Insight Editions · No. 96
Through Two Doors at Once
The Elegant Experiment That Captures the Enigma of Our Quantum Reality
Anil Ananthaswamy
Anil Ananthaswamy traces the double-slit experiment from its origins to modern tests, using its paradoxes to explain competing interpretations of quantum mechanics.
A study guide to Through Two Doors at Once by Anil Ananthaswamy. Shared free for personal reading; not for sale and not endorsed by the authors or publishers. Please read and buy the original.
The Book in Brief
The argument in brief
- One experiment holds the mystery. Particles go through a double slit one at a time and still build interference fringes; asking which slit kills them.
- The formalism works; its meaning is open. A wavefunction evolves smoothly, then collapses on measurement, and nobody defines measurement.
- Entanglement is the key. EPR and Bell show no local hidden variables can work; which-path detectors kill fringes by entangling.
- Information, not disturbance. Delayed-choice and eraser experiments show the photon's behaviour matches the final setup, whenever it is fixed.
- Every interpretation has a price. Bohm pays with nonlocality, collapse models with new physics, Everett with many worlds, QBism with a subjective ψ.
- Some prices can be tested. Bigger molecules and mirrors probe collapse; triple slits probe the Born rule.
The argument map: from one experiment through its paradoxes to five ways of paying for it.
| Ch | Title | In one line |
|---|---|---|
| P | Prologue: The Story of Nature Taunting Us | The bomb puzzle; the plan of the book. |
| 1 | The Case of the Experiment with Two Holes | Feynman's lecture; Newton, Huygens, Young; single photons. |
| 2 | What Does It Mean "To Be"? | Maxwell to Solvay: quanta, Bohr, matrices, waves, Born, Copenhagen. |
| 3 | Between Reality and Perception | Single photons, electrons, Mach-Zehnder, the cat, delayed choice. |
| 4 | From Sacred Texts | EPR, Hermann, Bohm, Bell, Aspect: entanglement in the slit. |
| 5 | To Erase or Not to Erase | Erasers on Earth and across 144 km; bomb tester; Hardy. |
| 6 | Bohmian Rhapsody | Pilot waves, droplets, weak measurement, surreal paths. |
| 7 | Gravity Kills the Quantum Cat? | GRW, Penrose, giant molecules, mirrors in superposition. |
| 8 | Healing an Ugly Scar | Everett, DeWitt, Carroll, Wallace; QBism. |
| E | Epilogue: Ways of Looking at the Same Thing? | Feynman's six pictures; interacting worlds; Born-rule tests. |
The Story of Nature Taunting Us
The bomb puzzle
Hardy starts at the blackboard: "Imagine you have a factory and they make bombs." The puzzle carries the names of two Israeli physicists, Avshalom Elitzur and Lev Vaidman. A faulty assembly line makes "good" bombs, whose triggers are so sensitive that a single photon sets them off, and "bad" duds with no trigger at all.
The task is to pick out good bombs without detonating them. Looking means shining light, and light fires a live trigger, so ordinary inspection leaves only duds. One concession is allowed: some bombs may be sacrificed, provided some good ones survive unexploded.
- Classical verdict. Impossible: any check that sees the trigger touches it.
- Quantum verdict. Possible: with a simple setup a share of the good bombs can be certified without a single photon striking them (Chapter 5 gives the exact odds).
The plan of the book
The double slit took centre stage again when Albert Einstein and Niels Bohr argued about reality in the 1920s, and in the 1960s Richard Feynman said it contained all the mysteries of the quantum world. A high-school student can follow its workings, yet it still bewilders the best minds.
Ananthaswamy follows the experiment from thought experiments by "luminous minds" to the basement labs where variants are built, one of which solves the bomb puzzle.
The bomb as a preview of every later price
The Prologue opens with a warehouse of bombs that look identical: most are duds, a few are live. A live bomb has a photon-sensitive detonator; a dud has no such fuse. Classical inspection would destroy every live bomb. Quantum mechanics, via an Elitzur-Vaidman Mach-Zehnder, lets you certify some live bombs without the probe photon ever meeting the detonator. That single puzzle foreshadows the book's themes: complementarity, the role of which-path information, and the fact that a null outcome can still be a measurement (Renninger, 1960).
Ananthaswamy's reporting plan is explicit: start with Feynman's "central mystery," reconstruct how Copenhagen became orthodoxy, then visit labs that turn thought experiments into hardware (Aspect, Zeilinger, Steinberg, Arndt, Bouwmeester), and only then hear the rival ontologies (Bohm, collapse, Everett, QBism) from their living champions.
Prologue map: from the bomb riddle to the book's five prices.
Nature taunting: every classical check has a quantum catch.
The Case of the Experiment with Two Holes: Richard Feynman Explains the Central Mystery
Feynman at Cornell, November 1964
Feynman was a year from his Nobel Prize and two decades from his best-selling memoir when he gave his Messenger Lectures at Cornell; the provost introduced him as a physicist and a bongo drummer. By the sixth lecture he skipped even a "Hello" and went straight to how intuition, built for things we can see and touch, fails at small scales.
Light and electrons, he said, "do not behave just like particles. They do not behave just like waves," but they behave "exactly the same" way: "they're both screwy." The difficulty is psychological, the "utterly vain" wish to see nature through a familiar analogy. "I will not describe it in terms of an analogy," he promised. "I'll simply describe it."
Sand, waves and the expected result
The setup is minimal: a source, an opaque sheet with two slits, a screen. Ananthaswamy swaps Feynman's bullets for grains of sand, which also "come in lumps."
- One slit open. Grains pile up behind the open slit, tapering off to either side.
- Both slits open. The distribution is the sum of the two single-slit patterns; pour sand from above and two mounds form.
- Newtonian light. If light were Newton's corpuscles, we would expect two bright strips. That is not what happens.
Book figure: particles (sand) through two open slits. The screen shows two humps, the plain sum of the one-slit patterns, as Newton's corpuscles would predict for light.
Newton against Huygens
Isaac Newton argued light is made of particles, partly because light, unlike sound, does not bend around corners. Christiaan Huygens argued for waves in an all-pervading ether, which explains refraction easily: a wave changes speed between air and glass, so its direction changes, whereas particles would need an unexplained force.
Huygens was formidable: he ground his own lenses, discovered Saturn's moon Titan (the 2005 Huygens probe honours him), independently found the Orion nebula and published Traité de la Lumière in 1690. Newton's prestige (motion, gravitation, calculus) still kept the corpuscular theory on top for more than a century.
Thomas Young, 24 November 1803
Thomas Young, "The Last Man Who Knew Everything," explained the eye's focusing at about 20 (from dissecting an ox's eye), became a Fellow of the Royal Society a year later, qualified in medicine in 1796 and later helped decipher the Rosetta stone. At the Royal Society on 24 November 1803 he described an experiment that can be repeated "whenever the sun shines."
Young's double slit: two waves overlap and leave light and dark fringes.
He let a sunbeam through a needle hole in a window shutter and held a card about one-thirtieth of an inch wide in it. Particles would cast a sharp shadow; waves would pass on both sides and recombine into interference fringes, with a bright fringe at the centre, exactly where particles predict darkness. Young saw coloured fringes around a white centre: light is a wave.
- Constructive interference. Crests meet crests, as with sea waves through two gaps in a breakwall: bright fringes.
- Destructive interference. Crest meets trough and the waves cancel: dark fringes.
- Diffraction. Each opening becomes a source of new spreading waves.
The barrister Henry Brougham (later Lord Chancellor, 1830) attacked Young anonymously in the Edinburgh Review as "destitute of every species of merit." Support soon followed, and Young's card became the standard double slit.
Book figure: a laser through two slits. Waves spread from each slit and overlap, giving bright and dark fringes and the many-peaked intensity curve of interference.
The quantum twist: one photon at a time
In 1905 Einstein argued that light comes in photons, the smallest indivisible units of energy at a given frequency, to explain the photoelectric effect (the basis of solar panels). With particles of light, the double slit turns strange.
One photon at a time: dots build fringes, and which-path checks erase them.
| Setup | What the screen shows |
|---|---|
| Intense red light, both slits | Interference fringes |
| One slit closed | Fringes vanish |
| Single photons, both slits | Random dots that build up fringes |
| Single photons, which-slit detector | No fringes: sum of two lumps |
| Detector removed | Fringes return |
Each photon is created as a particle and detected as a particle, yet between source and screen it behaves "as if it's interfering with itself." Photons avoid the dark-fringe locations when unobserved but land there once their paths are monitored. And no amount of initial information predicts where a single photon lands: quantum theory gives only probabilities.
Book figure: single particles arriving over 10, 20, 30 and 40 seconds. Individual hits look random; the fringes appear only in the accumulated pattern.
Feynman used electrons in his thought experiment; the book uses photons. That massless photons and massive electrons behave identically is its own puzzle. Single-photon double slits were not possible in 1964; it would take twenty more years.
What the sand-and-wave contrast is for
Feynman's Cornell lecture (Messenger series, November 1964) builds the mystery by contrast. A sand gun through two holes gives two piles. Water waves through two openings give diffraction from each opening plus constructive and destructive overlap: bright where crests meet, dark where crest meets trough. Classical light (Young) matches the wave case. Replace sand with single electrons (or, in the book's telling, photons) and the hits land one by one like sand, yet the accumulated pattern matches waves. Close either slit and the fringes vanish; open both and they return. Ask which hole and the wave pattern dies.
Huygens (Traité de la Lumière, 1690) needed a vibrating ether; he also discovered Titan while grinding his own lenses. Newton won the particle argument for a century. Young's 24 November 1803 Royal Society lecture used a card's edge to split a sunbeam; the bright central fringe sits where particles would cast a shadow. Henry Brougham's anonymous Edinburgh Review attack ("destitute of every species of merit") delayed acceptance; by mid-century Fresnel and others had settled the wave case for light.
Three regimes Feynman stacks before the quantum twist.
Einstein's light quantum and the open questions
Einstein (1905) made light arrive in lumps of energy E = hν, explaining the photoelectric effect. That restores a particle picture just when Young's fringes had seemed decisive. The book's open questions, which later chapters answer experimentally, are: can the choice of wave versus particle measurement be delayed until after the slits (Wheeler); can which-path information be stored and later erased (Scully); and does a particle always take one path while "something else" goes through both (Bohm, droplets, weak values).
Feynman's contrast: classical expectations versus the quantum buildup.
What Does It Mean "To Be"?: The Road to Reality, from Copenhagen to Brussels
Fields join particles
Newton's Principia (1687) built a world of particles moved by forces, with light's place in the ontology (the inventory of what exists) unsettled. Louis de Broglie later put the question plainly: light crosses empty space "not bound up with any motion of Matter," so what is its structure?
