big bang. But Price finds cosmologists, including Davies, Hawking and Penrose, repeating the nineteenth-century double standard when they try to explain that state. The basic dilemma: a time-symmetric physics that makes the big bang smooth seems bound to make a big crunch smooth too (Gold's universe), and one that does not leaves the smooth big bang unexplained. The usual objections to Gold's symmetric universe are themselves double standards.
The need for smoothness
What is special about the early universe is that its matter was distributed extremely smoothly, with nearly the same density everywhere. That sounds like the most disordered state, since a gas spreads evenly through its box. But a gas is dominated by pressure, which pushes molecules apart. The universe is dominated by gravity, which pulls matter together, so the natural, high-entropy state of a gravitating system is clumpy. (Compare water on a waxy surface: surface tension is attractive, so the natural state is droplets.)
For gravity, smooth means low entropy. Without early smoothness, gravity would have gathered matter into vastly larger clumps, huge black holes, and no galaxies could have formed. With too much smoothness, even galaxy-sized clumps would not form. The universe needed to be extremely but not completely smooth.
The conclusion first came from models of cosmic evolution; then the microwave background, known since the 1960s, gave dramatic support. Satellite studies (COBE, results announced 1992) showed the radiation is nearly identical in every direction, with tiny variations of just the size galaxy formation requires.
There are two puzzles: why so smooth, and why the small irregularities. The first is the one tied to temporal asymmetry. "The smoothness of the early universe is the big puzzle of temporal asymmetry, to which the little puzzles of the previous chapters all seem to lead." Smoothness alone does not account for every feature of the familiar arrows, but it is an essential and powerful prerequisite for all of them.
Precision cosmology. WMAP (2001–2010) and Planck (2009–2013, final results 2018) mapped the background to exquisite precision: temperature fluctuations of about 1 part in 100,000, a universe 13.8 billion years old, spatially flat to within about 0.2 percent, with a nearly scale-invariant spectrum (spectral index ns ≈ 0.965). Price's range of "ten to twenty billion years" is now pinned down. The smoothness-as-low-entropy point is the standard view, usually stated through Penrose's Weyl curvature hypothesis or the Past Hypothesis.
Gold universes and the basic dilemma
If the universe is dense enough, gravity will reverse the expansion and drive it to a big crunch. Would the crunch mirror the bang, equally smooth? It is hard to see how time-symmetric theories could make one end special without making both special.
Thomas Gold proposed in the early 1960s that entropy might be low at both ends. His motivation was a hoped-for link between the expansion and the second law: expansion might raise the maximum possible entropy by creating new possibilities for matter, and the thermodynamic arrow would be matter taking them up. Then contraction would shrink the possibilities and entropy would decrease. That directed link is untenable: the smooth early universe was incredibly special even by the standards of its time; its low entropy did not depend on fewer possibilities. But the symmetric model keeps its appeal.
In a Gold universe entropy is low at both extremities; observers in the contracting half would have the opposite arrow and would call the crunch their big bang.
Most cosmologists think Gold's view leads to absurdity: matter would have to behave in extremely unlikely ways as entropy fell. Price's reply: what Gold requires toward the future is exactly what the standard view requires toward the past. We know the improbability argument fails toward the past; entropy does decrease that way despite the unlikely arrangement it needs. So it cannot be conclusive toward the future.
The basic dilemma
- The laws of physics are (apart from tiny exceptions) time-symmetric.
- A time-symmetric argument that one extremity of the universe must be smooth applies equally to the other extremity.
- Horn one: both ends are smooth: the Gold universe, with the arrows reversing in a contracting phase.
- Horn two: neither end need be smooth: the smooth big bang is inexplicable by time-symmetric physics (without extra, asymmetric assumptions).
- Most cosmologists find both horns unsatisfactory but fail to see how hard it is to steer between them, because double standards hide the dilemma.
Smoothness: how surprising is it?
The natural first response to a demand for explanation is to show the feature is not surprising. Early on, Paul Davies wrote that a time-asymmetric universe "does not demand any very special initial conditions", but a creation "of a very general and random character", as expected from a completely unpredictable singularity.
Roger Penrose did most to expose the error. He compared the entropy of a smooth arrangement of matter with alternative arrangements in which most matter sits in large black holes, whose entropy is vastly greater. Since entropy measures probability, the actual early universe was special to the degree of about 1 in 1010123.
- 1 in 1010123: Penrose's estimate of the fraction of possible initial states as smooth as ours.
- 10123: roughly the entropy (in natural units) the observable universe's matter would have if collapsed into one black hole; the actual early entropy was smaller by an exponent of comparable size.
- 10–20 billion years: Price's figure for the time since the big bang (now known to be 13.8 billion).
The gravitational symmetry argument
Price turns the black-hole point into a direct argument closer to his theme: nobody would regard a collapse to a smooth late universe just before a crunch as statistically natural. Absent reason to the contrary, that applies equally at the other end.
The gravitational symmetry argument
- The natural end of collapse. A universe collapsing under its own weight is likely, in its late stages, to be very inhomogeneous, clumpy rather than smooth.
- Reverse the film. Viewed in reverse, the history of our universe is a universe collapsing under its own gravity, accelerating toward a final crunch.
- No privileged orientation. Nothing in physics says one orientation of the time coordinate is right, or that one end is objectively the start. So the reversed perspective is as valid for judging the natural condition of what we call the early universe as the usual one is for the late universe.
Conclusion: with double standards disallowed, a smooth big bang is just as unlikely as a smooth big crunch. If we treat the late stages by a theory of gravitational collapse, we must treat the early stages the same way; if the early stages obey some extra boundary constraint, the late stages may obey it too. We cannot assume the smooth start is unexceptional, nor that a smooth end (Gold) is impossible.
The appeal to inflation
The inflationary model (early 1980s: Alan Guth, then Linde, Albrecht and Steinhardt) is a "front end" to the big bang. When the universe is extremely small and young, perhaps the product of a chance quantum fluctuation, gravity is effectively repulsive and the universe doubles in size over and over in tiny fractions of a second. As it cools it undergoes a phase transition (like steam to water), gravity becomes attractive and the sedate ordinary expansion begins. Inflation seemed to explain features the standard model must assume, including smoothness: repulsive gravity "irons out" inhomogeneities. Davies argued in Nature in 1983 that the universe therefore "began in an arbitrary, rather than remarkably specific, state", as expected of a spontaneous quantum fluctuation from nothing.
Inflation's double standard. As in step 2 of the gravitational symmetry argument, view the process in reverse: a gravitational collapse toward what we call the big bang, which statistically should produce inhomogeneities at the transition to an inflationary (now deflationary) phase. The statistical reasoning is as good in either direction, so inflation cannot do the job unless one direction is already privileged. Davies also argued that a recollapsing universe would not "deflate" at the crunch, since that would need "an exceedingly improbable conspiracy of quantum coherence to reverse-tunnel through the phase transition". But viewed in reverse, the transition from ordinary big bang into inflation involves exactly that conspiracy. A universe that collapses without deflation just is a universe that expands without inflation: the same universe under an equally valid description.
Inflation and the entropy problem today. Inflation is now the leading account of the near-scale-invariant fluctuations measured by Planck, but Price's point has been widely accepted by foundations-minded cosmologists: inflation does not explain the low entropy of the initial state, because inflation itself needs a special, low-entropy patch to start (Penrose 1989 and later; Carroll and Tam 2010, "Unitary evolution and cosmological fine-tuning"; Albrecht's work on "de Sitter equilibrium"). Critics such as Ijjas, Steinhardt and Loeb (2013, 2017) argue Planck data disfavour simple inflation and that eternal inflation produces a measure problem ("multimess"). Searches for primordial gravitational waves (BICEP/Keck, limit on the tensor-to-scalar ratio r < 0.036 in 2021, tightened to about r < 0.032 with Planck) have ruled out the simplest models. The Simons Observatory (operating from 2024–25) and planned LiteBIRD aim to probe r down to about 0.001–0.003.
Hawking and the big crunch
Stephen Hawking's proposal, popularised in A Brief History of Time (1988), is the no boundary condition: restrict possible histories of the universe to those that "are finite in extent but have no boundaries, edges, or singularities". The dilemma bites him hard, because extra boundary conditions are against the spirit of his proposal.
- 1983 Hartle and Hawking: the no-boundary wave function of the universe.
- 1985 Halliwell and Hawking: perturbation modes "start off in their ground state". Hawking's paper "Arrow of Time in Cosmology" argues the arrow reverses on contraction, then concedes his "mistake" in a note added in proof.
- c. 1985 Don Page and Raymond Laflamme (Hawking's student) persuade him that disorder keeps increasing in contraction.
- 1988 A Brief History of Time: "I realized that I had made a mistake."
- 1988–89 Price writes to Hawking, Page and Laflamme; no reply.
- July 1989 Price's article on the puzzle appears in Nature; Dieter Zeh writes that he agrees with every word; Scientific American (October) carries comments from Hawking and Page that do not clear up the mystery.
- 1991 Conference on the arrow of time in Spain (Mazagón, Huelva): Hawking's account with Laflamme and Glenn Lyons of oscillating and non-oscillating perturbation modes.
Hawking initially thought the no-boundary condition implied Gold's view: that disorder would decrease in the contracting phase. Then he decided this was a mistake: the condition implies disorder continues to increase in contraction, and the thermodynamic and psychological arrows would not reverse in contraction or inside black holes. That avoids the usual objections to Gold, but impales him on the second horn: how does a time-symmetric proposal make entropy low near the bang without making it low near the crunch?
The corkscrew loophole
Three classes of universe
| Class | Extremity A | Extremity B | Status if Hawking is right |
|---|---|---|---|
| Order–order | smooth | smooth | Excluded (that was his "mistake") |
| Order–disorder | smooth | clumpy | Allowed, and the normal case |
| Disorder–disorder | clumpy | clumpy | Must be excluded, or our universe is unexplained |
Hawking needs to exclude disorder–disorder without excluding order–disorder. That is not incompatible with symmetric laws: a symmetric theory can have only (or mostly) asymmetric models.
The unbiased corkscrew factory. A factory produces equal numbers of left- and right-handed corkscrews. Every individual corkscrew is spatially asymmetric, but production as a whole is perfectly unbiased. Likewise an employer with no gender bias still employs only individuals who are male or female. A time-symmetric theory might likewise make every individual universe asymmetric in time, with one ordered end and one disordered end, and the weak anthropic argument would explain why observers call the ordered end the beginning (as Boltzmann argued).
J. J. Halliwell describes Hawking's view in these terms, and Davies (in About Time, 1995) says the loophole is Hawking's way out. But Price's question is whether Hawking has actually shown it. It cannot be done by examining one extremity in isolation: whatever works for "the initial state" works for "the final state", unless the argument has quietly assumed an objective initial/final distinction. Hawking needs a general argument that almost all universes have at least one ordered extremity, and at most one.
Price combed the papers. Hawking and Halliwell's calculation gives "an arrow of time": the universe is nearly homogeneous "when it is small" and irregular when large. Note that this is phrased by size, not time. Hawking's "great mistake" was to think perturbations would be small whenever the radius was small, at both ends. Page and Laflamme convinced him that at small radius there are two kinds of solution: one almost Euclidean, starting "like the north pole of a sphere" and expanding monotonically (the start of the expansion), and one with a long Lorentzian period of expansion followed by contraction to that radius (the end of the contraction). Non-oscillating perturbation modes, being far more common, are small when they enter the horizon during expansion, keep growing in contraction and become non-linear.
Where the asymmetry sneaks in. If it is not objective which end is expansion and which contraction, and nothing constrains the universe simply in virtue of its radius, why should the perturbations ever be small? Price could find no answer. Instead the papers say the modes "start off" or "start out" in their ground state (Halliwell and Hawking 1985), and that "at early times ... The Universe is in a state that is as ordered and homogeneous as it can be" (Hawking 1985). Either this assumes one extremity is objectively the start, which helps itself to the asymmetry, or it means "when the universe is small", which applies at both ends or neither. It cannot mean "the end observers will call the start", because that presupposes the result. So Hawking's real mistake is an ambiguity about the scope of the no boundary condition, trapping him between assuming an objective start and failing to see that a size-based condition applies at both extremities.
| If the no boundary condition... | then Hawking's mistake was... |
|---|---|
| excludes disorder at both extremities | changing his mind: contraction should reduce entropy (Gold) |
| excludes disorder at neither extremity | thinking it explains the low-entropy big bang at all |
| excludes it at exactly one (corkscrew) | not telling readers the argument, which is the crux |
A symmetric reading is not ruled out by Page's statistical point that most histories end in disordered collapse. Statistics defers to boundary conditions: the big bang is smooth although it is as much the end of a gravitational collapse as a crunch would be. Hawking could have said the no-boundary condition, applied symmetrically, overrides Page's statistics. Not doing so, he owes an explanation of why the same statistics do not apply toward the big bang.
Irony: Hawking criticised Penrose's explicitly asymmetric proposal for "putting in the thermodynamic arrow by hand". Price's verdict: the difference is that Penrose says so, while Hawking claims to do more. Still, like Boltzmann, Hawking thinks atemporally better than most (he once endorsed Gold), but not consistently.
After Hawking. Hawking's later work with Thomas Hertog ("top-down cosmology", 2006; their final paper on eternal inflation, 2018) treats the no-boundary state from the observer's present, which is closer to the anthropic horn. Hertog's On the Origin of Time (2023) recounts this. Technical disputes about whether the no-boundary path integral is even well defined (Feldbrugge, Lehners and Turok, 2017, versus Diaz Dorronsoro, Halliwell, Hartle, Hertog and Janssen) remain open. Price's point that a size-based boundary condition is symmetric is now often cited in discussions of "two-time" boundary conditions.
The basic dilemma and some ways to avoid it
Perhaps only Penrose fully appreciates the dilemma. He takes the second horn: physics must contain an asymmetric law that the initial extremities of the universe obey a smoothness constraint: the Weyl curvature hypothesis, that the Weyl curvature of spacetime approaches zero at initial singularities. Is "initial" already an illegitimate objective distinction? Superficially only: Penrose need say only that there is one temporal direction in which Weyl curvature goes to zero at the extremities; observers then call that direction the past, by the weak anthropic argument.
The symmetric alternative. A Gold supporter can accept Penrose's argument for a new law and make it symmetric: Weyl curvature approaches zero at the extremities in both directions. That explains the smooth bang just as well and introduces no asymmetry into physics. So Penrose's version is preferable only if there are good reasons to reject Gold, and the usual reasons are weak.
Escape 1: what if there is no big crunch?
If the universe expands forever, it has no future extremity, and a proof that all extremities are smooth would not imply Gold. Price thinks this is overrated:
- The coherence question is separate. What matters is whether Gold's view makes sense for a recollapsing universe, not whether ours recollapses, unless recollapse could be shown physically impossible. (Inflation predicts a density very close to critical, which might make recollapse impossible.)
- Black holes are local crunches. Massive stars collapse to black holes, miniature versions of the crunch and of the reversed big bang. If symmetric physics makes the bang smooth, it should make a black hole's collapse end smooth too. Hawking and Penrose conclude global recollapse is largely irrelevant.
- The real puzzle remains. Even with no second extremity, from nowhen there is no reason to describe our universe as expanding from a bang rather than contracting toward a crunch. Why does that endpoint lack the expected clumpiness of a gravitational collapse?
So the Gold universe is "a convenient way of thinking about a problem which arises independently": the symmetry of a recollapsing universe forces on us, without leaving our ordinary perspective, the question the atemporal view requires us to ask about the bang itself.
Will there be a crunch? In 1998 two supernova teams (Perlmutter; Riess and Schmidt; Nobel Prize 2011) found the expansion is accelerating, apparently driven by dark energy (about 68 percent of the cosmic energy budget). With a true cosmological constant, the universe never recollapses. But DESI baryon acoustic oscillation results (2024, and the DR2 release of March 2025) hint at evolving dark energy at roughly 3–4σ when combined with supernova and CMB data. Some models fitted to these hints (for example Lu, Qiu and Tye, "The Lifespan of our Universe", 2025) allow a negative cosmological constant and an eventual big crunch, about 20 billion years from now. The question Price treats as peripheral has become open again, and his black-hole point (local crunches) stands regardless.
Escape 2: the corkscrew model
The loophole above is perhaps the best prospect. Two cautions:
- No asymmetry by hand. The theory must imply that all solutions are asymmetric, not assume it. Since any derived asymmetry must be implicit somehow in the premises, the requirement is that it flow from principles not manifestly asymmetric and with independent justification.
- Do not prefer it for statistical reasons. The intuition that a clumpy collapse is the "likely fate" gives no prima facie advantage over Gold, because the statistics is symmetric: it is unreliable in the one case out of two in which we can test it (the big bang). Trusting it toward the crunch is the double standard. Only if the bang is a mere fluke can we expect flukiness at one end only, and that abandons the corkscrew strategy for the anthropic one.
Escape 3: the anthropic strategy
We can exist only in unusual regions with an entropy gradient, so we find ourselves in one. This is Boltzmann's idea again, with his difficulties.
The anthropic strategy: costs and loopholes
- Ontological cost. It needs a genuine multiplicity of actual regions or universes; merely possible worlds would not explain why ours is actual. On Penrose's figure, our universe would be about 1 in 1010123 of reality.
- Possible subsidy. Some inflationary theories already say universes are bubbles in a vast foam, so the cost might be paid anyway.
- Overkill objection (Penrose). Life needs only a smooth patch big enough for a galaxy or two; global smoothness is vastly more improbable than life requires. Compare Boltzmann: one galaxy is far cheaper than two million.
- Loophole. If inflation made a universe our size all or nothing, the argument revives, provided (1) a background grand universe has time enough for the rare quantum preconditions of inflation to occur, and (2) when they occur, a universe like ours, complete with its smooth boundary, is guaranteed.
Price grants that this is a possible escape that would explain a low-entropy history without implying a low-entropy future. But the price is a reality hugely larger than we imagine, a far less welcome result than a universe explicable as it stands.
What's wrong with a Gold universe?
A Gold universe doubles the boundary conditions to explain but makes a symmetric physics far more likely to be up to the job. Gold's original mechanism (expansion creates possibilities) failed: contraction alone would not make radiation converge on stars, and smoothness is anything but a natural product of contraction. So the extremities must be special in a way expansion does not explain. One option is a time-symmetric law in Penrose's spirit, perhaps grounded in a symmetric no boundary condition.
