Overview
A hallmark of Albert Einstein's career was his use of visualized thought experiments ( ) as a fundamental tool for understanding physical issues and for elucidating his concepts to others. Einstein's thought experiments took diverse forms. In his youth, he mentally chased beams of light. For special relativity, he employed moving trains and flashes of lightning to explain his theory. For general relativity, he considered a person falling off a roof, accelerating elevators, blind beetles crawling on curved surfaces and the like. In his debates with Niels Bohr on the nature of reality, he proposed imaginary devices that attempted to show, at least in concept, how the Heisenberg uncertainty principle might be evaded.
In a contribution to the literature on quantum mechanics, Einstein considered two particles briefly interacting and then flying apart so that their states are correlated, anticipating the phenomenon known as quantum entanglement.
Introduction
A thought experiment is a logical argument or mental model cast within the context of an imaginary (hypothetical or even counterfactual) scenario. A scientific thought experiment, in particular, may examine the implications of a theory, law, or set of principles with the aid of fictive and/or natural particulars (demons sorting molecules, cats whose lives hinge upon a radioactive disintegration, men in enclosed elevators) in an idealized environment (massless trapdoors, absence of friction). They describe experiments that, except for some specific and necessary idealizations, could conceivably be performed in the real world. As opposed to physical experiments, thought experiments do not report new empirical data. They can only provide conclusions based on deductive or inductive reasoning from their starting assumptions.
Thought experiments invoke particulars that are irrelevant to the generality of their conclusions. It is the invocation of these particulars that give thought experiments their experiment-like appearance. A thought experiment can always be reconstructed as a straightforward argument, without the irrelevant particulars. John D. Norton, a well-known philosopher of science, has noted that "a good thought experiment is a good argument; a bad thought experiment is a bad argument." When effectively used, the irrelevant particulars that convert a straightforward argument into a thought experiment can act as "intuition pumps" that stimulate readers' ability to apply their intuitions to their understanding of a scenario. Thought experiments have a long history.
Perhaps the best known in the history of modern science is Galileo's demonstration that falling objects must fall at the same rate regardless of their masses. This has sometimes been taken to be an actual physical demonstration, involving his climbing up the Leaning Tower of Pisa and dropping two heavy weights off it. In fact, it was a logical demonstration described by Galileo in Discorsi e dimostrazioni matematiche (1638). Einstein had a highly visual understanding of physics. His work in the patent office "stimulated him to see the physical ramifications of theoretical concepts." These aspects of his thinking style inspired him to fill his papers with vivid practical detail making them quite different from, say, the papers of Lorentz or Maxwell. This included his use of thought experiments.
Pursuing a beam of light
Late in life, Einstein recalled Einstein's recollections of his youthful musings are widely cited because of the hints they provide of his later great discovery. However, Norton has noted that Einstein's reminiscences were probably colored by a half-century of hindsight. Norton lists several problems with Einstein's recounting, both historical and scientific: :1. At 16 years old and a student at the Gymnasium in Aarau, Einstein would have had the thought experiment in late 1895 to early 1896. But various sources note that Einstein did not learn Maxwell's theory until 1898, in university. :2. A 19th century aether theorist would have had no difficulties with the thought experiment.
Einstein's statement, "...there seems to be no such thing...on the basis of experience," would not have counted as an objection, but would have represented a mere statement of fact, since no one had ever traveled at such speeds. :3. An aether theorist would have regarded "...nor according to Maxwell's equations" as simply representing a misunderstanding on Einstein's part. Unfettered by any notion that the speed of light represents a cosmic limit, the aether theorist would simply have set velocity equal to c, noted that yes indeed, the light would appear to be frozen, and then thought no more of it.
Magnet and conductor
In the first paragraph of Einstein's 1905 work introducing special relativity, he writes: This opening paragraph recounts well-known experimental results obtained by Michael Faraday in 1831. The experiments describe what appeared to be two different phenomena: the motional EMF generated when a wire moves through a magnetic field (see Lorentz force), and the transformer EMF generated by a changing magnetic field (due to the Maxwell–Faraday equation). Although Einstein calls the asymmetry "well-known", there is no evidence that any of Einstein's contemporaries considered the distinction between motional EMF and transformer EMF to be in any way odd or pointing to a lack of understanding of the underlying physics.