Building on Michael Faraday, James Clerk Maxwell unified electricity and magnetism and predicted that they travel together as one electromagnetic wave, presenting the theory to the Royal Society on 8 December 1864. The world now held particles (localized) and fields (diffuse, acting far from their source), and light was a wave of the field: ν = c/λ, with electric and magnetic fields vibrating at right angles to each other and to the direction of travel.
The photoelectric effect
Hertz noticed his receiver worked better when lit. His assistant Philipp Lenard showed that ultraviolet light knocks electrons out of metals, and that their speed does not depend on the light's intensity. Hertz called it a "very puzzling phenomenon" in a July 1887 letter; he died of blood poisoning on 1 January 1894, aged 37.
The photoelectric effect: colour, not brightness, decides whether electrons fly.
Book figure: the photoelectric effect. Below a threshold frequency no electrons leave the metal; more intensity ejects more electrons; higher frequency ejects more energetic ones.
- J. J. Thomson, 1897. Bent cathode rays with electric fields and showed they are negatively charged bits smaller than atoms: the electron (his "corpuscles"); one listener thought he was "pulling their legs."
- Max Planck, 1900. Explained black-body radiation only by assuming energy comes in quanta, a floor like the cent in a dollar: E = hν.
- Einstein, 1905. Light itself comes in quanta. An electron leaves the metal only if one quantum carries enough energy; extra sub-threshold quanta do nothing, and higher frequency gives faster electrons.
- Nobel Prizes. Lenard in 1905 (cathode rays), Einstein in 1921 (photoelectric law). Lenard, an anti-Semite who backed Hitler by 1924, branded relativity a "Jewish fraud."
Planck himself, recommending Einstein to the Prussian Academy in 1913, excused the light-quantum idea as overshooting "the target in his speculations." The wave-particle duality was now in plain view: frequency, a wave property, fixed the energy of a particle.
Taylor's faint-light experiment, 1909
Geoffrey Ingram Taylor, starting out in J. J. Thomson's Cambridge lab, tested Thomson's guess that very faint light through a slit would give blurry fringes. In his parents' children's playroom he scratched a slit in foil with a razor, used a gas flame dimmed through smoked glass to the brightness of a candle a mile away, and photographed a needle's shadow.
He timed one six-week exposure to coincide with a sailing cruise; the longest ran three months. The fringes came out as sharp as with bright light. Thomson was wrong, Taylor never followed up, and he went on to fame in fluid mechanics.
Bohr's quantized atom
Niels Bohr came to Thomson in 1911, then to Ernest Rutherford in Manchester, whose atom had a small positive nucleus orbited by electrons. Classically such orbiting electrons must radiate energy and spiral into the nucleus. In 1913 Bohr postulated stable "stationary" orbits with quantized energy and angular momentum and a lowest orbit with nowhere lower to fall.
Bohr's atom: fixed orbits, and light emitted only in jumps.
- Quantum jumps. Like a car that leaps from 10 to 60 mph in 10 mph steps and cannot go below 10, electrons jump between orbits, emitting or absorbing the energy difference.
- Slow acceptance. For about a decade Bohr insisted the emitted radiation was classical, before accepting photons with E = hν.
- De Broglie, 1924. His PhD thesis gave matter the same duality: an electron's allowed orbits are those that fit whole wavelengths around the nucleus.
Discreteness, continuity and indeterminism (no one can predict when a radioactive atom will decay) all needed one framework. The mid-1920s produced two.
Matrix mechanics: Helgoland, 1925
Bohr founded his Institute of Theoretical Physics in Copenhagen in 1921 (today the Niels Bohr Institute), having become a professor there in 1916 at 31. He met Werner Heisenberg in Göttingen in June 1922, when the 20-year-old student questioned him so sharply that Bohr took him for a walk and invited him to Copenhagen.
In spring 1925, fleeing hay fever, Heisenberg went to pollen-free Helgoland. Between walks and reading Goethe's West-östlicher Divan, he finished the calculations near 3 a.m., felt he was looking at "a strangely beautiful interior," and climbed a sea rock to wait for sunrise.
Max Born recognized his strange symbols, where A×B ≠ B×A, as matrices. Born, Heisenberg and Pascual Jordan built matrix mechanics within months; Paul Dirac independently added insight and the notation still used.
- Observables. A quantity such as position is a matrix listing the values that can be observed; jumps are built in and orbits cannot be pictured.
- Probabilities. A state that is x parts A and y parts B yields A with probability x² and B with y², where x² + y² = 1 (moduli once x and y are complex).
- No hidden ignorance. The theory claims to hold all available information, so the odds are not ignorance; only ensembles (a million identical runs) show the frequencies.
Wave mechanics: Arosa, 1925-26
Erwin Schrödinger was "discouraged, if not repelled" by matrix "transcendental algebra." He read de Broglie's thesis (he wrote to Einstein on 3 November 1925) and, over a Christmas holiday in Arosa with an unnamed old girlfriend and pearls in his ears against noise, found his wave equation, in hand by 9 January 1926. Four papers in Annalen der Physik followed.
The equation evolves a wavefunction ψ: spread out, complex-valued, given at every point in space. Schrödinger hoped ψ pictured the electron; Born showed in summer 1926 that it encodes probabilities.
Schrödinger showed the two mechanics equivalent (John von Neumann later proved it rigorously) but claimed victory for continuity: no quantum jumps. Heisenberg called his theory "Mist" (rubbish) and Wolfgang Pauli spoke of "local Zurich superstitions," while telling Schrödinger the conviction tormented him too.
Copenhagen's crucible, 1926-27
When Schrödinger visited in September 1926, Bohr argued from the railway station onward, even at his feverish guest's bedside while Margrethe Bohr nursed him; Heisenberg saw Bohr as "a relentless fanatic." Biographer Walter Moore: Schrödinger was a "visualizer," Bohr a "nonvisualizer."
Bohr and Heisenberg then argued late into the night in Heisenberg's attic, trying, Heisenberg said, to "concentrate the poison of the paradox," whose quintessence was "the electron with the two holes." In February 1927 Bohr went skiing in Norway; walking in the Fælledpark, Heisenberg found the uncertainty principle.
- Uncertainty. Paired quantities (position and momentum, energy and time) cannot both be sharp: Δx · Δp ≥ ħ/2 in modern form.
- Complementarity (Bohr). Wave and particle are mutually exclusive aspects; the choice of experiment reveals one, never both. Bohr saw uncertainty as one consequence of it.
Brussels, October 1927
The Fifth Solvay Conference in Brussels drew 29 physicists, 17 of whom became Nobel laureates; Benjamin Couprie's photograph seats Einstein, Planck and Marie Curie in front. Ananthaswamy ranks the debate with Copernicus against Ptolemy, Fred Hoyle's lonely steady state and Popper versus Kuhn.
Solvay 1927: the rival pictures of quantum reality laid side by side.
At the Hotel Metropole, Einstein brought a new thought experiment to breakfast, and by dinner Bohr had answered it; "in his heart," said Heisenberg, Einstein "was not convinced."
Book figure: Einstein's thought experiment in its modern form, with a movable ("recoiling") double slit between a fixed single slit and the screen.
Experiment eventually sided with Bohr, though historians caution that his arguments were often inscrutable, so "Bohr was right" needs care. Complementarity would prove deeper than the uncertainty principle, as later chapters show.
Born's rule and Heisenberg's pairs
Max Born (1926) read Schrödinger's wave as a probability amplitude: the chance of finding a particle is the square of the amplitude (more carefully, |ψ|²). "The motion of particles follows probability laws but the probability itself propagates according to the law of causality." Deterministic Schrödinger evolution of ψ; stochastic outcomes for detectors.
Heisenberg's uncertainty principle pairs observables (position and momentum; energy and time): sharpening one blurs the other. Bohr treated uncertainty as a special case of complementarity: wave and particle are mutually exclusive experimental aspects, never shown together. Einstein pressed for a deeper description that would restore definite properties independent of the apparatus.
From wave equation to Copenhagen's two pillars.
Solvay 1927: the photograph and the fight
The Fifth Solvay Conference (Brussels, October 1927) gathered 29 physicists; Benjamin Couprie's photograph puts Einstein, Planck and Marie Curie in front, with younger faces behind. de Broglie offered a pilot-wave picture and was pushed back, chiefly by Pauli. Bohr defended complementarity in long private exchanges with Einstein, who devised successive thought experiments meant to beat uncertainty; Bohr answered each within the new rules. The meeting fixed Copenhagen as the working orthodoxy for decades, even though Einstein never accepted incompleteness as the final word (the 1935 EPR paper is his next major strike).
What "Copenhagen" actually committed to
As used in the book, the package includes: (1) the wavefunction as the complete state for prediction; (2) the Born rule for probabilities; (3) complementarity of incompatible experimental arrangements; (4) a collapse (or "reduction") when a classical apparatus registers an outcome; (5) refusal of definite trajectories between measurements. Bohr and Heisenberg did not agree on every metaphysical gloss; the single label is a 1950s convenience, as the chapter's A closer look notes.
The Carlsberg exchange ("to be") is the chapter's hinge: if an electron need not "be somewhere" between source and screen, then Feynman's mystery is not a puzzle about hidden paths but about what existence claims the theory licenses. Jørgensen's outburst ("damn it, not reduce the whole of philosophy to a screen with two holes") is the book's ironic thesis statement.
Planck's floor and Lenard's electrons
Planck (1900) faced the black-body spectrum: classical theory predicted an "ultraviolet catastrophe" of infinite energy at short wavelengths. He saved the curve by assuming energy at each frequency comes in indivisible packets E = hν, a floor like the cent under a dollar. He treated the move as a formal fix; Einstein (1905) took quanta as real for light itself.
Philipp Lenard showed ultraviolet light knocks electrons from metals with a speed independent of intensity, which classical waves cannot explain (brighter waves should push harder). Einstein's light quanta fit: each electron absorbs one quantum, so frequency sets the kick and intensity only sets how many electrons. That is the photoelectric effect the book pairs with Young's fringes as the particle side of light.
From black-body quanta to light as particles.
Solvay 1927: the settlement the later labs keep testing.
