One of the interesting historical aspects of modern relativity theory is that, although it is often regarded as the highly original and even revolutionary contribution of a single individual, almost every idea and formula of the theory had been anticipated by others. For example, Voigt formally derived the Lorentz transformations in 1887 based on general considerations of the wave equation. In the context of electro-dynamics, Fitzgerald, Larmor, and Lorentz had all, by 1892, arrived at the Lorentz transformations, including all the peculiar "time dilation" and "length contraction" effects (with respect to the transformed coordinates) associated with Einstein's special relativity. By 1905, Poincare had even demonstrated that these transformations constitute a group, in the same sense as do Galilean transformations. In view of this, is it correct to regard Einstein as the sole originator of modern relativity?
The question is complicated by the fact that relativity is traditionally split into two separate theories, the special and general theories, corresponding to the two phases of Einstein's historical development, and the interplay between the ideas of Einstein and those of his predecessors and contemporaries are different in the two cases. The "special theory" of 1905 can, with some justification, be regarded as an interpretation of Lorentz's theory of electrodynamics. Indeed, Wilhelm Wein proposed that the Nobel prize of 1912 be awarded jointly to Lorentz and Einstein, saying
The principle of relativity has eliminated the difficulties which existed in electrodynamics and has made it possible to predict for a moving system all electrodynamic phenomena which are known for a system at rest... From a purely logical point of view the relativity principle must be considered as one of the most significant accomplishments ever achieved in theoretical physics... While Lorentz must be considered as the first to have found the mathematical content of relativity, Einstein succeeded in reducing it to a simple principle. One should therefore assess the merits of both investigators as being comparable.
As it happens, the physics prize for 1912 was awarded to the Nils Gustaf Dalen (for the "invention of automatic regulators for lighting coastal beacons and light bouys during darkness or other periods of reduced visibility"), and neither Einstein, Lorentz, nor anyone else was ever awarded a Nobel prize for either the special or general theories of relativity. This is sometimes considered to have been an injustice to Einstein, although in retrospect it's conceivable that a joint prize for Lorentz and Einstein in 1912, as Wein proposed, assessing "the merits of both investigators as being comparable", might actually have diminished Einstein's subsequent popular image as the sole originator of both special and general relativity.
On the other hand, despite the fact that special relativity can, in a sense, be regarded as "just" an interpretation of Lorentz's theory, it is clearly an extraordinarily profound interpretation, with consequences extending far beyond Lorentz's electrodynamics. As Einstein later recalled,
The new feature was the realization that the bearing of the Lorentz transformation transcended its connection with Maxwell's equations and was concerned with the nature of space and time in general.
This is the aspect of Einstein's 1905 theory that prompted Witkowski, after reading vol. 17 of Annalen der Physic, to exclaim: "A new Copernicus is born! Read Einstein's paper!" The comparison is apt, because the contribution of Copernicus was, after all, essentially nothing but an interpretation of Ptolmey's astronomy, just as Einstein's theory was an interpretation of Lorentz's electrodynamics. Only subsequently did men like Kepler, Galileo, and Newton, taking the Copernican insight even more seriously than Copernicus himself had done, develop a substantially new physical theory. It's clear that Copernicus was only one of several people who jointly created the "Copernican revolution" in science, and we can argue similarly that Einstein was only one of several individuals (including Maxwell, Fitzgerald, Lorentz, Planck, Mach, and Minkowski) responsible for the "relativity revolution".
The historical parallel between special relativity and the Copernican model of the solar system is not merely superficial, because in both cases the starting point was a pre-existing theoretical structure based on the naive use of a particular system of coordinates lacking any inherent physical justification. On the basis of these traditional but eccentric coordinate systems it was natural to imagine certain consequences, such as that both the Sun and the planet Venus revolve around a stationary Earth in separate orbits. However, with the newly-invented telescope, Galileo was able to observe the phases of Venus, clearly showing that Venus moves in (roughly) a circle around the Sun. In this way the intrinsic patterns of the celestial bodies became better understood, but it was still possible (and still is possible) to regard the Earth as stationary in an absolute extrinsic sense. In fact, for many purposes we continue to do just that, but from an astronomical standpoint we now almost invariably regard the Sun as the "center" of the solar system. Why? The Sun too is moving among the stars in the galaxy, and the galaxy itself is moving relative to other galaxies, so on what basis do we decide to regard the Sun as the "center" of the solar system?