Maxwell, for instance, had repeatedly discussed Faraday's laws of induction, stressing that the magnitude and direction of the induced current was a function only of the relative motion of the magnet and the conductor, without being bothered by the clear distinction between conductor-in-motion and magnet-in-motion in the underlying theoretical treatment. Yet Einstein's reflection on this experiment represented the decisive moment in his long and tortuous path to special relativity. Although the equations describing the two scenarios are entirely different, there is no measurement that can distinguish whether the magnet is moving, the conductor is moving, or both.
In a 1920 review on the Fundamental Ideas and Methods of the Theory of Relativity (unpublished), Einstein related how disturbing he found this asymmetry: Einstein needed to extend the relativity of motion that he perceived between magnet and conductor in the above thought experiment to a full theory. For years, however, he did not know how this might be done. The exact path that Einstein took to resolve this issue is unknown. We do know, however, that Einstein spent several years pursuing an emission theory of light, encountering difficulties that eventually led him to give up the attempt. Einstein's wording of the first postulate was one with which nearly all theorists of his day could agree. His second postulate expresses a new idea about the character of light. Modern textbooks combine the two postulates.
One popular textbook expresses the second postulate as, "The speed of light in free space has the same value c in all directions and in all inertial reference frames."
Trains, embankments, and lightning flashes
The topic of how Einstein arrived at special relativity has been a fascinating one to many scholars: A twenty-six year old patent officer (third class), largely self-taught in physics and completely divorced from mainstream research, nevertheless in the year 1905 produced four extraordinary works (Annus Mirabilis papers), only one of which (his paper on Brownian motion) appeared related to anything that he had ever published before. A routine supposition among historians of science is that, in accordance with the analysis given in his 1905 special relativity paper and in his popular writings, Einstein discovered the relativity of simultaneity by thinking about how clocks could be synchronized by light signals. The Einstein synchronization convention was originally developed by telegraphers in the middle 19th century.
The dissemination of precise time was an increasingly important topic during this period. Trains needed accurate time to schedule use of track, cartographers needed accurate time to determine longitude, while astronomers and surveyors dared to consider the worldwide dissemination of time to accuracies of thousandths of a second. Following this line of argument, Einstein's position in the patent office, where he specialized in evaluating electromagnetic and electromechanical patents, would have exposed him to the latest developments in time technology, which would have guided him in his thoughts towards understanding the relativity of simultaneity. He never mentioned thought experiments about clocks and their synchronization. The routine analyses of the Fizeau experiment and of stellar aberration, that treat light as Newtonian corpuscles, do not require relativity.
But problems arise if one considers light as waves traveling through an aether, which are resolved by applying the relativity of simultaneity. It is entirely possible, therefore, that Einstein arrived at special relativity through a different path than that commonly assumed, through Einstein's examination of Fizeau's experiment and stellar aberration. We therefore do not know just how important clock synchronization and the train and embankment thought experiment were to Einstein's development of the concept of the relativity of simultaneity. We do know, however, that the train and embankment thought experiment was the preferred means whereby he chose to teach this concept to the general public.
Relativistic center-of-mass theorem
Einstein proposed the equivalence of mass and energy in his final Annus Mirabilis paper. Over the next several decades, the understanding of energy and its relationship with momentum were further developed by Einstein and other physicists including Max Planck, Gilbert N. Lewis, Richard C. Tolman, Max von Laue (who in 1911 gave a comprehensive proof of from the stress–energy tensor ), and Paul Dirac (whose investigations of negative solutions in his 1928 formulation of the energy–momentum relation led to the 1930 prediction of the existence of antimatter ). Einstein's relativistic center-of-mass theorem of 1906 is a case in point.