"To be"
At the Carlsberg mansion, with philosophers Harald Høffding and Jørgen Jørgensen, someone insisted the electron "must be somewhere on its road from source to observation screen." Bohr answered that it depends on what "to be" means. Jørgensen exploded: "One can, damn it, not reduce the whole of philosophy to a screen with two holes." The rest of the book argues that, in a sense, one can.
| Year | Step | Who |
|---|---|---|
| 1864 | Light as electromagnetic wave | Maxwell |
| 1887 | Radio waves; photoelectric hint | Hertz |
| 1897 | Electron | J. J. Thomson |
| 1900 | Energy quanta, E = hν | Planck |
| 1905 | Light quanta | Einstein |
| 1909 | Faint-light fringes | G. I. Taylor |
| 1913 | Quantized atom | Bohr |
| 1924 | Matter waves | de Broglie |
| 1925 | Matrix mechanics | Heisenberg, Born, Jordan |
| 1926 | Wave equation; Born rule | Schrödinger; Born |
| 1927 | Uncertainty; complementarity; Solvay | Heisenberg; Bohr |
Between Reality and Perception: Doing the Double Slit, One Photon at a Time
Dinosaurs in the zoo
Stefan Hell, chemistry Nobel laureate in 2014, quoted Schrödinger at his banquet: we will no more experiment with single particles "than we will raise dinosaurs in the zoo." Hell's moral: predict that something will never happen and you will be remembered in a Nobel speech decades later.
Aspect's road to Bell
After his master's degree, Aspect spent his early-1970s French military service teaching in Cameroon, where he read Cohen-Tannoudji's new Quantum Mechanics "from page one to... page 1,300" (Cohen-Tannoudji became his PhD adviser and won the 1997 Nobel). Back in France in 1974 he read John Bell's 1964 paper in a two-hour sitting: "This is unbelievable."
- Local hidden variables. Bell made Einstein's question testable: are there variables missing from the formalism that obey the speed-of-light limit (local) and complete the theory?
- Bell's warning. Visiting CERN, Aspect heard that the topic was considered "crackpot physics"; Bell first asked whether he had a permanent job. He did.
- Feynman's request, 1984. After Aspect's Caltech talk on Bell tests, Feynman asked whether his single photons could do the double slit; Aspect said his student Grangier was on it.
Electrons first: biprism to Hitachi
Feynman's 1961-62 Caltech lectures called the electron double slit impossible to build.
Early 1950s: Gottfried Möllenstedt (Tübingen) sees a charged tungsten wire split an electron microscope's beam into two images.
1954: with Heinrich Düker, using gold-plated quartz wires about 3 microns thick (first gold-plated spider silk), a 30-second exposure shows fine fringes, confirming de Broglie's λ = h/p.
1961: Claus Jönsson does a true electron double slit.
1974: Merli, Missiroli and Pozzi (Bologna) film single electrons building fringes; the 16 mm film wins a prize in Brussels in 1976.
1989: Akira Tonomura's Hitachi team records electrons one by one over 20 minutes.
When Physics World readers later voted the single-electron double slit "the most beautiful experiment," the article omitted the Bologna team, which protested. Tonomura replied that Hitachi's was the first with "no chance of finding two or more electrons" in the apparatus. On single photons, nobody disputes priority.
The Mach-Zehnder interferometer
A beam splitter (half-silvered glass, like a train window that both reflects the carriage and shows the lit buildings outside) splits a light beam in half. A single photon cannot split: it is wholly reflected (detector D1 clicks) or wholly transmitted (D2 clicks), each with probability 0.5, and the two detectors never click together.
The Mach-Zehnder interferometer: a photon split by one beam splitter and rejoined by another.
Add mirrors and a second beam splitter where the paths cross, and each detector can be reached two ways: rt or tr to D1, rr or tt to D2. The paths are now indistinguishable, exactly as in a double slit. Naive bookkeeping predicts 5,000 / 5,000 for 10,000 photons.
Book figure: the Mach-Zehnder interferometer. Reflected (R) and transmitted (T) paths recombine at a second beam splitter; rt and tr lead to D1, rr and tt to D2.
Ludwig Mach (son of Ernst Mach) improved in 1892 an instrument Ludwig Zehnder had designed a year earlier. Anything a double slit can do, this interferometer can do, which is why experimenters use it: "It's just smarter," says Aspect.
Aspect and Grangier's single photons
The team laser-excited calcium atoms, which decay by emitting a green photon (551.3 nm) followed within nanoseconds by a blue one (422.7 nm). The green photon heralds the blue, so detectors open just in time and the chance of a second blue photon is "peanuts."
| Configuration | Result (equal arms) |
|---|---|
| Beam splitter 1 only | D1 or D2, 50:50, never both |
| Both beam splitters | All 10,000 at D1, none at D2 |
| One arm blocked | Half lost; rest split 50:50 |
| Arm lengths shifted | D1/D2 odds vary with path difference |
- The wave account. A reflected wave lags a transmitted one by a quarter wavelength, so rr trails tt by half a wavelength and they cancel at D2, while rt and tr arrive in phase at D1.
- The puzzle. That account works for a beam; it works equally for single photons, which cannot split. Something goes through both arms.
- The block. A blocked arm acts as a which-way detector, and interference vanishes.
Asking which slit the particle went through is like asking "the marital status of the number five or the weight in grams of Catholicism." It is a category mistake.
David Albert, philosopher, Columbia University
The photon is in a superposition of two path states, which is not the same as taking both paths, one path or neither. Albert calls superposition "just a name for something we don't understand," and the story of how objects enter and leave it "the most unsettling story" in physical science since the seventeenth century.
The measurement problem, and two morbid cats
In the formalism, ψtotal = a1·ψD1 + a2·ψD2 with |a1|² + |a2|² = 1; for equal arms the probabilities are 1 and 0. A measurement at D1 or D2 collapses ψ to one outcome, but Copenhagen never defines a measurement or says where quantum ends and classical begins.
The measurement problem: smooth evolution versus sudden collapse.
If detectors obey quantum mechanics too, the photon-plus-detector system is itself in superposition, and so is the next device, without end. Does a conscious observer finish the chain? Copenhagen avoids consciousness but demands a classical apparatus, and with it denies any reality between measurements.
The cat was meant to expose incompleteness, yet superposition is real enough to explain single-photon fringes. Dirac's phrase that "a particle interferes with itself" is too narrow: two states of the system interfere. With five slits, five path states interfere and give a different pattern.
Aspect remains on Einstein's side: "I think there is a real world," independent of observers, though he accepts quantum mechanics as an accurate account.
Wheeler's dragon and the delayed choice
John Wheeler (with Warner Miller) pictured the "great smoky dragon": a sharp tail (the photon entering), a sharp head (the click at D1 or D2) and a smoky body we have "no right to speak" of.
Wheeler's delayed choice: the setup is fixed only after the photon is inside, and the photon still matches it.
His delayed-choice thought experiment asks when the photon "decides." Decide whether the second beam splitter is in place only after the photon has passed the first. If the photon had "chosen" one path, inserting the splitter would force it to have taken both; removing it, the reverse.
- 1985 limits. Aspect's arms were about 6 metres, crossed in 20 ns, too little time to switch. Arms of 50 m would give 165 ns, but a non-point-like source would need lenses metres across.
- 2005 experiment. With a near point-like single-photon source and 48-metre arms, Aspect's team switched the setup after entry (results published February 2007).
- Result. The photon behaved as a particle without the splitter and as a wave with it, whenever the choice was made.
The choice and the photon's entry were space-like separated, so no disturbance could pass between them. Complementarity therefore does not rest on clumsy measurements disturbing the system; it is a deeper principle than Bohr's uncertainty argument implied. Bohr's dictum that measurement determines what you see "should not be taken in a too naive [manner]," says Aspect.
From "dinosaurs" to single-electron movies
Schrödinger (1933) doubted anyone would experiment with single particles "any more than we will raise dinosaurs in the zoo." Stefan Hell (2014 chemistry Nobel) opened his banquet speech by noting that the dinosaurs had arrived. Möllenstedt and Düker's electron biprism, Jönsson's 1961 electron double slit (German report; slow to reach English, so Feynman still called it a thought experiment), and Tonomura's Hitachi film (1989) of electrons arriving one by one made the buildup visible without storing the first hit until the last.
Aspect and Grangier's single-photon proof
Ordinary lamps and even attenuated lasers emit photons in bunches; a photographic plate is not a true single-photon source. Aspect's student Philippe Grangier used atomic cascades so that a first photon heralds a second. The antibunching parameter g²(0) < 1 certifies that two detectors almost never fire together: there is at most one photon in the apparatus. Those heralded photons then show Mach-Zehnder interference. Ghirardi's rough count for a 100 W lamp into a 1 cm² aperture at 1 m shows why "dim the bulb" is not enough: huge photon rates remain.
How a single photon earns the name before it meets the slits.
Two cats and the measurement problem
Schrödinger's cat (1935) couples a microscopic decay to a macroscopic poison: the joint wavefunction is a superposition of live and dead until observation. Wigner later put a friend inside the lab and asked when collapse occurs: at the Geiger counter, the cat, the friend, or Wigner's own awareness. The chapter treats both as symptoms of the same disease: the theory has two evolution rules and no sharp criterion for when each applies. Aspect's delayed-choice result (2007 paper; 48 m arms, space-like switching) shows the "decision" cannot be blamed on a clumsy earlier disturbance.
Mach-Zehnder as the book's workhorse
A Mach-Zehnder interferometer is the double slit rebuilt with mirrors. BS1 splits the photon into two arms; mirrors redirect; BS2 recombines. With BS2 in place and phases set for a bright port, every photon goes to D1 (wave behaviour). With BS2 removed, D1 and D2 each fire half the time (particle behaviour). The same device hosts delayed choice, the bomb tester, and Hardy's paradox. Aspect's 48 m arms finally left enough flight time to switch BS2 after the photon had passed BS1, with the switching event space-like separated from the entry.
Mach-Zehnder: one device, wave or particle by whether BS2 is present.
Wheeler's dragon: known head and tail, unknown body.
The next step, the delayed-choice quantum eraser, needs entanglement, identified in 1935 by Einstein (the EPR paper, his most cited) and named by Schrödinger the same year. Aspect calls what followed "the second quantum revolution."
From Sacred Texts: Revelations About Spooky Action at a Distance
Einstein's first worry, 1927
Philosopher Tim Maudlin (NYU) recalls pacing his college room after reading Bernard d'Espagnat's Scientific American article on Bell, whose subtitle said realism conflicts "with Facts Established by Experiment." Einstein had seen the tension at Solvay in 1927: if a spread-out wavefunction is a complete description, detecting the particle at one spot means it vanishes everywhere else at once, a nonlocal collapse at odds with special relativity.
The EPR paper, 1935
"EINSTEIN ATTACKS QUANTUM THEORY," said The New York Times on 4 May 1935, after Boris Podolsky leaked the paper; Einstein deprecated "advance publication... in the secular press." David Mermin's later quip gives the chapter its title: if the Times is the secular press, "the sacred text is the Physical Review." The four-page paper appeared on 15 May 1935.