The answer is that the Sun is the inertial center. In other words, the Copernican revolution (as carried to its conclusion by the successors of Copernicus) can be summarized as the adoption of inertia as the prime organizing principle for the understanding and description of nature. The concept of physical inertia was clearly identified, and the realization of its significance evolved and matured through the works of Kepler, Galileo, Newton, and others. Nature is most easily and most perspicuously described in terms of inertial coordinates. Of course, it remains possible to adopt some non-inertial system of coordinates with respect to which the Earth can be regarded as the stationary center, but there is no longer any imperative to do this, especially since we cannot thereby change the fact that Venus circles the Sun, i.e., we cannot change the intrinsic relations between objects, and those intrinsic relations are most readily expressed in terms of inertial coordinates.
Likewise the pre-existing theoretical structure in 1905 described events in terms of coordinate systems that were not clearly understood and were lacking in physical justification. It was natural within this framework to imagine certain consequences, such as anisotropy in the speed of light, i.e., directional dependence of light speed resulting from the Earth's motion through the (assumed stationary) ether. This was largely motivated by the idea that light consists of a wave in the ether, and therefore is not an inertial phenomenon. However, experimental physicists in the late 1800's began to discover facts analogous to the phases of Venus, e.g., the symmetry of electromagnetic induction, the "partial convection" of light in moving media, the isotropy of light speed with respect to relatively moving frames of reference, and so on. Einstein accounted for all these results by showing that they were perfectly natural if things are described in terms of inertial coordinates - provided we apply a more profound understanding of the definition and physical significance of such coordinate systems and the relationships between them.
As a result of the first inertial revolution (initiated by Copernicus), physicists had long been aware of the existence of a preferred class of coordinate systems - the inertial systems - with respect to which inertial phenomena are isotropic. These systems are equivalent up to orientation and uniform motion in a straight line, and it had always been tacitly assumed that the transformation from one system in this class to another was given by a Galilean transformation. The fundamental observations in conflict with this assumption were those involving electric and magnetic fields that collectively implied Maxwell's equations of electromagnetism. These equations are not invariant under Galilean transformations, but they are invariant under Lorentz transformations. Lorentz invariance was similar to the phases of Venus, in the sense that it irrevocably altered our awareness of the intrinsic relations between events. We can still go on using coordinate systems related by Galilean transformations, but we now realize that only one of those systems (at most) is a truly inertial system of coordinates.
(The electrodynamic theory of Lorentz has something in common with Tycho Brahe's proposed model of the solar system, in which the planets revolve around the Sun, but the Sun revolves around a stationary Earth. Tycho's model was kinematically equivalent to Copernicus' Sun-centered model, the only difference being that Tycho chose to use a coordinate system with respect to which the Earth is stationary, i.e., a non-inertial coordinate system.)
It's worth noting that we define inertial coordinates just as Galileo did, i.e., systems of coordinates with respect to which inertial phenomena are isotropic, so our definition hasn't changed. All that has changed is our understanding of the relations between inertial coordinate systems. Einstein's famous "synchronization procedure" (which was actually first proposed by Poincare) was expressed in terms of light rays, but the physical significance of this procedure is due largely to the empirical fact that it yields the same synchronization as does Galileo's procedure based on mechanical inertia. To establish simultaneity between spatially separate events while floating freely in empty space, throw two identical objects in opposite directions with equal force, so that the thrower remains stationary in his original frame of reference. These objects then pass equal distances in equal times, i.e., they serve to assign inertially simultaneous times to separate events as they move away from each other. In this way we can theoretically establish complete slices of inertial simultaneity in spacetime. Also, someone moving uniformly relative to us can carry out this same procedure with respect to his own inertial frame of reference and establish his own slices of inertial simultaneity throughout spacetime. The unavoidable intrinsic relations that were discovered at the end of the 19th century show that these two sets of simultaneity slices are not identical. The two main approaches to the interpretation of these facts were discussed in Sections 1.5 and 1.6. The approach advocated by Einstein was to adhere to the principle of inertia as the basis for organizing our understanding and descriptions of physical phenomena - which was certainly not a novel idea.
