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Albert Einstein Historical and Cultural Perspectives
The Centennial Symposium in Jerusalem
By Gerald Holton, Yehuda Elkana
PRINCETON UNIVERSITY PRESSCopyright © 1982 Princeton University Press
All rights reserved.
Arthur I. Miller
THE SPECIAL RELATIVITY THEORY: EINSTEIN'S RESPONSE TO THE PHYSICS OF 1905
Imagine that you are on the editorial board of a prestigious physics journal and that you receive a paper that is unorthodox in style and format. Its title has little to do with most of its content; it has no citations to current literature; a significant portion of its first half seems to be philosophical banter on the nature of certain basic physical concepts taken for granted by everyone; the only experiment explicitly discussed could be explained adequately using current physical theory and is not considered to be of fundamental importance. Yet, with a minimum of mathematics, the little-known author deduces exactly a result that has heretofore required several drastic approximations. Furthermore, you are struck by certain of the author's general principles, and you feel that they promise additional simplifications. So you decide to publish the paper. This could well have been the frame of mind of the most eminent theoretical physicist on the Guratorium of the Annalen der Physikl Max Planck, when he received from the editor's office Albert Einstein's 1905 paper "On the Electrodynamics of Moving Bodies" — the relativity paper.
The kind of title Einstein had given his paper customarily signaled a discussion of the properties of moving bulk matter, either magnetic or dielectric. Einstein analyzed neither of these topics. In fact, the paper's first quarter contains a philosophical analysis of the notions of time and length. The paper's second half dispatches quickly certain problems of such fundamental importance that they generally rate separate papers — for example, the characteristics of radiation reflected from a moving mirror — and he concludes with certain results from the dynamics of electrons that generally appear at the beginning of papers in which electrons are discussed. The only experiment developed in detail is at the paper's beginning and concerns the generation of current in a closed circuit as a result of the circuit's motion relative to a magnet, that is, electromagnetic induction.
The phenomenon of electromagnetic induction had ushered the Western world into the age of technology because it is fundamental to electrical dynamos. Everyone knew dynamos worked, but there remained fundamental problems concerning their operation. This essay discusses the connection that Einstein realized in 1905 between problems concerning huge electrical dynamos, radiation, moving electrical bulk media, the dynamics of electrons, and the nature of space and time. In order to set the stage for Einstein's bold approach to the physics of 1905, let us review the treatment of these topics by scientists and philosophers of whom Einstein has acknowledged he was aware before 1905.
THE NATURE OF SPACE AND TIME
In his Science of Mechanics (1883) the philosopher-scientist Ernst Mach leveled a devastating critique at the Newtonian notions of absolute space and time. According to Newton, absolute space was the ultimate receptacle in which all phenomena occurred, and absolute time flowed independent of the motion of clocks. Mach considered these notions to be "metaphysical obscurities" because they were unavailable to our sense perceptions. Consequently, Mach disagreed with Immanuel Kant, who by 1781 had elevated Newton's notions of absolute space and time to knowledge that we possessed before all else, that is, a priori intuitions. According to Kant, these intuitions serve as basic organizing principles that enable our minds to construct knowledge from the potpourri of sense perceptions. Thus, for example, we are driven irresistibly toward a three-dimensional Euclidean geometry and the law of causality, and then to such higher-order organizing principles as Newton's physics. Although the discovery of non-Euclidean geometries in 1827 had dealt the Kantian view a serious blow, Kant's emphasis on the role of a priori organizing principles was nevertheless considered important to an understanding of how exact laws of nature are possible. A priori organizing principles played an important role in the neo-Kantian frameworks of such influential philosopher-scientists as Hermann von Helmholtz, Heinrich Hertz, and Henri Poincaré, whose writings impressed Einstein no less than did Mach's "incorruptible skepticism."
Although Mach and Poincaré probed the relation between time and sense perceptions, in their work time remained absolute because there was no reason for it to depend on motion. But Mach and Poincaré insisted on replacing motion relative to Newton's absolute space with motion relative to the distant stars or, even better, motion relative to the substance that electrodynamicists assumed to fill Newton's cosmic receptacle — the ether. This brings us to electromagnetism.
Newton's mechanics of 1687 had unified terrestrial and extraterrestrial phenomena. The next great synthesis occurred not quite two hundred years later, when James Clerk Maxwell unified electromagnetism and optics. Whereas in the Newtonian mechanics disturbances propagated instantaneously through empty space, in Maxwell's theory disturbances propagated at a large but finite velocity through an ether, like ripples in a pond. In 1892 there appeared the result of over two decades of elaborations and purifications of Maxwell's theory — the electromagnetic theory of that master of theoretical physics, Hendrik Antoon Lorentz.
