Einstein's thought experiments
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 most penetrating insights. 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 intended to show, at least in concept, how the Heisenberg uncertainty principle might be evaded. In a profound 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: 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 very first paragraph of Einstein's seminal 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 of which he could be sure. Expressed in contemporary physics vocabulary, his postulates were as follows: Einstein's wording of the second postulate was one with which nearly all theorists of his day could agree. His wording is a far more intuitive form of the second postulate than the stronger version frequently encountered in popular writings and college textbooks. Trains, embankments, and lightning flashes. The topic of  how Einstein arrived at special relativity has been a fascinating one to many scholars: A lowly, 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: 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. However, all of the above is supposition. In later recollections, when Einstein was asked about what inspired him to develop special relativity, he would mention his riding a light beam and his magnet and conductor thought experiments. He would also mention the importance of the  Fizeau experiment and the observation of stellar aberration. "They were enough", he said. 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 formula_1 and length formula_2, (b) with some sort of arrangement for sending a quantity of radiative energy (a burst of photons) formula_3 from the left to the right. The radiation has momentum formula_4 Since the total momentum of the system is zero , the cylinder recoils with a speed formula_5 (c) The radiation hits the other end of the cylinder in time formula_6 (assuming formula_7), bringing the cylinder to a stop after it has moved through a distance (d) The energy deposited on the right wall of the cylinder is transferred to a massless shuttle mechanism formula_9 (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 formula_10 cannot be massless while transferring energy from the right to the left. If energy formula_3 possesses the inertia formula_12 the contradiction disappears. Modern analysis suggests that neither Einstein's original 1905 derivation of mass-energy equivalence nor the alternate derivation implied by his 1906 center-of-mass theorem are definitively correct. 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 formula_13 (as viewed from the material strip). Imagine two observers, A and B, standing on the "x"-axis and separated by the distance formula_2. They stand next to the material strip, which is not at rest, but rather is moving in the "negative" "x"-direction with speed formula_15. A uses the strip to send a signal to B. From the velocity composition formula, the signal propagates from A to B with speed formula_16. The time formula_17 required for the signal to propagate from A to B is given by The strip can move at any speed  formula_19. Given the starting assumption formula_20, one can always set the strip moving at a speed formula_15 such that formula_22. 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: General relativity. 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. In 1911, Einstein returned to this subject, in part because he had realized that certain predictions of his nascent theory were amenable to experimental test. 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 formula_3, then the increase in its inertial mass is formula_24 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. To show that the equivalence principle necessarily implies the gravitation of energy, Einstein considered  a light source formula_25 separated along the "z"-axis by a distance formula_26 above a receiver formula_27 in a homogeneous gravitational field having a force per unit mass of 1 formula_28 A certain amount of electromagnetic energy formula_3 is emitted by formula_25 towards formula_31 According to the equivalence principle, this system is equivalent to a gravitation-free system which moves with uniform acceleration formula_32 in the direction of the positive "z"-axis, with formula_25 separated by a constant distance formula_26 from formula_31 In the accelerated system, light emitted from formula_25 takes (to a first approximation) formula_37 to arrive at formula_31 But in  this time, the velocity of formula_27 will have increased by formula_40 from its velocity when the light was emitted. The energy arriving at formula_27 will therefore not be the energy formula_42 but the greater energy formula_43 given by According to the equivalence principle, the same relation holds for the non-accelerated system in a gravitational field, where we replace formula_45 by the gravitational potential difference formula_46 between formula_25 and formula_27 so that The energy formula_43 arriving at formula_27 is greater than the energy formula_52 emitted by formula_25 by the potential energy of the mass formula_54 in the gravitational field. Hence  formula_55 corresponds to the gravitational mass as well as the inertial mass of a quantity of energy. To further clarify that the energy of gravitational mass must equal the energy of inertial mass, Einstein proposed the following cyclic process: (a) A light source formula_25 is situated a distance formula_26 above a receiver formula_27 in a uniform gravitational field. A movable mass formula_1 can