In his later years Einstein observed "there is no doubt that the Special Theory of Relativity, if we regard its development in retrospect, was ripe for discovery in 1905". The person (along with Lorentz) who most nearly anticipated Einstein's special relativity was undoubtedly Poincare, who had already in 1900 proposed an explicitly operational definition of clock synchronization and in 1904 suggested that the ether was in principle undetectable to all orders of v/c. Those two propositions and their consequences essentially embody the whole of special relativity. Nevertheless, as late as 1909 Poincare was not prepared to say that the equivalence of all inertial frames combined with the invariance of (two-way) light speed were sufficient to infer Einstein's model. He maintained that one must also stipulate a particular contraction of physical objects in their direction of motion. This is sometimes cited as evidence that Poincare still failed to understand the situation, but there's a sense in which he was actually correct. The two famous principles of Einstein's 1905 paper are not sufficient to uniquely identify special relativity, as Einstein himself later acknowledged. One must also stipulate, at the very least, homogeneity, memorylessness, and isotropy. Of these, the first two are rather innocuous, and one could be forgiven for failing to explicitly mention them, but not so the assumption of isotropy, which serves precisely to single out Einstein's simultaneity convention from all the other - equally viable - interpretations. (See Section 4.5). This is also precisely the aspect that is fixed by Poincare's postulate of contraction as a function of velocity.
In a sense, the failure of Poincare to found the modern theory of relativity was not due to a lack of discernment on his part (he clearly recognized the Lorentz group of space and time transformations), but rather to an excess of discernment and philosophical sophistication, preventing him from subscribing to the young patent examiner's inspired but perhaps slightly naive enthusiasm for the symmetrical interpretation, which is, after all, only one of infinitely many possibilities. Poincare recognized too well the extent to which our physical models are both conventional and provisional. In retrospect, Poincare's scruples have the appearance of someone arguing that we could just as well regard the Earth rather than the Sun as the center of the solar system, i.e., his reservations were (and are) technically valid, but in some sense misguided.
As for Lorentz, his reluctance to fully embrace the relativity principle that he himself did so much to uncover is partly explained by his belief that "Einstein simply postulates what we have deduced... from the equations of the electromagnetic field". If this were true, it would be a valid reason for preferring Lorentz's approach. However, if we closely examine Lorentz's electron theory we find that agreement with experiment (to the second order in v/c) was achieved only by means of Fitzgerald's contraction hypothesis, which Lorentz adopted only when it became necessary to account for the null result of Michelson and Morely. It's true that, after Poincare complained about the proliferation of hypotheses, Lorentz subsequently explained how the contraction can be deduced from more fundamental principles (as discussed in Section 1.5), but this was based on yet another hypothesis, the co-called molecular force hypothesis, which simply asserts that all physical forces and configurations (including the unknown forces that maintain the shape of the electron) transform according to the same laws as do electromagnetic forces. Now, it obviously cannot follow deductively "from the equations of the electromagnetic field" that the necessarily non-electromagnetic forces which hold the electron together must transform according to the same laws. Lorentz's molecular force hypothesis is simply a disguised form of the postulate of universal Lorentz invariance - which is precisely what Lorentz claims to have deduced rather than postulated. In essence his program consisted of performing a great deal of deductive labor, at the end of which it was still necessary, in order to arrive at results that agreed with experiment, to simply postulate the same principle that forms the basis of special relativity. (To his credit, Lorentz candidly acknowledged that his deductions were "not altogether satisfactory".)
In contrast, Einstein recognized the necessity of invoking the principle of relativity and Lorentz invariance at the start, and then demonstrated that all the other "constructive" labor involved in Lorentz's approach was superfluous, because once we have adopted these premises, all the experimental results arise naturally from the simple kinematics of the situation, with no need for molecular force hypotheses or any other exotic and dubious conjectures regarding the ultimate constituency of matter. On some level Lorentz grasped the superiority of the purely relativistic approach, as is evident from the words he included in the second edition of his "Theory of Electrons" in 1916:
If I had to write the last chapter now, I should certainly have given a more prominent place to Einstein's theory of relativity by which the theory of electromagnetic phenomena in moving systems gains a simplicity that I had not been able to attain. The chief cause of my failure was my clinging to the idea that the variable t only can be considered as the true time, and that my local time t' must be regarded as no more than an auxiliary mathematical quantity.