The consequences sound absurd. In the contracting phase, radiation would converge on stars, apples would assemble in compost heaps and leap into trees, and humanoids would rise from their ashes, grow younger and become unborn. Davies himself makes the right point: this "is simply a description of our present world given in reversed-time language"; the difference is "purely semantic and not physical".
Objection 1: the special initial conditions of the turnaround
Davies says the remarkable thing is the transition: a very special set of microscopic motions in the big bang, "each little particle ... Set off along a carefully chosen path", requiring "an extraordinary degree of cooperation between countless numbers of atoms". Price: the conventional asymmetric view itself requires that the final conditions be arranged so that, viewed in reverse, countless atoms cooperate over billions of years to produce the low-entropy bang. The statistical argument "is an instrument with two possible uses"; it fails glaringly in one, so neither symmetry nor caution licenses trusting it in the other.
Objection 2: Penrose's astronaut
The astronaut in the black hole. Penrose imagines an astronaut falling into a black hole of about 1010 solar masses, giving him roughly a day inside the horizon with negligible tidal forces to do leisurely experiments. In a Gold-type view tied to collapse, his apparatus and metabolism are determined by the hole's singularity as much as by the big bang, so his experiments should run entropy-decreasingly and he should believe he is coming out of the hole rather than falling in. Absurd, so Gold is wrong.
Price's reply rests on a distinction between two ways the products of two low-entropy boundaries could relate.
| The meeting model | The mixing model |
|---|---|
| Every piece of structure is a natural product of both extremities | Each piece of structure is normally the product of one extremity or the other, not both |
| Assumed by Penrose's astronaut and by Hawking (the astronaut would not notice because his time sense would reverse) | Price's preferred principle: any piece of low-entropy structure needs explaining as a product of either the past or the future singularity, but no piece needs both |
| The astronaut must have a reverse evolutionary history inside the hole | Relative to the hole's reversed time sense, the astronaut is simply an improbable "miracle", imported structure |
The astronaut is the product of a billion years of biology and ten billion of cosmology; he can only exist at that temporal distance from a suitable bang, and a "bang" needs mass enough to produce structure, not just low entropy. So he meets no time-reversed humanoids, unevolving life or unforming stars inside a small hole. Proportions of each kind of structure vary by place; near our bang and far from black holes almost everything comes from the bang. In a hole without the time or mass to produce much structure, the experience might be much less odd than Penrose suggests.
Approaching a reverse star. Near a big enough sink (the crunch itself), reverse structure would eventually affect us. From the reverse viewpoint, our ship is leaving a normal star: warmed by it, cooling as we recede, radiating into space. From our viewpoint, photons converge on us "inexplicably" from empty space, increasingly, while our craft reradiates toward one direction, a giant radiation sink. The wall facing the reverse star would feel cold to the touch, reflecting heat flowing toward the star in our time sense. Bizarre, but within the Gold model neither unexpected nor inexplicable. An objection needs incoherence, not mere strangeness.
Objection 3: black holes and white holes
Penrose later preferred a stronger argument: a symmetric view must either disallow black holes in the future, which "requires physically unacceptable teleology", or allow a proliferation of white holes in the past, contradicting the smooth early universe. The teleology objection is statistical: it would take "remarkably improbable" coincidences to forbid black holes, and would place "unreasonable" constraints on what matter may do in the past. Price: another double standard. The smooth past shows something overrides the natural behaviour of gravitational collapse; once that is admitted, there are no non-question-begging grounds to exclude, or even doubt, the same factor operating in the future.
A telescope to look into the future?
Suppose our universe is a Gold universe. The contracting phase contains reverse galaxies and reverse stars, sinks of coherent radiation in our time sense. What happens if we point a telescope toward one?
The telescope that cools. A reverse astronomer would say light from her galaxy is being absorbed by our distant telescope, slightly heating a black plate at its back. In our time sense absorption looks like emission and heat flows reverse. So when we point the telescope at the reverse galaxy, radiation flows out of the telescope into space, and the plate shows an apparent cooling: it is actually hotter than its surroundings but behaves like a cooler object, taking in heat from its environment and sending it off as light. A photographic plate over the aperture would not record the outgoing light; from the reverse view it shades the telescope, so in our view the light leaves from the back of the plate, facing the reverse galaxy.
The effects may be insignificant in practice, given the vast interval between eras, but in-principle analysis might reveal an incoherence and rule out Gold for good.
Plate temperature when a future reverse source shines on our telescope: in our time sense the change comes before we open the telescope and ends before we close it, an apparent advanced effect.
The bilking policy
The temperature appears to rise before we open the telescope and fall before we close it: an advanced effect. That invites the classic argument against backward causation (chapter 7): adopt the policy "open the telescope only if the plate's temperature has not just risen significantly". Does that generate contradiction?
Price thinks not. Grant that under the policy the temperature never rises on an occasion when we could have opened but did not. That leaves the possibility that on every relevant trial the temperature does not rise and the telescope is opened. The predicted profile was statistical, the most likely behaviour inferred from heat-flow direction, and statistics can be overridden by boundary conditions. Here there are two: our policy (constant temperature before opening) and the future reverse source. The system is constrained in both temporal directions, so we should not expect the behaviour predicted on the assumption that it has its normal freedom in one direction. Price suspects this loophole is always available, not least because quantum indeterminism may make it impossible to constrain both boundaries enough for outright contradiction.
Gell-Mann and Hartle's night-sky objection
Murray Gell-Mann and James Hartle argue: starlight from our epoch, in a transparent universe, reaches the final epoch; if much of it passes the reverse stars toward the final singularity, then by symmetry a corresponding amount must have come from the big bang, so the night sky should be brighter than observed (Davies and Jason Twamley: "a difficulty reminiscent of Olbers' paradox").
Looking at the back of your own head. Could we detect that extra radiation? It is already arranged to converge on its future sinks, not on our instruments. A reverse galaxy at +x emits (in its time sense) toward a distant point at −x. We stand at the origin and look toward −x for light that, in our time sense, travels from −x toward +x. We will not see it, because we are in the way: if we stand at the origin, the reverse galaxy's light falls on us and never reaches the sky at −x. The relevant radiation comes not from the sky but "from the back of our own head". And our choice to stand there influences the past: because we interpose ourselves, some photons are not emitted from a surface at −x that otherwise would have emitted them.
General lesson: our asymmetric ways of thinking are tied up with the thermodynamic asymmetry and cannot be trusted where it is not universal. Even counterfactuals change: if event B follows deterministically from A, we may be unable to say "had A not happened, B would not have", not because of a backup earlier cause (preemption) but because B is guaranteed by later events.
Two tentative conclusions. First, whether Gold's view is inconsistent is still open, and will not be settled until we learn to think about it the right way. Second, the contents of the contracting half of a Gold universe might be observable now, in principle, though they lie in what we call the distant future. The methods look bizarre, but that is only the oddity of ordinary asymmetries running the other way.
Conclusion
Modern cosmology gives Boltzmann's puzzle a concrete form, why was the early universe so ordered?, but its practitioners are prone to the same double standards. Price's summary of the options:
| Option | Big bang is... | Cost / problem | Price's verdict |
|---|---|---|---|
| Corkscrew model | an extremity of a mostly-asymmetric model of a symmetric theory | must derive, not assume, the asymmetry | attractive, but not for the usual statistical reasons |
| Gold universe | smooth by a symmetric constraint that also governs the crunch | arrows reverse in contraction; consistency still open | if anything more plausible on symmetry grounds |
| Anthropic | a freak but natural outcome of collapse, once in 1010123 tries | reality vastly larger than the observable universe | possible escape, with inflation's help |
| Penrose's asymmetric law | smooth by a time-asymmetric law (Weyl curvature → 0) | ad hoc asymmetry | a symmetric law would do as well |
All except the anthropic view say the big bang is not a natural product of gravitational collapse: something (boundary conditions, global constraints on models) overrides generic reasoning about collapse. What favours Gold is that, once that concession is made at one extremity, there is no objection in principle to applying it more widely, and symmetry is a considerable advantage.
A twist that undercuts the statistics. If statistical reasoning is unreliable in cosmology, does that undercut the reason for thinking the low-entropy past is unusual and needs explaining? Price's answer: the smooth early universe needs explaining not because it is statistically unlikely but because it is so distinctive and important, essential to galaxy formation and the familiar arrows. Critics note that this weakens the force of Penrose's 1010123 argument, which relies on a probability measure over initial states whose legitimacy is itself debated (Callender, Earman, Wallace on the "measure problem" for initial conditions).
Symmetric and cyclic cosmologies since 1996. Gold-style symmetric arrows remain a minority view, but two-time boundary conditions are studied seriously: Lawrence Schulman's Time's Arrows and Quantum Measurement (1997) models consistent two-boundary systems; Carroll and Chen (2004) propose a universe with entropy rising in both directions from a middle; Barbour, Koslowski and Mercati (2014) find a "Janus point" with arrows pointing away on both sides. Penrose turned the Weyl curvature hypothesis into Conformal Cyclic Cosmology (Cycles of Time, 2010): each aeon's remote, massless future is conformally identified with the next aeon's smooth big bang. His claimed observational signatures (concentric low-variance circles, 2010; "Hawking points", 2018) have been disputed by several groups who find them consistent with random Gaussian fluctuations in Planck data, and most cosmologists regard CCC as unsupported. Price's general moral, that explaining the low-entropy past without a double standard is hard, is now mainstream in philosophy of cosmology.
Innocence and Symmetry in Microphysics
This chapter is the hinge of the book. Price identifies an asymmetric assumption so natural that physics barely notices it: μInnocence, the principle that microscopic systems are uncorrelated before they interact. Unlike the macroscopic asymmetry of thermodynamics, it has no observational support, so it cannot be explained away as a matter of boundary conditions and it conflicts with T-symmetry. Drop μInnocence on symmetry grounds and quantum mechanics starts to look like exactly the theory we should have expected: its nonlocality and indeterminacy follow only from QM plus μInnocence.
Chapters 2–4 concerned a specialised topic, the arrows of time. Price now claims the atemporal standpoint matters for mainstream physics. It reveals a presupposition that is temporally asymmetric, plays a central role in every standard reading of quantum mechanics, and without which quantum mechanics looks far less bizarre. Dropping it gains "on both the swings and the roundabouts": we lose a puzzling asymmetry and dent the mysteries of quantum theory. The path ahead has two parts: the philosophy of dependence and causation (chapters 6–7, skippable on first reading) and quantum mechanics (chapters 8–9).
Conflicting intuitions in contemporary physics
The orthodox picture, held for about a century:
- T-symmetry. The laws are (except for the tiny kaon effect) blind to the direction of time: any interaction allowed with one orientation is allowed with the other.
- Boundary conditions. The observed arrows come from asymmetric boundary conditions, chiefly the special state after the big bang, not from asymmetric laws.
- Statistical character. The arrows are large-scale manifestations of the average behaviour of huge numbers of constituents, not asymmetries in individual microprocesses.
Minority dissenters want asymmetric laws (Ritz for radiation, Penrose for the low-entropy bang), but for most physicists T-symmetry is close to obvious. Yet one asymmetric principle almost universally assumed cannot fit this picture: the extrapolation of PI3 to microphysics. As a macroscopic principle, PI3 can be credited to boundary conditions. As a microscopic principle it cannot, because it has no observational basis. So there is a real conflict between two "intuitive" principles.
| Resolution A | Resolution B |
|---|---|
| Keep micro-PI3 (μInnocence) | Keep T-symmetry |
| Conclude the orthodoxy is wrong: not all asymmetry is statistical or due to boundary conditions | Abandon μInnocence |
| Cost: an unexplained lawlike asymmetry in microphysics | Benefit: symmetry, plus a much more classical quantum mechanics (it undercuts a key premise of Bell's theorem) |
Price's verdict: T-symmetry wins, on symmetry grounds and with strong indirect support from quantum mechanics.
Preinteractive "innocence": the intuitive asymmetry
We assume that when two systems meet for the first time, "innocence precedes experience": they are blissfully unaware of each other until they meet. The principle has been stated explicitly:
- O. Penrose and I. C. Percival (1962): the law of conditional independence, in Davies's gloss "influences emanating from different directions in space are uncorrelated". They note it is time-asymmetric: outgoing influences, having "learned something from the experience", are correlated.
- Hans Reichenbach, The Direction of Time (1956, posthumous): the principle of the common cause. When spatially separated events are correlated without direct causal connection, they are jointly correlated with a third event, a common cause, in their common past.
The fork asymmetry
- A fork is the V-shaped structure in which two separated events are correlated through their joint correlation with a third event at the vertex.
- Example: the bodily similarities of identical twins come from their shared history; the zygote is the vertex.
- The asymmetry: forks open to the future (V-shaped, vertex in the past) are very common; forks open to the past (Λ-shaped, vertex in the future) are rare or absent.
- Macroscopically, it rides on thermodynamics: view the world in reverse and you see correlated incoming influences converging in entropy-decreasing processes, the fragments of a wine glass hurling themselves together into an unbroken glass.
The fork asymmetry: correlations between separated events are common when they share a past vertex and rare when they share only a future one.
So macroscopically PI3 is just another face of the special past, as chapter 2 and 3 argued, and is compatible with T-symmetry. But we also assume the asymmetry for individual microscopic interactions.
The particle and the box. A particle passes through a box or instrument of some kind. Afterwards, its state might reflect that fact: natural. Before it reaches the box, with no previous contact direct or indirect, its state could not possibly be correlated with the box's contents. We treat this as obvious without knowing anything about the particle or the box. We say it anthropomorphically: systems are ignorant of each other until they meet, then each "learns" about the other. That intuition, applied to the microscopic case, is μInnocence.
Two kinds of innocence in physics
Price shows there really are two distinct principles by looking first at correlations after interactions.
Macroscopic versus microscopic innocence
| Macroscopic innocence | μInnocence | |
|---|---|---|
| What it denies before interactions | Entropy-reducing correlations | Any microscopic correlation of the kind interaction produces afterwards |
| Its post-interactive mirror | Widespread correlations that, viewed in reverse, lead to lower entropy | Pairwise correlations between particles that have just interacted, even in equilibrium |
| Observed asymmetry? | Yes: every manifestation of the second law | None |
| Can boundary conditions explain it? | Yes (low-entropy past) | Only by begging the question |
The separating case is a gas sealed in a chamber for a very long time, at equilibrium. Its molecules show no entropy-reducing correlations in either direction (unless there is a low-entropy state somewhere in the far past or future we know nothing of). Yet we still say that a pair of molecules that have just collided are not independent because they have interacted. So microscopic post-interactive correlation is a different thing from entropy-related correlation. By symmetry, there is a coherent notion of microscopic pre-interactive correlation that would not violate the second law: the time-inverse of the post-collision correlation. μInnocence is the assumption that there are no such correlations: particles about to interact are as innocent of each other as particles that never meet.
Is μInnocence observable?
Where the asymmetry of μInnocence has been noticed, it has been lumped with macroscopic innocence as a product of boundary conditions (unsurprising, since the distinction was never drawn). But the cases differ.
The argument that μInnocence conflicts with T-symmetry
- Macroscopic innocence is supported by direct observation: entropy-reducing correlations are common in one temporal orientation and rare in the other.
- μInnocence is not observed. We do not observe that the incoming particle is uncorrelated with the box; we assume that interaction produces correlations only toward the future.
- Without an observational basis, μInnocence's status in physics can rest only on its being treated as a fundamental principle in its own right: physics assumes an asymmetry in boundary conditions because it assumes an asymmetric dynamics of correlation.
- An asymmetric dynamics of correlation violates T-symmetry.
- To claim instead that μInnocence is "merely boundary conditions" would remove the only reason for believing there is any such asymmetry.
- So μInnocence, as it operates in physics, is a free-standing asymmetric principle, in conflict with T-symmetry.
Objection 1: violations would need "miraculous" correlations
Unless this merely restates μInnocence, it appeals to statistical, option-counting considerations, which are symmetric. Post-interactive correlations do not seem miraculous only because we already assume the asymmetric principle at issue.
Objection 2: μInnocence is indirectly observed
Physicists (including Penrose and Percival) cite cases where assuming it explains observed asymmetries, such as scattering of intersecting beams.
Two water jets. Two narrow jets of water intersect and water scatters in all directions. Supposedly explained by assuming colliding molecule pairs, one from each jet, are uncorrelated. Run it backwards: water assembles itself into two narrow jets converging on two small nozzles. Pairwise post-interactive correlations between molecules are not enough to explain that; you need widespread entropy-reducing correlations. By symmetry, what explains forward scattering is the absence of entropy-reducing correlations, which is macroscopic innocence. The example never needs μInnocence. Price thinks the same holds for every example offered.
There is no observational evidence for any temporal asymmetry in pre- and post-interactive correlations other than the macroscopic kind tied to the thermodynamic arrow. The appearance of support came from failing to distinguish entropy-related correlation, where observation does reveal an asymmetry, from the microscopic correlation produced by interaction, where μInnocence posits one.
Symmetry or innocence?
If observation were irrelevant, T-symmetry would win on symmetry grounds: symmetric solutions are the default in science and departures need justification. So, absent reason to think otherwise, we should hold that an interaction in the future is just as much a reason to think two systems correlated as one in the past (and no more). Deeply counterintuitive, Price concedes, but once the two asymmetries are distinguished the intuition is groundless and in conflict with symmetry.
But observation might still bear on the question. What should the world look like if μInnocence failed, so that interacting systems were correlated both before and after interacting? Price's striking answer: "We should expect the world to be the kind of world we find in quantum mechanics."
μInnocence and quantum mechanics
Quantum mechanics is the most successful and most puzzling theory physics has produced, and its interpretations largely come down to a choice between evils: problems avoided in one place break out in another (chapter 8). But some results are agreed to embody its strangeness, above all Bell's theorem, due to John Bell (1930–1990), taken to show that the quantum world involves nonlocality, which sits uneasily with special relativity.
Where μInnocence enters the quantum puzzles
- Bell's theorem assumes quantum systems are not correlated with the settings of measurement devices before they interact with them. Thanks to μInnocence this seemed uncontentious. Bell's own relaxation, superdeterminism, posited an extra common cause in the past, which respects μInnocence (chapter 9).
- Later nonlocality arguments (e.g. GHZ) make the same assumption: incoming particle states are uncorrelated with settings of instruments they are yet to meet.
- Copenhagen indeterminacy. Bohr held reality is indeterminate until measured. Without μInnocence one could instead posit a reality fully determinate before measurement but partly constrained by the nature of that measurement.
