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100 YEARS of RELATIVITY: CRUCIAL POINTS ∗ V.A

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100 YEARS of RELATIVITY: CRUCIAL POINTS ∗ V.A 100 YEARS of RELATIVITY: CRUCIAL POINTS ∗ V.A. Petrov Division of Theoretical Physics, Institute for High Energy Physics, Protvino, Russia This is a concise review of the main steps in the process of making the relativity theory. §1. Introduction The theory of relativity is, probably, a unique theory in the history of human knowledge that attracted so much attention of the general public. The reasons of such an interest are quite diverse and we are not going to discuss them here. We have only to regret that at present physics seems to lose the credit it had not so many years ago. That is why it was very to the point that the year 2005 was declared the World Year of Physics as a sign of a worldwide celebration of the “Annus Mirabilis”, i.e. 1905, the year marked by many outstanding discoveries including the theory of relativity. Unfortunately this very good move was largely spoiled and depreciated by reducing this celebration to glorification of one single person while other contributors to the powerful break- through in physics which happened in the beginning of the XXth century were unfairly put in oblivion. I am aware that I can hardly improve the general trend but I will try, at least in my talk, to correct this unfairness and to give a more balanced vision of the genesis of the theory of relativity. §2. Prehistory Relativity was known in physics long before 1905. Some vague ideas on this subject can be found already in writings of ancient Greek and Arab philosophers or of medieval European scholastics. Actually the principle of relativity can be traced back to Galileo Galilei. In his famous “Dialogo sopra i due Massimi Sistemi del Mondo, Tolemaico e Copernicano”(“Dialogue con- cerning the two Chief World Systems, Ptolemaic and Copernican”), appeared in 1632 and banned by Pope Urban VIII, the great Italian wrote: “...have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still “[1]. In modern language the mentioned observation of “all the effects” meant all possible physical experiments inside a uniformly moving ship. Galileo Galilei (1564-1642) ∗[email protected] 182 Sir Isaac Newton was also aware of the relativity of the uniform rectilinear motion. He wrote in his famous “Philosophia Naturalis Principia Mathematica” (1687) [2]: “The motions of bodies included in a given space are the same among themselves, whether that space is at rest, or moves uniformly forwards in a right line without any circular motion.” Sir Isaac Newton (1642-1727) Nonetheless Newton devoted special attention to the fundamental concepts of absolute time and absolute space. “Absolute Space, in its own nature, without regard to anything external, remains al- ways similar and immovable.” “Absolute, True and Mathematical Time, of itself and from its own nature flows equa- bly without regard to anything external, and by another name is called Duration.” These Newton’s basic statements survived till the end of the XIXth century. Why did he keep so to these fundamentals? He must have a serious reason for that. The reason was that while one can relatively easily accept the equivalence of the reference systems moving rectilinearly and uniformly relative to each other, it is impossible for reciprocally accelerated systems. The famous “bucket argument” of Newton was quite impressive and persuasive. There just must exist “some- thing” relative to which the rotation proceeds. And this was the Newton Absolute Space. Many years later Ernest Mach dared to challenge this notion and pushed forward some (a bit vague) argument that the acceleration has to be referred to “distant fixed stars” the interaction with which should give to “ponderable bodies” their inertia. He also was quite severe to the abso- lute time: “This absolute time can be measured by comparison with no motion; it has therefore neither a practical nor a scientific value; and no one is justified in saying that he knows aught about it. It is an idle metaphysical conception.” Ernest Mach was neither the first nor the only, who treated these notions quite critically. Nonetheless his writings rendered quite a strong impression on his contemporaries and gave a definite new impetus to further speculations on fundamental issues of time and space. Ernest Mach (1838-1916) 183 §3. Aether Newton, who expressed interbody interactions quantitatively in his Second Law and gave a uni- versal gravitation law, accepted the action at a distance because he, probably, saw that for practi- cal purposes it is quite sufficient while the very nature of the interaction asks for new hypotheses which he endeavoured to