Still, it's clear that neither Lorentz nor Poincare ever whole-heartedly embraced special relativity, for reasons that may best be summed up by Lorentz when he wrote
Yet, I think, something may also be claimed in favor of the form in which I have presented the theory. I cannot but regard the aether, which can be the seat of an electromagnetic field with its energy and its vibrations, as endowed with a certain degree of substantiality, however different it may be from all ordinary matter. In this line of thought it seems natural not to assume at starting that it can never make any difference whether a body moves through the aether or not, and to measure distances and lengths of time by means of rods and clocks having a fixed position relatively to the aether.
This passage implies that Lorentz's rationale for retaining a substantial aether and attempting to refer all measurements to the rest frame of this aether (without, of course, specifying how that is to be done) was the belief that it might, after all, make some difference whether a body moves through the aether or not. In other words, we should continue to look for physical effects that violate Lorentz invariance (by which we now mean local Lorentz invariance), both in new physical forces and at higher orders of v/c for the known forces. A century later, our present knowledge of the weak and strong nuclear forces and the precise behavior of particles at 0.99999c has vindicated Einstein's judgement that Lorentz invariance is a fundamental principle whose significance and applicability extends far beyond Maxwell's equations, and apparently expresses a general attribute of space and time, rather than a specific attribute of particular physical entities.
In addition to the formulas expressing the Lorentz transformations, we can also find precedents for other results commonly associated with special relativity, such as the equivalence of mass and energy. In fact, the general idea of associating mass with energy in some way had been around for about 25 years prior to Einstein's 1905 papers. Indeed, as Thomson and even Einstein himself noted, this association is already implicit in Maxwell's theory. With electric and magnetic fields e and b, the energy density is (e2 + b2)/(8p) and the momentum density is (e x b)/(4pc), so in the case of radiation (when e and b are equal and orthogonal) the energy density is E = e2/(4p) and the momentum density is p = e2/(4pc). Taking momentum p as the product of the radiation's "mass" m times its velocity c, we have
and so E = mc2. Indeed, in the 1905 paper containing his original deduction of mass-energy equivalence, Einstein acknowledges that it was explicitly based on "Maxwell's expression for the electromagnetic energy of space". We can also mention the pre-1905 work of Poincare and others on the electron mass arising from it's energy, and the work of Hasenohrl on how the mass of a cavity increases when it is filled with radiation. However, these suggestions were all very restricted in their applicability, and didn't amount to the assertion of a fundamental equivalence such as emerges so clearly from Einstein's relativistic interpretation. Hardly any of the formulas in Einstein's two 1905 papers on relativity were new, but what Einstein provided was a single conceptual framework within which all those formulas flow quite naturally from a simple set of general principles.
Occasionally one hears of other individuals who are said to have discovered one or more aspect of relativity prior to Einstein. For example, in November of 1999 there appeared in newspapers around the world a story claiming that "The mathematical equation that ushered in the atomic age was discovered by an unknown Italian dilettante two years before Albert Einstein used it in developing the theory of relativity...". The "dilettante" in question was named Olinto De Pretto, and the implication of the story was that Einstein got the idea for mass-energy equivalence from "De Pretto's insight". There are some obvious difficulties with this account, only some of which can be blamed on the imprecision of popular journalism. First, the story claims that Einstein used the idea of mass-energy equivalence to develop special relativity, whereas in fact the suggestion that energy has inertia appeared in a very brief note that Einstein submitted for publication toward the end of 1905, after the original paper on special relativity.
The report goes on to say that "De Pretto had stumbled on the equation, but not the theory of relativity... It was republished in 1904 by Veneto's Royal Science Institute... A Swiss Italian named Michele Besso alerted Einstein to the research and in 1905 Einstein published his own work..." Now, it's certainly true that Besso was Italian, and worked with Einstein at the Bern Patent Office during the years leading up to 1905, and it's true that they discussed physics, and Besso provided Einstein with suggestions for reading (for example, it was Besso who introduced him to the works of Ernst Mach). However, the idea that Einstein's second relativity paper in 1905 (let alone the first) was in any way prompted by De Pretto's obscure and unfounded comments is bizarre.