The EPR argument: either quantum theory is incomplete or influences are nonlocal.
- Entanglement. After two particles interact, there is one joint wavefunction, not one per particle (the idea grew from a teatime talk between Einstein and Nathan Rosen).
- Locality. No influence travels faster than light; general relativity makes even gravity obey it (Earth would notice a vanished Sun after about eight minutes).
- Realism. Theories should describe "the objective reality, which is independent of any theory."
- Reality criterion. "If, without in any way disturbing a system, we can predict with certainty... the value of a physical quantity, then there exists an element of physical reality corresponding to" it.
Von Neumann's proof and Grete Hermann
In 1932 John von Neumann had "proved" no hidden-variable theory could match quantum predictions, and the Copenhagen camp gladly accepted it. In 1935 the philosopher Grete Hermann, a doctoral student of Emmy Noether, showed the proof assumes what it sets out to prove: "the proof is circular." Her paper, in an obscure German journal, was ignored, perhaps through sexism (philosopher Patricia Shipley thinks this secondary), politics or partisanship.
Einstein around 1938 asked of the same assumption, "Why should we believe in that?" Determinism mattered less to him than legend says: his "God does not play dice" is overquoted, and he accepted indeterminism as the theory matured. Realism and locality were what he would not give up.
Then David Bohm in 1952 built a working hidden-variable theory.
Bell's theorem as an experiment
Light's polarization is the plane in which its electric field vibrates (vertical, horizontal or any angle). A source sends polarization-entangled photon pairs to Alice, who tests direction A or B, and Bob, who tests C or D, each choosing independently and getting YES or NO. Same directions give perfectly opposite answers.
Bell's test: local hidden variables predict a limit that experiments break.
Book figure: a Bell test. Switches at each end pick the polarization direction (A or B for Alice, C or D for Bob) after the entangled photons have left the book.
For different directions, Bell computed the maximum correlation any local hidden-variable theory allows: an inequality. Quantum mechanics predicts more, so it violates the inequality. Bell called it "a piece of historical silliness" that a variable as ordinary as position got called "hidden."
1964: Bell's theorem.
1972 onward: Stuart Freedman and John Clauser (Berkeley), Richard Holt and Francis Pipkin (Harvard), Edward Fry and Randall Thompson (Texas A&M).
By 1976: seven experiments, two disagreeing with quantum mechanics; consensus for quantum theory.
1980: Aspect's source, after five years' work: "What Clauser would do in one day, what Fry would do in one hour, I could do in one minute."
Early 1980s: settings switched while photons fly, measurements space-like separated; violation confirmed.
Remaining loopholes were "for the purists"; for most physicists Aspect "sealed the deal." Einstein, who died in 1955, had written to Max Born on 3 March 1947 that physics should be "free from spooky actions at a distance."
EPR in four pages, and the secular press
Einstein, Podolsky and Rosen published on 15 May 1935 in Physical Review. Podolsky leaked the claim to the New York Times two weeks early; Einstein complained about announcement in the "secular press." David Mermin later joked that if the Times is secular, the sacred text is the Physical Review. The argument: if two systems are entangled, measuring one quantity on A lets you predict the same quantity on B without disturbing B; by locality B must have had a definite value already; quantum mechanics does not assign that value; therefore the theory is incomplete.
Bohr's reply defended complementarity: the very conditions that define one measurement exclude the conjugate one, so EPR's "elements of reality" are not jointly meaningful. Einstein never accepted that as a restoration of locality-plus-realism. His 3 March 1947 letter to Born still demanded physics "free from spooky actions at a distance."
From EPR incompleteness claim to Bell's testable limit.
Hermann's gap and Bell's escape
John von Neumann's no-hidden-variables proof was treated as gospel. Grete Hermann (1935), a philosopher-mathematician and Noether student, showed the proof assumes what it claims to show (an additivity condition that already rules out the interesting theories). Bell's 1964 inequality turned the philosophical fight into a lab protocol on polarization correlations.
Why entanglement kills fringes
Maudlin's apartment mime: the two halves of the wavefunction leave the slits, and a hit at one screen point is at once a miss everywhere else. A which-slit detector does not need to "kick" the particle hard; it entangles detector states with path states, so the reduced state of the particle alone no longer carries a stable relative phase. Fringes are an entanglement casualty. That is Schrödinger's claim that entanglement, not merely uncertainty, is the distinctive quantum relation, and it is why Chapter 5's erasers must disentangle (or erase the record) to bring fringes back in sorted data.
Which-path detection as entanglement, not a classical kick.
Closing Bell loopholes after Aspect.
Entanglement inside the double slit
In his New York apartment, Maudlin mimed the two halves of a wavefunction leaving the slits. When a particle registers at one spot on the plate, it simultaneously fails to appear everywhere else: "How puzzling is that?" The bigger surprise is what happens when we look for the path: the which-slit detector becomes entangled with the particle, and that is why the fringes vanish.
"Schrödinger said that what was really new about quantum mechanics was entanglement," says Maudlin, so the truly quantum effect is the disappearance of the interference. That insight opened a new wave of double-slit experiments, starting with the quantum eraser.
To Erase or Not to Erase: Mountaintop Experiments Take Us to the Edge
Two islands, one experiment
On La Palma, at the Roque de los Muchachos observatory (about 2,400 m), physicists in a shipping container sent photons to the European Space Agency's one-metre telescope on Tenerife, beside Mount Teide, 144 km away. They needed moonless nights; a single cigarette lit on the mountain could saturate the receiver, and Saharan dust could kill the link.
Book figure: the La Palma-Tenerife quantum eraser. The system photon runs through an interferometer on La Palma; its entangled partner flies 144 km to Tenerife, where a random choice keeps or scrambles its which-path information.
The leader was Anton Zeilinger, who shared the 2010 Wolf Prize with Aspect and Clauser. "The probabilities are the reality we have... full stop," he says, and he finds interpretation labels "silly." His institute stands on Vienna's Boltzmanngasse. The Erwin Schrödinger Institute moved to the same street in 1996, from Pasteurgasse; in a Vienna that names streets after physicists, history is close at hand. The book also recalls an older mountain crossing: Einstein hiked over the Maloja Pass (about 1,800 m) with Marie Curie in 1913. Zeilinger speaks of Einstein with respect while siding with the probabilities.
Customs was its own obstacle: the Canaries are an autonomous part of Spain, yet sit outside the EU's VAT area, so every crate crossed a customs border. Between moonless runs they decompressed on the beaches of Las Teresitas, built with imported Saharan sand, and El Bollullo.
Scully, the quantum cowboy
Marlan Scully grew up working a Wyoming farm, studied under Willis Lamb at Yale (a "dumb kid from Wyoming," Lamb first assumed), and later moved between MIT, Arizona, New Mexico and Texas A&M. With Kai Drühl in Munich he proposed the quantum eraser (published 1982).
The context is the measurement problem. Von Neumann treated measuring devices quantum mechanically, so collapse can be placed anywhere along the chain; Bohr split the world into big classical and small quantum; Eugene Wigner in 1961 argued consciousness completes the measurement, and abandoned the view by about 1970.
Kim and Scully's delayed-choice eraser, 2000
Yoon-Ho Kim (University of Maryland, Baltimore County) and Scully's team (Physical Review Letters, January 2000) used two atoms, A and B, as a virtual double slit. An excited atom emits a system photon toward a screen detector and an entangled environment photon into a beam-splitter network.
The delayed-choice quantum eraser: sorting later reveals fringes, with no signal back in time.
Book figure: Kim's delayed-choice quantum eraser. Environment photons from atom A or B reach D3 or D4 (path known) or are mixed at the central beam splitter and reach D1 or D2 (path erased).
| Environment photon at | Path | System-photon subset |
|---|---|---|
| D3 (via BSA) | atom A known | no fringes |
| D4 (via BSB) | atom B known | no fringes |
| D1 (central BS) | erased | fringes |
| D2 (central BS) | erased | anti-fringes |
- Delayed. The environment photon can be detected after the system photon has hit the screen; in principle the delay is arbitrary.
- No signal. The total screen pattern never shows fringes; they emerge only when data are sorted by coincidence with D1 or D2, which needs a classical message. Nothing travels back in time.
La Palma to Tenerife
Xiao-Song Ma, Rupert Ursin and colleagues shipped about two-thirds of a ton of equipment through Canary Islands customs (the islands sit outside the EU VAT area). The La Palma interferometer was so sensitive that opening the container door smeared the fringes; piezo-electric controls kept it stable.
On Tenerife a quantum random number generator chose for each environment photon: 0 kept which-path information, 1 scrambled it. The choice came about 0.5 ms after the system photon's detection on La Palma, space-like separated from it. Sorted by the choice, the "erased" subset showed wave behaviour and the "kept" subset particle behaviour.
Interpretations are "for gray-haired people."
Rupert Ursin, Austrian Academy of Sciences, Vienna
Wheeler had concluded, quoting Gertrude Stein (possibly misquoting), that there is "no there there" before a measurement. Ma, now in China, wants a better interpretation; Wheeler called the issue unfinished business. Even collapse at a detector is slippery: a silicon avalanche photodiode turns one photon into billions of electrons, effectively irreversible, while a single-atom detector could in principle be reversed. As Aephraim Steinberg says, nothing forbids un-scrambling an egg except practicality.
The bomb tester
Avshalom Elitzur, an autodidact without a high-school diploma, met Lev Vaidman in 1991. Elitzur built on Mauritius Renninger's 1960 negative-result measurement: if one arm of an interferometer takes 1 second and the other 5 seconds, a missing click after 1 second tells you the path without any interaction.
Elitzur-Vaidman bomb test: a live bomb can be found without a photon touching it.
Book figure: the Elitzur-Vaidman bomb tester. A bomb whose trigger absorbs one photon sits on one arm of a Mach-Zehnder interferometer between BS1 and BS2.
Bomb-tester odds for one photon and a live bomb. A dud lets interference send every photon to D1.
- The trick. A live bomb is a which-path detector, so it destroys interference; a click at D2, impossible with a dud, certifies a live bomb that no photon touched.
- Publication. Physical Review Letters and Physics Letters A rejected it (one referee a "very big shot"); it appeared in Foundations of Physics in 1993. Roger Penrose's Shadows of the Mind (1994) spread it, renaming the device a "Shabbos switch."
- Vaidman's lesson. "Collapse has nonlocality and randomness." He prefers a theory with neither, which leads him to many worlds (Chapter 8).
Hardy's paradox
Lucien Hardy, then a PhD student of Euan Squires at Durham, overlapped an electron interferometer and a positron interferometer so that one arm of each crosses: if both particles take those arms, they annihilate.