In 1900, Henri Poincaré had noted a paradox in modern physics as it was then understood: When he applied well-known results of Maxwell's equations to the equality of action and reaction, he could describe a cyclic process which would result in creation of a reactionless drive, i.e. a device which could displace its center of mass without the exhaust of a propellant, in violation of the conservation of momentum. Poincaré resolved this paradox by imagining electromagnetic energy to be a fluid having a given density, which is created and destroyed with a given momentum as energy is absorbed and emitted. The motions of this fluid would oppose displacement of the center of mass in such fashion as to preserve the conservation of momentum. Einstein demonstrated that Poincaré's artifice was superfluous.
Rather, he argued that mass-energy equivalence was a necessary and sufficient condition to resolve the paradox. In his demonstration, Einstein provided a derivation of mass-energy equivalence that was distinct from his original derivation. Einstein began by recasting Poincaré's abstract mathematical argument into the form of a thought experiment: Einstein considered (a) an initially stationary, closed, hollow cylinder free-floating in space, of mass M and length L , (b) with some sort of arrangement for sending a quantity of radiative energy (a burst of photons) E from the left to the right. The radiation has momentum E/c. Since the total momentum of the system is zero, the cylinder recoils with a speed v = -E/(Mc).
(c) The radiation hits the other end of the cylinder in time \Delta t = L/c, (assuming v ), bringing the cylinder to a stop after it has moved through a distance : \Delta x = - \frac . (d) The energy deposited on the right wall of the cylinder is transferred to a massless shuttle mechanism k, (e) which transports the energy to the left wall (f) and then returns to re-create the starting configuration of the system, except with the cylinder displaced to the left. The cycle may then be repeated. The reactionless drive described here violates the laws of mechanics, according to which the center of mass of a body at rest cannot be displaced in the absence of external forces. Einstein argued that the shuttle k cannot be massless while transferring energy from the right to the left. If energy E possesses the inertia m = E/c^2, the contradiction disappears.
For instance, the center-of-mass thought experiment regards the cylinder as a completely rigid body. In reality, the impulse provided to the cylinder by the burst of light in step (b) cannot travel faster than light, so that when the burst of photons reaches the right wall in step (c), the wall has not yet begun to move. Ohanian has credited von Laue (1911) as having provided the first truly definitive derivation of .
Impossibility of faster-than-light signaling
In 1907, Einstein noted that from the composition law for velocities, one could deduce that there cannot exist an effect that allows faster-than-light signaling. Einstein imagined a strip of material that allows propagation of signals at the faster-than-light speed of W (as viewed from the material strip). Imagine two observers, A and B, standing on the x-axis and separated by the distance L . They stand next to the material strip, which is not at rest, but rather is moving in the negative x-direction with speed v . A uses the strip to send a signal to B. From the velocity composition formula, the signal propagates from A to B with speed (W-v) /(1 -(Wv/c^2)) . The time T required for the signal to propagate from A to B is given by : T = L 1 - (Wv/c^2) \over W-v . The strip can move at any speed v .
Given the starting assumption W > c , one can always set the strip moving at a speed v such that T . In other words, given the existence of a means of transmitting signals faster-than-light, scenarios can be envisioned whereby the recipient of a signal will receive the signal before the transmitter has transmitted it. About this thought experiment, Einstein wrote:
Falling painters and accelerating elevators
In his unpublished 1920 review, Einstein related the genesis of his thoughts on the equivalence principle: The realization "startled" Einstein, and inspired him to begin an eight-year quest that led to what is considered to be his greatest work, the theory of general relativity. Over the years, the story of the falling man has become an iconic one, much embellished by other writers. In most retellings of Einstein's story, the falling man is identified as a painter. In some accounts, Einstein was inspired after he witnessed a painter falling from the roof of a building adjacent to the patent office where he worked. This version of the story leaves unanswered the question of why Einstein might consider his observation of such an unfortunate accident to represent the happiest thought in his life.