In essence, De Pretto's "insight" was the (hardly novel) idea that matter consists of tiny particles (of what he does not say), agitated by their exposure to the ultra-mundane ether particles of George LeSage's "shadow theory" of gravity. Since the particles in every aggregate of matter are in motion, every quantity of mass contains an amount of energy equal to Leibniz's "vis viva", the living force, which Leibniz defined as mv2. Oddly enough, De Pretto seems to have been under the impression that mv2 was the kinetic energy of macroscopic bodies moving at the speed v. On this (erroneous) basis, and despite the fact that De Pretto did not regard the speed of light as a physically limiting speed, he noted that LeSage's ether particles were thought to move at approximately the speed of light, and so (he reasoned) the particles comprising a stationary aggregate of matter may also be vibrating internally at the speed of light. In that case, the vis viva of each quantity of mass m would be mc2, which, he alertly noted, is a lot of energy. Needless to say, this bears no resemblance at all to the path that Einstein actually followed to mass-energy equivalence.
Furthermore, there were far more accessible and authoritative sources available to him for the idea of mass-energy equivalence, including Thomson, Lorentz, Poincare, etc. (not to mention Isaac Newton, who famously asked "Are not gross bodies and light convertible into one another...?"). After all, the idea that the electron's mass was electromagnetic in origin was one of the leading hypotheses of research at that time. It would be like saying that some theoretical physicist today had never heard of string theory! Also, the story requires us to believe that Einstein got this information after submitting the paper on Electrodynamics of Moving Bodies in the summer of 1905 (which contained the complete outline of special relativity but no mention of E = mc2) but prior to submitting the follow-up note just a few months later. Reader's can judge for themselves from a note that Einstein wrote to his close friend Conrad Habicht as he was preparing the mass-energy paper whether this idea was prompted by De Pretto's musings in an obscure Italian publication:
One more consequence of the paper on electrodynamics has also occurred to me. The principle of relativity, in conjunction with Maxwell's equations, requires that mass be a direct measure of the energy contained in a body; light carries mass with it. A noticeable decrease of mass should occur in the case of radium [as it emits radiation]. The argument [which he intends to present in the paper] is amusing and seductive, but for all I know the Lord might be laughing over it and leading me around by the nose.
These are clearly the words of someone who is genuinely working out the consequences of his own recent paper, and wondering about their validity, not someone who has gotten an idea from seeing a formula in someone else's paper. Of course, the most obvious proof that special relativity did not arise from an equation borrowed from Mr. De Pretto is the wonderfully lucid thought process presented by Einstein in his 1905 paper, beginning from first principles and a careful examination of the physical significance of time and space, and leading to the kinematics of special relativity, from which the inertia of energy follows naturally.
Nevertheless, we shouldn't underestimate the real contributions to the development of special relativity made by Einstein's predecessors, most notably Lorentz and Poincare. In addition, although Einstein was remarkably thorough in his 1905 paper, there were nevertheless important contributions to the foundations of special relativity made by others in the years that followed. For example, in 1907 Max Planck greatly clarified relativistic mechanics, basing it on the conservation of momentum with his "more advantageous" definition of force. Planck also critiqued Einstein's original deduction of mass-energy equivalence, and gave a more general and comprehensive argument. (This led Johannes Stark in 1907 to cite Planck as the originator of mass-energy equivalence, prompting an angry letter from Einstein saying that he "was rather disturbed that you do not acknowledge my priority with regard to the connection between mass and energy". In later years Stark became an outspoken critic of Einstein's work.)
Another crucially important contribution was made by Hermann Minkowski (one of Einstein's former professors), who recognized that what Einstein had described was simply ordinary kinematics in a four-dimensional spacetime manifold with the pseudo-metric
(dt)2 = (dt)2 - (dx)2 - (dy)2 - (dz)2
This was vital for the generalization of relativity which Einstein (with the help of his old friend Marcel Grossmann) developed on the basis on the theory of curved manifolds developed in the 19th century by Gauss and Riemann. The tensor calculus and generally covariant formalism employed by Einstein in his general theory had been developed by Gregorio Ricci-Curbastro and Tullio Levi-Civita around 1900 at the University of Padua, building on the earlier work of Riemann, Beltrami, and Christoffel. In fact, the main technical challenge that occupied Einstein in his efforts to find a suitable field law for gravity, which was to construct from the metric tensor another tensor whose covariant derivative automatically vanishes, had already been solved in the form of the Bianchi identities, which lead directly to the Einstein tensor as discussed in Section 5.8.