shuttle between formula_25 and formula_31 (b) A pulse of electromagnetic energy formula_3 is sent from formula_25 to formula_31 The energy formula_65 is absorbed by formula_31 (c) Mass formula_1 is lowered from formula_25 to formula_69 releasing an amount  of work equal to formula_70 (d) The energy absorbed by formula_27 is transferred to formula_72 This increases the gravitational mass of formula_1 to a new value formula_74 (e) The mass is lifted back to formula_25, requiring the input of work formula_76 (e) The energy carried by the mass is then transferred to formula_77 completing the cycle. Conservation of energy demands that the difference in work between raising the mass and lowering the mass, formula_78, must equal formula_79 or one could potentially define a perpetual motion machine. Therefore, In other words, the increase in gravitational mass predicted by the above arguments  is precisely equal to the increase in inertial mass predicted by special relativity. Einstein then considered sending a continuous electromagnetic beam of frequency formula_81 (as measured at formula_25) from formula_25 to formula_27 in a homogeneous gravitational field. The frequency of the light as measured at formula_27 will be a larger value formula_86 given by Einstein noted that the above equation seemed to imply something absurd: Given that the transmission of light from formula_25 to formula_27 is continuous, how could the number of periods emitted per second from formula_25 be different from that received at formula_91 It is impossible for wave  crests to appear on the way down from formula_25 to formula_27. The simple answer is that this question presupposes an absolute nature of time, when in fact there is nothing that compels us to assume that clocks situated at different gravitational potentials must be conceived of as going at the same rate. The principle of equivalence implies gravitational time dilation. It is important to realize that Einstein's arguments predicting gravitational time dilation are valid for "any" theory of gravity that respects the principle of equivalence. This includes Newtonian gravitation. 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. 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. Stachel has identified Einstein's analysis of the rigid relativistic rotating disk as being key to this realization. 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 formula_94 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. Einstein realized that he did not have the mathematical skills to describe the non -Euclidean view of space and time that he envisioned, so he turned to his mathematician friend, Marcel Grossmann, for help. After researching in the library, Grossman found a review article by Ricci and Levi-Civita on absolute differential calculus (tensor calculus). Grossman tutored Einstein on the subject, and in 1913 and 1914, they published two joint papers describing an initial version of a generalized theory of gravitation. Over the next several years, Einstein used these mathematical tools to generalize Minkowski's geometric approach to relativity so as to encompass curved spacetime. Quantum mechanics. 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 well-known 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. Therefore, Einstein before 1925 originated most of the key concepts of quantum theory: light quanta, wave-particle duality, the fundamental randomness of physical processes, the concept of indistinguishability, and the probability density interpretation of the wave equation. In  addition, Einstein can arguably be considered the father of solid state physics and condensed matter physics. He provided a correct derivation of the blackbody radiation law and sparked the notion of the laser. What of "after" 1925? 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 formula_96 in a  small volume formula_15 of a cavity filled with thermal radiation in the frequency interval between formula_98 and formula_99 to be a function of frequency and temperature: where formula_101 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 formula_95). From this, Einstein concluded that radiation had simultaneous wave and particle aspects. Bubble paradox. Einstein  from 1905 to 1923 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" and maintained this attitude even after Einstein's photoelectric law was validated. The citation for Einstein's 1922 Nobel Prize very deliberately avoided all mention of light-quanta, instead stating that it was being awarded for "his services to theoretical physics and especially for his discovery of the law of the photoelectric effect". This dismissive stance contrasts sharply with the enthusiastic manner in which Einstein's other major  contributions were accepted, including his work on Brownian motion, special relativity, general relativity, and his numerous other contributions to the "old" quantum theory. Various explanations have been given for this neglect on the part of the physics community. First and foremost was wave theory's long and indisputable success in explaining purely optical phenomena. Second was the fact that his 1905 paper, which pointed out that certain phenomena would be more readily explained under the assumption that light is particulate, presented the hypothesis only as a "heuristic viewpoint". The paper offered no compelling, comprehensive alternative to existing electromagnetic theory. Third  was the fact that his 1905 paper introducing light quanta and his two 1909 papers that argued for a