- No hidden variable theorems. These assume a single hidden state must reproduce the quantum predictions for any possible next measurement. Without μInnocence, otherwise similar systems facing different future measurements would have different hidden states, and the hidden-variable problem becomes "relatively trivial".
- Bohm's theory. David Bohm's hidden-variable theory escapes the theorems by letting measurement affect the hidden variables instantaneously; μInnocence is what makes "instantaneous" seem the only option rather than "in advance".
Price compresses the logical situation into a schema:
QM + μInnocence ⇒ Nonlocality, Indeterminacy, ...Price's schema
The right-hand list varies with interpretation, but virtually everyone agrees there are such consequences.
The counterfactual history of physics. Imagine that physicists had questioned μInnocence on symmetry grounds before quantum mechanics, which is not far-fetched, since T-symmetry got its main impetus from classical statistical mechanics. Quantum mechanics would then have looked like a dramatic confirmation of the hypothesis that μInnocence fails: given QM, keeping μInnocence implies absurdities like nonlocality and indeterminacy. The experimental confirmations of Bell-type predictions would have seemed observational data whose only reasonable explanation is that μInnocence fails, as symmetry had predicted.
Today that is hard to see: talk of nonlocality and indeterminacy no longer sounds absurd, and our commitment to μInnocence is strong. Price's claim is that we have reason to doubt μInnocence on purely classical, symmetry grounds, so it is unwise to keep insisting that quantum mechanics is radically nonclassical in the accepted ways.
Is the symmetry argument as strong as Price thinks? Critics (for example Tim Maudlin and many Bell theorists) reply that statistical independence of hidden states from settings is not a contingent "innocence" intuition but a precondition of experimental science: if it fails, randomised trials and controls lose their point. Others argue μInnocence is supported indirectly by the overwhelming success of models that assume it, or that its asymmetry is ultimately grounded in the low-entropy past via the same route as macroscopic innocence (the line taken in Albert's and Loewer's Mentaculus, where all such asymmetries derive from the Past Hypothesis). Price's rejoinder is that such derivations work for macroscopic, entropy-linked correlations, not for the micro-correlations at issue.
"Measurement independence" is now the named target. The assumption Price calls μInnocence is now standardly labelled statistical independence or measurement independence in Bell's theorem, and violating it is recognised as one of three logically possible escapes from Bell nonlocality (with nonlocality and giving up single outcomes). Two families pursue it: retrocausal models (Price, Ken Wharton, Argaman, Sutherland, Evans) and superdeterministic models (Gerard 't Hooft's cellular automaton interpretation, 2016; Sabine Hossenfelder and Tim Palmer, "Rethinking Superdeterminism", 2020; Palmer's invariant set theory). Experiments have tried to squeeze the room for past common causes: the BIG Bell Test (2018) used choices made by about 100,000 human volunteers, and "cosmic Bell tests" (2017 with Milky Way stars; 2018 with quasar light emitted 7.8 and 12.2 billion years ago) push any common cause of settings and particles back billions of years. These constrain superdeterminism of Bell's kind but, as Price would stress, not future-input dependence, since retrocausal correlations run through the particles' own worldlines, not through a common past.
μInnocence and backward causation
Many will feel it absurd that physical systems might "know" about each other before they meet. A full reply needs the analysis of physical dependence in chapters 6–7, but Price previews one consequence that turns out less objectionable than it looks.
Suppose we control one member of a pair of interacting systems, for instance the setting of the box before the particle arrives. If the particle's state is correlated with the box's, then by controlling the box we control the particle's earlier state. This is not action at a distance (the correlation is carried continuously along the interacting worldlines), but it is a kind of backward or advanced causation.
The bilking argument and why it fails here
The bilking argument (against advanced causation)
- Suppose a later event C is claimed to cause an earlier event E.
- Observe whether E has occurred, and arrange for C to occur exactly when E has not occurred, and vice versa.
- Then no consistent outcome is possible given the claimed link.
- So the claimed backward link is refuted. Applied here: observe the incoming particle's state, then set the box to defeat the claimed correlation.
To bilk, we must observe the particle before it reaches the box, with a second box or measuring device in its path. If μInnocence is in doubt, that observation is compromised twice over:
- Measurement may alter the past. If measurements can affect earlier states, what a measurement reveals is not in general what would have been there without it. Even if the correlation failed with the second device present, we could not infer it would fail without it.
- Correlations last only since the last interaction. A correlation established by interaction normally survives only until the system interacts with something else. Failure of μInnocence requires a correlation between the box setting and the particle's state from the time of the particle's last interaction. Interposing a measuring device confines the advanced effect to the interval between that measurement and the main interaction, and the contradiction slips out of reach.
These escapes would close if we could observe the particle without disturbing it. Classical physics is often said to have assumed perfectly non-intrusive measurement is possible or approachable without limit. Quantum mechanics overturned exactly that: almost everyone agrees it shows measurement cannot be separated from the behaviour of the observed system. So symmetry alone might have led us to predict the demise of classical measurement, since non-intrusive measurement is incompatible with microscopic T-symmetry once μInnocence goes.
The next step
Two plausible principles conflict: microscopic T-symmetry and microscopic innocence. One must go. Quantum mechanics already supplies indirect evidence for the symmetric option, but "familiarity has bred contentment in physics, and the reductio has lost its absurdum." Choosing between T-symmetry and μInnocence must be done anyway; if we favour symmetry, the quantum dividends come at no extra cost, unlike the usual trade-offs between interpretations.
Two tasks follow. One is quantum (chapters 8–9). The other is philosophical: μInnocence is entangled with our intuitions about causation, and causation has its own striking arrow (causes precede effects). Is the asymmetry of μInnocence the same as the arrow of causation? If so, attacking μInnocence would mean attacking all ordinary causal intuitions, raising the stakes "by several orders of magnitude". Price thinks not: they are separate issues. His account (chapters 6–7) will be that causal asymmetry rests on a subjective, perspectival element in the concept. Ironically, physicists' belief that causal direction is subjective has made the backward-causation approach harder to see: if direction is perspectival, how can quantum mechanics show there is backward causation? The answer is that abandoning μInnocence is a thoroughly objective proposal that is naturally described, from our asymmetric perspective, as backward causation.
Audit your independence assumptions. In statistics and machine learning, "the inputs are independent of what will later be done with them" is usually treated as obvious. Price's analysis is a reminder that independence assumptions have a direction, and that the evidence for them may be evidence for a different, macroscopic principle. When a model produces bizarre conclusions (here, nonlocality), check whether an unexamined independence assumption is doing the work.
In Search of the Third Arrow
We take for granted that events depend on the past and not the future, that causes precede effects, and that we can affect only what comes later. Price asks where these asymmetries come from, given symmetric physics. The leading answer, a physical "third arrow" (the fork asymmetry) mediating between time and causation, fails: the fork asymmetry is macroscopic and vanishes at the micro level, exactly where our causal intuitions remain firmest. Rejecting eliminativism and hyperrealism, Price defends the perspectival (agency) view: causal asymmetry is a projection of our asymmetric situation as deliberating agents, something like a secondary quality.
Sunglasses at night. You wear sunglasses on a cloudless summer evening (the kind of neighbourhood where people wear sunglasses at night, drink serious coffee and dress in black). Photons from a distant star pass through your polarising lenses onto your retina. Some passed long ago through sunglasses discarded by an alien astronaut near the star. Near the end of their journey, does their state depend on the lens they will pass through in a moment? Intuition: no. On the lens they passed long ago? Possibly. It may depend on the past but not the future. Yet in the photon's world, with no objective direction of travel, what could sustain the difference?
This is the box-and-particle puzzle of chapter 5 with a face. But the asymmetry of dependence also shows up in mundane cases: after a collision, the red billiard ball's motion depends on having been struck by the white ball, after the collision but not before. If that too were μInnocence, μInnocence would hardly be controversial. Price's long-range aim is to separate the uncontroversial asymmetry (billiard balls) from μInnocence (photons).
Three target asymmetries
- Dependence. Events often depend on what happens earlier, never (or almost never) on what happens later.
- Causation. Effects occur after, never (or almost never) before, their causes.
- Agency. Human actions influence later events, not earlier ones.
The third looks anthropocentric and derivative, but Price will argue it is the key to the other two.
Physicists who preach but do not practise
Many physicists regard causation as partly subjective and so physically uninteresting; the respectable notion is the symmetric one of deducibility under deterministic laws. Stephen Hawking recalled being disappointed by Reichenbach's The Direction of Time: if A evolves into B, one could equally say B caused A, "so causality does not define a direction of time".
But such physicists rarely notice how these very notions constrain which theories they find acceptable:
- The photon case. If the asymmetry of dependence were merely subjective, physics should treat dependence on the past and on the future polarizer alike. Almost nobody does.
- Standard quantum mechanics. The photon's quantum state reflects the past polarizer but not the future one: a concrete representation of the dependence asymmetry, flatly at odds with calling it subjective. (Price thinks this is a defect of the standard model, chapter 8.)
- Wheeler's delayed choice. In John Wheeler's version of the two-slit experiment, the choice between one-slit and two-slit arrangements is made after the particle passes. The predictions are unchanged. Wheeler asks whether present choice influences past dynamics "in contravention of every principle of causality", and concludes instead that "the past has no existence except as it is recorded in the present."
Wheeler's case shows two things. The "principles of causality" are not in the physics: they are a metaphysical constraint on interpretation. And they are so powerful that a theorist would rather sacrifice the observer-independent existence of the past than violate them. Price's demand is not that physicists change their tune about causal subjectivity but that they practise what they preach, which requires understanding the intuitions ("know one's enemy").
Delayed choice in the lab. Wheeler's thought experiment has been realised: Jacques et al. (2007) with single photons and a randomly, space-like-separated chosen interferometer configuration; the delayed-choice quantum eraser (Kim et al. 2000; Ma et al., entanglement-swapping versions, 2012); and a satellite version over 3,500 km (Vedovato et al. 2017). The quantum predictions hold in every case. Interpretations still divide exactly as Price describes: Copenhagen-style readings deny a determinate past, Bohmian and many-worlds readings keep a past without retrocausality, and retrocausal readings (Price, Wharton, Sutherland) take the later setting to constrain the earlier state.
Causal asymmetry: the nature of the problem
The question presupposes that the cause–effect relation is itself asymmetric: a compass needle identical at both ends cannot be said to point north. So there are two sub-problems: what distinguishes causes from effects (the relation's internal arrow), and why that arrow aligns with the arrow of time.
Humean conventionalism
One can "kill two birds with one fiat": the relation is symmetric and "cause" simply labels the earlier member. On the orthodox reading of David Hume (1711–1776), causation is constant conjunction, a symmetric notion, and "cause/effect" mark earlier/later. Compare numbering the acts of a play: Act 1 is performed first by convention; plays could be numbered like countdowns.
Standard objections to conventionalism
- Too weak. It makes it a merely linguistic matter that we can affect the future and not the past; intuitively there is more to it.
- Too strong. It makes backward and simultaneous causation logically impossible, true by definition like "a spouse is a marital partner", though they seem merely non-actual.
- No causal theory of time. It blocks explaining temporal order by causal order.
Price will defend a more sophisticated conventionalism (chapter 7) that meets 1 and 2. He welcomes 3: since time has no intrinsic direction, causation should not be asked to supply one.
A third arrow?
The third arrow strategy: the causal relation can be characterised in physical terms, and that physical relation happens (de facto, not by law) to hold asymmetrically in our world, aligned with time.
The fork asymmetry
The only plausible candidate is the asymmetry met in earlier chapters: outgoing processes from a common centre tend to be correlated, incoming ones meeting at a centre are not. It must be characterised without causal notions. It has two ingredients:
- Sufficiency: if there is a suitable central event in the common past, we tend to find correlations between separated, not directly connected events (forks with prongs to the future).
- Necessity (converse): we find such correlations only under these conditions.
So in pre-causal terms we find V-shaped forks open to the future, not Λ-shaped forks open to the past, and every non-local correlation of the relevant sort belongs to a V-fork. Two ways to link it to causation: define causes by the independence of combining causal factors (look at the prongs and say "these are effects"), or define causes by their role of explaining non-local correlations (look at the vertices and say "these are causes").
Reichenbach's common cause principle (formal)
Whenever A and B are correlated, P(AB) > P(A)·P(B), and neither causes the other, there is an earlier event C such that:
- P(AB | C) = P(A | C)·P(B | C) (C screens off A from B)
- P(AB | ¬C) = P(A | ¬C)·P(B | ¬C)
- P(A | C) > P(A | ¬C)
- P(B | C) > P(B | ¬C)
For the third arrow strategy, the order matters: a non-causal statistical asymmetry must come first, and causation is defined from it.
Too few forks
Price's central charge: there are not enough asymmetric forks to go around. Two reasons:
- Microphysical symmetry (the main one, below): the fork asymmetry is macroscopic, depending on coordinated behaviour of huge numbers of components that are themselves symmetric.
- Rare or weak common causes. Many common causes are too infrequent or insignificant to produce actual correlations above background noise.
The only fire in history. A fire causes heat and smoke. Perhaps heat and smoke are correlated in the world. But the causal fact does not depend on that: had this been the only fire in the history of the universe, it would still have caused both. Or suppose heaters and smoke machines produced so much independent heat and smoke that fire-produced correlations were negligible: still no difference to the fact that this fire caused both. Causal facts are insensitive to the amount of actual correlation. Even if every non-local correlation has a common cause, not every common cause produces a non-local correlation.
The reply that common causes tend to produce correlations, or would if instantiated, introduces modal notions (tendency, what would be) that are likely to carry temporal asymmetries of their own.
Two ways to misuse a fork
- Disguised conventionalism. Slipping a definitional temporal asymmetry into the account, so that it collapses into Hume's view after all. Example: defining causes as preconditions and effects as postconditions, then noting the fork pattern. The right method is to define causes by the independence feature and discover they are generally preconditions.
- Passing the buck. Appealing to a notion whose own temporal asymmetry is as mysterious as causation's. Not always fatal, since a problem may be more tractable in new form, but one must be clear what has been achieved.
How probability smuggles in direction
- Evidential probability that conditions on evidence available before a time builds in a conventional asymmetry.
- Objective chance is usually taken to be forward-looking, dependent on past not future: an asymmetry as mysterious as causation's (buck-passing).
- Frequencies are symmetric and Reichenbach's own choice, but conditional probabilities defined as "the frequency with which A succeeds B" are asymmetric by convention.
Arntzenius and the hundred coins. Frank Arntzenius proposes relating causation to Markov transition probabilities invariant under changes of initial distributions. Price's counterexample: 100 fair coins are each tossed once at time t. P(heads after | heads before) = 0.5, whatever the initial distribution. The reverse transition probability is not invariant: if 99 coins began heads, P(heads before | heads after) = 0.99; if 99 began tails, 0.01. An asymmetry. But specify the final distribution instead: told that after t, 99 coins show heads, the evidential P(heads after | heads before) becomes 0.99 and P(heads before | heads after) becomes 0.5. The asymmetry simply tracks the choice of initial rather than final boundary conditions. Defending that choice either assumes it (conventionalism) or rests on some further asymmetric notion of probability (buck-passing).
Changing frequencies, two friends, and God's fires
A common formulation:
(6-1) Changing the frequency of a common cause changes the frequency of its joint effects; changing the frequency of a common effect does not change the frequency of its joint causes.
"Changing" is ambiguous.
- As natural variation, it avoids conventionalism but captures no real asymmetry, and says nothing about causes whose frequency never changes.
Friends by chance. Two friends who work in the same part of town sustain their friendship entirely on chance encounters, once or twice a month. When they meet, their prior movements were correlated (both entered the same café at about the same time). In months with more meetings, there are correspondingly more of the earlier "coincidences". Natural changes in the frequency of a common effect go with changes in the frequency of its contributory causes, contrary to 6-1.
- As intervention, 6-1 is plausible, but it embodies our perspective as agents, who can affect the future and not the past.
God's millennium fires. Imagine God choosing among possible histories, with a fancy to mark January 2001 by many millions of tiny accidental fires around the globe. In the histories She might choose, there are vastly more "accidental" conjunctions of combustibles, oxygen and ignition just before that date. By opting for such a history, God increases the frequency of a common effect (fire) and thereby produces a correlation among its joint causes. From God's perspective, 6-1 fails. Its plausibility for us reflects only that for us the past is fixed and unmanipulable, which chapter 7 will argue is a convention, one we are not free to change.
A fourth arrow? Lewis's counterfactuals
David Lewis analyses causation counterfactually: A caused B roughly when if A had not happened, B would not have happened. Causal asymmetry then traces to an asymmetry of counterfactual dependence: "the way things are later depends on the way things are earlier. Not so in reverse." Illustration: if Price's parents had not met in the 1940s, this book would not have been written; but "if Time's Arrow and Archimedes' Point had not been written, Huw Price's parents would not have met" is absurd.
Lewis is careful: this fourth arrow only transfers the burden. He explains it by the asymmetry of overdetermination: events have few earlier determinants but very many later ones (A is a determinant of B if just sufficient, given the laws, to ensure B). Whatever happens leaves "widespread and varied traces at future times", most too minute or dispersed for any detective, and many disjoint combinations of traces each determine the fact. Lewis cites the expanding spherical wave as a special case: countless tiny samples of the wave each determine the emission event.
The symmetry of micro-forks
Here Lewis illustrates vice. Chapter 3 showed that radiation's asymmetry comes from an imbalance between big coherent sources and big coherent sinks; represented atomistically, it vanishes.
The atom-source and atom-sink argument
- Take a single atom-source i at time t. Its presence makes a difference after t: an outgoing ring of correlated changes in the field.
- To detect that ring we must correct for the background: know the field's state just before t (its state independent of i). Given that, and that i is the only variable, i is overdetermined by the later field.
- Take an atom-sink i at t. In the sink-based representation, its presence makes a difference before t*: an incoming ring of correlated changes.
- To detect that ring we must know the field just after t. Given that, i is overdetermined by the earlier field.
- So at the micro level there is no asymmetry of overdetermination. The macro asymmetry arises because big coherent sources exist and big coherent sinks do not.
- Size matters only because it lets us ignore the background: big coherent sources are so improbable that background is negligible, which is why one segment of the pond ripple tells us what happened at the centre without knowledge of initial conditions.