avoid (“Hypotheses non fingo”). The problem had been identified long before Newton. Say, Aristotle ( in contrast with Leukippus and Democritus) argued that the empty space is absurd and there must exist some medium which fills the whole space and which was considered as a “ fifth element” or “ quintessence”. The idea of “aether” (below we will use the simplified spelling “ether” as well) was strongly advocated by René Descartes and then by one of the founders of the wave theory of light Christiaan Hyugens (followed by Thomas Young and Augustin Fresnel more than hundred years later). Newton, who vigorously objected Hyugens’ theory, later himself advanced some aether-like model to explain optical phenomena. There were many attempts to construct a mechanical model of the ether (they still con- tinue in our days). Great Scottish physicist James Clerk Maxwell, who systematized a huge num- ber of various results concerning electromagnetic phenomenae and formulated his famous sys- tem of differential equations for electric and magnetic fields, invented quite a complicated model of ether to mechanically interpret his equations. Now some “wise and clever” historians of sci- ence often consider these attempts in a quite arrogant manner as evidently wrong and naïve. We can hardly agree with such an attitude if we try to place ourselves into the XIII-XIX centuries marked by enormous successes of Newton’s mechanics. Moreover mechanical models of the ether were, even if transient, unavoidable and necessary trial steps towards new horizons. And the very idea of the ether played a progressive role. Some discontent had been felt, though, about this important element of nature. Thereof the growing need in more direct manifestations of the ether. As the aether was associated with Newton’s absolute space it was understood quite early that one could detect the effects of motion through the aether experimentally. And this concerned first of all the light propagation which was identified as a propagation of perturbations of the aether. §4. New turn And it was J.C. Maxwell who initiated a new turn in the search for the ether effects when he sug- gested (1878) to measure the effect of the “aether wind”. James Clerk Maxwell (1831-1879) 184 He did this in a year to his death as if indicating to his successors the way to unravel the mystery hidden in his legacy, the Maxwell equations. The way led them in the right direction. The experiment was conducted by American Albert Abraham Michelson in 1881 and later, with better accuracy, in 1887 (together with Edward Williams Morley). Albert A. Michelson (1852-1931) and Edward W. Morley (1838-1923) The scheme of experiment was remarkably simple but Michelson and Morley had to use all their skill and exert their every effort to achieve the necessary accuracy to measure the shift of the interference fringes due to would-be the “aether wind”. Just look at their facility and the scheme of the experiment. 185 The data obtained indicated that within the error bars the effect of the shift was absent, i.e. there was no an “ether wind”. The conclusion was: “It appears, from all that precedes, reasonably certain that if there be any relative motion between the earth and the luminiferous ether, it must be small; quite small enough entirely to refute Fresnel’s explanation of aberration (So called “partial ether drift” hypothesis with help of which A. Fresnel explained the visible position of stars accounting for the Earth movement. V.P.). And further: “If now it were legitimate to conclude from the pre- sent work that the ether is at rest with regard to the earth’s surface, according to Lorentz there could not be a velocity potential, and his own theory also fails.” What was the theory of Lorentz mentioned above? We shall concern it a bit later. Just the same year 1887 as of the Michelson - Morley experiment an article of Göttingen professor Woldemar Voigt appeared. This article dealt with some “elastic theory of light” and was not devoted to the problem of the “aether wind”. But in the course of consideration of the invariance of the wave equation in moving reference systems Voigt has found that corresponding transformations from a system at rest to a system moving with constant velocity v included not only the change of coordinates (Galilei transformations) but also the change of time! Here are Voigt’s transformations (c stands for the velocity of light): 2 x = x – vt, y = y 1 - v 2/c2 , z = z 1 - v 2/c2 , t = t – vx/c ( V ) Woldemar Voigt (1850-1919) For the first time in history of physics time was subjected to a non-trivial change depend- ent on space. What was the meaning of this new time t ? Voigt did not provide an answer, he even did not pose the question.
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