wave-particle fusion theory approached their subjects via statistical arguments that his contemporaries "might accept as theoretical exercise—crazy, perhaps, but harmless". Most of Einstein's contemporaries adopted the position that light is ultimately a wave, but appears particulate in certain circumstances only because atoms absorb wave energy in discrete units. Among the thought experiments that Einstein presented in his 1909 lecture on the nature and constitution of radiation was one that he used to point out the implausibility of the  above argument. He used this thought experiment to argue that atoms emit light as discrete particles rather than as continuous waves: (a) An electron in a cathode ray beam strikes an atom in a target. The intensity of the beam is set so low that we can consider one electron at a time as impinging on the target. (b) The atom emits a spherically radiating electromagnetic wave. (c) This wave excites an atom in a secondary target, causing it to release an electron of energy comparable to that of the original electron. The energy of the secondary electron depends only  on the energy of the original electron and not at all on the distance between the primary and secondary targets. All the energy spread around the circumference of the radiating electromagnetic wave would appear to be instantaneously focused on the target atom, an action that Einstein considered implausible. Far more plausible would be to say that the first atom emitted a particle in the direction of the second atom. Although Einstein originally presented this thought experiment as an argument for light having a particulate nature, it has been noted that this thought experiment, which has been termed the "bubble paradox , 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. In a letter to Born, he wrote: The Solvay Debates between Bohr and Einstein began in dining-room discussions at the "Fifth Solvay International Conference on Electrons and Photons" in 1927. Einstein's issue with the new quantum mechanics was not just that, with the  probability interpretation, it rendered invalid the notion of rigorous causality. After all, as noted above, Einstein himself had introduced random processes in his 1916 theory of radiation. Rather, by defining and delimiting the maximum amount of information obtainable in a given experimental arrangement, the Heisenberg uncertainty principle denied the existence of any knowable reality in terms of a complete specification of the momenta and description of individual particles, an objective reality that would exist whether or not we could ever observe it. Over dinner, during after-dinner discussions, and at breakfast, Einstein debated with Bohr and his followers on the  question whether quantum mechanics in its present form could be called complete. Einstein illustrated his points with increasingly clever thought experiments intended to prove that position and momentum could in principle be simultaneously known to arbitrary precision. For example, one of his thought experiments involved sending a beam of electrons through a shuttered screen, recording the positions of the electrons as they struck a photographic screen. Bohr and his allies would always be able to counter Einstein's proposal, usually by the end of the same day. On the final day of the conference, Einstein revealed that the uncertainty principle  was not the only aspect of the new quantum mechanics that bothered him. Quantum mechanics, at least in the Copenhagen interpretation, appeared to allow action at a distance, the ability for two separated objects to communicate at speeds greater than light. By 1928, the consensus was that Einstein had lost the debate, and even his closest allies during the Fifth Solvay Conference, for example Louis de Broglie, conceded that quantum mechanics appeared to be complete. At the Sixth Solvay International Conference on Magnetism (1930), Einstein came armed with a new thought experiment. This involved a box with a shutter that  operated so quickly, it would allow only one photon to escape at a time. The box would first be weighed exactly. Then, at a precise moment, the shutter would open, allowing a photon to escape. The box would then be re-weighed. The well-known relationship between mass and energy formula_103 would allow the energy of the particle to be precisely determined. With this gadget, Einstein believed that he had demonstrated a means to obtain, simultaneously, a precise determination of the energy of the photon as well as its exact time of departure from the system. Bohr was shaken by  this thought experiment. Unable to think of a refutation, he went from one conference participant to another, trying to convince them that Einstein's thought experiment could not be true, that if it were true, it would literally mean the end of physics. After a sleepless night, he finally worked out a response which, ironically, depended on Einstein's general relativity. Consider the illustration of Einstein's light box: After finding his last attempt at finding a loophole around the uncertainty principle refuted, Einstein quit trying to search for inconsistencies in quantum mechanics. Instead, he shifted his focus to the  other aspects of quantum mechanics with which he was uncomfortable, focusing on his critique of action at a distance. His next paper on quantum mechanics foreshadowed his later paper on the EPR paradox. Einstein was gracious in his defeat. The following September, Einstein nominated Heisenberg and Schroedinger for the Nobel Prize, stating, "I am convinced that this theory undoubtedly contains a part of the ultimate truth." 