Lorentz assumed that the sources of the electromagnetic fields were as yet undiscovered electrons, which moved about in an all-pervasive, absolutely resting ether. The five fundamental equations of Lorentz's theory are:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
where [??] and [??] are the electric and magnetic fields, respectively, and [??] is the electron's volume density of charge. Since Lorentz's fundamental equations are written relative to a reference system at rest in the ether, which we shall call S, then c is the velocity of light measured in S, and [??] is the electron's velocity relative to S. The Maxwell-Lorentz equations possess the property expected of a wave theory of light, namely, that relative to S the velocity of light is independent of the source's motion and is always c. But this may not necessarily be the result of measuring the velocity of light in a reference system moving with a uniform linear velocity relative to the ether, that is, in an inertial reference system. Therefore, the reference systems in the ether are preferred reference systems. To be sure, despite much effort, experiments had not revealed that the earth's motion through the ether had any effect on optical or electromagnetic phenomena.
Concerning the velocity of light, Newtonian mechanics predicted that the velocity of light emitted from a moving source should differ from the velocity of the light emitted from a source at rest by the amount of the source's velocity; consequently, the velocity of light c' from a source moving with velocity ? is given by Newton's law for the addition of velocities,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
On the other hand, according to the wave theory of light, the quantity c' measured by an observer at rest in the ether is
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
and Lorentz's equations agreed with this requirement. But the effect of the ether on the measuring apparatus was expected to yield a result in agreement with (6), where c' is the velocity of the light relative to the earth and v is the ether's velocity relative to the earth. However, experiments accurate to second-order in the ratio v/c, where v is the velocity of a body that is moving relative to the ether and c is the velocity of light, led to (7). To this order of accuracy, optical and electromagnetic phenomena occurred on the moving earth as if the earth were at rest in the ether. Therefore, to second-order accuracy in v/c, Newtonian mechanics and electromagnetism are inconsistent with optical phenomena occurring in inertial reference systems.
In an 1895 monograph titled Treatise on a Theory of Electrical and Optical Phenomena in Moving Bodies, Lorentz responded fully to the failure of the first-order experiments to detect any effects of the earth's motion on optical and electromagnetic phenomena; these experiments were called ether-drift experiments.
For regions of the ether that are free of matter, or within neutral matter that is neither magnetic nor dielectric, the Lorentz equations in the ether-fixed reference system are the set of equations (S) (see Fig. 1). Applying the modified space and time transformations to (S), Lorentz obtained their analogues in the inertial reference system Sr.
We can appreciate Lorentz's achievement at a glance because to first-order accuracy in the quantity v/c, the Maxwell-Lorentz equations have the same form in the inertial system Sr as in the ether-fixed system S, and thus the same physical laws pertain to both these reference systems; in other words, to this order of accuracy neither optical nor electromagnetic experiments could reveal the motion of the system Sr. Lorentz called this stunning and desirable result the "theorem of corresponding states." It rested on the hypothesis of the mathematical "local time coordinate" tL; the real or physical time was still Newton's absolute time. Hence, to order v/c, the velocity of light in Sr was the same as in S, that is, c' = c. To this order of accuracy, then, Lorentz's theorem of corresponding states removed the inconsistency between Newton's prediction and that of electromagnetic theory in favor of electromagnetic theory.
But Lorentz had not yet explained the only reliable experiment accurate to second-order accuracy in v/c, namely, the 1887 experiment of Albert A. Michelson and Edward Williams Morley, in which light had been found to take the same time to race back and forth along each of two orthogonal rods of equal length that were at rest on the moving earth. He discussed this experiment in the final chapter of the 1895 treatise, which contained two other experiments that, as the chapter's title indicated, could "not be explained without further ado." In order to explain the Michelson-Morley experiment, Lorentz indulged in a physics of desperation. From Newton's law for the addition of velocities, which the theorem of corresponding states was supposed to have obviated, he proposed the hypothesis that the dimensions of the rod in the direction of the earth's motion contracted by an amount [square root](1 – v2/c2). In short, Lorentz's contraction hypothesis was admittedly ad hoc. This blemish on Lorentz's theory was emphasized in the philosophic-scientific criticism of that titan of international science, Henri Poincaré. Nevertheless, Poincaré was impressed with Lorentz's theorem of corresponding states because he eschewed absolute motion.