Turn down the transmitter. As a signal weakens it merges into noise, and recovering the source needs more spatial sampling or more knowledge of the prior field, until in the limit we need complete information, as in the atom case. Overdetermination is a matter of degree that fades out at the micro level; it is implausible that causation and dependence fade in the same way.
Micro-forks are symmetric: hold a micro-event fixed and conservation laws correlate its successors and its predecessors alike.
The micro-fork fallacy
Take micro-events P, F1, F2. Holding P fixed, F1 and F2 may be correlated (by conservation of momentum, say): had F1 differed, F2 would have. That looks like a fork asymmetry, but the same holds in reverse: hold F fixed and its predecessors P1 and P2 are correlated. Temporal direction is irrelevant.
The fork asymmetry in the world is an asymmetry of gross forks. Like a picture on a computer screen that dissolves into pixels under close inspection, it is "not pictorial all the way down". It depends on the ordered alignment of vast numbers of micro-events. At the micro level there are forks in both directions, but only relative to a perfectly fixed background. So if causal asymmetry needs the fork asymmetry, there is no fact about whether the incoming photon caused the electron to leave the electrode or vice versa. The fork asymmetry disappears where it is needed most. μInnocence obscured this, but it is a powerful intuitive asymmetry with no physical grounding, so it compounds the mystery instead of solving it.
Two extreme proposals
We want microphysical events to have causes and effects, yet micro-physics is symmetric. Two extreme responses:
| Eliminativism (error theory) | Hyperrealism | |
|---|---|---|
| Claim | There is no real causation, at least in physics. Bertrand Russell: the law of causality is "a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm." | Causation is a real ingredient of the world over and above physics; physics is symmetric only because it ignores causal relations. |
| Appeal | Popular among physicists | Saves causal talk from the eliminativist |
| Problem | The damage spreads: macro-causation decomposes "horizontally" into chains and "vertically" into micro-relations, so no micro-asymmetry means no asymmetry anywhere, and we lose the right to say actions affect the future not the past. Even Russell lapses into conventionalism ("a mere tautology": an effect is defined as subsequent). | Epistemically inaccessible: we could never tell whether our causal ascriptions are back to front, since neither micro-physics nor (cosmologically explained) thermodynamics bears on it. And irrelevant to agency: if there were no such extra-physical facts, would anything seem different? |
The perspectival view
Price's recommendation is "modest and pragmatic": perhaps causal asymmetry is not in the world, but its appearance is a product of our standpoint, like the warmth seen through rose-tinted spectacles, or, in Kant's analogy, the apparent motion of the heavens that Copernicus showed to be the motion of the viewpoint.
Why perspectivalism beats the alternatives
- Economy. Like the apparent motion of the stars, which is far more widespread than the real motion of the Earth that explains it, apparent causal asymmetry can be far more widespread than the actual asymmetry that explains it. This handles the shortage of forks.
- Not eliminativism. The eliminativist assumes causal talk tries to do what physics does and condemns it when nothing physical matches. The perspectivalist reads the discovery as showing causal talk and physics are "in different lines of work". Compare "here" and "now": perspectival, yet not in error, and not in need of surgery.
- We are strikingly asymmetric. We remember the past and act for the future. It is unsurprising that this asymmetry is entrenched in how we describe the world, and that it does not wear its origins on its sleeve.
- Secondary qualities as model. Colours, smells and tastes are partly products of our sensory apparatus; seeing this took a Galileo, and their status is still debated. So (a) appearance and reality are hard to separate, and (b) even once separated, abandoning the vocabulary is not a serious option, even in science.
The agency theory of causation
The relevant feature of our perspective is that we are agents. Roughly, to think of A as a cause of B is to think of A as a potential means of bringing about B (or making it likelier). The idea goes back to Frank Ramsey (1903–1930), in his later paper on laws: "from the situation when we are deliberating seems to ... Arise the general difference of cause and effect." This agency or manipulability theory has been unpopular, but its standard objections are overrated, no stronger than parallel objections to standard theories of colour.
On the agency view, the asymmetry of causation is the asymmetry of the means–end relation. Causes are potential means and effects potential ends. In circumstances where we can do one thing to achieve another, we cannot reverse the order, bringing about the second to achieve the first. That gives the causal arrow. Its alignment with time follows from the fact that we normally cannot achieve an earlier end by a later means. "The reason that we see asymmetry everywhere we look is that we are always looking through an asymmetric lens."
Escaping a circle, projecting an arrow
The circularity objection: the asymmetry of agency depends on that of causation; we can act only for later ends because causes precede effects.
Price's reply in four steps
- If the alternative is to ground causal asymmetry in some objective physical asymmetry (as third-arrow theorists do), that same asymmetry is available to explain agency.
- So: first explain the asymmetry of agency using ordinary causal notions freely ("knowledge is an effect, actions are causes").
- Then rewrite the explanation, replacing each appeal to causal asymmetry with the objective physical asymmetry third-arrow theorists favour. The result explains agency without appealing to causation.
- Paul Horwich shows how: the fork asymmetry underpins the knowledge asymmetry (we know more about the past), since "the processes that give us knowledge about the past are typically [future-directed open forks]", stated in terms of processes and correlation, not causation.
Why is this immune to the micro-fork objection? Because agents are essentially macroscopic and depend on the very thermodynamic asymmetry that is the source of the physical asymmetries third-arrow theorists invoke. The account uses only the correct part of its rivals' theory and succeeds where the third arrow does well (common, macroscopic cases) and also where it fails (rare and microscopic cases): "a small objective change in one's viewpoint can alter the apparent character of one's entire surroundings".
The price is that causal asymmetry becomes anthropocentric, like a secondary quality. Price accepts that and denies it is a loss: if what we seemed to lose was illusory, our ontology is unchanged and our epistemology has gained, since we now understand the source of the illusion.
Is the agency theory too anthropocentric? Critics object that it cannot account for causation before agents existed (the big bang caused the CMB), and that it seems to make causal facts mind-dependent. Price's answer (developed in chapter 7 and in later work, "Causal perspectivalism", 2007, and with Brad Weslake) is that the concepts are perspectival while the truth-conditions, fixed by our conventions, are objective: just as "red" applies to things nobody sees. Interventionist accounts (James Woodward, Making Things Happen, 2003; Judea Pearl's Causality, 2000) took the manipulability idea mainstream by defining causation through hypothetical interventions, not human actions, though critics note that the asymmetry of interventions still needs grounding. Statistical-mechanical accounts (Albert, Loewer, Kutach, Fernandes) try instead to derive the asymmetry of influence and of records from the Past Hypothesis, a modern form of the third-arrow strategy that Price regards as explaining the agent's situation, not causation itself.
Summary
- We have powerful intuitions about the asymmetries of causation and dependence, even in simple physical cases.
- They are not "merely subjective" in the sense of irrelevant to physics: they shape current theory centrally.
- The fork asymmetry is the only plausible objective basis, and it is insufficiently general; above all it fails in microphysics. The models of radiation and thermodynamics suggest it is essentially macroscopic.
- This has been hidden by μInnocence and by disguised conventionalism and buck-passing, especially through modal notions such as probability and counterfactual dependence.
- Eliminativism and hyperrealism are heroic options: one convicts causal talk of massive error, the other posits reality beyond physics.
- The perspectival view makes both unnecessary. Causal asymmetry reflects an asymmetry in us. "In accounting for appearances, a little asymmetry goes a very long way."
- The agency theory provides the best basis: deliberation has the right intrinsic asymmetry and temporal orientation, and since we all occupy the agent's perspective all the time, it colours our view of the world in ways hard to detect.
Causal claims in analytics are agent-relative. The interventionist descendant of Price's view is the working theory behind A/B tests, uplift models and causal machine learning: "X causes Y" means intervening on X changes Y. Price's warning applies directly: observational correlations (forks) are thin, noisy and macroscopic evidence of causal structure, and the direction you read into them may come from your own position as the one who acts, not from the data.
Convention Objectified and the Past Unlocked
Price recasts the perspectival view in terms of counterfactuals and answers objectors on both flanks. Against philosophers who say conventionalism makes causal asymmetry too weak, he shows how a convention we cannot choose to change yields an asymmetry that is objective relative to our orientation. Against those who say it rules out backward causation by fiat, he shows that a convention of holding fixed only the accessible past leaves room for it, via Dummett's loophole in the bilking argument. When the subjective strands are pruned away, an objective possibility remains, advanced action, and symmetry favours it: it is "the proper default option for reality".
Physicists are tempted to dismiss causation as subjective but do not practise what they preach; philosophers tend to treat it as fully objective. Price's strategy is to focus on the asymmetry of dependence (why the future depends on the past) and to read it through counterfactual conditionals, which separates the convention itself from the features of our situation that make us adopt it.
Asymmetry conventionalized
Back to the photon from a distant star. Intuitively:
- (7-1) If the distant polarizer had been oriented differently, the state of the incoming photon might have been different (or it might not have arrived): true.
- (7-2) If the local polarizer had been oriented differently, the state of the incoming photon might have been different: false.
The standard semantics for a counterfactual (7-3) "If X had happened at t₁, Y would have happened at t₂": hold fixed the course of events before t₁, add X, and see whether Y at t₂ follows from the laws. On this reading 7-2 is false trivially: the supposition holds fixed the photon's state before it reaches the local polarizer, so of course that state does not change.
The photon's path. 7-1 holds Region 1 fixed and varies the distant polarizer; its true temporal mirror would hold Region 3 fixed and vary the local polarizer. 7-2 instead holds Region 2 fixed, so it is not the mirror of 7-1.
No physical asymmetry is needed. The mirror image of 7-1 would hold Region 3 fixed and vary the local polarizer. Claim 7-2 holds Region 2 fixed. So 7-1 and 7-2 are not temporal inverses, and their different truth values need no asymmetry in the world. Why doesn't the present affect the past? Because "if the present had been different, the past would have been different" means "suppose the present different while the past is the same; then the past is different", which is false on logical grounds.
The two-pronged objection to conventionalism
- Too weak. It makes our ability to affect the future and not the past terminological: couldn't we hold the future fixed instead, and say the present depends on the future? Then how can one way be right?
- Too strong. It makes backward dependence impossible by definition. David Lewis: it "gives us more of an asymmetry than we ought to want"; readers make sense of time-travel stories, and physicists seriously consider tachyons, advanced potentials and closed timelike curves. "It will not do to declare them impossible a priori."
Convention objectified
Reply to objection 1: the "choice" of convention is constrained by circumstances we cannot control, so familiar that we mistake the resulting asymmetry for an objective feature of the world. Things may seem more objective than they are when the source of the subjectivity is not obvious.
The key constraint: counterfactuals are used in deliberation, and deliberation is temporally asymmetric. As structures in spacetime, agents are orientable, and an agent cannot choose or change her orientation. Our orientation may be contingent, not fixed by law (Gold's universe allows oppositely oriented creatures), but we depend on the thermodynamic gradient and cannot move to a region where it runs the other way. So we must hold the past fixed. It is objectively true from our perspective that we cannot affect the past; missing the relevance and contingency of orientation, we take a relational truth for an absolute one. The result is quasi-objectivity.
The one-way locomotive. A locomotive that cannot reverse runs on the transcontinental line between Perth and Sydney, with no turntables or loops. Which stations it may visit in future is an objective matter, depending on two things: its location and its orientation (facing east or west). Accessibility shows a marked east–west asymmetry, from the locomotive's point of view, only because of the imposed one-way condition. Deliberation is the same: given our orientation in time, one direction is accessible. Turn us round and different parts of reality would seem accessible; make us symmetric and there would be no apparent asymmetry (though deliberation seems essentially asymmetric).
The asymmetry of agency
Two complementary ways to characterise it:
- Formal. Map an ideal deliberative process atemporally, steps laid out en bloc, and point to an intrinsic asymmetry along its time axis: little more than rewriting dynamic models of deliberation in an atemporal key.
- Phenomenological. Objectively, an agent is a natural system correlating inputs (environmental data) with outputs (behaviour), modulated by internal state. From a detached view that is broadly symmetric: a "black box" mediating otherwise unlikely correlations between events on its two temporal sides. The asymmetry belongs to the internal perspective: inputs feel fixed or given, outputs feel open, subject to our control. An "Augustinian god" just sees a nexus of correlations.
The role of counterfactuals
Deliberation takes what is given or fixed (in practice, what is known of what is taken as fixed), adds an option hypothetically, and considers what follows by known laws. So what we hold fixed in counterfactuals is what presents itself as fixed from the agent's perspective. As long as counterfactuals keep their link to deliberation, the "hold the past fixed" convention is dictated by our contingent but unchangeable orientation. We have no choice in the matter.
Are lemons really sour? We could have been built to find lemons sweet; between differently equipped communities there is no fact about who is right. Yet it seems wrong to say lemons are "really tasteless". From the neutral perspective one can only say lemons taste sweet to group A and sour to group B; the absolute form of speech makes sense only from within, and from our perspective it is simply true that lemons are sour. Likewise: reverse-oriented creatures would see dependence running, in our terms, from future to past; from nowhen there is no fact about which orientation is right; but given what we mean, it is straightforwardly true that we can affect the future and not the past.
The account fits microphysical T-symmetry, and while anthropocentric it is not conventional in the problematic sense: we cannot change it by fiat. "Normally we look through our internal constraints, not at them." The more basic they are, the harder they are to spot, and temporal orientation is among the most basic. "We would have to have been gods, Augustinian gods at that, to have seen this all along."
Could the past depend on the future?
Reply to objection 2. It is tempting to say backward causation is impossible anyway, because of paradox. But that is self-defeating for the conventionalist: if the paradox arguments are unconvincing, backward causation's impossibility is not merely terminological; if they are convincing, no conventionalist confirmation is needed. Better to show that conventionalism leaves a loophole, which turns out to be the same one that answers the causal paradoxes.
Escaping the paradoxes of backward causation
Time-travel stories: the heroine goes back and kills her young self, or introduces her mother-to-be to contraception. Contradiction follows, and so (in physical mode) if there were time travel we could design an experiment with contradictory results. Backward causation inherits the same argument: causing your young self to have been pushed under a bus is as suicidal as travelling back to do it yourself.
The bilking argument, formally
- Claim: a later event of type B brings about an earlier event of type A, so there is a reliable positive correlation between B and A on occasions when we can produce B.
- Build a device that detects whether A occurred, giving a positive correlation between A and a third event C.
- Arrange that B occurs if and only if C does not, giving a negative correlation between B and C.
- The triangle of correlations (A–B positive, A–C positive, B–C negative) is logically impossible.
- So in the presence of the A–C and B–C correlations, the claimed A–B correlation must fail. It is "bilked": no reliable correlation can hold between past states and independently determined future states.
The qualification matters. Bilking does not refute ordinary forward correlations, because every reliable correlation holds only in appropriate circumstances, and bilking destroys them.
Cocktails and hangovers. Drinking cocktails is correlated with relaxation and with morning-after headaches. We could bilk the latter by giving nervous subjects headache-inducing medication and relaxed subjects headache-preventing medication. That does not refute the drinking–hangover correlation: the intervention is incompatible with the circumstances in which it holds.
In the backward case the A–B correlation is claimed to hold even when B is independently sensitive to outside factors. But there is still the third side: perhaps the mechanism of the A–C correlation (observing A) disturbs the circumstances required for the A–B correlation. The usual presentation assumes it does not. With that assumption, one reaches Michael Dummett's conclusion (about thirty years before the book): claims to affect the past are coherent so long as it is not possible to find out whether the earlier effect occurred before the later cause.
Dummett's dancing chief. A tribe performs a ritual to ensure the success of a hunt that has already taken place, while the hunters are still away. Their belief is coherent as long as they regard it as impossible to find out whether the hunt succeeded before performing the ritual, which makes bilking appear impossible to them. (Coherent, not necessarily true.)
Price refines Dummett. The perfect parallel with the forward case is not that past events cannot be observed, but that observing them inevitably disturbs the system so that the claimed correlation fails: the ritual works only under conditions any attempt to learn the outcome would defeat. (Another tradition argues bilking fails even with normal access; Price thinks Dummett's route is the strongest and the one that matters for physics.)
The past unlocked
It is a matter of definition that we cannot affect what we know about when we deliberate. It is not a matter of definition that what we can know about is whatever lies in the past. Experience shows that what we know via memory and senses lies in the past; it does not show that everything past is knowable. The link between temporal location and epistemic accessibility is contingent in both directions and underdetermined by experience: some of the past may be inaccessible, some of the future accessible.
Apply it to the photon. Suppose its present state φ depends on the next polarizer it meets. To bilk, we must measure φ before it arrives; but if the only way to measure φ is to pass it through a polarizer, that measurement becomes the next polarizer, and the conditions of the claimed dependence no longer hold. By the claim under test, such a measurement cannot reveal the value φ would have had without it. Bilking becomes impossible.
| Convention for counterfactuals | Hold fixed... | Photon's earlier state depends on the later polarizer? |
|---|---|---|
| Strong | the entire past before the antecedent | No, by definition |
| Weak | only the accessible past (without disturbing the background of the claimed correlation) | May do so, if the world is so structured |
Ordinary usage, Price argues, has a systematic indeterminacy here: it never clearly chose between the two conventions because it rarely meets cases where they diverge. Is this cheating, defining "dependence" to permit backward dependence? No, for two reasons. First, it does not redefine but points to an existing ambiguity. Second, and more important, it exposes an objective question about the correlational structure of the world that does not depend on how the ambiguity is resolved: a possible world-structure physics has almost entirely ignored, partly because it thought the relevant concepts "metaphysical".
Advanced action: its objective core
Price borrows a physicist's term for that structure: advanced action. Triangulate it via the two conventions. Advocates of both might agree that there is a one-to-one correlation between some feature of the incoming photon and the later polarizer setting (the photon "knows" the setting in advance). They disagree only about whether "had the setting differed, the photon's prior state would have differed" is true: false by definition on the strong convention, possibly true on the weak. That disagreement is verbal. A world with advanced action is a world in which the two conventions disagree, one that forces us to choose. Dividing through by convention leaves a physical remainder, and one can even concede the strong convention to opponents and fall back on it.
Counterfactuals: what should we fix?
Why the weak convention is better (in an advanced-action world)
- Suppose all agree on a strict correlation between polarizer setting S and earlier photon state φS.
- Under "hold the entire past fixed", these cannot both be true: (7-4) if we were to bring about S, φS would obtain; (7-5) if we were to bring about not-S, not-φS would obtain. One consequent is false given the fixed past.