Book figure: Hardy's paradox. Electron and positron interferometers share a site of potential explosion; detectors C+/D+ and C-/D- record each particle.
Quantum mechanics predicts that D+ and D- click together one-sixteenth of the time, about 62,500 per million runs. Each click alone implies its particle took the crossing arm, yet no annihilation occurred. Hardy's 1992 PRL cited the "Tel Aviv Report, 1991." Mermin (1994) called it "one of the strangest and most beautiful gems to be found in the deep mine of quantum mechanics." Irvine, Hodelin, Simon and Bouwmeester realized it with photons at UC Santa Barbara (2005). Hardy's argument also proves nonlocality without inequalities.
Renninger's negative result and the bomb arithmetic
Mauritius Renninger (1960) showed that a missing detector click can be a measurement. Put a source, a beam splitter, and two detectors at unequal arm lengths: if D1 has not clicked after the shorter flight time, the photon must be on the longer arm, yet no interaction with D1 has occurred. Elitzur and Vaidman turned that logic into a factory test.
For a live bomb on one arm of a Mach-Zehnder set for a dark port:
- 1/2 of trials: the photon takes the bomb arm and the bomb explodes.
- 1/4: the photon takes the free arm and D1 clicks (inconclusive; retest).
- 1/4: the photon takes the free arm and D2 clicks: a live bomb is certified without being touched.
A dud restores interference, so D2 never clicks. Retesting inconclusive bombs raises the yield of salvaged live bombs toward one-third. Paul Kwiat and colleagues demonstrated interaction-free measurement in 1995 at about 50% efficiency, then used the quantum Zeno effect (repeated weak "looks" that freeze evolution) to push the efficiency higher. The Prologue's "about half" matches that later Zeno version, not the simple one-photon interferometer.
Bomb-tester outcomes for one photon and a live bomb.
What erasing really changes
Scully and Kai Drühl (1982) asked whether which-path information can be stored without kicking the particle, and whether erasing that information restores fringes. Kim's 2000 delayed-choice eraser answered yes: the total screen pattern never shows fringes; fringes and anti-fringes appear only in coincidence-sorted subsets. The Tenerife choice, made ~0.5 ms after the La Palma detection and space-like separated from it, showed the same complementarity over 144 km.
Xiao-Song Ma, Angus and Rupert Ursin shipped about two-thirds of a ton of gear through Canary customs. Opening the La Palma container door was enough to smear fringes; piezo locks held the interferometer. Between moonless runs the team rested on Las Teresitas (Saharan sand) and El Bollullo. Ursin jokes that interpretation is "for gray-haired people." Wheeler, quoting Gertrude Stein, said there is "no there there" before a measurement; Ma wants a better story.
Zeilinger's street and Einstein's hike
Zeilinger's institute sits on Vienna's Boltzmanngasse, a short walk from the Donaukanal. The Erwin Schrödinger Institute moved to the same street in 1996 from Pasteurgasse; Vienna names streets after physicists. The book pairs the mountaintop eraser with an older alpine crossing: Einstein hiked the Maloja Pass (~1,800 m) with Marie Curie in 1913. Zeilinger shared the 2010 Wolf Prize with Aspect and Clauser and later the 2022 Nobel; he finds interpretation labels "silly" and takes probabilities as "the reality we have... full stop."
From Scully's eraser idea to a 144 km delayed choice.
Scully the Quantum Cowboy
Marlan Scully, nicknamed the "Quantum Cowboy" for combining quantum optics with beef-cattle farming on a Civil War-era Texas cotton farm, grew up in rural Wyoming and married into a farming family. At Yale he sought out Willis Lamb. With Kai Drühl he invented the quantum eraser thought experiment (1982), pushing past Wheeler: store which-path information without kicking the particle, then ask whether erasing that information restores fringes. Kim's delayed-choice eraser and the Canary Islands link are laboratory descendants of that ranch-desk idea.
Eraser lineage from Scully's thought experiment.
Hardy's paradox in one pass.
Bohmian Rhapsody: Obvious Ontology Evolving the Obvious Way
The exile
Bohm studied under Robert Oppenheimer at Berkeley, where "Bohr was God and Oppie was his Prophet." A former Communist Party member, he was barred from Los Alamos; his thesis was classified, and he received his PhD on Oppenheimer's word. At Princeton he was subpoenaed by the House Un-American Activities Committee in 1949, pleaded the Fifth, was indicted and then acquitted, but Princeton did not renew his contract in 1951.
That year his textbook Quantum Theory defended orthodoxy: "no theory of mechanically determined hidden variables can lead to all of the results of the quantum theory." Months later he wrote one. In October 1951 he left for the University of São Paulo, where his passport was confiscated; he moved to Israel in 1955 and then Britain, ending at Birkbeck College, London.
Goldstein and the hoodwinking
Sheldon Goldstein (Rutgers), whose office door is plastered with clippings on the Sokal hoax and who wears a "Keepin' it real" T-shirt, came to Bohm through Edward Nelson's stochastic mechanics and Bell's Speakable and Unspeakable. "We were all hoodwinked," he says of the claim that hidden variables were impossible.
Bohmian mechanics in three ingredients.
Louis de Broglie had proposed a pilot wave at Solvay in 1927; Wolfgang Pauli attacked it and de Broglie dropped it. When Bohm sent his work, Pauli again objected; Bohm answered that every objection had been met, and that pursued to its logical conclusion each one failed. De Broglie, meanwhile, returned to his double-solution idea, begun in 1926.
Walking droplets
John Bush (MIT, raised in London, Ontario) studies the work of Yves Couder and Emmanuel Fort (Paris), who in 2006 showed that a millimetre oil droplet bouncing on a vibrating bath just below the Faraday threshold rides its own wave, a classical pilot-wave system. Their double slit, with 75 trajectories, appeared to give interference.
Walking droplets: a classical analogue of a particle guided by its own wave.
- Doubt. Tomas Bohr (DTU, Niels Bohr's grandson) found the statistics too thin; MIT's repeats showed no interference or diffraction, which Bush attributes to air currents and "boundary conditions," and he says "do not close the door."
- Successes. Droplets in corrals reproduce quantum-like statistics, and a droplet "senses" when a slit closes. Bush calls the de Broglie match a "hell of a coincidence."
- Limit. Goldstein objects that droplets live in 3D space; Bohm's wave lives in configuration space, where its nonlocality comes from.
Configuration space and nonlocality
Bohm's theory is, in Goldstein's phrase, "obvious ontology evolving the obvious way." Basil Hiley and Peter Holland developed it at Birkbeck; Detlef Dürr, Goldstein and Nino Zanghì named it Bohmian mechanics (Hiley dislikes the name). For N particles the wavefunction lives in 3N dimensions (two particles: six), so a measurement here instantly changes the guidance there.
| Feature | Bohmian mechanics |
|---|---|
| Positions | always definite |
| Evolution | deterministic |
| Uncertainty | ignorance, like weather |
| Collapse | effective, not real |
| Locality | explicitly nonlocal |
| Predictions | same as standard QM |
Bell tried to remove the nonlocality and instead proved any such theory must have it; Bell tests rule out local hidden variables only. For the cat, the empty part of the wavefunction stops mattering, an effective collapse. Goldstein calls the theory "a clarification" of quantum mechanics.
| Question | Copenhagen | Bohm |
|---|---|---|
| Which slit? | meaningless | one, always |
| What interferes? | probability amplitudes | the guiding wave |
| Why random? | nature is chancy | unknown start positions |
| Measurement | primitive, undefined | ordinary interaction |
| Price | no reality between looks | explicit nonlocality |
Uncertainty, on this view, is like weather forecasting: the dynamics are deterministic, but sensitivity to initial conditions and our ignorance of them make outcomes look random. The Born rule follows if the initial positions are distributed as |ψ|², which the theory treats as a kind of equilibrium. Even critics grant that it answers the which-slit question Copenhagen forbids.
Trajectories on punch cards
Chris Dewdney, inspired by Belinfante's survey of hidden variables, wrote to Bohm and was taken on by Hiley; with Chris Philippidis he computed Bohmian double-slit trajectories on punch cards, plotting them via film canisters (published 1979). He is now at Portsmouth.
Book figure: Bohmian trajectories for a double slit (after Dewdney and colleagues). Paths from slits A and B bunch into fringes and never cross the midline.
Weak measurement and average paths
Yakir Aharonov (Bohm's student), David Albert and Lev Vaidman introduced weak measurement in 1988: couple so gently that each reading is noisy but disturbs little, then average. Howard Wiseman (Griffith, 2007) showed weak measurements of momentum at each position give average trajectories, matching Bohm's.
Steinberg's weak measurements: average photon paths matching Bohmian trajectories.
Book figure: Steinberg's 2011 setup. Single photons from fibers form a virtual double slit; a calcite crystal weakly rotates polarization as a proxy for momentum, read on a CCD at successive planes.
Aephraim Steinberg's Toronto group (Kocsis et al., Science 2011) did it with photons: a thin calcite crystal weakly rotated polarization by an amount tied to direction, plane after plane. The average paths looked like Dewdney's; Physics World named it Breakthrough of the Year 2011. Steinberg jokes that some colleagues assume he was "brainwashed."
Hiley objects that photons are relativistic and lack Bohmian trajectories; with Robert Flack (UCL) he is building a version with metastable argon atoms (about 100-second lifetime) and a magnetic weak stage, still incomplete at the time of writing.
Surreal trajectories, explained
Bohmian paths never cross the midline, so a particle detected on the left came through the left slit. In 1992 Englert, Scully, Süssmann and Walther (ESSW) showed that a which-path detector can then fire for the wrong slit, and called Bohmian trajectories "surrealistic."
Book figure: surreal trajectories tested (Mahler et al., 2016). The entangled probe photon's polarization changes along the system photon's Bohmian path, crossing the midline in its record.
Steinberg's 2016 experiment (Mahler et al., Science Advances) entangled the system photon with a probe photon, whose polarization (H/V, or read at +45° to erase) marked the path. The probe's polarization changed along the trajectory, because of nonlocal influence from the system photon. The "surreal" trajectories are real Bohmian trajectories plus nonlocality: Bohm's theory survives, and its nonlocality is made visible. The result means trajectories "cannot be ruled out, yet."
From textbook orthodoxy to the 1952 paper
Bohm's 1951 textbook Quantum Theory was, in the book's phrase, not only orthodox but one of the clearest Copenhagen presentations ever published. He still wrote that "no theory of mechanically determined hidden variables can lead to all of the results of the quantum theory," using EPR and the uncertainty principle. After talks with Einstein he reversed course. The 1952 Physical Review paper thanks only Einstein; it is the theory Bohm had said could not be conceived, and it shows von Neumann's no-go claim was not the last word.