So successful had been Newton's physics that many scientists had attempted to reduce all of physical theory to it; that is, they pursued a mechanical world-picture. For example, they attempted to simulate the contiguous actions of the ether with increasingly complex mechanical models. But these attempts paled before the successes of Lorentz's theory. Thus, in 1900 Wilhelm Wien suggested the "possibility of an electromagnetic foundation for mechanics," that is, pursuance of an electromagnetic world-picture based on Lorentz's electromagnetic theory. A far-reaching implication of this program was that the electron's mass originated in its own electromagnetic field and should therefore be a velocity-dependent quantity. From studying the behavior of fast electrons that had been injected transversely into parallel electric and magnetic fields, Walter Kaufmann gave data for a dependence of the electron's mass on its velocity that increased without limit as the electron's velocity approached that of light. Kaufmann's colleague at Gottingen, Max Abraham, developed the first field-theoretical description of an elementary particle. Depending on whether his rigid-sphere electron experienced a force transverse or parallel to its motion, and with certain severe restrictions placed on the electron's acceleration, Abraham predicted that it had transverse (mT) and longitudinal [mL] masses:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)
where moe = e2/2Rc2 is the electron's electrostatic (that is, rest) mass and β = v/c. The transverse mass of Abraham's theory agreed with Kaufmann's data, and the goal of an electromagnetic world-picture appeared to be within reach. However, Abraham's theory offered no explanation for the Michelson-Morley experiment, and by 1904 it was in violent disagreement with the new optical experiments of Lord Rayleigh and D. B. Brace, which were accurate to second-order in v/c.
Prompted by the new second-order data and by Kaufmann's measurements, as well as by Poincaré's criticisms, Lorentz proposed his own theory of the electron in which the contraction hypothesis was deemed no longer to be ad hoc, because it became one of several hypotheses that could explain more than one experiment. Lorentz's electron can be likened to a balloon smeared with a uniform distribution of charge. While at rest, Lorentz's electron is assumed to be a sphere; but moving, it undergoes a Lorentz contraction, and its mass becomes a two-component quantity:
mT = 4/3 meo/[square root of (1 - β2)] (10)
mL = 4/3 meo/(1 - β2(3/2 (10)
where moe = e2/2Rc2 is the electron's electrostatic (that is, rest) mass and β = v/c.
Lorentz's mT agreed with Kaufmann's data as well as did Abraham's. But Abraham mT immediately leveled a severe fundamental criticism at Lorentz's theory: Lorentz's deformable electron was unstable because it could explode under the enormous repulsive forces among its constituent parts. From newly discovered Lorentz-Poincaré correspondence we know that Poincaré had recognized this problem independently and then cracked it with his unmatched arsenal of mathematics. Poincaré's resulting papers were the penultimate effort toward an electromagnetic world-picture based on Lorentz's electromagnetic theory. They included such advanced notions of mathematics as group-theoretical methods and four-dimensional spaces. Using a term familiar from fundamental studies in geometry, Poincaré renamed Lorentz's 1904 theorem of corresponding states that embraced all extant data — and, it was hoped, future ones as well — the "principle of relativity." Einstein, we know, had not encountered Poincaré's 1905 version of Lorentz's theory of the electron when he wrote the relativity paper.
To summarize, by 1905 physicists believed that electromagnetic theory was proceeding in the correct direction. Many of them felt sure that with a little more tinkering, Lorentz's theory of the electron could serve as the cornerstone for a unified field-theoretical view of nature. Lorentz's was a dynamical theory that explained such effects as the presumed contraction of length, the observed variation of mass with velocity, and the fact that the measured velocity of light always turned out to be the same — all explained as resulting from the interaction of electrons with the ether. The stage was set for a great new era in science to emerge from what everyone considered to be the cutting edge of scientific research. But, as we shall see, this turned out not to be the case. We move next to an area of science and engineering whose basic problems were deemed unimportant for progress in basic physical theory: the area of electromagnetic induction. In German-speaking countries problems in this area combined technology and basic research. They received a particularly interesting treatment because, as the intellectual historian J. T. Merz has written, the "German man of science was a philosopher."
In 1831 Michael Faraday discovered that relative motion between a wire loop and a magnet produces a current in the wire. Faraday interpreted this result as follows: the magnet affects the wire loop through its lines of force, which emanate from the magnet's north pole and enter through its south pole,· consequently, relative motion between the loop and the magnet results in the loop's cutting the lines of force. Faraday's law states that the rate at which the lines of force are cut determines the strength of the current induced; furthermore, the direction and magnitude of the induced current depend on only the relative velocity between the loop and magnet.
Excerpted from Albert Einstein Historical and Cultural Perspectives by Gerald Holton, Yehuda Elkana. Copyright © 1982 Princeton University Press. Excerpted by permission of PRINCETON UNIVERSITY PRESS.
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