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. Einstein's beliefs had evolved over the years from those that he had held when he was young, when, as a logical positivist heavily influenced by his reading of David Hume and Ernst Mach, he had rejected such unobservable concepts as absolute time and space. Einstein believed: Einstein  considered that realism and localism were fundamental underpinnings of physics. After leaving Nazi Germany and settling in Princeton at the Institute for Advanced Study, Einstein began writing up a thought experiment that he had been mulling over since attending a lecture by Léon Rosenfeld in 1933. Since the paper was to be in English, Einstein enlisted the help of the 46-year-old Boris Podolsky, a fellow who had moved to the institute from Caltech; he also enlisted the help of the 26-year-old Nathan Rosen, also at the institute, who did much of the math. The result of  their collaboration was the four page EPR paper, which in its title asked the question "Can Quantum-Mechanical Description of Physical Reality be Considered Complete?" After seeing the paper in print, Einstein found himself unhappy with the result. His clear conceptual visualization had been buried under layers of mathematical formalism. Einstein's thought experiment involved two particles that have collided or which have been created in such a way that they have properties which are correlated. The total wave function for the pair links the positions of the particles as well as their linear momenta. The figure depicts the spreading  of the wave function from the collision point. However, observation of the position of the first particle allows us to determine precisely the position of the second particle no matter how far the pair have separated. Likewise, measuring the momentum of the first particle allows us to determine precisely the momentum of the second particle. "In accordance with our criterion for reality, in the first case we must consider the quantity P as being an element of reality, in the second case the quantity Q is an element of reality." Einstein concluded that the second particle, which we have never  directly observed, must have at any moment a position that is real and a momentum that is real. Quantum mechanics does not account for these features of reality. Therefore, quantum mechanics is not complete. It is known, from the uncertainty principle, that position and momentum cannot be measured at the same time. But even though their values can only be determined in distinct contexts of measurement, can they both be definite at the same time? Einstein concluded that the answer must be yes. The only alternative, claimed Einstein, would be to assert that measuring the first particle instantaneously affected  the reality of the position and momentum of the second particle. "No reasonable definition of reality could be expected to permit this." Bohr was stunned when he read Einstein's paper and spent more than six weeks framing his response, which he gave exactly the same title as the EPR paper. The EPR paper forced Bohr to make a major revision in his understanding of complementarity in the Copenhagen interpretation of quantum mechanics. Prior to EPR, Bohr had maintained that disturbance caused by the act of observation was the physical explanation for quantum uncertainty. In the EPR thought experiment, however , Bohr had to admit that "there is no question of a mechanical disturbance of the system under investigation." On the other hand, he noted that the two particles were one system described by one quantum function. Furthermore, the EPR paper did nothing to dispel the uncertainty principle. Later commentators have questioned the strength and coherence of Bohr's response. As a practical matter, however, physicists for the most part did not pay much attention to the debate between Bohr and Einstein, since the opposing views did not affect one's ability to apply quantum mechanics to practical problems, but only  affected one's interpretation of the quantum formalism. If they thought about the problem at all, most working physicists tended to follow Bohr's leadership. So stood the situation for nearly 30 years. Then, 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. Successive experiments improved the accuracy of observation and closed loopholes. To date, it is virtually certain that local realist theories have been falsified. So Einstein was wrong. But after decades of relative neglect, the EPR paper has been recognized as prescient, since it identified the phenomenon of quantum entanglement. It has several times been the case that Einstein's "mistakes" have foreshadowed and provoked major shifts in scientific research. Such, for instance, has been the case with his proposal of the  cosmological constant, which Einstein considered his greatest blunder, but which currently is being actively investigated for its possible role in the accelerating expansion of the universe. In his Princeton years, Einstein was virtually shunned as he pursued the unified field theory. Nowadays, innumerable physicists pursue Einstein's dream for a "theory of everything." The EPR paper did not prove quantum mechanics to be incorrect. What it did prove was that quantum mechanics, with its "spooky action at a distance," is completely incompatible with commonsense understanding. Furthermore, the effect predicted by the EPR paper, "quantum entanglement", 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.