Pauli raised the same objections he had used against de Broglie in 1927. Bohm answered every one and, when Pauli said the draft was too long to read, wrote: if the paper is short enough to read it cannot answer the objections; if it answers them it is too long. To Pauli he also used the diamond metaphor: if one man finds a diamond, throws it away as worthless, and another later recognizes its value, the stone belongs to the second. De Broglie, once alerted, left Copenhagen and returned to his 1926 double-solution idea.
Bohm's path from orthodoxy to pilot-wave theory.
Quantum equilibrium and the Born rule
In Bohmian mechanics the Born rule is not an axiom about measurement. If the initial particle positions are distributed as |ψ|² (quantum equilibrium), the guidance equation preserves that distribution, so outcomes match standard quantum statistics. Uncertainty is then like weather forecasting: deterministic dynamics plus ignorance of precise initial conditions. Detlef Dürr, Sheldon Goldstein and Nino Zanghì made this precise; Basil Hiley dislikes the name "Bohmian mechanics" but agrees on the ontology. Peter Holland's The Quantum Theory of Motion is the standard monograph.
For Schrödinger's cat, the N particles that make up the cat end in a dead or alive configuration regardless of observation. The dead and alive parts of the wavefunction diverge in configuration space and stop influencing each other: an effective collapse with a mapped physical process. Goldstein: the theory is "a clarification" of the rules, not a repudiation.
Surreal trajectories and the 2016 reply
Englert, Scully, Süssmann and Walther (ESSW, 1992) argued that a which-path detector can fire for the wrong slit if Bohmian paths never cross the midline, dubbing the paths "surrealistic." Steinberg's 2016 experiment (Mahler et al., Science Advances) entangled a system photon with a probe whose polarization marked the path. The probe's polarization record crossed the midline along the Bohmian trajectory of the system photon, because of nonlocal influence. The "surreal" paths are ordinary Bohmian paths plus the theory's nonlocality made visible.
Hiley objects that photons are relativistic and lack true Bohmian trajectories. With Robert Flack (UCL) he planned a version with metastable argon atoms (~100 s lifetime) and a magnetic weak stage; the book leaves it incomplete. Steinberg jokes colleagues assume he was "brainwashed"; he still waits for a reason to privilege position over other observables and notes Bohm "doubled the number of entities."
ESSW surreal claim and Steinberg's nonlocal reply.
Dewdney's punch cards and Steinberg's 2011 breakthrough
Chris Dewdney, working with Bohm and Hiley in the late 1970s and early 1980s, computed double-slit trajectories on punch cards: submit the deck, wait, retrieve a film canister, hold the frames to the light. Particles went through one slit or the other, then zigzagged under the pilot wave into the fringe bands. No path crossed the midline. That numerical picture is what Steinberg's photons later traced on average.
Wiseman (2007) stressed that weak values do not let you follow one particle without spoiling the experiment; they reconstruct ensemble-average paths. Steinberg's calcite-polarization method (Science 2011; Physics World Breakthrough of the Year) matched Dewdney's plots. Critics (including Hiley) note photons are relativistic; the planned metastable argon version would speak more directly to nonrelativistic Bohmian mechanics.
From computed Bohm paths to measured average photon paths.
Bohmian package: what is added and what is derived.
Gravity Kills the Quantum Cat?: The Case for Adding Spacetime into the Mix
Penrose's broken entrance
Roger Penrose lectures with hand-drawn overhead transparencies; one maps physics with "Our broken down entrance" where quantum theory meets gravity. Quantum mechanics works with spacetime as a fixed stage; general relativity makes spacetime dynamic. He wants an "even-handed marriage" rather than quantizing gravity, because superposing two spacetimes "doesn't really make sense."
Penrose's idea: superposed masses curve space-time two ways, and the strain forces collapse.
His image gives the book its title: a cat facing two doors, one opened by a photon reflected at a beam splitter, so the cat is in superposition of going through both doors at once. A cat, or a pair of glasses, in two places means two different curvatures of spacetime.
Penrose admits the argument is "hand-waving," but it removes Bell's "shifty split" between quantum and classical: no observers, a physical mechanism. He reminds audiences that Newtonian mechanics reigned for longer than quantum mechanics has so far, and was still superseded; a theory's success is no proof it is final.
GRW and CSL
In 1986 Giancarlo Ghirardi, Alberto Rimini and Tullio Weber proposed that each particle's wavefunction is occasionally multiplied by a sharply localized function, at random: about once in 100 million years per particle. A measuring device with about 10²⁰ particles entangled together collapses in tens of nanoseconds or less.
GRW collapse: rare random hits that add up quickly for big objects.
| Model | Collapse trigger | Key parameter |
|---|---|---|
| GRW (1986) | random hits per particle | rate, localization width |
| CSL (1990) | continuous, mass-density | rate λ, width ~100 nm |
| Diósi-Penrose | gravitational self-energy | mass-density cutoff R0 |
- CSL. Another variant (the continuous spontaneous localization of Pearle, Ghirardi and Rimini, which the book leaves unnamed) fixes GRW's trouble with identical particles. The parameters are tunable.
- Bell's verdict. With GRW, "the cat is not both dead and alive for more than a split second"; such theories are "honest attempts to replace the woolly words."
- The cost. Collapse is still nonlocal and random, and the Schrödinger equation is no longer the whole story.
The biggest Schrödinger cat
Markus Arndt (Vienna) wants "the biggest Schrödinger cat," measured by mass and by criteria such as being as warm as a cat or containing a biomolecule.
1983: David Pritchard (MIT) diffracts atoms.
1991: Jürgen Mlynek (Konstanz) sends helium atoms through slits 1 µm wide, 8 µm apart.
1992: Fujio Shimizu (Tokyo) does neon.
1999: Arndt and Zeilinger interfere C60 buckyballs (~1 nm, ~200 m/s, de Broglie wavelength ~350 times smaller than the molecule).
2013 (book's record): a molecule of 810 atoms, 10,123 amu.
The record molecule (284 carbon, 190 hydrogen, 320 fluorine, 4 nitrogen, 12 sulphur atoms) came from Marcel Mayor (Basel), wrapped in a Teflon-like shell, evaporated at 220 °C. A velocity selector of three slits on a parabola kept speeds within 10-15%, accepting only about 1 in 10 million molecules. Gratings with 266 nm slits; a 1 mm beam spans ~4,000 slits; molecules land on reconstructed silicon and are counted. Decoherence by stray gas molecules or emitted heat would destroy the fringes, hence ultra-high vacuum.
Penrose's self-energy argument in numbers
Penrose applies an energy-time uncertainty idea to the gravitational self-energy difference between two superposed mass distributions. The collapse time is roughly τ ≈ ħ / E_G. A pair of glasses in two places collapses almost at once; a single microscopic particle could last about the age of the universe. He calls the argument "hand-waving" but insists it removes Bell's "shifty split": no observers, a physical mechanism. Lajos Diósi proposed a related gravitational criterion slightly earlier; together they form the Diósi-Penrose family. Penrose wants an "even-handed marriage" of quantum theory and gravity rather than simply quantizing spacetime, because superposing two geometries "doesn't really make sense."
Diósi-Penrose: gravitational strain forces collapse.
GRW rates and CSL's fix
GRW (1986) multiplies the wavefunction by a sharply localized function at random, about once per 10⁸ years per particle. A device with ~10²⁰ entangled particles collapses in tens of nanoseconds. CSL (Pearle; Ghirardi and Rimini, 1990), which the book leaves unnamed, replaces discrete hits with a continuous stochastic process tied to mass density and handles identical particles cleanly. Parameters (λ, localization width ~100 nm) remain tunable, which is why Arndt complains that theorists can "change their parameters" when experiments approach a threshold.
Bell welcomed GRW as an "honest attempt to replace the woolly words": the cat is not both dead and alive for more than a split second. The cost is the same nonlocality and randomness Vaidman calls an "ugly scar."
Buckyballs, Basel chemistry, and free fall
Arndt and Zeilinger's 1999 C60 experiment put ~1 nm buckyballs (named for Buckminster Fuller's geodesic dome) at ~200 m/s through a grating; the de Broglie wavelength was ~350× smaller than the molecule. The book's 2013 record, 810 atoms / 10,123 amu, came from Marcel Mayor (Basel): 284 C, 190 H, 320 F, 4 N, 12 S, wrapped in a Teflon-like shell and evaporated at 220 °C. A three-slit velocity selector on a parabola kept speeds within 10-15%, accepting ~1 in 10⁷ molecules. Gratings with 266 nm slits; a 1 mm beam spans ~4,000 slits. Stray gas or emitted heat would decohere the fringes, hence ultra-high vacuum.
A tobacco mosaic virus (~10⁷ amu) is in the lab's hypothetical range but broke apart in tests. Beyond ~10⁸ amu, flight times grow until Earth's rotation matters, or one drops the apparatus in Bremen's 146 m tower (~4 s free fall). Penrose's space proposal put three satellites ~10,000 miles apart; Bouwmeester, Christoph Simon and William Marshall (PRL 2003) shrank it to cavities where radiation pressure displaces a micro-mirror cooled below 1 mK in a dilution refrigerator. Bouwmeester expects no collapse, then would take many worlds seriously.
Two experimental roads to testing collapse.
Why bigger objects make collapse models nervous.
Arndt admits "occasionally you think as a Bohmian," though Vienna's mood is non-realist. GRW's boundary has moved: theorists revised the mass where collapse should bite from about 10⁹ to 10¹⁶ amu; "Theorists... can change their parameters." Lab limits sit near 10⁸ amu, about 10,000 times the record; a tobacco mosaic virus (~10⁷ amu) broke apart in tests. Bigger masses need longer flight, meaning Earth's rotation matters, or free fall (Bremen's 146 m drop tower, about 4 s). "In either case, you win."
The mass frontier: interference holds at every rung tested; GRW's revised threshold lies far above.
Arndt frames it as a win-win: finding the point where interference fails would be the discovery of new physics; pushing past every predicted threshold squeezes collapse models into corners and strengthens the case that the Schrödinger equation holds at all scales.
Mirrors in superposition
Dirk Bouwmeester met Penrose by chance at an airport talk about knotted light and twistors, became his Oxford postdoc, worked on teleportation in Innsbruck, and returned to Oxford. Penrose had proposed a space test: three satellites about 10,000 miles apart, an X-ray photon in superposition of hitting or missing a tiny movable mirror, displaced by ~10⁻¹³ m, recombined in a Michelson interferometer.
