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.
Special relativity 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.
Rather than the thought experiment being at all incompatible with aether theories (which it is not), the youthful Einstein appears to have reacted to the scenario out of an intuitive sense of wrongness. He felt that the laws of optics should obey the principle of relativity. As he grew older, his early thought experiment acquired deeper levels of significance: Einstein felt that Maxwell's equations should be the same for all observers in inertial motion. From Maxwell's equations, one can deduce a single speed of light, and there is nothing in this computation that depends on an observer's speed. Einstein sensed a conflict between Newtonian mechanics and the constant speed of light determined by Maxwell's equations.
Regardless of the historical and scientific issues described above, Einstein's early thought experiment was part of the repertoire of test cases that he used to check on the viability of physical theories. Norton suggests that the real importance of the thought experiment was that it provided a powerful objection to emission theories of light, which Einstein had worked on for several years prior to 1905.
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). James Clerk Maxwell himself drew attention to this fact in his 1861 paper On Physical Lines of Force. In the latter half of Part II of that paper, Maxwell gave a separate physical explanation for each of the two phenomena.
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.
That decision ultimately led to his development of special relativity as a theory founded on two postulates. Einstein's original expression of these postulates was:
"The laws governing the changes of the state of any physical system do not depend on which one of two coordinate systems in uniform translational motion relative to each other these changes of the state are referred to. Each ray of light moves in the coordinate system "at rest" with the definite velocity V independent of whether this ray of light is emitted by a body at rest or a body in motion."
In their modern form: 1. The laws of physics take the same form in all inertial frames. 2. In any given inertial frame, the velocity of light c is the same whether the light be emitted by a body at rest or by a body in uniform motion. [Emphasis added by editor]
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.
Einstein's paper, On the Electrodynamics of Moving Bodies, is a polished work that bears few traces of its gestation. Documentary evidence concerning the development of the ideas that went into it consist of, quite literally, only two sentences in a handful of preserved early letters, and various later historical remarks by Einstein himself, some of them known only second-hand and at times contradictory.
In regards to the relativity of simultaneity, Einstein's 1905 paper develops the concept vividly by carefully considering the basics of how time may be disseminated through the exchange of signals between clocks. In his popular work, Relativity: The Special and General Theory, Einstein translates the formal presentation of his paper into a thought experiment using a train, a railway embankment, and lightning flashes. The essence of the thought experiment is as follows: Observer M stands on an embankment, while observer M rides on a rapidly traveling train. At the precise moment that M and M coincide in their positions, lightning strikes points A and B equidistant from M and M. Light from these two flashes reach M at the same time, from which M concludes that the bolts were synchronous. The combination of Einstein's first and second postulates implies that, despite the rapid motion of the train relative to the embankment, M measures exactly the same speed of light as does M. Since M was equidistant from A and B when lightning struck, the fact that M receives light from B before light from A means that to M, the bolts were not synchronous. Instead, the bolt at B struck first.