Several other individuals are often cited as having anticipated some aspect of general relativity, although not in any sense of contributing seriously to the formulation of the theory. John Mitchell wrote in 1783 about the possibility of "dark stars" that we so massive light could not escape from them, and Laplace contemplated the same possibility in 1796. Based on Newton's laws and treating light as corpuscles of matter, Johann von Soldner in 1801 predicted a deflection of 0.84 seconds of arc (half the relativistic value) for light rays passing near the Sun. William Clifford wrote about a possible connection between matter and curved space in 1873.
Interestingly, the work of Soldner had been virtually forgotten until being rediscovered and publicized by Philipp Lenard in 1921, along with the claim that Hasenohrl should be credited with the mass-energy equivalence relation. Similarly in 1917 Ernst Gehrcke arranged for the re-publication of a 1898 paper by a secondary school teacher named Paul Gerber which contained a formula for the precession of elliptical orbits identical to the one Einstein had derived from the field equations of general relativity. Gerber's approach was based on the premise that the gravitational potential propagates at the speed of light, and that the effect of the potential on the motion of a body depends on the body's velocity through the potential field. His potential was similar in form to the Gauss-Weber theories. However, Gerber's "theory" was (and still is) regarded as unsatisfactory, partly because the form of the potential can be arbitrarily manipulated to match any desired precession by adjusting the parameters, and partly because the combination of Gerber's proposed gravitational potential with the rest of (nonrelativistic) physics results in predictions (such as 3/2 the relativistic prediction for the deflection of light rays near the Sun) which are inconsistent with observation. Also, Gerber's free mixing of propagating effects with some elements of action-at-a-distance tended to undermine the theoretical coherence of his proposal.
There is also the delicate matter of Hilbert's priority in publishing the final field equations of general relativity on 20 November 1915, just five days ahead of Einstein's paper. The previous summer Einstein had given a series of lectures at Gottingen on the general theory, on which he'd been working for nearly ten years. During these talks he apparently succeeded in convincing both Hilbert and Klein that he was close to an important discovery (despite the fact that the details of Einstein's theory at that time were not yet completely correct). Hilbert took up the problem from an axiomatic standpoint, and carried on an extensive correspondence with Einstein until the 19th of November. On the 20th, Hilbert submitted a paper to the Gesellschaft der Wissenschaften in Gottingen with a derivation of the field equations. Einstein submitted his paper with the correct form of the field equations to the Prussian Academy on 25 November.
Incidentally, historians have recently found proofs of Hilbert's paper, dated 6 December, which do not contain the final form of the field equations, although it appears in the paper when it was finally published early in 1916. If this is the correct interpretation of events, it seems that Hilbert did not precede Einstein in arriving at the actual field equations (at least not in explicit form), and may even have availed himself of the results from Einstein's paper submitted on 25 November, which he had surely seen by early December. Whatever the sequence of events, it seems that Einstein initially had some feelings of resentment toward Hilbert, perhaps thinking that Hilbert had acted ungraciously and stolen some of his glory, but by December 20 he was able to write a conciliatory note to Hilbert, saying "I think of you again with untroubled friendliness, and ask you to do the same regarding me." Thereafter they remained on friendly terms, and Hilbert never publicly claimed any priority in the discovery of general relativity.
As it turned out, Einstein can hardly have been dissatisfied with the amount of popular credit he received for the theories of relativity, both special and general. Nevertheless, one senses a bit of annoyance when Max Born mentioned to Einstein in 1953 (two years before Einstein's death) that a second edition of Whittaker's book has just appeared, in which the entire credit for special relativity is given to Lorentz and Poincare, with barely a mention of Einstein except to say that "in the autumn of [1905] Einstein published a paper which set forth the relativity theory of Poincare and Lorentz with some amplifications, and which attracted much attention". Einstein replied to his old friend Born
Everybody does what he considers right... If he manages to convince others, that is their own affair. I myself have certainly found satisfaction in my efforts, but I would not consider it sensible to defend the results of my own work as being my own 'property', as some old miser might defend the few coppers he had laboriously scrapped together. I do not hold anything against him [Whittaker], nor of course, against you. After all, I do not need to read the thing.