Book figure: Penrose's satellite proposal. An X-ray photon split between satellites A, B and C, about 10,000 miles apart, nudges or misses a movable mirror; interference reveals whether the mirror's superposition survived.
With Christoph Simon and William Marshall (proposal 2002, PRL 2003) Bouwmeester shrank it to a tabletop: optical cavities in which a photon's radiation pressure displaces a tiny mirror.
Book figure: the tabletop version. A photon in superposition of two optical cavities nudges a movable micro-mirror in one; after release, interference shows whether the mirror's superposition persisted.
- Engineering. The mirror must be cooled below 1 millikelvin in a dilution refrigerator; mirrors cut by focused ion beam are glued upside down on silicon nitride. Costs run to "several millions."
- Decoherence vs collapse. Decoherence leaks phase into the environment and can be shielded; a true collapse cannot.
- Expectation. Bouwmeester expects no collapse; then he would take many worlds seriously.
The ugly scar
Vaidman sees collapse as "an ugly scar" on a beautiful theory. On a bus in China (retold at Waterloo's Institute for Quantum Computing) he described a patent watch whose YES or NO display is set by a photon at a beam splitter: in his view both outcomes happen, in different worlds, as Hugh Everett proposed in 1957.
Healing an Ugly Scar: The Many Worlds Medicine
Everett's thesis
Everett took a chemical engineering degree (1953) and began a Princeton PhD in 1955 under John Wheeler, who later coined "black hole" and "wormhole." Standard theory has two processes: smooth Schrödinger evolution, and collapse on measurement. Everett asked: "What actually does happen in the process of measurement?" His answer: apply the equation to everything, observer included, in one universal wavefunction.
Everett's move: no collapse; observer and system become entangled branches.
Everett's branching: a beam-splitter photon, the detector and the observer evolve into two branches, both real.
- The split. For ψ = a·ψreflected + b·ψtransmitted, the observer ends up in a superposition of seeing each result; each branch contains an observer who sees one outcome.
- Statistics. Along a tree of measurement sequences, Born-rule frequencies hold "for almost all" branches.
- The cost. "Abandonment of the concept of the uniqueness of the observer." Everett likened it to an amoeba's life tree of splitting.
Wheeler was "bashful about showing it to Bohr." Everett submitted in 1956, calling Copenhagen an "objectionable" dualism, but Bohr's circle disliked it. At Alexander Stern's seminar in May 1956 the work was said to "lack meaningful content" and verge on theology; Wheeler apologized for Everett, misdescribing his view, and the thesis was cut to about a quarter of its length to make it "javelin proof" before the 1957 paper.
DeWitt makes it "many worlds"
Bryce DeWitt, editing Reviews of Modern Physics, objected: "I simply do not branch." Everett answered that Copenhagen was a "philosophic monstrosity" and that all branches are equally actual. At a Cincinnati meeting in October 1962 (Rosen, Podolsky, Dirac, Shimony, Wigner), Podolsky spoke of "parallel worlds that science fiction likes"; Everett replied that each branch is a "perfectly respectable world." DeWitt's 1970 Physics Today article popularized the name, and the image of "10¹⁰⁰+ slightly imperfect copies" of oneself: "schizophrenia with a vengeance."
Carroll and Wallace
Sean Carroll, then at Caltech beneath a Feynman-diagram mural, points to the Universe Splitter app, which sends a request to a photon lab in Geneva and splits the world on your behalf: "Take a chance." Bohr's language, he says, is "complete nonsense"; Everettians are "suckers for mathematical beauty."
- Decoherence. Interaction with the environment turns a superposition into a mixed state (a density matrix) for local observers; branches become orthogonal and "exponentially hard to find" again. Decoherence does not by itself say why we see one outcome; many worlds says we see all of them.
- Path integrals. Steinberg notes that Feynman's sum over histories already speaks of "two different states of the universe."
David Wallace (then at USC, formerly Oxford with David Deutsch) calls many worlds "extremely conservative": it takes the equation literally and changes neither physics nor philosophy.
Book figure: Wallace's quadrant. Change physics? Change philosophy? Copenhagen and QBism change philosophy; Bohm, GRW and Penrose change physics; Everett changes neither; changing both is crossed out.
The probability problem
Unequal amplitudes break naive counting. Make a beam splitter 75/25: each photon still yields two branches, so counting worlds gives 50/50, not 75/25. Howard Wiseman calls Everett's derivation a sleight of hand.
| Approach | Born rule from | Status |
|---|---|---|
| Counting worlds | number of branches | fails for 75/25 |
| Deutsch-Wallace | decision theory: rational betting | disputed |
| Carroll-Sebens | self-locating uncertainty | disputed |
Carroll and Charles Sebens note that decoherence (~10⁻²⁰ s) splits you before you know which branch you are in, so probability is self-locating uncertainty. Deutsch and Wallace derive the Born rule from rational decision-making. Wiseman remains unconvinced.
QBism
Christopher Fuchs lives in an 1886 house of quartersawn oak with a shelf of Daniel Dennett labelled "the enemy." Steeped in William James, he met Wheeler at UT Austin ("elementary acts of observer-participancy") and did his PhD under Carlton Caves (New Mexico), where the argument was frequentist versus Bayesian probability.
QBism: the wave function as an agent's beliefs about future experiences.
Fuchs illustrates with a simple wager. An agent who assigns odds of 1/3 and 2/3 to two outcomes writes amplitudes 1/√3 and √2/√3; new data change her odds to 1/2 and 1/2, and she rewrites ψ accordingly. Nothing physical "collapsed": the change is in her expectations, as when a forecaster revises a rain probability. The uniqueness of quantum theory, for QBists, is not in the states but in the rules linking an agent's bets on different measurements, rules that no classical probability theory obeys.
- Not Copenhagen in disguise. The agent, not a classical apparatus, is central, and any physical system can be treated quantum mechanically.
- Not solipsism. David Mermin (Cornell), a convert, stresses there is a world that pushes back; quantum theory is each agent's guide to it.
- Locality. Fuchs and Mermin call QBism "explicitly local." Wallace's Emergent Multiverse claims locality for many worlds too.
1955: Everett begins under Wheeler.
1956: thesis submitted; Stern's seminar in May.
1957: short paper, "'Relative State' Formulation of Quantum Mechanics."
1962: Cincinnati conference.
1970: DeWitt's Physics Today article names "many worlds."
1970s-1980s: decoherence theory (Zeh, Zurek) explains why branches stop interfering.
2000s-2010s: Deutsch-Wallace and Carroll-Sebens attack the probability problem.
The quantum-classical divide moves with the interpretation: nowhere for Everett, at the agent for QBism, at the collapse threshold for GRW. Each side dismisses the other. After one Fuchs talk Mermin called "the worst" he had heard, Zeilinger advised Fuchs to "look to the back rows." The chapter closes on the cracks in each account, through which light passes through two doors.
Stern's seminar and the javelin-proof thesis
Wheeler was "bashful about showing it to Bohr." Everett submitted in 1956; at Alexander Stern's seminar that May the work was said to "lack meaningful content" and verge on theology. Wheeler apologized and misdescribed Everett's view. The thesis was cut to about a quarter of its length to make it "javelin proof" before the 1957 paper, "'Relative State' Formulation of Quantum Mechanics." Everett called Copenhagen an "objectionable" dualism: two processes, Schrödinger evolution and collapse, with no clear rule for when each applies.
At the Cincinnati meeting in October 1962 (Rosen, Podolsky, Dirac, Shimony, Wigner), Podolsky spoke of "parallel worlds that science fiction likes." Everett answered that each branch is a "perfectly respectable world." Abner Shimony asked whether awareness attaches to one branch or all; the uniqueness of the observer was already the price Everett had named. Bryce DeWitt's 1970 Physics Today article coined "many worlds" and the image of 10¹⁰⁰+ slightly imperfect copies of oneself: "schizophrenia with a vengeance."
Everett from thesis to popular name.
Universe Splitter and the 75/25 problem
Carroll's Universe Splitter app queries a photon lab in Geneva: say "Take a chance" or "Play it safe" and, on the Everettian reading, the world branches. A beam splitter alone already splits the universal wavefunction into transmitted and reflected components; adding the rest of a Mach-Zehnder only reunites them if coherence survives.
Unequal amplitudes break naive world-counting. A 75/25 beam splitter still yields two branches per photon, so counting worlds gives 50/50, not 75/25. Howard Wiseman calls Everett's original frequency argument a sleight of hand. Carroll and Charles "Chip" Sebens treat |a|² as self-locating uncertainty: decoherence (~10⁻²⁰ s) splits you before you know which branch you occupy. Deutsch and Wallace derive the Born rule from decision theory (rational betting). Both remain disputed.
Carroll quotes the Hilbert-space dimension of our universe as roughly e^(10¹²⁰), room enough for branching. Frank Wilczek raises the bookkeeping of energy across branches. How fast splitting spreads, and its fit with relativity, stay open. Deutsch to Paul Davies: many worlds is "cheap on assumptions but expensive on universes." Wallace: simplicity counts laws, not objects.
QBism's Jamesian roots and locality claim
Christopher Fuchs, steeped in William James, met Wheeler at UT Austin ("elementary acts of observer-participancy") and did his PhD under Carlton Caves at New Mexico, where the fight was frequentist versus Bayesian probability. The 2002 Caves-Fuchs-Schack paper made quantum probabilities personal degrees of belief. Fuchs's 1886 house holds a shelf of Daniel Dennett labelled "the enemy," because QBism keeps the agent in the theory while Dennett wants awareness dissolved.
David Mermin (Cornell), a convert, stresses the world pushes back; quantum theory is each agent's guide to it, not solipsism. Fuchs and Mermin call QBism "explicitly local": no single agent experiences space-like separated events, so the theory does not assign spooky correlations to them. Wallace's The Emergent Multiverse claims locality for many worlds too. After one Fuchs talk Mermin called "the worst" he had heard; Zeilinger advised Fuchs to "look to the back rows."
Two collapse-free answers to the ugly scar.
What QBism keeps and drops
QBists keep the Born rule as a normative constraint on an agent's gambling commitments, not as a law about frequencies in an ensemble. They drop the demand that ψ represent the world as it is independently of any agent. Measurement outcomes are experiences for the agent who acts; two agents can assign different states to the same system until they communicate. The "scar" of collapse becomes ordinary Bayesian updating after a new experience.
Fuchs's research programme asks whether the Born rule, written in a special form, can reconstruct the rest of the quantum formalism from simpler axioms about probability and measurement. The book presents that ambition without claiming it is finished. Against Everett, QBism refuses a god's-eye universal wavefunction; against Copenhagen, it refuses a privileged classical cut enforced by physics rather than by the agent's perspective.
