Einstein's thought experiments

• 1. Introduction

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  Einstein's thought experiments began at the Gymnasium in Aarau. A sixteen-year-old asked himself what a beam of light would look like if he could travel alongside it. That question stayed with him for a decade. It eventually pointed him toward a theory that overturned three centuries of physical certainty.

  He called this kind of mental exercise a Gedankenexperiment. His job reviewing electromagnetic patents at a Bern office taught him, as he recalled, to see "the physical ramifications of theoretical concepts." His scientific papers were consequently filled with concrete, practical detail, quite unlike the work of contemporaries such as Lorentz or Maxwell.

  What kinds of imaginary scenarios did he build? What battles did they fuel with the greatest physicists of the twentieth century? And how did mental images of sealed elevators, racing trains, and glowing boxes help push physics into territory no one had foreseen?

• 2. The Unbearable Asymmetry

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  Michael Faraday's experiments of 1831 revealed a puzzle that most physicists accepted without question. Move a magnet near a conducting wire: a current flows. Move the wire near a stationary magnet: a current flows again, in the same direction and the same amount. The observable results are identical. The theoretical explanations for the two cases, however, are completely different from each other.

  James Clerk Maxwell had noted this in his 1861 paper On Physical Lines of Force. He gave a separate physical account for each scenario without finding it strange. None of Einstein's contemporaries found it troubling either. Einstein found it intolerable. In an unpublished 1920 review, he confessed that two fundamentally different explanations for the same observable outcome felt "unbearable" to him.

  No measurement could reveal whether the magnet was moving or the wire was moving. To Einstein, this meant the theoretical distinction had to be illusory. Maxwell's equations predicted a single, fixed speed of light with no dependence on any observer's velocity. Newtonian mechanics gave no such constant. The two frameworks could not both be right.

  For years Einstein pursued an emission theory of light as a way to resolve the conflict. He gave it up in failure. "Gradually I despaired of the possibility of discovering the true laws by means of constructive efforts based on known facts," he wrote. The solution came from proposing two postulates. The laws of physics look identical in every frame moving at constant velocity. The speed of light is always the same for all observers, regardless of the source's motion. From those two ideas, special relativity followed.

  A consequence arrived in 1907. Einstein imagined a material capable of transmitting signals faster than light. Using the formula for combining velocities, he showed that such signals could, in certain conditions, reach their destination before they were sent. He wrote that this result, though not logically contradictory, "conflicts with the character of all our experience to such an extent that this seems sufficient to prove the impossibility of the assumption."

• 3. The Relativity of Now

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  At twenty-six, largely self-taught in physics and far from the mainstream of academic research, Einstein produced four extraordinary papers in 1905. His paper On the Electrodynamics of Moving Bodies was polished and complete. The documentary evidence of how it developed amounts to only two sentences in a handful of preserved early letters.

  What is known is how Einstein taught the concept of simultaneity to others. In his popular book Relativity: The Special and General Theory, he explained it through a train scenario. One observer stands on a railway embankment. Another rides a rapidly moving train. As the two pass each other at the same point, lightning strikes two locations, A and B, that are equidistant from both observers. The embankment observer sees both flashes arrive at the same instant and concludes the bolts struck simultaneously. The train observer is moving toward B and away from A. Since both observers measure exactly the same speed of light, the flash from B reaches the train observer first. To her, the bolt at B struck before the bolt at A.

  Two observers in equally valid frames of motion reach opposite but equally correct conclusions about when the strikes occurred. There is no universal now.

  A routine supposition among historians connects this insight to the precision-time technology of the era. Telegraphers had developed conventions for synchronizing clocks by light signals since the middle of the nineteenth century. Railroads needed accurate schedules; cartographers needed precise time to determine longitude; astronomers were aiming for synchronization accurate to thousandths of a second.

  Yet when asked directly about the roots of special relativity, Einstein never mentioned any of this. He cited the Fizeau experiment, the observation of stellar aberration, and the thought experiments he had been working through for years. "They were enough," he said.

• 4. The Happiest Thought

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  In 1907, Einstein was writing a summary article for the Jahrbuch der Radioaktivitat und Elektronik. There, he was struck by what he later called "the happiest thought of my life." It began with a falling man. A person stepping off a rooftop would feel no gravitational field whatsoever. Any object released from his hands would float alongside him, obeying no apparent force, regardless of its material or composition. The falling man, Einstein realized, was justified in concluding that he was at rest.