- Say the photon is not in φS, so 7-4 fails. Options: call 7-4 false (the agreed correlation does not support counterfactuals) or meaningless (means–end reasoning breaks down: we cannot suppose we do S).
- Both are unsatisfactory: all agree the correlation always obtains, even on future occasions when we do S. Refusing the counterfactuals looks wilful while we claim to bring about S at will.
- Denying free will does not help: the phenomenology is unchanged, we go through the motions of "quasi-deliberation", and the same question about quasi-counterfactuals recurs.
- Holding fixed only what is accessible avoids the problem; "it will be difficult to see why this course was not chosen from the beginning."
This normative question is separate from the empirical one: whether the world has the correlational structure that would force the choice.
Advanced action and μInnocence: the apparent backfire
Is advanced action the same as giving up μInnocence (chapter 5)? If so, the symmetry argument against μInnocence becomes a symmetry argument for advanced action. But a worry arises: perhaps the counterfactual convention explains μInnocence away entirely.
Two Newtonian billiard balls. Frictionless balls X and Y collide at t. Knowing the total momentum before, conservation gives it after, so afterwards their momenta are correlated. But knowing the total after (the same quantity) correlates them before just as well. Still we accept (7-6) "if X's momentum after t had been larger, Y's would have been correspondingly smaller" and reject (7-7) "if X's momentum before t had been larger, Y's would have been smaller". The difference is the convention: for 7-6 we hold fixed the total momentum before t; for 7-7 we do not hold fixed the total after t. Had we done so, we would get the same answer.
7-6 and 7-7 look like what we mean by "correlated after interacting, not before". So the asymmetry of μInnocence seems explained without any objective asymmetry, which would devastate chapter 5. The attempt to find a symmetry argument for advanced action seems to have "backfired in a spectacular way".
Why can't a photon be more like a billiard ball?
First impressions mislead: there is another asymmetry tied to μInnocence that is not reducible to the counterfactual convention, present in our picture of photons but not of billiard balls.
The video quiz. You are shown diagrammatic video clips of micro-interactions and asked: (1) does this process occur naturally? (2) does its reverse occur naturally? For a few Newtonian particles, both answers always match: that is T-symmetry. Now a clip of photons passing a polarizer: each emerges in a state exactly reflecting the polarizer's orientation, and none is correlated with it beforehand. Question 1: yes, natural. Played backwards, photons arrive already matching the polarizer and leave uncorrelated. Question 2: no. Since the counterfactual convention applies equally to billiard balls and photons, it cannot explain this difference. (It does not matter whether the clip shows photons as they really are; the point concerns our intuitions.)
So ordinary "innocence" bundles two principles. For billiard balls, "incoming systems are independent" just means the conventional counterfactual asymmetry, with no asymmetry in the objects. For photons, our sense of a plausible model is guided by a further principle: systems are correlated after but not before they interact, in a non-counterfactual sense that lets us tell forward from reverse videos. Price now restricts "μInnocence" to this second principle. It stays in conflict with T-symmetry after the first is explained away. Newtonian billiard balls, even microscopic ones, do not exhibit μInnocence in this restricted sense.
Does dropping μInnocence force advanced action? Billiard balls lack μInnocence yet seem to involve no advanced action: surely we cannot influence one ball before the collision by fiddling with the other. But defending that would lean on the bilking argument, which assumes we can observe the remote ball first. We can, because real billiard balls are not isolated: they interact with countless things, some of which we exploit to observe them. With all those interactions included, it is far from clear the balls form a symmetric system. So they are no counterexample.
Symmetry and advanced action I: the three-legged diagram
Represent a first interaction as a three-legged diagram: two past legs (incoming systems A and B) and one future leg (the combined system C). Change something on leg A: where does the change show up?
The three-legged diagram: a change on incoming leg A is normally assumed to be absorbed entirely on the future leg C; advanced action is the hypothesis that part of it shows up on the other incoming leg B.
For billiard balls, increase A's momentum. We assume the increase all appears in C. But conservation of momentum alone would equally allow a matching decrease in B, or any mix. Why assume the extreme point? If we have access to B's properties at the time of the change, bilking forces the whole change onto C. Without access, only μInnocence forces the choice.
Advanced action defined, and the symmetry argument
- Definition. Advanced action is the hypothesis that changes on one past leg are not absorbed entirely on the future leg.
- Billiard balls. Rejecting μInnocence allows but does not mandate advanced action; it would be mandated only if a change in A were not fully absorbed in C, and nothing suggests that.
- Photon and polarizer. Let A be the polarizer's history, B the incoming photon, C the joint future. "Changes in A absorbed only in C" means A and B vary independently in real cases with futures like C: that is μInnocence, strongly asymmetric (time-reversed cases with uncorrelated outgoing photon and polarizer look absurd).
- Conclusion. Restoring T-symmetry means allowing photon–polarizer correlations in both temporal directions, and if correlations toward the past are allowed to match those we accept toward the future, advanced action is the result.
Symmetry and advanced action II: the counterfactual route
Reach the same point via counterfactuals. Take the two-polarizer photon, and suppose what is accessible is at most the photon's state before the distant polarizer. On the weak convention, the orthodox independence intuition reads:
- (7-8) With the history before the past polarizer held fixed, changes in the future polarizer's setting do not change φ between the polarizers.
Its temporal inverse:
- (7-9) With events after the photon passes the future polarizer held fixed, changes in the past polarizer's setting do not change φ between them.
7-9 has no intuitive appeal.
The patinated artefact. An artefact known to be a year old could have been made by one of two processes. Given its present condition, does our view of its condition six months ago depend on which process made it? Obviously it may: in one case the distinctive patina came from manufacture, in the other it built up gradually with age. Holding the later state fixed, the intermediate state depends on the earlier history. So we reject 7-9.
Endorsing 7-8 but not 7-9 is a genuine temporal asymmetry, not the trivial one behind 7-1/7-2. Standard quantum mechanics has exactly this shape: knowing the photon's state before the distant polarizer, varying the local setting changes nothing in between; knowing its state after the local polarizer, varying the distant setting changes the inferred intermediate state. The orthodox view is thoroughly asymmetric (wave functions localise after measurement, not before). Advanced action restores symmetry by rejecting 7-8 as well as 7-9.
Why was so simple an argument missed? Partly because we think in counterfactuals with the simpler "hold the past fixed" convention, under which the question collapses into the innocent 7-1/7-2 contrast. And partly because we take classical measurement for granted: with it, bilking gives a reason to accept 7-8 and so underwrites the asymmetry. Perhaps we should have turned this around and been suspicious of classical measurement because it conflicts with symmetry. Where the world lacks non-disturbing measurement, the past and the accessible past come apart and "Dummett's strategy allows us to unlock a little of the past".
Taxonomy and T-symmetry
Another angle: we assume physics cannot sort systems into different kinds just because they have different futures. "Taxonomy is blind to the future", which is close to μInnocence. As a human practice this is understandable: we classify by what we can find out, which concerns the past, so our taxonomy reflects our asymmetry as knowers, as causal talk reflects our asymmetry as agents. But why think the taxonomy of objects in themselves obeys that asymmetry, rather than being, from our standpoint, partly teleological? Only the assumption that the entire past is knowable (which, with bilking, blocks future-based distinctions) stands in the way, and symmetry should make us suspicious of that assumption.
Backward causation is not forward causation backwards
Four patterns of dependence (agent legs on the left, object-system legs on the right; time runs upward; thick coloured legs show where the agent's intervention makes a difference). Advanced action adds influence on the system's past leg but keeps the agent's own orientation, so it is not ordinary causation reversed.
With a four-legged diagram (agent and object system, each before and after), ordinary causation shows the agent's influence on the two future legs. Advanced action adds influence on the object system's past leg, but the direction on the agent's own past leg does not change, because it is fixed by the agent's perspective. Full reversal of the ordinary pattern is something else: the normal case for an agent with opposite orientation (at the other end of a Gold universe). So backward causation in Price's sense is a subtle possibility, compatible with causal direction being perspectival: the world is objectively patterned so that, from our standard perspective, our influence extends as in the advanced-action panel.
Inverted forks and distant effects
A symmetric world would let us affect distant states of affairs indirectly: influencing one past leg of a Λ-fork lets us affect the other. Changing the local polarizer would influence photons yet to arrive. Should symmetry let us do the same with ordinary V-forks, influencing the distant prong by influencing the near one? In theory yes, in practice no, because we cannot influence the near leg between ourselves and the vertex, which lies in our past.
God and the lost message. Suppose God created the world by first fixing the Earth circa 1996 and then choosing earlier, later and more distant parts consistent with it. In 1996 we "remember" that in 1976 we sent a message out of the solar system by rocket, but in 1986 our records of its content were lost. Couldn't God, pencilling in the past, pick a history in which the pre-1986 records show the message we now wish we had sent? In choosing the records She chooses the message in the distant spacecraft, since the craft "rendezvoused" with Earth in 1976 and its message matches the records. Logically, then, the advanced-action view treats both directions alike: if we could affect our past, ordinary V-forks would give us influence at a space-like distance, just as Λ-forks do. The practical difference comes from our orientation on paths between forks, not from any global asymmetry in the pattern of forks.
Summary: saving the baby
Where chapter 7 leaves us
- Too weak? No. Conventionalism is as strong as it needs to be: it explains why the asymmetry of dependence looks objective from our point of view, via a convention our orientation forces on us.
- Too strong? No. Conventionalism allows backward dependence if the convention is sensitive to how we actually engage with the world (hold fixed the accessible past); ordinary usage is ambiguous here.
- The ironic bonus. Asking what world could coherently admit past-on-future dependence is a question about the world itself: a live objective possibility almost invisible to folk intuition and almost ignored by physics.
- Saving the baby. Pruning anthropocentrisms into a basket marked ANTHROPOCENTRISMS leaves an embarrassing anomaly in view: a proposition about the correlational structure of the microworld. Worlds that look unidirectionally causal and worlds that look bidirectionally causal differ objectively.
- Default status. We never had good reason to exclude the bidirectional structure; on symmetry grounds it is "the proper default option for reality, from which departures need to be approved".
Advanced action is just what we should have expected in the world, and quantum mechanics simply shows us how God managed to pull it off!Price, with "Archimedean gall"
Contested moves. (1) Many philosophers resist the claim that counterfactual asymmetry is conventional; Lewis's own account and its statistical-mechanical successors (Albert, Loewer: the Past Hypothesis makes records of the past abundant and makes the past "fixed" in a physical sense) aim to ground it objectively. (2) Critics of retrocausality argue that "unobservable dependence on the future" is either fine-tuned (the correlations conspire to hide themselves, which Wood and Spekkens, 2015, showed is required of any classical causal explanation of Bell correlations) or empirically idle. Price and Wharton reply that the hiding is a natural consequence of the dependence running only through the inaccessible past, exactly as Dummett's loophole requires. (3) The claim that ordinary usage is "systematically indeterminate" between two conventions is a philosophical thesis about meaning, not something the data of usage settle.
Time travel and consistency since 1996. The bilking argument's physics cousins have developed: Novikov's self-consistency principle (billiard balls through wormholes, Echeverria, Klinkhammer and Thorne 1991, finding consistent solutions to every "paradoxical" setup they tried); David Deutsch's 1991 model of quantum closed timelike curves, which avoids paradox by allowing mixed states; and Seth Lloyd and colleagues' post-selected CTCs (2011, simulated optically), in which paradoxical histories simply get zero probability. These support Price's general point that consistency constraints, not logic, decide whether influence on an inaccessible past is coherent. Price's own later work refines the agency view as "causal perspectivalism" (2007), and with Ken Wharton develops "interventionist retrocausality" (2015–2024).
Einstein's Issue: The Puzzle of Contemporary Quantum Theory
Before making the case for advanced action, Price surveys the conventional debate about quantum mechanics as an "impartial spectator", organised around Einstein's issue: is the quantum description complete? His verdict, even before advanced action enters, is that Einstein's incompleteness view is much healthier than its reputation: Bell's theorem rules out only local hidden variables, and the rival complete-description views are just as nonlocal, while also facing the measurement problem and an unexplained temporal asymmetry. No-collapse and many-minds views buy locality at exorbitant metaphysical prices, and decoherence has been attached to the wrong programme.
Einstein helped found quantum theory (the photoelectric effect, light's particle-like aspect) and then rejected what became its standard interpretation, becoming the "great reactionary" in a long dispute with Niels Bohr (1885–1962). Bohr won the popular vote; Einstein was never convinced, to his death in 1955. Two generations on, the theory is unequalled as a tool and its meaning still unclear: the debate is "an auction of lesser evils" in which players downplay their own disabilities. Price diagnoses a deeper cause: the theory has been "grafted onto diseased classical rootstock", the root being temporal asymmetry, and he intends to prune it.
He also flags a dialectical double standard (not temporal this time): Einstein's opponents demand locality of his programme, a constraint almost all their own views fail.
- 1905 Einstein explains the photoelectric effect with light quanta.
- 1925–27 Matrix and wave mechanics; Born rule; Heisenberg uncertainty; the Copenhagen interpretation takes shape.
- 1935 Einstein, Podolsky and Rosen, "Can Quantum-Mechanical Description of Physical Reality be Considered Complete?"; Schrödinger's cat, in reply.
- 1952 David Bohm's hidden-variable theory (and Bohm's spin version of EPR).
- 1957 Hugh Everett's relative-state ("many worlds") formulation.
- 1964 Aharonov, Bergmann and Lebowitz on the time symmetry of measurement.
- 1964–65 John Bell's theorem.
- 1967 Kochen–Specker no-hidden-variable theorem.
- 1982 Aspect's Bell tests with fast-switched settings.
- 1989–90 Greenberger, Horne, Zeilinger (with Shimony): GHZ "Bell without statistics".
- 1990 Bell dies (October).
The quantum view: basic elements
A system is described by a state function or wave function ψ, which generally assigns probabilities to measurement outcomes rather than predicting them uniquely. Hence the question: is the indeterminism fundamental, or does ψ simply not tell the whole story?
The two modes of evolution
- No measurement: ψ evolves smoothly and deterministically by Schrödinger's equation.
- Measurement: ψ "collapses" discontinuously and indeterministically into a state that depends on what was measured and reflects the result (repeat a position measurement and you get the same answer: the new state is "position-definite").
On the complete-description reading, before measurement the particle has no determinate position at all; collapse makes it acquire one.
A tom split in thought experiment!
(Price's heading is a pun: a tom-cat split between life and death, in thought.) The complete-description view became the Copenhagen interpretation. Erwin Schrödinger (1887–1961) objected with the most famous thought experiment in physics.
Schrödinger's cat and the measurement ladder. A cat is shut in a box with a device that kills it if a radioactive atom decays. If the atom is objectively indeterminate until measured, so is the cat, neither alive nor dead until the box is opened. Schrödinger: indeterminacy has been "transferred from the atomic to the crude macroscopic level"; there is a difference "between a blurred or poorly focussed photograph and a picture of clouds or fog patches." The standard reply, that the cat or apparatus itself measures, only postpones the problem. Build two series of variants: replace the cat with ever more complex systems up to a human observer, and with ever simpler recorders down to a few atoms. At the simple end the box's contents are surely isolated and evolve continuously; at the cat end we want collapse inside the box. Where, in a series as finely graded as you like, does collapse switch on?
The two stances (outsider: box isolated until opened; inside instrument: "I am measuring") give incompatible mathematical descriptions, differing on when the discontinuous change happens. This is the measurement problem: if quantum mechanics is universal, it applies to measuring devices, whose interaction with the object should then follow Schrödinger's equation, flatly incompatible with collapse at measurement. Price judges it unsolved.
The measurement problem is entirely a consequence of the complete-description view. If ψ is a fuzzy picture of a sharp reality, the change at measurement is a change in our information, a new photograph showing more detail, not a change in the world. Abandon the assumption that the picture shows everything "and his cat becomes a toothless tiger". This is the ignorance interpretation, or hidden variable view. Its own problems are real, but "the sins of one's enemies do not atone for one's own."
The EPR argument
EPR experiments: two particles interact and separate; quantum theory then lets measurement on one predict the corresponding measurement on the other (position from position, momentum from momentum). Einstein, a realist who disliked Bohr's view that reality depends on what we choose to observe, wanted to show the uncertainty restriction is epistemological only.
The EPR–Bohm setup behind Bell's theorem: two particles from a common source are measured at space-like separation with independently chosen settings.
The EPR argument for incompleteness (1935)
- Perfect correlation. For a suitable pair, measuring position (or momentum) on particle 2 lets us predict with certainty the result of the same measurement on particle 1.
- Locality. What we choose to measure on particle 2 cannot affect the distant particle 1.
- Reality criterion. If, without disturbing a system, we can predict a quantity with certainty, there is an element of reality corresponding to it.
- So particle 1 has a definite position and a definite momentum, whatever we do to particle 2.
- Quantum mechanics assigns no state with both.
- Therefore quantum mechanics is incomplete.
The Copenhagen camp was unmoved, more because its reply was obscure than because it found a compelling counterargument. With hindsight we would say Einstein was right, had Bell not found a "sting in the tail" thirty years later: other EPR predictions show any more complete theory must be nonlocal, rejecting premise 2, the very premise the argument needs.
What Bell does not show. A common misconception is that Bell excludes hidden variables tout court. It does not. Even setting advanced action aside, it counts only against local hidden variables; and nonlocality can hardly be a decisive failing of hidden variables if rival views need it too. It "simply saves his opponents from what would otherwise be a very serious objection."
Even without the original argument, EPR cases favour hidden variables intuitively: if nothing is "there" but a fog until measurement, why does what materialises on one side always stand in the same relation to what materialises on the other? The reply "the particles share one combined state function" describes the correlation without explaining it. Claiming to have reached explanatory bedrock is a prima facie disadvantage, like painting oneself into a corner while the opponent's pieces are still free.
EPR and special relativity: the cost of nonlocality
On the complete-description view, a measurement here produces a real change there, however far away, and the correlations hold at space-like separation. So collapse cannot respect special relativity's constraints.
Two observers, two histories. Measure position on particle 1 and momentum on particle 2, space-like separated. An observer for whom the position measurement comes first says: ψ → both particles position-definite → particle 2 later momentum-definite (particle 1 stays position-definite). An observer for whom the momentum measurement comes first says: ψ → both momentum-definite → particle 1 later position-definite. They disagree about whether there was ever a stage at which a position measurement on particle 2 would have had a definite result. Unless there is a privileged frame in which collapse is instantaneous, the "complete truth" is frame-dependent, unlike special relativity itself, which supplies an objective reality underlying frame-dependent mass, length and time.