Einstein later refined his thought experiment to consider a man inside a large enclosed chest or elevator falling freely in space. While in free fall, the man would consider himself weightless, and any loose objects that he emptied from his pockets would float alongside him. Then Einstein imagined a rope attached to the roof of the chamber. A powerful "being" of some sort begins pulling on the rope with constant force. The chamber begins to move "upwards" with a uniformly accelerated motion. Within the chamber, all of the man's perceptions are consistent with his being in a uniform gravitational field. Einstein asked, "Ought we to smile at the man and say that he errs in his conclusion?" Einstein answered no.
Rather, the thought experiment provided "good grounds for extending the principle of relativity to include bodies of reference which are accelerated with respect to each other, and as a result we have gained a powerful argument for a generalised postulate of relativity." Through this thought experiment, Einstein addressed an issue that was so well known, scientists rarely worried about it or considered it puzzling: Objects have "gravitational mass," which determines the force with which they are attracted to other objects. Objects also have "inertial mass," which determines the relationship between the force applied to an object and how much it accelerates. Newton had pointed out that, even though they are defined differently, gravitational mass and inertial mass always seem to be equal. But until Einstein, no one had conceived a good explanation as to why this should be so.
From the correspondence revealed by his thought experiment, Einstein concluded that "it is impossible to discover by experiment whether a given system of coordinates is accelerated, or whether...the observed effects are due to a gravitational field." This correspondence between gravitational mass and inertial mass is the equivalence principle. An extension to his accelerating observer thought experiment allowed Einstein to deduce that "rays of light are propagated curvilinearly in gravitational fields."
Early applications of the equivalence principle
Einstein's formulation of special relativity was in terms of kinematics (the study of moving bodies without reference to forces). Late in 1907, his former mathematics professor, Hermann Minkowski, presented an alternative, geometric interpretation of special relativity in a lecture to the Göttingen Mathematical society, introducing the concept of spacetime. Einstein was initially dismissive of Minkowski's geometric interpretation, regarding it as überflüssige Gelehrsamkeit (superfluous learnedness). As with special relativity, Einstein's early results in developing what was ultimately to become general relativity were accomplished using kinematic analysis rather than geometric techniques of analysis.
In his 1907 Jahrbuch paper, Einstein first addressed the question of whether the propagation of light is influenced by gravitation, and whether there is any effect of a gravitational field on clocks. By the time of his 1911 paper, Einstein and other scientists had offered several alternative demonstrations that the inertial mass of a body increases with its energy content: If the energy increase of the body is E , then the increase in its inertial mass is E / c^2 . Einstein asked whether there is an increase of gravitational mass corresponding to the increase in inertial mass, and if there is such an increase, is the increase in gravitational mass precisely the same as its increase in inertial mass? Using the equivalence principle, Einstein concluded that this must be so.
Experiments such as the Pound–Rebka experiment, which have firmly established gravitational time dilation, therefore do not serve to distinguish general relativity from Newtonian gravitation. In the remainder of Einstein's 1911 paper, he discussed the bending of light rays in a gravitational field, but given the incomplete nature of Einstein's theory as it existed at the time, the value that he predicted was half the value that would later be predicted by the full theory of general relativity.
Non-Euclidean geometry and the rotating disk
led Einstein to consider that gravitation curves spacetime. By 1912, Einstein had reached an impasse in his kinematic development of general relativity, realizing that he needed to go beyond the mathematics that he knew and was familiar with. The rigid rotating disk had been a topic of lively discussion since Max Born and Paul Ehrenfest, in 1909, both presented analyses of rigid bodies in special relativity. An observer on the edge of a rotating disk experiences an apparent ("fictitious" or "pseudo") force called "centrifugal force". By 1912, Einstein had become convinced of a close relationship between gravitation and pseudo-forces such as centrifugal force: In the accompanying illustration, A represents a circular disk of 10 units diameter at rest in an inertial reference frame.