QBism's move: from ontic ψ to agent-centered belief.
Everett's relative states without a collapse postulate.
Ways of Looking at the Same Thing?
Feynman's six or seven pictures
At Werner Erhard's est-funded physics conferences of the late 1970s (recounted in David Kaiser's How the Hippies Saved Physics), Leonard Susskind watched Feynman and Sidney Coleman take apart two philosophers at dinner; yet Susskind calls Feynman "the most philosophical" physicist he knew. Feynman's theories A and B, mathematically equivalent but suggesting different next steps, led him to say that "every theoretical physicist who is any good knows six or seven different theoretical representations for exactly the same physics."
Many interacting worlds
Howard Wiseman, with Dirk-André Deckert and Michael Hall, proposed many interacting worlds: a large but finite set of classical worlds, each with definite particle positions, that repel each other, like a starling murmuration. There is no wavefunction; quantum effects emerge from the interaction, and trajectories resemble Bohm's.
Book figure: double-slit trajectories in the many-interacting-worlds model. Each line is one world's particle, pushed by the others into fringe-like bands.
Wiseman also reads collapse theories as hidden-variable theories with the variables entangled, and notes that locality in configuration space can look nonlocal in 3D space. Seen through the epilogue's four axes, no two interpretations make the same set of sacrifices, and only some of them (collapse models, Born-rule tests, perhaps gravity) leave fingerprints in the lab. The rest remain, in Feynman's sense, different ways of looking at the same predictions, valuable for the next theory they might suggest.
| Interpretation | Deterministic | Realist | Wavefunction only | Local |
|---|---|---|---|---|
| Copenhagen | no | no | plus classical world | obscure |
| Bohmian | yes | yes | no: plus particles | no |
| Collapse (GRW, DP) | no | yes | yes | no |
| Many worlds | yes | yes | yes | tends local |
| Many interacting worlds | yes | yes | no wavefunction | no |
| QBism | silent | yes, with caveat | ψ subjective | dismisses issue |
Testing the Born rule
"If Born's rule fails, everything goes to hell," Wojciech Zurek has said. Urbasi Sinha (formerly at Waterloo's IQC, now at the Raman Research Institute, Bengaluru) notes: "There is no formal proof" of the rule. Squaring amplitudes means interference comes only in pairs of paths; three open slits should add nothing beyond pairwise terms.
Sinha's triple-slit test of the Born rule: a nonzero three-path term would mean the rule is not exactly squaring.
Book figure: a nonclassical path in the triple slit, from one slit to its neighbour and on to the screen, with top views of the slits and baffle.
A subtlety: light can take nonclassical paths that loop between slits, mimicking a three-path term; a baffle helps separate the two effects. Feynman, on the double slit: "You remember the case of the experiment with the two holes?" The book's last line: "The case remains unsolved."
Four axes, not one winner
The epilogue refuses a verdict. It sorts interpretations by whether they are deterministic, realist about the microscopic, treat the wavefunction alone as the state, and remain local. No two popular options match on all four. Feynman's lesson from the est-funded dinners and from theories A and B is pragmatic: keep six or seven representations of the same physics, because each suggests different next experiments.
Many interacting worlds (Wiseman, Deckert, Hall) drops ψ entirely: a large finite swarm of classical worlds with definite positions repel each other; interference-like bands emerge as in a murmuration. Trajectories resemble Bohm's, but the ontology is different and the authors present it as an existence proof of alternatives, not a claim of truth.
Epilogue: keep many pictures; test what can be tested.
Sorkin's parameter and nonclassical paths
Sinha's triple-slit program asks whether probabilities are exactly |sum of amplitudes|². A nonzero three-path (Sorkin) term would mean the Born rule's exponent is not exactly two. Sinha et al. (Science, 2010) bounded that term below ~10⁻² of ordinary two-path interference. A confound: light can take looped nonclassical paths between slits that mimic a third-order term; baffles and later work (Sawant et al., PRL 2014) separate that optics from a true Born-rule failure. So far the rule holds. The book's last line stands: "The case remains unsolved."
Keep multiple pictures; demand lab fingerprints where possible.
Main Points
Twenty-two takeaways
- Single particles interfere. Photons, electrons and molecules sent one at a time still build fringes; any path information destroys them.
- Entanglement explains the vanishing fringes. A which-path detector becomes entangled with the particle; no disturbance is needed.
- No local hidden variables. Bell's theorem and loophole-free tests (2015) rule out theories that are both local and realist; nonlocal ones survive.
- Every interpretation has a price. Give up realism (Copenhagen), locality (Bohm), the pure equation (collapse), one world (Everett) or an objective ψ (QBism).
- Delayed choice cannot fool the photon. Its behaviour matches the final setup whenever the setup is fixed, even space-like separated.
- Collapse models are testable. GRW and Diósi-Penrose predict new physics; underground detectors have already ruled out the simplest DP version.
- Measurement is undefined. Copenhagen never says what counts as a measurement or where the classical world begins.
- Superposition is not "both paths." Albert: asking which path is a category mistake; the states, not the particle, interfere.
- The Mach-Zehnder is the smart double slit. Two beam splitters, two indistinguishable routes per detector, and all photons at D1.
- Erasers show information matters. Kim (2000) and La Palma-Tenerife (2013) restore fringes by erasing path marks, but only after sorting the data.
- No retrocausal signal. The total screen pattern never changes; fringes emerge only from coincidence sorting.
- Interaction-free measurement is real. The bomb tester certifies a live bomb one time in four per photon without touching it.
- Hardy's paradox proves nonlocality without inequalities. Clicks that cannot both happen classically happen 1/16 of the time.
- Einstein's worry was locality, not dice. He accepted indeterminism; he rejected nonlocal collapse and anti-realism.
- Bohmian mechanics is a full theory. Positions plus a guiding ψ reproduce all quantum predictions, with explicit nonlocality.
- Average trajectories can be measured. Weak measurement (Steinberg, 2011) traced Bohm-like average paths; surreal paths are nonlocality made visible.
- The mass frontier keeps moving. From C60 (1999) to 810 atoms (2013) to over 7,000 atoms (2026), interference holds.
- Many worlds is conservative about physics. It keeps the Schrödinger equation alone, at the cost of branching universes.
- Probability is many worlds' hardest problem. Counting branches fails for 75/25; decision-theory and self-location derivations remain disputed.
- QBism makes ψ a belief. Collapse becomes Bayesian updating, keeping locality but making the theory agent-centred.
- The Born rule is still being tested. Triple-slit experiments bound any three-path term below 1% of normal interference.
Five interpretations and the price each pays for the double slit.
Frameworks and mental models
| Name | What it says | Use it when |
|---|---|---|
| Which-path versus fringes | Path information and interference trade off | Reading any two-path experiment |
| EPR reality criterion | Certain prediction without disturbance implies an element of reality | Following the incompleteness argument |
| Bell inequality | Local hidden variables cap correlations | Judging what experiments rule out |
| Mark and erase | Fringes depend on available information | Analysing erasers and delayed choice |
| Wallace's quadrant | Change physics, philosophy, or neither | Sorting interpretations by cost |
| Diósi-Penrose time | τ ≈ ħ / E_G | Estimating where collapse would bite |
| Interpretation axes | Determinism, realism, locality, ψ-only | Comparing interpretations side by side |
Who's who
| Person | Role in the book |
|---|---|
| Thomas Young | Showed light interference, 1801-1803 |
| Richard Feynman | Called the double slit "the only mystery" |
| Niels Bohr, Werner Heisenberg | Complementarity, uncertainty, Copenhagen |
| Albert Einstein | EPR; defended locality and realism |
| Erwin Schrödinger | Wave equation, cat, named entanglement |
| Grete Hermann | Refuted von Neumann's proof, 1935 |
| John Bell | 1964 theorem on local hidden variables |
| Alain Aspect | Bell tests, single photons, delayed choice |
| John Wheeler | Delayed choice; Everett's adviser |
| Anton Zeilinger, Rupert Ursin | Vienna; La Palma-Tenerife eraser |
| Marlan Scully, Yoon-Ho Kim | Quantum eraser theory and experiment |
| Avshalom Elitzur, Lev Vaidman | Bomb tester; Vaidman a many-worlder |
| Lucien Hardy | Hardy's paradox |
| Tim Maudlin, David Albert | Philosophers of physics |
| David Bohm, Basil Hiley | Pilot-wave theory, Birkbeck |
| Sheldon Goldstein | Bohmian mechanics advocate |
| John Bush, Yves Couder | Walking droplets |
| Aephraim Steinberg | Weak-measurement trajectories |
| Roger Penrose, Lajos Diósi | Gravity-induced collapse |
| Ghirardi, Rimini, Weber | Spontaneous collapse (GRW) |
| Markus Arndt | Molecule interferometry, Vienna |
| Dirk Bouwmeester | Mirror superposition experiment |
| Hugh Everett, Bryce DeWitt | Many worlds and its naming |
| Sean Carroll, David Wallace | Modern Everettians |
| Christopher Fuchs, David Mermin | QBism |
| Howard Wiseman | Many interacting worlds; probability critic |
| Urbasi Sinha | Triple-slit Born-rule tests |
Coverage checklist against the book
Frameworks preserved in full where the book lists them: bomb-tester fractions; Bell's local-realism limit versus quantum violations; GRW rarity versus macroscopic certainty; Everett's relative states versus QBism's agent-centered ψ; the epilogue's four-axis table; Sinha's Born-rule test logic. Numbers and dates called out in the chapters (1803, 1905, 1927, 1935, 1952, 1964, 1982-89, 1999-2017, 2015, 2022, 2025-26 updates) are repeated in timelines rather than left only in prose.
Master map: phenomena saved, prices paid, tests left.
About this book
Through Two Doors at Once: The Elegant Experiment That Captures the Enigma of Our Quantum Reality by Anil Ananthaswamy, 2018. 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
- Single particles interfere. Photons, electrons and molecules sent one at a time still build fringes; any path information destroys them.
- Entanglement explains the vanishing fringes. A which-path detector becomes entangled with the particle; no disturbance is needed.
- No local hidden variables. Bell's theorem and loophole-free tests (2015) rule out theories that are both local and realist; nonlocal ones survive.
- Every interpretation has a price. Give up realism (Copenhagen), locality (Bohm), the pure equation (collapse), one world (Everett) or an objective ψ (QBism).
- Delayed choice cannot fool the photon. Its behaviour matches the final setup whenever the setup is fixed, even space-like separated.
- Collapse models are testable. GRW and Diósi-Penrose predict new physics; underground detectors have already ruled out the simplest DP version.