The temporal asymmetry objection
On the orthodox complete-description view, between measurements ψ reflects the previous measurement (say, a localised position) and not the next one (say, momentum). Viewed in reverse, a particle would evolve toward a state tailored to a future interaction, which looks odd: a sign of an asymmetry we overlook. Can it be harmless?
- Thermodynamic origin? Unlikely: on this view ψ describes the intrinsic behaviour of individual systems, not statistics of ensembles.
- Anthropocentric (chapters 6–7)? Incompatible with the spirit of complete description: in the photon case ψ between polarizers is correlated with the earlier polarizer and not the later; if ψ is objective, so is that asymmetry.
The fish bone. A 35-year-old man of average weight with high blood pressure and recent stomach pain sees his doctor. At each stage her description reflects tests already done, not tests to come; she does not yet describe him as having a fish bone wedged in his oesophagus, because the X-ray has not been taken. That asymmetry belongs to knowledge acquisition: the bone was there all along. On the ignorance interpretation, ψ is a summary of what could be known from a system's past interactions, so its past-dependence is equally harmless. Only on the complete-description view is it an objective asymmetry in the world, a concrete form of μInnocence.
Aharonov, Bergmann and Lebowitz (1964) argued that the apparent time asymmetry of "reduction of the wave packet" relates to how statistical ensembles are constructed. But that presupposes the ensemble (incomplete) view, on which assigning ψ locates a system in a class, like "35-year-old male with stomach pain". It solves the problem only for Einstein's side; later writers wrongly took it to solve it for the complete-description view.
Three problems for complete description
- The measurement problem (peculiar to it; the most serious).
- EPR nonlocality and conflict with relativity (shared, it turns out, with hidden variables).
- Temporal asymmetry of collapse (peculiar to it).
Price: the measurement problem alone is so serious that the view "would simply not be regarded as a serious contender, if there seemed to be a viable alternative."
The consequences of superposition
Why, then, was Einstein's view rejected even before Bell? Because of the superposition principle: if ψ₁ and ψ₂ are allowed states, so is any aψ₁ + bψ₂ (a, b complex).
In the two-slit experiment, the pattern with both slits open is not the sum of the one-slit patterns, which suggests particles lack definite trajectories: a particle with a trajectory goes through one slit, and its behaviour there should not depend on whether the other is open. Hidden-variable projects aimed to (1) account for the result of any possible measurement from the system's underlying state, and (2) recover quantum probabilities from a distribution over those states. A series of theorems culminating in Kochen and Specker (1967) showed that for simple systems no such set of underlying states exists.
The shell game. Three upturned cups; you may turn over any two. You always find one black and one white stone. Can a prior arrangement explain this? Each cup must hold exactly one stone (never more or fewer), each black or white. But with three stones and two colours, two must share a colour, so some pair of cups would show the same colour. Contradiction. Price's twist: "If the stones know in advance which cups are to be turned over, it is a trivial matter to have them arrange themselves so that one of each colour appears."
Escapes multiplied. Kochen–Specker assume the result for measurement M does not depend on which other measurements accompany it (the colour under a cup does not depend on which other cup is turned). Drop that and contextual hidden-variable theories become possible. The best known is Bohm's (early 1950s), long ignored; as David Albert remarks, many physicists dismissed it because the theorems had "shown" what Bohm had done was impossible. Bell himself championed and reformulated it in the early 1980s, so he did not think his own theorem ruled out contextual theories.
A more basic assumption underlies all the no-hidden-variable theorems: that hidden states do not depend on future measurement interactions, i.e. That the photon's true state does not depend on the future polarizer. Contextualists keep that assumption and multiply variables to suit every measurement combination, preserving the benign classical view that observation simply reads off a pre-existing reality. Price's alternative (chapter 9) abandons that view of measurement, and with it the demand that one hidden state reproduce the results of any possible next measurement.
Bell's theorem
Bell (mid-1960s) examined Bohm's spin version of EPR and found "one of the most puzzling discoveries in the history of physics". Price explains it with a parable adapted from David Mermin.
Ypiaria 1: the Twin Paradox. In Ypiaria (pronounced "E-P-aria"), police could detain anyone at random and ask one question, chosen at random from three: (1) Are you a murderer? (2) Are you a thief? (3) Have you committed adultery? Records survive. The psychologist Alexander Graham Doppelgänger studied cases where both twins of a pair were questioned and found:
- (8-1) Asked the same question, twins always gave the same answer.
- (8-2) Asked different questions, they gave the same answer only about 25 percent of the time.
Doppelgänger's reasoning (Bell's inequality, in miniature)
- By 8-1, whatever disposes a twin to answer Y or N to each question is shared by both twins. Call a disposition by its answers, e.g. YYN.
- There are 8 dispositions: homogeneous YYY, NNN and inhomogeneous YYN, YNY, NYY, YNN, NYN, NNY.
- There are 6 ways to ask different questions: 1:2, 2:1, 1:3, 3:1, 2:3, 3:2.
- For inhomogeneous twins (e.g. YYN), exactly 2 of 6 pairings (1:2 and 2:1) give matching answers: 33 percent. For homogeneous twins, 6 of 6: 100 percent.
- So whatever the mix of dispositions, matching answers in different-question cases must be at least 33 percent.
- The records show about 25 percent. Contradiction: no shared, pre-set dispositions can explain 8-1 and 8-2 together, unless a twin's answer depends on the other twin's question.
Doppelgänger first suspected collusion, but twins were questioned separately, questions chosen at random after separation, and the interrogations were space-like separated (light travelled more slowly in Ypiaria: the speed of a modern carrier pigeon is the best estimate). He reluctantly favoured telepathy (instant influence, at odds with relativity). He knew of a relativity-friendly alternative: precognition, the twins knowing in advance what they would be asked. He rejected it as making the police automatons, unfree to choose; others reject it as causally paradoxical. Price thinks neither objection is sound (chapter 9).
- Twins ↔ spin-½ particles in the singlet state; each question ↔ a spin measurement along one of three directions 120° apart, perpendicular to the flight line.
- P(opposite spin results) = cos²(α/2) for detectors at angle α.
- α = 0°: probability 1 (8-1). α = ±120°: probability ¼ (8-2).
- "Same answer" ↔ opposite spin results (Y/N map to up/down on one side, down/up on the other).
Bell is often hailed as "the man who proved Einstein wrong" (John Gribbin's tribute after Bell's death in October 1990). Price: one-sided. Leaving advanced action aside, Bell shows only that a hidden-variable theory must be nonlocal. Since complete-description views are nonlocal too, "to the extent that nonlocality is a defect, both views are equally at fault"; Copenhagen escapes notice only because of "the comfortable cushion of obscurity" around its commitments about reality.
Bell tests since 1996. After Aspect (1982), Weihs et al. (1998) closed the locality loophole with fast random switching; the detection loophole was closed separately (2001 with ions, 2013 with photons). In 2015 three groups closed both at once: Hensen et al. (Delft), electron spins in diamond 1.3 km apart; Giustina et al. (Vienna) and Shalm et al. (NIST) with photons, at very high significance. The 2022 Nobel Prize in Physics went to Alain Aspect, John Clauser and Anton Zeilinger for these experiments. Remaining logical escapes are exactly the assumptions Price targets: measurement independence (μInnocence), the "freedom-of-choice" loophole squeezed by cosmic and human-choice Bell tests, plus single-outcome assumptions questioned by Everettians. Bell inequality violation now underpins device-independent quantum key distribution and certified randomness, demonstrated over the 2020s.
EPR for triplets: the GHZ argument
The Greenberger–Horne–Zeilinger results achieve Bell's conclusion without statistics, combining the combinatorics of the no-hidden-variable theorems with Bell's multi-particle setting.
Ypiaria 2: the triplet tapes. Triplets, excused adultery for "diminished childhood responsibility", were asked only (1) Are you a thief? Or (2) Are you a murderer? When all three were questioned:
- (8-3) All three asked question 1: an odd number said "no".
- (8-4) Two asked question 2 and one asked question 1: an even number (two or none) said "no".
The GHZ contradiction
- Assign each triplet local dispositions ai (answer to Q1) and bi (answer to Q2), valued +1 (yes) or −1 (no).
- By 8-3: a₁a₂a₃ = −1.
- By 8-4: a₁b₂b₃ = b₁a₂b₃ = b₁b₂a₃ = +1.
- Multiply all four: (a₁a₂a₃)(a₁b₂b₃)(b₁a₂b₃)(b₁b₂a₃) = (−1)(+1)(+1)(+1) = −1.
- But every factor appears exactly twice on the left, so the product must be +1.
- Contradiction: no local dispositions can produce the pattern. The quantum GHZ state of three spin-½ particles, measured along a or b directions, predicts exactly 8-3 and 8-4.
As with Bell, GHZ rules out only local hidden variables, and its objection is to locality, not to hidden variables. It also assumes no advanced action (chapter 9). "Nonlocality is a hook on which both sides of the debate about completeness seem currently impaled."
GHZ and contextuality in the lab. Pan, Bouwmeester, Daniell, Weinfurter and Zeilinger observed three-photon GHZ correlations in 2000, violating the local-realist prediction in single runs. Kochen–Specker contextuality has been tested with neutrons, ions and photons from 2009 onward. A 2012 theorem by Pusey, Barrett and Rudolph (PBR) showed, given a preparation independence assumption (another relative of μInnocence), that the quantum state cannot be merely a representation of ignorance about an underlying state: a blow to "ψ-epistemic" readings like Price's medical analogy, unless that independence assumption is dropped, which retrocausal models do.
What if there is no collapse?
One tradition dodges the measurement problem by denying collapse: the cat is alive and dead after the box is opened, and there is a version of us seeing each. We see only one branch; from the Archimedean standpoint, ψ always obeys Schrödinger's equation. This is the no collapse interpretation, best known as many worlds (reality "splits"), better put as Everett's relative state view, stressing perspective. It is popular in quantum cosmology, since the universe as a whole has no external measuring device to collapse it.
Two difficulties. The recognised one: why does the many-branched reality look classical? The unrecognised one: probability.
The probability problem for no-collapse views
- If all outcomes occur, what can "outcome O has probability p" mean?
- Branch counting: p is the proportion of branches with O (or a generalised measure).
- Classical objection: proportions of alternatives give probabilities only if the alternatives are equiprobable, which makes the analysis circular.
- Illustration: repeated coin tosses grow a tree in which almost all long branches show about 50 percent heads. But the tree is identical for a biased coin. Branch frequencies match real probabilities only if we assume each branching is governed by those probabilities.
- The alternative, defining probability via rational decision, meets strange consequences in a world where every outcome happens.
Quantum Russian roulette (Zeh). A benefactor offers a fortune to be Wigner's friend: to take the cat's place while asleep, so you notice nothing in branches where you die. On a no-collapse view you are guaranteed to wake in some branch, however small the chance of the quantum safety switch, so subjectively it is exactly like a free gift. By the same logic the whole human race should gamble its existence for any benefit: a power station that works with odds of one in a billion and destroys the universe in every other branch would be rational to build. The view even becomes testable: survive quantum roulette far longer than the orthodox half-life predicts and you have strong evidence for it (though skeptical colleagues must play too, or they will say "I told you so" to your corpse in most of their branches; give each a private game and each finds they outlive everyone else). But since no-collapse is a sport of the complete-description view, if there is a viable incomplete alternative it answers a nonexistent problem, so "funding for quantum suicide missions would be a little premature".
Everett and probability since 1996. The probability problem has driven the main Everettian research programme: David Deutsch (1999) and David Wallace (The Emergent Multiverse, 2012) derive the Born rule from decision theory for rational agents in a branching world; Sebens and Carroll (2018) from self-locating uncertainty; Zurek from "envariance". Critics (Albert, Kent, Maudlin, Price himself in a 2010 paper "Decisions, decisions, decisions: can Savage salvage Everettian probability?") argue the derivations smuggle in the very assumptions at issue, close to Price's 1996 complaint. Max Tegmark (1998) popularised "quantum suicide" as a test, which almost everyone now regards as unpersuasive to anyone but the survivor. Many worlds has grown markedly in popularity among physicists since the 1990s.
Many minds?
No-collapse theorists claim to evade nonlocality: Bell correlations hold between outcomes, and on this view outcomes never occur objectively; correlations exist only in a single observer's records within one branch. The extreme form is the many minds interpretation of David Albert and Barry Loewer, in which branches are mental. Albert: what Bell proved is that there can be no local account of correlations between outcomes, but "the idea that there ever are matters of fact about the 'outcomes' ... Is just what this sort of picture denies!"
| Cost of many minds | Price's assessment |
|---|---|
| Radical mind–matter dualism | Very expensive |
| Every sentient system has a continuous infinity of minds | Very expensive |
| Our experience is compatible with the universe being in the vacuum state for all time (Albert) | Disturbing epistemology |
| Locality is saved only for the physics, not the appearances | If locality constrains what we observe (as classical phenomenalists would read it), nonlocality remains; classical physics gives not even nonlocal appearances. These views explain nonlocality rather than eliminate it. |
Advanced action, by contrast, promises to show Bell correlations are not really nonlocal at all, depending on purely local interactions between particles and devices, with no Platonic split between real world and appearances, and with independent motivation from symmetry. Even within the conventional debate, is nonlocality so implausible that many worlds or many minds beats a modest nonlocal theory like Bohm's? Bell thought not.
The decoherence approach
Why does the macro world look classical? Decoherence: uncontrollable interactions with the environment act as measurements, suppressing interference so quantum systems behave like classical mixtures, which is why no Bell experiment works with non-microscopic components. Price notes the parallel with Burbury's "disturbances coming at haphazard" in chapter 2.
Price's critique of how decoherence is used
- Not a collapse mechanism. W. Zurek says decoherence can define Everett's branches and "delineate the border that is so central to Bohr's point of view". But "the environment explains why collapse happens where it does" differs from "the environment explains why collapse seems to happen". The first fails for the universe as a whole (no environment) and faces a slippery slope: no single added particle of environment could "break the wave function's back".
- Undermotivated within no-collapse. Zurek suggests without decoherence we might be "conscious of quantum goings-on". But who knows what being in a superposition feels like, least of all those who say it never happens? Branches are equally real either way; decoherence only yields an ersatz mixture with small interference terms.
- Preferred basis. A superposition can be decomposed in many bases (like choosing grid directions on a map). Decoherence privileges some. That matters if worlds literally split (they need to know where), but less for a relative-state view where reality "can be carved in many ways".
- Its real home. Understood as the study of when classical equations of motion approximate quantum theory, and when Bell-type effects can be neglected, decoherence serves every interpretation, including hidden variables and advanced action, which will need to explain why its effects do not show up more widely.
Decoherence and collapse after 1996. Decoherence is now textbook physics (Zurek's "quantum Darwinism", Joos and Zeh, Schlosshauer's Decoherence and the Quantum-to-Classical Transition, 2007) and has been observed directly (Haroche's cavity experiments, 1996; Nobel 2012; matter-wave interference with molecules of tens of thousands of atomic mass units). It is widely agreed, as Price argued, that decoherence alone does not solve the measurement problem. Objective collapse theories (GRW 1986, CSL, Diósi–Penrose gravity-induced collapse) have been tested: a 2020 underground radiation experiment at Gran Sasso ruled out the simplest parameter-free Diósi–Penrose model. Frauchiger and Renner (2018) and related "extended Wigner's friend" no-go results sharpened the tension among universality, single outcomes and consistency.
Summary: Einstein's live issue
| Objection | Against | Status in Price's survey |
|---|---|---|
| Schrödinger's cat | Complete description | Answered by "early collapse", which leads to... |
| Measurement problem | Complete description | Profound, unresolved; vanishes on incompleteness |
| EPR nonlocality | Complete description | Needs a preferred frame; forbids any explanation of the correlations |
| Temporal asymmetry of collapse | Complete description | Not conventional, not thermodynamic; objective μInnocence |
| No hidden variable theorems | Hidden variables | Leave contextual theories (Bohm) open |
| Bell and GHZ | Hidden variables | Require nonlocality, which rivals share |
| Probability, preferred basis | No collapse | New problems; answers a problem incompleteness never had |
Each side's case consists mainly of arguments against the other. Both are troubled by nonlocality, so it is puzzling that the hidden-variable approach is not more popular. Critics of orthodoxy have mostly fled the other way, into no-collapse views, because the complete-description view was already orthodox: "having already turned their backs on Einstein's alternative", they "pressed on into deeper water". Contemporary physicists "would do well to pay more attention to the cautious voice of the century's great revolutionary." And advanced action will vindicate Einstein's incompleteness view and Bohr's claim that what we find depends partly on our looking, leaving "the two great antagonists of quantum theory ... Arm-in-arm".
The Case for Advanced Action
Bell himself saw a way to keep realism, locality and special relativity: give up the assumption that hidden variables are independent of future measurement settings. He rejected it as incompatible with free will. Price argues that Bell ran together two different ways of dropping independence: a common past (a vast conspiratorial substructure, rightly rejected) and a common future (advanced action, the measurement interaction itself as the vertex of a Λ-shaped fork). The common future hypothesis explains the Bell and GHZ correlations locally, escapes the bilking and fatalist objections, dissolves the no-hidden-variable theorems, and restores microscopic time symmetry: "Bell saw how Einstein could be right about quantum mechanics, but didn't understand what he saw."
Bell's Faustian bargain
Bell's intuitions were unfashionably realist, like Einstein's and Schrödinger's, and he appreciated the irony that from that standpoint his theorem seemed to show objective nonlocal connections, against the spirit of special relativity. His "cheapest resolution" was to go back to relativity "as it was before Einstein", with Lorentz and Poincaré's undetectable aether: a preferred frame in which things do go faster than light.
He noted one way to save locality: drop the assumption that "hidden variables are independent of later measurement settings". But he found this even worse, because it seemed to deny free will: if the experimenter's intervention is "determined in advance, the difficulty disappears."
Nature, as Bell describes it, offers an almost Faustian choice: keep realism, locality and special relativity, but surrender free will. Many philosophers deny free will anyway, or reconcile it with determinism (who is Bell, Price asks, to teach philosophy what is incompatible with free will?). Price's stronger claim: the offer is better than Bell thought. We can take locality and Einsteinian realism and keep free will, via advanced action.