The circumference of the disk is \pi times the diameter, and the illustration shows 31.4 rulers laid out along the circumference. B represents a circular disk of 10 units diameter that is spinning rapidly. According to a non-rotating observer, each of the rulers along the circumference is length-contracted along its line of motion. More rulers are required to cover the circumference, while the number of rulers required to span the diameter is unchanged. Note that we have not stated that we set A spinning to get B. In special relativity, it is not possible to set spinning a disk that is "rigid" in Born's sense of the term. Since spinning up disk A would cause the material to contract in the circumferential direction but not in the radial direction, a rigid disk would become fragmented from the induced stresses.
In later years, Einstein repeatedly stated that consideration of the rapidly rotating disk was of "decisive importance" to him because it showed that a gravitational field causes non-Euclidean arrangements of measuring rods. Over the next several years, Einstein used these mathematical tools to generalize Minkowski's geometric approach to relativity so as to encompass curved spacetime.
Background: Einstein and the quantum
Many myths have grown up about Einstein's relationship with quantum mechanics. Freshman physics students are aware that Einstein explained the photoelectric effect and introduced the concept of the photon. But students who have grown up with the photon may not be aware of how revolutionary the concept was for his time. The best-known factoids about Einstein's relationship with quantum mechanics are his statement, "God does not play dice with the universe" and the indisputable fact that he just did not like the theory in its final form. This has led to the general impression that, despite his initial contributions, Einstein was out of touch with quantum research and played at best a secondary role in its development.
Concerning Einstein's estrangement from the general direction of physics research after 1925, his scientific biographer, Abraham Pais, wrote: In hindsight, we know that Pais was incorrect in his assessment. Einstein was arguably the greatest single contributor to the "old" quantum theory. Einstein created the quantum theory of light. His proposal that light exists as tiny packets (photons) was so revolutionary, that even such major pioneers of quantum theory as Planck and Bohr refused to believe that it could be true. * In his 1906 theory of specific heats, Einstein was the first to realize that quantized energy levels explained the specific heat of solids.
In this manner, he found a rational justification for the third law of thermodynamics (i.e. the entropy of any system approaches zero as the temperature approaches absolute zero): at very cold temperatures, atoms in a solid do not have enough thermal energy to reach even the first excited quantum level, and so cannot vibrate. Basically, he demonstrated that the Brownian motion experienced by a mirror in thermal equilibrium with black-body radiation would be the sum of two terms, one due to the wave properties of radiation, the other due to its particulate properties. This paper, well known for broaching the possibility of stimulated emission (the basis of the laser), changed the nature of the evolving quantum theory by introducing the fundamental role of random chance. He provided a correct derivation of the blackbody radiation law and sparked the notion of the laser.
In 1935, working with two younger colleagues, Einstein issued a final challenge to quantum mechanics, attempting to show that it could not represent a final solution. Despite the questions raised by this paper, it made little or no difference to how physicists employed quantum mechanics in their work. Of this paper, Pais was to write: In contrast to Pais' negative assessment, this paper, outlining the EPR paradox, has become one of the most widely cited articles in the entire physics literature. It is considered the centerpiece of the development of quantum information theory, which has been termed the "third quantum revolution."
Wave–particle duality
All of Einstein's major contributions to the old quantum theory were arrived at via statistical argument. This includes his 1905 paper arguing that light has particle properties, his 1906 work on specific heats, his 1909 introduction of the concept of wave–particle duality, his 1916 work presenting an improved derivation of the blackbody radiation formula, and his 1924 work that introduced the concept of indistinguishability. Einstein's 1909 arguments for the wave–particle duality of light were based on a thought experiment. Einstein imagined a mirror in a cavity containing particles of an ideal gas and filled with black-body radiation, with the entire system in thermal equilibrium. The mirror is constrained in its motions to a direction perpendicular to its surface. The mirror jiggles from Brownian motion due to collisions with the gas molecules.
Since the mirror is in a radiation field, the moving mirror transfers some of its kinetic energy to the radiation field as a result of the difference in the radiation pressure between its forwards and reverse surfaces. This implies that there must be fluctuations in the black-body radiation field, and hence fluctuations in the black-body radiation pressure. Reversing the argument shows that there must be a route for the return of energy from the fluctuating black-body radiation field back to the gas molecules. Given the known shape of the radiation field given by Planck's law, Einstein could calculate the mean square energy fluctuation of the black-body radiation.