  The realization, he recalled, "startled" him. It set off an eight-year investigation that he would later regard as his greatest work. Over the years, this founding insight acquired a legend of its own. Most retellings identify the falling man as a painter. Some accounts claim Einstein was inspired after watching a painter fall from a rooftop adjacent to where he worked. This version leaves unanswered why he would consider witnessing such an accident the happiest thought of his life.

  He refined the scenario into something more systematic. He imagined a man sealed inside a large chest or elevator, drifting freely in space far from any mass. Floating, the man finds himself weightless. Then a powerful "being" begins pulling the chest upward with constant force. Everything the man experiences becomes consistent with a uniform gravitational field. Einstein asked whether the man erred in concluding he stood on solid ground. He answered: no. The physics inside an accelerating chamber is identical to the physics inside a gravitational field.

  This correspondence resolved a mystery that Newton had noticed but never explained. Objects have gravitational mass, which determines the pull they feel from other bodies. They also have inertial mass, which determines how strongly they resist acceleration. The two quantities are always exactly equal, but no one had ever given a reason why. Einstein's thought experiment made the equality necessary rather than coincidental. From it, he deduced that rays of light must propagate curvilinearly in gravitational fields.

  By 1912, Einstein had reached an impasse. He had been developing general relativity using kinematic methods and realized he needed different mathematics. Stachel has identified a specific thought experiment, the rigid rotating disk, as the moment Einstein understood why. Max Born and Paul Ehrenfest had both analyzed rigid rotating bodies in special relativity in 1909. An observer on the rim of a spinning disk experiences centrifugal force, which Einstein had become convinced was closely analogous to a gravitational field. A non-rotating observer would find that rulers along the spinning disk's circumference contract in length while rulers spanning the diameter do not. The geometry is non-Euclidean.

  Einstein turned to his mathematician friend Marcel Grossmann for help. Grossmann searched the literature and found a review article by Ricci and Levi-Civita on absolute differential calculus, later called tensor calculus. He tutored Einstein on the subject. In 1913 and 1914, they published two joint papers on an initial version of a generalized theory of gravitation.

• 5. Light as Particle and Wave

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  For the eighteen years between 1905 and 1923, Einstein stood nearly alone among physicists in treating light as a stream of discrete particles. His 1905 paper had presented the hypothesis only as a "heuristic viewpoint," offering no comprehensive alternative to wave theory. His contemporaries found his statistical arguments plausible as exercises but unconvincing as physics.

  The dismissal was stark. In 1922, Einstein received the Nobel Prize in Physics. The citation carefully avoided all mention of light-quanta. It named instead "his services to theoretical physics and especially for his discovery of the law of the photoelectric effect." The discovery most dependent on treating light as particles was honored without acknowledging that light was particles.

  His 1909 work on wave-particle duality rested on a thought experiment. Einstein imagined a mirror inside a cavity filled with black-body radiation and a small quantity of ideal gas. The entire system was held at thermal equilibrium. The mirror jiggles from Brownian motion; it also exchanges energy with the radiation field through pressure fluctuations. When Einstein calculated those fluctuations using the known spectrum of black-body radiation, he found two terms. One matched the classical wave description of light. The other matched the behavior expected from discrete particles with energy proportional to frequency. Both terms were necessary to account for the observed spectrum. Radiation, he concluded, had simultaneous wave and particle aspects.

  He pressed the argument further in a 1909 lecture on the nature and constitution of radiation. He described a scenario later called the bubble paradox. An electron in a dim beam strikes a target atom. The atom emits a spherical electromagnetic wave spreading outward in all directions. At a secondary target far away, that wave excites another atom, which releases an electron with energy comparable to the original. The energy of the secondary electron does not depend on the distance between the two targets. All the energy distributed across the expanding sphere appears to converge instantaneously on a single atom. Einstein considered this implausible. The cleaner account was that the first atom had fired a particle directly toward the second.

  The question was ultimately settled by experiment rather than argument. In 1923, Arthur Compton studied the scattering of high-energy X-rays from a graphite target and found that scattered X-rays were shifted in wavelength. This was a sign of inelastic collisions between X-rays and individual electrons, impossible to explain with wave theory. The Compton effect changed the field rapidly. By 1926, the concept of the photon was in general use.

• 6. The Light Box

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  The Fifth Solvay International Conference on Electrons and Photons convened in 1927. Its most consequential arguments began not in the lecture hall but over dinner. Einstein had written to Born that quantum mechanics was "very impressive," but that an inner voice told him "it is not yet the real thing."