Price diagnoses two sources of the apparent free-will problem: physicists who considered dropping independence thought of a different possibility (common causes in the past), which does raise worries; and, given advanced action, the remaining worry comes from reading the correlation between the earlier state and the experimenter's choice in the wrong direction. Read it the other way and the experimenter stays in control.
Two ways to drop independence
The set-up. A hidden-variable theory gives each system S an underlying state λ beyond its quantum state. S approaches a measuring device M with various possible settings (a polarizer rotatable through 180°). The independence assumption: λ does not depend on M's setting. Suppose, for simplicity, that it fails completely: certain values of λ are perfectly correlated with certain settings. That is a correlation between two spatially distant states (incoming system, device or its precursors), and to save locality we stipulate that neither acts on the other directly. Then how does the correlation arise?
| Common past hypothesis | Common future hypothesis | |
|---|---|---|
| Fork shape | V: vertex in the past | Λ: vertex in the future |
| What sustains the correlation | Some factor in the common past of λ and the setting | The future interaction between system and device itself |
| Motivated by | Reichenbach's common cause principle, μInnocence | Rejecting μInnocence on symmetry grounds |
| Today's name | Superdeterminism | Retrocausality |
| Bell's view | What he usually had in mind; "mind boggling", "conspiratorially entangled" | Never clearly distinguished |
| Price's verdict | Rejected: needs a vast, all-pervasive substructure | Defended: elegant, economical, local, symmetric |
The advanced-action "zigzag" (Costa de Beauregard's term): influence from one setting runs back along particle 1's worldline to the source and forward along particle 2's, staying inside light cones throughout.
Locality saved in the past
Bell's most explicit published comment: even if settings come from "apparently random radioactive devices, or by the Swiss national lottery machines, or by elaborate computer programmes, or by apparently free willed physicists", we cannot be sure they are not influenced by the same factors λ that influence results; but that "would be even more mind boggling than one in which causal chains go faster than light. Apparently separate parts of the world would be conspiratorially entangled, and our apparent free will would be entangled with them."
Why the common past hypothesis fails (Price)
- The free will objection is puzzling. Compatibilists hold free will is compatible with Laplacian determinism; this would be no worse. Why raise it here and not against classical mechanics?
- Bell was probably moved by two other things: a fatalist thought (if the incoming state "already" reflects the setting, we are not free to choose it), dealt with below; and the idea that the common cause would have to be something wholly new.
- The real objection: it needs a universal mechanism of extraordinary scope and discrimination, steering every possible way of choosing settings (lotteries, starlight, physicists) toward the same endpoint. That is "a vast hidden substructure underlying what we presently think of as physical reality". The cure is worse than the disease.
Locality saved in the future
The alternative: a brute correlation between the present λ and the future setting, explained not by an extra common cause but by the existing interaction in the future. The vertex of a Λ-shaped fork is the future meeting of object and device; the prongs are the present λ and the setting.
Ypiaria 3: the interrogators strike back. Recall: same question, always the same answer; different questions, the same answer 25 percent of the time, versus the 33 percent minimum for shared pre-set dispositions. Note first that even inferring shared dispositions from the same-question cases uses the independence assumption (we learn only one disposition per case, and assume it would have been there whatever was asked). Grant it anyway and drop independence later. Suppose twins about to be asked questions 2 and 3: the fact that the questions differ makes it less likely they are in states giving the same answer to 2 and 3 (YYY, YNN, NYY, NNN) and more likely they are in states giving different answers (YYN, YNY, NYN, NNY). Then 25 percent instead of 33 is trivially explained.
Why does this seem implausible? Because we assume events are independent unless they share a causal history: μInnocence. With it in place, only the common past remains, and that can be made very implausible (randomise settings by lotteries, or by light from regions too distant to have interacted). But μInnocence has no physical credentials: PI3 is a macroscopic fact about coherent organisation toward our past. Drop it, and the twins' states can depend on their fate, their future history: "at the time when the two twins separate, they already know, in effect, what questions they are going to be asked."
Was Bell told?
Bell can hardly have been unaware of the idea: backward causation as an explanation of Bell correlations is an old idea on the fringes, as in Olivier Costa de Beauregard's "zigzag causality", which Bell knew. But Price suspects Bell never separated the two hypotheses.
The 1988 letter. Price wrote to Bell in 1988, enclosing two early papers on advanced action. Bell replied: "I have not myself been able to make any sense of the notion of backward causation. When I try to think of it I lapse quickly into fatalism." For his own view he referred Price to a published discussion with Clauser, Horne and Shimony, which turns out to treat the common past hypothesis, with no mention of backward causation. Bell there characterises free variables as having "implications only in their future light cones", being "in no sense a record of ... What has gone before". Both hypotheses violate that, but they tell very different stories about what sustains the correlation, with very different implications for freedom.
The benefits of backward forks
Advantages of the common future hypothesis
- Over the common past: no vast universal mechanism of common causes.
- Over all major rivals: no conflict with special relativity. In Ypiaria, the twins' coupling (conception, birth or a later meeting) lies within the light cones of both interrogations. The effect is not instantaneous, not space-like, and needs no mysterious carrier: the twins "bear the marks of their future as they bear the marks of their past."
- Over everything on offer: it explicitly abandons μInnocence, an unjustified temporal asymmetry, and so respects a symmetry the others ignore.
Why the neglect? Partly because the common cause principle is so reliable elsewhere that people dropping independence assumed common past causes; only on investigating its background do we see it should fail in microphysics. Partly because earlier symmetry arguments for advanced action were misdirected: the ordinary asymmetry of dependence is anthropocentric and violates no physical symmetry; only μInnocence does. And mainly because of two objections: causal paradox (bilking) and fatalism.
Ypiaria 4: causal paradox?
The Ypiarian Euthanasia Society. Could Y.E.S. exploit backward influence for painless retroactive deaths? The claimed earlier effect: if twins Tdum and Tdee will be asked questions 2 and 3, they were (say, with certainty) not in YYY, YNN, NYY or NNN when they last met. A suicide machine must be wired to kill if the twins were in one of those states, so it must detect the twins' states before they are interrogated. But why think such a detector is possible? The states are dispositions to answer interrogation; we know they are revealed by interrogation, not that they are ever revealed any other way. This is Dummett's loophole again. Compare the old argument that space must be infinite, since at the edge of a finite space one could stretch out an arm: the experiment may be physically impossible, because a finite space need have no edge.
Ypiaria 5: the fatalist objection
If the interrogators' choices are correlated with the twins' earlier states, isn't their freedom illusory, their "choice" already written in the twins' minds?
Price's reply to fatalism
- It slides back into bilking. If "already determined" means "accessible", we have the paradox argument, already answered. So take "already determined" to mean only "already true, though not knowable".
- It is strictly weaker than the paradox argument. At best it shows advanced action is incompatible with free will, not that it is physically impossible. Then theoretical simplicity might favour concluding there is no free will, another piece of conceptual anthropocentrism.
- It has a familiar twin: if statements about our future actions are already true or false, we are not free. Physicists, favouring the block universe, have more reason than most to grant future statements truth values.
- Dilemma. If the ordinary (forward) fatalist argument is sound, there is no free will anyway, so it is no objection that advanced action implies none. If it is unsound, so is the backward version, since the arguments are formally parallel.
- Diagnosis. Future statements have truth values, and some describe events that stand in dependence relations with our present actions. What makes us say our actions fix those events, not vice versa, is that they are our free actions. "The fatalist's basic mistake is to fail to notice the degree to which our talk of (directed) dependence rides on the back of our conception of ourselves as free agents." That applies in reverse too, wherever bilking is blocked.
- What the objection needs: both (i) the forward fatalist argument is valid, and (ii) past-tense statements have truth values but future-tense ones do not. (i) is unpopular in an ancient debate; (ii) is something modern physicists have special reason to reject. "An unhealthy foundation for an objection to an otherwise promising scientific theory."
Advanced action in quantum mechanics
As in Ypiaria, Bell's results are easy to explain if particle states depend on their fate. For instance, suppose pair production obeys:
(9-1) In those directions G and H (if any) in which the spins are going to be measured, the probability that the particles have opposite spins is cos²(α/2), where α is the angle between G and H.Price's illustrative constraint
This explicitly makes present properties depend partly on future conditions, violating Bell's independence assumption.
Quantum mechanics builds in the loophole. To bilk, we must detect the claimed earlier effect, the arrangement of spins along G and H, before the later cause. But detecting it is a spin measurement along G and H, exactly the kind of event claimed to produce the earlier effect. "By the time the earlier effect has been detected its later cause has already taken place." And the particles themselves convey the influence: if a particle's fate is a property of it, influence runs back along one worldline to the source and forward along the other, confined to past light cones. No action at a distance, no new field, no conflict with relativity.
Why not simply accept Bell's faster-than-light influence?
All agree Bell correlations cannot be used to signal faster than light, but causal influence is another matter. One worry about space-like influence is that relativity makes it backward in some frame, and backward influence "introduces great problems, paradoxes of causality". If that were the only problem, rejecting the bilking argument would also rescue Bell's own view. But there is a second problem: a space-like influence picks out a unique frame in which it is instantaneous, contradicting the physical equivalence of inertial frames. Bell accepted that ("Einstein local causality fails, and we must live with this"). Advanced action needs no reconstruction of relativity.
Einstein reissued?
Without advanced action, Bell is roughly neutral between Einstein and his rivals. With it, the balance swings strongly to Einstein: standard quantum mechanics does not embody the backward influence needed to avoid nonlocality (its complete-description reading embodies μInnocence), so only a theory that adds to it, an incompleteness theory, can represent advanced action. And such a view keeps the old virtue: by denying that collapse is a real physical change, it has no measurement problem, the point of Schrödinger's cat.
Two objections to "Einstein reissued", and replies
- A new measurement problem? If later measurement settings affect earlier hidden variables, don't we need a principled account of "measurement"? Reply: a satisfactory development must make advanced effects products of physical interactions in general, not of a special class of measurements.
- Is it really realism? If our measurement choices affect the prior state of what we observe, isn't the world observer-dependent, as Einstein disliked in Copenhagen? Reply: (a) human activity affects the world in ordinary ways (trains, planes, laser beams) without threatening realism; (b) an empiricist realist like Einstein might well hold that the direction of causation is for physics to discover; (c) the claim is that physical interactions have earlier effects, not that specifically human acts do. It extends to the past a form of dependence realists accept toward the future.
A deeper issue remains: classically, the state of a system is the sum of its dispositions to respond to future circumstances; if the present state depends on future circumstances, that conception needs rethinking (see "The atemporal view").
Advanced action and the GHZ argument
GHZ, too, assumes independence. In Rob Clifton, Constantine Pagonis and Itamar Pitowsky's presentation (whose terms Price borrowed for the Ypiarian triplets), λ is assumed compatible with all four measurement combinations if (a) settings are fixed just before measurement, so λ lies in the backward light cones of the setting events, and (b) settings come from random generators "sufficiently disentangled" from λ. Advanced action denies that independence follows from (a); (b) only excludes the common past hypothesis. Clifton, Pagonis and Pitowsky argue nonlocality follows "whether or not quantum mechanics is complete"; in effect, GHZ shows only a hidden-variable view could escape nonlocality, and only advanced action lets hidden variables escape independence. "Advanced action provides the only serious alternative to nonlocality." (Price notes the experiment was not yet feasible in 1996; it was done in 2000.)
Advanced action and superposition
The no-hidden-variable theorems presuppose that one set of hidden variables must predict the result of any possible next measurement. On advanced action, hidden variables depend on the actual next measurement or interaction; had it differed, they might have differed. So we should not expect them to reproduce the results of merely possible measurements.
Putnam's superposition puzzle (1965). In "A Philosopher Looks at Quantum Mechanics", written just before Bell, Hilary Putnam describes a system S of many atoms with incompatible properties R and T. In state A, 100 percent have R; in state B, 100 percent have T. In a superposition C of A and B, quantum mechanics might predict that 60 percent have R and also that 60 percent have T: impossible classically, saved only because you cannot test both on the same system. Putnam's Principle of No Disturbance (ND): measurement does not disturb the observable measured, i.e. "the observable has almost the same value an instant before the measurement as it does at the moment the measurement is taken". He claims ND is incompatible with quantum mechanics.
Price: Putnam's formulation is blind to advanced action. Advanced action does say measurement disturbs the observable, yet it satisfies Putnam's explication: the value an instant before matches the value measured. Quantum mechanics actually predicts only (3′) when C is in place and an R-measurement is made, 60 percent have R; and (4′) likewise for T. ND conflicts with quantum mechanics only if the proportion with R is the same for atoms about to be R-measured as in general, which is just Bell's independence assumption again.
The precognitive cat. My house has two outer doors, each with a doormat. My dog sleeps on the mats, moving occasionally; his state is a pair of probabilities of finding him at each door, e.g. (0.5, 0.5), summing to 1 (or less): ordinary classical ignorance. My cat has the same habits but knows in advance which door I will choose, and as she gets hungrier through the day she tends to place herself on the right mat to greet me. In early afternoon her state is (0.6, 0.6): whichever door I choose, a 60 percent chance of finding her behind it. Two incompatible outcomes each with probability 0.6: Putnam's statistics exactly, given a perfectly classical reading as conditional probabilities under each of two incompatible hypotheses. And ND holds: open a door and find her, and she was on that mat an instant before.
| Interpretation | The cat's position before the door is opened | Price's comment |
|---|---|---|
| Copenhagen | Indeterminate: no fact about which mat until a door opens | Had we not looked, there would be no value at all |
| Discontinuous hidden variables (Bohm) | Definite, but opening a door instantly moves the cat; we see the value produced by measurement | Gives up ND; non-classicality confined to the moment of measurement, hence its popularity |
| Advanced action | Definite and continuous; the cat's earlier position depends on the door I will choose | Keeps determinateness, continuity, locality and symmetry |
Instantaneously affecting the present, even the distant present, is thought more plausible than affecting the past. Price sees no sound basis for that preference, and good reasons for the opposite, chiefly that only advanced action reconciles nonlocality with special relativity.
Evidence will always be indirect. Price concedes that advanced-action phenomena "will never be free of alternative explanations": since advanced action requires that classical "leave everything as it is" observation fail, it cannot be observed directly. Even 100 percent correlations would admit other readings. The case must rest on theoretical virtues: relativity-compatibility, time symmetry, determinateness and continuity. Price argues this is legitimate and well motivated, not ad hoc. Critics reply that in 1996 there was no worked-out retrocausal model reproducing all of quantum mechanics, only toy illustrations like 9-1, and that a theory whose key posit is in principle unobservable risks being idle. That is the main gap later work has tried to fill.
The key fits an ancient lock. Recall Wheeler on delayed choice: rather than accept present choice influencing past dynamics, he concluded "the past has no existence except as it is recorded in the present". Physicists have long known "the key might fit the lock" but thought it too fantastic. Price's claim: there are independent reasons for the key, and had they led us to it first, "quantum mechanics seems to be the kind of lock we ought to have expected to find."
The atemporal view
From the Archimedean standpoint these conclusions look natural. Ordinary practice assumes our categories are not forward-looking: photons that passed a given polarizer in the past form a significant kind; photons about to pass a given polarizer do not.
Photons in reverse. View the same class of photons in reverse. They now seem to have many different histories: some arrive via up–down polarizers, some via left–right, and so on. It seems absurd to require them to be blind to those differences, which is exactly what the independence assumption demands; and absurd that all should be in the same state because of an interaction that, from this perspective, lies in their future. The reversal exposes the double standard: familiarity is not a justification, since it is our familiar intuitions that are on trial.
| Uncharitable verdict | Irenic verdict (Price's preference) |
|---|---|
| Physicists have let an assumption "as groundless as the geocentric foundations of ancient cosmology" guide their science, so physics is "likely to be grossly in error" | The assumption makes physics seriously partial, not simply wrong: correct as a description of reality from a particular standpoint, as geocentric astronomy is correct from Earth |
Quantum mechanics as a perspectival theory. Quantum mechanics may be "an idealized codification of all the information about a system available to an observer who is herself embedded in time", gathered through interactions in her past: complete from that standpoint, "though an incomplete one to God". The classical mistake was to assume our temporal perspective is not significantly partial: "In principle, classical observation makes us gods."
An atemporal physics would need to audit its concepts for hidden temporal direction. Notions such as degree of freedom, potential and disposition presuppose an open future for which systems are prepared (we never say a body is disposed to behave a certain way if conditions have obtained in the past). The very notion of a state often looks forward, which partly explains why the independence assumption is so rarely challenged; and the idea that measurement activates pre-existing dispositions must go too, with no clear replacement yet. These problems do not undercut advanced action; seeing them is seeing the perspectival character of ordinary thought. "Once we reach this point, then, there is no going back."
Retrocausality in quantum foundations, 1996–2026. Price's programme has become a recognised research area.
- Symmetry theorems. Price (2012, Studies in History and Philosophy of Modern Physics) proved that a realist model with time symmetry and discrete outcomes plus a plausible "no-retrocausality" assumption cannot reproduce even simple quantum polarisation statistics: time symmetry implies retrocausality. Leifer and Pusey (2017, Proceedings of the Royal Society A) strengthened this into a theorem: any ontological model satisfying a natural time-symmetry condition and reproducing quantum predictions must be retrocausal (or violate their "λ-mediation" assumption).
- Models. Ken Wharton and Nathan Argaman's review "Colloquium: Bell's theorem and locally mediated reformulations of quantum mechanics" (Reviews of Modern Physics, 2020) surveys retrocausal, "all-at-once" Lagrangian models; Roderick Sutherland's Lagrangian retrocausal model; Kastner's transactional interpretation; Wharton's and Sen's toy models reproducing Bell statistics.
- Collider bias. Price and Wharton (2021–2024) recast entanglement swapping and Bell correlations as products of "constrained colliders": correlations induced by a future common effect (a Λ-fork), echoing this chapter's common future hypothesis.
- Two-state vector formalism. Aharonov, Bergmann and Lebowitz (1964) were the seed of the two-state vector formalism (Aharonov and Vaidman), in which a system between measurements is described by a forward-evolving state from the past and a backward-evolving state from the future; weak measurements (Aharonov, Albert and Vaidman, 1988) and "weak values" give it an operational face, though whether they show genuine retrocausality is disputed.
- Critiques. Wood and Spekkens (2015) showed any classical causal explanation of Bell correlations, retrocausal included, requires fine-tuning to prevent signalling; retrocausalists answer that the tuning reflects which variables are accessible. Most physicists still prefer nonlocality, many worlds or operational views, but measurement independence is now universally recognised as a genuine assumption, which is Price's central 1996 point.