He found the root mean square energy fluctuation \left\langle \epsilon ^2 \right\rangle in a small volume v of a cavity filled with thermal radiation in the frequency interval between \nu and \nu + d\nu to be a function of frequency and temperature: : \left\langle \epsilon ^2 (\nu, T) \right\rangle = \left( h \nu \rho + \frac c^3 8 \pi \nu ^2 \rho^2 \right) v d\nu , where \rho v d\nu would be the average energy of the volume in contact with the thermal bath. The above expression has two terms, the second corresponding to the classical Rayleigh-Jeans law (i.e. a wavelike term), and the first corresponding to the Wien distribution law (which from Einstein's 1905 analysis, would result from point-like quanta with energy h \nu ). From this, Einstein concluded that radiation had simultaneous wave and particle aspects.
Bubble paradox
From 1905 to 1923, Einstein was virtually the only physicist who took light-quanta seriously. Throughout most of this period, the physics community treated the light-quanta hypothesis with "skepticism bordering on derision" foreshadows the famous 1935 EPR paper. In his 1927 Solvay debate with Bohr, Einstein employed this thought experiment to illustrate that according to the Copenhagen interpretation of quantum mechanics that Bohr championed, the quantum wavefunction of a particle would abruptly collapse like a "popped bubble" no matter how widely dispersed the wavefunction. The transmission of energy from opposite sides of the bubble to a single point would occur faster than light, violating the principle of locality. In the end, it was experiment, not any theoretical argument, that finally enabled the concept of the light quantum to prevail.
In 1923, Arthur Compton was studying the scattering of high energy X-rays from a graphite target. Unexpectedly, he found that the scattered X-rays were shifted in wavelength, corresponding to inelastic scattering of the X-rays by the electrons in the target. His observations were totally inconsistent with wave behavior, but instead could only be explained if the X-rays acted as particles. This observation of the Compton effect rapidly brought about a change in attitude, and by 1926, the concept of the "photon" was generally accepted by the physics community.
Einstein's light box
Einstein did not like the direction in which quantum mechanics had turned after 1925. Although excited by Heisenberg's matrix mechanics, Schroedinger's wave mechanics, and Born's clarification of the meaning of the Schroedinger wave equation (i.e. that the absolute square of the wave function is to be interpreted as a probability density), his instincts told him that something was missing.
EPR paradox
Einstein's fundamental dispute with quantum mechanics was not about whether God rolled dice, whether the uncertainty principle allowed simultaneous measurement of position and momentum, or even whether quantum mechanics was complete. It was about reality. Does a physical reality exist independent of our ability to observe it? To Bohr and his followers, such questions were meaningless. All that we can know are the results of measurements and observations. It makes no sense to speculate about an ultimate reality that exists beyond our perceptions. The EPR paper forced Bohr to make a major revision in his understanding of complementarity in the Copenhagen interpretation of quantum mechanics.
In 1964, John Stewart Bell made the groundbreaking discovery that Einstein's local realist world view made experimentally verifiable predictions that would be in conflict with those of quantum mechanics. Bell's discovery shifted the Einstein–Bohr debate from philosophy to the realm of experimental physics. Bell's theorem showed that, for any local realist formalism, there exist limits on the predicted correlations between pairs of particles in an experimental realization of the EPR thought experiment. In 1972, the first experimental tests were carried out that demonstrated violation of these limits. Successive experiments improved the accuracy of observation and closed loopholes. To date, it is virtually certain that local realist theories have been falsified.
The EPR paper has recently been recognized as prescient, since it identified the phenomenon of quantum entanglement, which has inspired approaches to quantum mechanics different from the Copenhagen interpretation, and has been at the forefront of major technological advances in quantum computing, quantum encryption, and quantum information theory.
External links
* NOVA: Inside Einstein's Mind (2015) — Retrace the thought experiments that inspired his theory on the nature of reality.