  His concern went beyond probability. The Heisenberg uncertainty principle denied the existence of any complete specification of individual particles. Position and momentum could not be known simultaneously. To Einstein, this was not merely a practical limitation; it was a claim that no underlying reality existed to be measured. That claim, he found unacceptable.

  Over the conference's sessions and dinner discussions, Einstein proposed thought experiment after thought experiment, each designed to show that position and momentum could in principle be determined simultaneously. Bohr and his collaborators found a refutation each time, usually by the end of the same day. By 1928, the consensus was that Einstein had lost the debate. Even Louis de Broglie, one of Einstein's closest allies during the conference, conceded that quantum mechanics appeared complete.

  At the Sixth Solvay International Conference on Magnetism in 1930, Einstein arrived with a new device. He imagined a box equipped with a shutter mechanism so swift it could release exactly one photon at a time. The box would be weighed precisely. At a known moment, the shutter would open and a photon would escape. The box would then be re-weighed. The known relationship between mass and energy would allow the escaped photon's energy to be determined precisely. Since the shutter opened at a precisely known moment, both the photon's energy and its departure time could be known simultaneously. This, Einstein believed, violated the Heisenberg uncertainty relation between energy and time.

  Bohr was shaken. Unable to find an immediate refutation, he went from one conference participant to another, insisting the argument could not be correct. Physics, he said, could not survive it. After a sleepless night, he found a reply built on Einstein's own theory of general relativity. The loss of the photon's mass causes the box to rise in a gravitational field. Returning the box to its original height takes time. The precision of that return is limited by the spring-mass dynamics of the weighing mechanism. General relativity predicts that a clock at a different height ticks at a different rate. The accumulated uncertainty in the clock's reading, combined with the uncertainty in the mass measurement, restored the uncertainty relation exactly.

  Modern analysis has since complicated Bohr's original reply. Later physicists showed that the photon box does not require general-relativistic arguments to resolve. Opening the shutter entangles the box's internal clock with its energy. Any subsequent attempt to weigh the box disturbs the clock state through a quantum mechanism alone.

• 7. Entanglement and Reality

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  After leaving Nazi Germany, Einstein settled at the Institute for Advanced Study in Princeton. A lecture by Leon Rosenfeld in 1933 had set a thought experiment in motion that he had been refining ever since. To write it up in English, he enlisted two colleagues. Boris Podolsky, forty-six, had recently moved to the institute from Caltech. Nathan Rosen, twenty-six, worked through much of the mathematics. The result was a four-page paper asking whether quantum mechanics could be considered a complete description of physical reality.

  Einstein was unhappy with the published version. His conceptual argument had been buried under layers of formalism. The thought experiment at the paper's heart was precise: two particles interact and then separate, leaving their states correlated. Measuring the first particle's position fixes the second particle's position exactly, no matter how far apart they have traveled. Measuring the first particle's momentum fixes the second particle's momentum.

  Einstein concluded that the second particle must possess a definite position and a definite momentum at every moment, regardless of whether anyone measures them. Quantum mechanics accounts for neither. The only alternative was to accept that measuring one particle instantaneously altered the reality of the other. Distance, in that view, would be irrelevant. "No reasonable definition of reality could be expected to permit this," he concluded.

  Bohr spent more than six weeks framing a response, giving it the exact same title as the EPR paper. The argument had forced him into a significant revision. Before 1935, Bohr had maintained that the physical disturbance caused by measurement explained quantum uncertainty. In the EPR scenario, he had to concede that "there is no question of a mechanical disturbance of the system under investigation." He fell back on the claim that the two particles, however distant, remained a single system described by one quantum function.

  Most working physicists paid little attention. The debate seemed to have no bearing on practical calculations. That judgment reversed. In 1964, John Stewart Bell showed that Einstein's local realist world view made experimentally testable predictions that conflicted with those of quantum mechanics. The first experimental tests of Bell's theorem were carried out in 1972, and successive experiments closed the remaining loopholes. Local realist theories are now considered to have been falsified.

  Abraham Pais, Einstein's scientific biographer, predicted that the EPR paper would largely be forgotten. He believed only a single phrase expressing discomfort with instantaneous action at a distance would survive. The paper has since become one of the most widely cited in the physics literature. It is now recognized as the founding document of quantum entanglement, a phenomenon that sits at the heart of quantum computing, quantum encryption, and what some researchers have called the third quantum revolution.