When two explanations share the mathematics, compare their ontological bills. Price's dissection of Bell's loophole into a common-past and a common-future story is a model for any modelling dispute: identical predictive mathematics can carry very different commitments (a universe-wide conspiracy versus a local, symmetric dependence). In architecture reviews the same move applies: two designs with identical behaviour can differ hugely in the hidden infrastructure they require.
Summary of the case
- Bell's loophole is real. Dropping the independence of hidden variables from future settings saves locality, realism and relativity at once.
- Choose the right version. A common past (superdeterminism) needs a conspiratorial substructure; a common future (advanced action) needs only local dependence along worldlines.
- The objections fail. Bilking is blocked because detecting the earlier effect requires the very measurement that produces it; fatalism is no worse backward than forward.
- The dividends are broad. Bell, GHZ and the no-hidden-variable theorems all assume μInnocence; drop it and the precognitive cat makes superposition statistics classical.
- The evidence is indirect but legitimate. Symmetry, locality, determinateness and continuity are the grounds, and quantum mechanics is "the kind of lock we ought to have expected to find."
Overview
Price closes by restating the book's conclusions chapter by chapter, setting an agenda for physics and philosophy, and defending the point of the whole exercise. We cannot step outside time, but we can understand how our position within time shapes our concepts, and so, "by subtraction", understand better what lies outside us; the view from nowhen is a campaign for self-improvement, not an attempt to become gods.
The book began with the two opposing views of time (objective present and flow versus the block universe) and has explored the consequences of the block view in two directions: for the physical arrows of time, and for the time-asymmetric presuppositions behind standard thinking about quantum mechanics. Throughout, the question has been how much of the asymmetry we see is objective and how much a by-product of our own asymmetry.
Main conclusions of the book
Price's own summary, by chapter
- Ch 2, the second law. Explain the low-entropy past, not the high-entropy future; the H-theorem and its descendants largely address a pseudo-problem. The traditional criticism (asymmetry in disguise) is well motivated but misdirected: the question is why PI3 fails toward the past. Guard against the double standard. The best tool is imagined time reversal: if an acceptable-looking argument looks counterintuitive reversed, a double standard is in play.
- Ch 3, radiation. The real asymmetry is that there are large coherent sources in the past and not (apparently) in the future. Deriving it from thermodynamics (pond edges) assumes the absence of the very boundary conditions (coherent advanced sources) it seeks to exclude, and the fallacy is worse in Wheeler–Feynman, which assumes advanced radiation exists. The radiative arrow is parallel to, not reducible to, the thermodynamic one; reinterpreted Wheeler–Feynman shows radiation is symmetric at the micro level.
- Ch 4, cosmology. Both arrows depend on the smooth early universe, highly ordered when gravity dominates. Cosmologists underestimate the basic dilemma (explain a smooth bang without a smooth crunch) because of double standards, and reject Gold's symmetric universe with statistics that would equally exclude a low-entropy bang. The consistency and observability of a time-reversing collapse have been neglected on spurious grounds.
- Ch 5, microphysics. Distinguish macroscopic PI3 (low-entropy past) from μInnocence (systems uncorrelated before first interacting). μInnocence has no observational basis and conflicts with T-symmetry. It underlies the arguments that quantum mechanics is strange, so quantum mechanics is in effect empirical confirmation that it fails. Its failure suggests backward causation, whose paradoxes quantum mechanics seems to block.
Price's summary, continued
- Ch 6, causation. Causal asymmetry shapes physics, so it matters. The third arrow strategy fails: the candidate physical asymmetries fail at the micro level. The best account is anthropocentric: causal asymmetry is a projection of our asymmetry as agents.
- Ch 7, convention. Expressed through counterfactuals, conventionalism seems too weak and too strong. It answers the first by showing the convention is not chosen; the second by a loophole allowing backward dependence where access to the past is limited. Choosing a convention is linguistic; whether the world forces the choice is objective. Symmetry favours a world that does: advanced action.
- Ch 8, quantum theory. Hidden-variable views are stronger than usually recognised (all conventional views are nonlocal); the contextualist route is underexplored. No-collapse views face a worse probability problem than recognised.
- Ch 9, advanced action. Bell's independence assumption can fail via a common past (implausible substructure) or a common future (advanced action: elegant, economical, symmetric). Quantum mechanics supplies the needed limits on classical observation. The proposal also undercuts the no-hidden-variable theorems and GHZ. Quantum mechanics may be complete from our temporal standpoint and incomplete from the Archimedean one.
Directions for further work
| Price's agenda (1996) | What has happened since |
|---|---|
| Models incorporating advanced action in quantum mechanics | A recognised subfield: Price 2012 and Leifer–Pusey 2017 link time symmetry to retrocausality; Wharton–Argaman review (2020); Sutherland's Lagrangian model; Kastner's transactions; Price–Wharton "constrained colliders" (2021–24). No consensus model of full quantum theory yet. |
| Consistency and observability of time-reversing cosmologies and future low-entropy boundaries | Studied mainly in models: Schulman's two-time boundary conditions (1997), Carroll–Chen (2004), Janus-point cosmology (2014), Penrose's CCC (2010). Accelerating expansion made a crunch seem unlikely, but DESI (2024–25) hints have revived it. |
| Explaining the low-entropy big bang with the basic dilemma in view | Now framed as the Past Hypothesis (Albert 2000) and the Weyl curvature hypothesis; inflation is widely agreed not to solve it by itself; Boltzmann brains are a standard constraint on cosmological models. |
| The proper conceptual framework for an atemporal physics | Debates over "all-at-once" Lagrangian formulations, block-universe treatments of laws (Chen, Goldstein), and Humean versus non-Humean views of laws without dynamical "production". |
| An atemporal metaphysics of causation and dependence | Causal perspectivalism (Price 2007), interventionism (Woodward 2003), statistical-mechanical accounts of the asymmetry of influence (Albert, Loewer, Kutach), work by Jenann Ismael on agents' self-location in the block. |
Why it matters
Why not ignore the view from nowhen? We cannot climb out of time as we climb a tree for a better view.
Knowledge by subtraction. We can understand how our situation within time is reflected in how we talk, think and conceptualise, and thereby gain a deeper understanding of ourselves and, "by subtraction", of what is external to us. This knowledge is reflective, ultimately "a sense-from-within" of what things are like from without. The reflexivity is not vicious: understanding is enhanced, not overturned. Science has always stood proxy for creatures whose epistemic links to the world are "tenuous, patchy, contingent, and parochial", and each advance brings a new picture of how the world looks from nowhere and a new appreciation of our limits.
It is tempting to think our standpoint is devalued by each such step. Price disagrees: if we had a choice of standpoints we might choose another, but to be swayed by that "would be like wanting to be someone else". Since our standpoint is no more a matter of choice than who we are, it cannot coherently be undermined this way. The campaign for a view from nowhen "promises only to enhance our understanding of ourselves and our world, and not to make us gods."
The portable technique. The single most transferable tool in the book is imagined time reversal: run the argument backwards and see whether you would still accept it. It is a cheap audit for any reasoning that produces an asymmetry, from statistical arguments about entropy to models that assume their inputs are independent of what will later be done with them.
Master Takeaways
The book's lessons, ranked. The first six are the strongest; the rest are the arguments, tools and corrections that make them work.
- The real puzzle of time's arrow is the low-entropy past, not the rising entropy of the future. High entropy is the natural condition of matter and needs no explanation; the H-theorem tradition has been explaining the wrong end of the gradient for over a century.
- The double standard fallacy is the master error. An argument that works in both temporal directions but is applied in only one yields an asymmetric conclusion that merely restates its asymmetric input; imagined time reversal is the test that exposes it.
- All the physical arrows lead to one place: the smooth, low-entropy early universe. Thermodynamics and radiation are siblings, not parent and child; both point to cosmological boundary conditions.
- Time-symmetric physics faces a basic dilemma. Whatever explains a smooth big bang seems bound to make a big crunch smooth too (Gold's universe), and the standard objections to that symmetric option are themselves double standards.
- μInnocence, the assumption that micro-systems are uncorrelated before they interact, has no observational support and conflicts with T-symmetry. It is the hidden premise behind quantum nonlocality and indeterminacy: QM plus μInnocence gives the strangeness.
- Advanced action is the symmetric default, and it makes quantum mechanics local and Einsteinian. A common future (not a conspiratorial common past) explains Bell and GHZ correlations within light cones, keeps realism, and leaves free will intact.
- The asymmetry of time is mostly an asymmetry of things in time. Like a long dinner table, time may be symmetric while its contents are arranged asymmetrically along it.
- Statistical arguments are symmetric weapons. Microstate counting predicts higher entropy toward the past as strongly as toward the future; once it fails in one direction (the low-entropy past), trusting it in the other needs independent justification (Keen and Able).
- Boltzmann's fluctuation hypothesis was a great atemporal insight with a fatal flaw. It makes direction an artefact of our orientation, but implies our records are almost certainly false (the Boltzmann brain problem).
- Radiation is symmetric at the micro level. Reinterpreted Wheeler–Feynman shows the same field can be described as diverging from a source or converging on absorbers; what is asymmetric is that sources clump into stars and galaxies.
- State the asymmetry correctly before explaining it. "Organised waves are emitted, disorganised waves absorbed" sets a different contrast class from "emitters produce retarded waves", and the wrong one sends physics after a non-problem.
- Inflation and the no-boundary proposal do not, by themselves, explain the low-entropy start. Run backwards, their statistical reasoning predicts a clumpy endpoint, and a size-based boundary condition applies at both ends or neither.
- The fork asymmetry is macroscopic and fades at the micro level, so it cannot ground causal direction where our intuitions are firmest; micro-forks are symmetric relative to a fixed background.
- Causal asymmetry is perspectival, like a secondary quality. It reflects the means–end structure of deliberating agents; "a little asymmetry goes a very long way" in explaining appearances.
- Counterfactual asymmetry is a convention we cannot choose to change. Holding the past fixed is forced on us by our orientation, which is why it feels objective (the one-way locomotive; sour lemons).
- The bilking argument fails wherever observing the past disturbs it. Dummett's loophole lets the inaccessible past depend on the future without paradox, and quantum measurement supplies exactly that inaccessibility.
- Abandoning μInnocence is not attacking ordinary causation. Billiard balls only show the conventional asymmetry; photons and polarizers show an objective one (the video quiz), and only the latter conflicts with symmetry.
- Backward causation is not forward causation reversed. The agent's own orientation stays fixed; only the object system's past leg acquires dependence on the agent's action.
- Bell's theorem rules out local hidden variables, not hidden variables. Since rival views are nonlocal too, Bell is neutral between Einstein and Bohr until advanced action breaks the tie in Einstein's favour.
- The measurement problem belongs to the complete-description view. Treat the wave function as incomplete and Schrödinger's cat becomes "a toothless tiger".
- No-collapse views face a deep probability problem. Branch counting is circular, and quantum Russian roulette shows how strangely decision theory behaves when every outcome happens.
- The no-hidden-variable theorems assume one hidden state must serve every possible next measurement. The precognitive cat shows how Putnam's paradoxical 60/60 statistics become classical once states may depend on the actual next measurement.
- Fatalism is no special objection to advanced action. The backward fatalist argument is formally parallel to the forward one; if one fails, so does the other.
- Quantum mechanics may be complete from our standpoint and incomplete from nowhen. It codifies everything available to an observer embedded in time, gathered from past interactions.
- Physics' concepts carry hidden temporal direction. State, disposition, potential and degree of freedom all presuppose an open future; an atemporal physics must rebuild them.
Frameworks & mental models
| Name | What it says | Use it when |
|---|---|---|
| View from nowhen | Describe the world from an atemporal, Archimedean standpoint; quarantine features due to our temporal location | Deciding which temporal features are objective |
| Double standard fallacy | Applying a direction-neutral argument in one temporal direction only yields an asymmetry you put in | Auditing any explanation of an arrow of time |
| Imagined time reversal | Run the argument with time reversed; if you reject it, a double standard is present | Fast check on asymmetric reasoning |
| Asymmetry of vs in time | Time itself (the table) versus its contents (the setting) | Clarifying what "time's arrow" means |
| Taxonomy vs genealogy | Catalogue the arrows and their relations; then explain why any exist given symmetric laws | Structuring the problem of time asymmetry |
| PI3 | Incoming influences are independent; outgoing ones correlated | Spotting hidden asymmetry in statistical mechanics |
| Explain departures from the natural | Equilibrium is normal; explain deviations, not the default | Choosing which end of a gradient needs explanation |
| Keen and Able | A principle that failed in one direction needs independent support in the other | Extrapolating statistical reasoning to the future |
| 3-1 vs 3-6 contrast classes | Different statements of an asymmetry imply different "symmetric" alternatives | Before explaining any asymmetry |
| Basic dilemma | Symmetric physics makes both cosmic ends special or neither | Evaluating cosmological explanations of the arrow |
| Gravitational symmetry argument | A reversed bang is a collapse, so a smooth bang is as unlikely as a smooth crunch | Assessing "the early universe was not special" claims |
| Corkscrew model | A symmetric theory may have only asymmetric models | Looking for a non-ad hoc asymmetric cosmology |
| Meeting vs mixing models | Structure in a two-boundary universe comes from one boundary, not both | Thinking about Gold universes and reverse stars |
| μInnocence | Micro-systems are uncorrelated before interacting; unobserved and anti-symmetric | Examining assumptions behind quantum no-go theorems |
| Fork asymmetry | V-forks common, Λ-forks rare; macroscopic only | Testing physical accounts of causation |
| Disguised conventionalism / buck-passing | Smuggling asymmetry by definition, or into an equally mysterious notion | Reviewing analyses of causation and probability |
| Perspectival (agency) view of causation | Causes are potential means; causal direction projects agents' asymmetry | Explaining why causal asymmetry seems objective |
| Two conventions for counterfactuals | Hold fixed the whole past vs the accessible past | Making sense of backward dependence |
| Bilking argument and Dummett's loophole | Backward causation is refutable only if the earlier effect can be observed without disturbance | Assessing paradox objections to retrocausality |
| Three-legged diagram | Is a change on one incoming leg absorbed only on the future leg? | Defining advanced action precisely |
| Common past vs common future | Two ways to break Bell's independence: superdeterminism vs retrocausality | Classifying escapes from Bell nonlocality |
The book as a whole. Price's diagnosis of double standards in thermodynamics, radiation and cosmology has aged very well: the Past Hypothesis framing, the Boltzmann brain problem and doubts about inflation as an entropy explanation are now mainstream. His positive programme is more contested. (1) The block universe is assumed, not defended. (2) The perspectival account of causation is one view among several; interventionist and statistical-mechanical accounts claim objective grounding for the asymmetry Price calls conventional. (3) In 1996 no full retrocausal model of quantum mechanics existed; the book offers a strategy and toy constraints (9-1), and critics say a theory whose key posit is in principle unobservable risks being idle or fine-tuned. Thirty years on there are theorems (Leifer–Pusey) and partial models, but no consensus formulation. (4) The physics chapters simplify, as Price warns; his treatment of Hawking's papers is a reading of their wording, and Hawking's camp later recast its view in observer-relative terms. (5) The case is avowedly one-sided in emphasis: it argues for neglected options rather than weighing all interpretations evenly.
Who's who
| Person | Role in the book |
|---|---|
| Ludwig Boltzmann | H-theorem, entropy as probability, the symmetric fluctuation view: the first atemporal thinker, imperfectly |
| Loschmidt, Culverwell, Burbury, Zermelo, Poincaré | Reversibility and recurrence objections; Burbury's "haphazard" environmental disturbances |
| Wheeler and Feynman | Absorber theory of radiation: right mathematics, wrong use |
| Thomas Gold | Proposed entropy is low at both ends of a recollapsing universe |
| Roger Penrose | Quantified the specialness of the big bang; asymmetric Weyl curvature hypothesis; the astronaut objection to Gold |
| Stephen Hawking | No-boundary proposal; first endorsed then abandoned the Gold view, without (Price argues) explaining the asymmetry |
| Paul Davies | Influential expositor whose inflationary and statistical arguments Price uses to illustrate double standards |
| Hans Reichenbach | Common cause principle and the fork asymmetry |
| David Lewis | Counterfactual analysis of causation; asymmetry of overdetermination |
| Michael Dummett | Coherence of affecting the unknowable past; the loophole in bilking |
| Einstein, Podolsky, Rosen | The incompleteness argument |
| Niels Bohr | Copenhagen complete-description view |
| Erwin Schrödinger | The cat; incompleteness ("blurred photograph" not "fog") |
| John Bell | Bell's theorem; saw the independence loophole but feared it cost free will |
| David Bohm | Contextual, nonlocal hidden-variable theory |
| Hilary Putnam | 1965 analysis of superposition and the no-disturbance principle |
| John Cramer, O. Costa de Beauregard | Early advanced-action approaches: transactional interpretation, zigzag causality |
Connect it
- Look-ahead bias is the double standard in reverse. In credit-risk and trading models, letting information from after the decision date leak into features is the classic way an asymmetric "explanation" smuggles in what it claims to find; Price's time-reversal audit is a disciplined way to check which direction each assumption runs.
- Independence assumptions carry direction. μInnocence is a sharp example of an independence assumption treated as obvious without evidence. In model risk management, assumptions such as "applicants are independent of the policy that will score them" (performative prediction, reject inference) deserve the same scrutiny Price gives Bell's measurement independence.
- Interventionist causation is the working theory of causal AI. The agency view's descendants (Woodward, Pearl) underpin uplift modelling and causal inference in banking analytics: causal claims are claims about what an intervention would change, and the direction of the arrow reflects the decision-maker's position.
- "Complete from a standpoint" is a useful lens for architecture. Price's reading of quantum mechanics as complete from an embedded observer's view and incomplete from nowhen mirrors how each system's data model is complete for its own consumers yet partial for the enterprise; integration problems often come from treating a perspectival model as the whole truth.
About this book
Time’s Arrow and Archimedes’ Point: New Directions for the Physics of Time by Huw Price, 1996. This is a chapter-by-chapter study of the book, with summaries, maps, tables and diagrams; short quotations keep their page references. It is shared free for personal study, is not for sale, and is not endorsed by the author or publisher. Please read and buy the original.
Insight Editions · rajeshrmahapatra.com/insight-editions