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1905 and all that John Stachel
How Einstein claimed his place in the changing landscape of physics during his annus mirabilis.
A
t the end of 1904, a reader who happened to glance over the contributions to the Annalen der Physik(the premier German physics journal) of one Albert Einstein, an obscure clerk at the Swiss patent office, would have found just five articles — the first published in 1901, when its author was 22 years old. These articles constituted Einstein’s entire published oeuvre, and none was sufficiently distinguished for our hypothetical reader to anticipate the nature or significance of Einstein’s next five papers1–5, all submitted to the Annalen in 1905, his annus mirabilis. Someone privy to Einstein’s correspondence or in close contact with him — his fellow physics student and wife Mileva Maric´ or his old friend and fellow patent office clerk Michele Besso, for example — would have been better prepared. These people knew that, at least since his student days at the Swiss Federal Polytechnic (1896–1900), the young Einstein had been concerned with the foundations of theoretical physics. He had been probing the edifice erected by his predecessors in this field for its strengths and weaknesses, and was already beginning to suggest modifications of some core assumptions6.
Newton’s legacy in question During the nineteenth century, the mechanistic world-view — based on Isaac Newton’s formulation in the Principia (1687) of the kinematics and dynamics of corpuscles of matter, and crowned by his stunningly successful theory of gravitation — was challenged first by the optics, then by the electrodynamics of moving bodies. By the mid 1800s Newton’s corpuscular theory of light was no longer tenable. To explain Snell’s law of refraction, this theory assumed that light corpuscles speed up on encountering a medium of higher refractive index. But in 1849, Léon Foucault and Hippolyte Fizeau showed that, in fact, light slowed down, as predicted by the rival wave theory espoused by Newton’s contemporary Christiaan Huygens. The problem now was to fit the wave theory of light into the newtonian picture of the world. Indeed, the ether — the medium through which light waves were assumed to propagate in the absence of ordinary, ponderable matter — seemed to provide a physical embodiment of Newton’s absolute space. But elucidating the relation between ether and ponderable matter presented grave problems: did moving matter drag the ether with it — either totally or partially — or did the ether remain immobile? It proved impossible to reconcile the consequences of any of these hypotheses with all the experimental results on the optics of moving bodies. By the last third of the nineteenth century, many physicists were acutely aware of this problem7. By 1865, James Clerk Maxwell had showed that light could be interpreted as wave-like oscillations of the electric and magnetic fields, obeying what we now call the Maxwell equations for these fields. It was realized that the optical problems were only a special case of similar problems in reconciling the electrodynamics of moving bodies with newtonian kinematics and dynamics. Towards the end of the century, however, Hendrik Antoon Lorentz seemed to
overcome all these problems through his interpretation of Maxwell’s equations. Lorentz assumed that the electromagnetic ether is entirely immobile, in which case there would be no dragging of the ether. Although in newtonian mechanics it is impossible to distinguish any preferred inertial frame (this result is often referred to as the galileian principle of relativity), at first the situation seemed different for electrodynamics and optics. The rest frame of the ether provided a preferred inertial frame, and motion through it should have been detectable. Yet all attempts to detect the translational motion of the Earth through the ether by means of optical, electrical or magnetic effects consistently failed. Lorentz succeeded in explaining why: according to his theory, no such effect should be detectable by any experiment sensitive to first order in (v/c), where v is the speed of the moving object through the ether and c is the speed of light in that medium. Until the 1880s, no experiment with greater sensitivity had been performed, and Lorentz’s explanation of the failure of all previous experiments was a crowning achievement of his theory. Newton’s mechanics now seemed to have successfully met the challenge of optics and electrodynamics. But the seeds of its downfall had already been planted. Lorentz’s explanation led him to introduce a transformation from newtonian absolute time to a new time variable in each inertial frame moving through the ether. As the relation between absolute time and this time varied from place to place in each inertial frame, Lorentz called this new variable the ‘local time’ of that frame, regarding the local time as a purely formal expression. But Henri Poincaré, the great mathematician who concerned himself extensively with problems of physics, was able to give a physical interpretation of this time variable within the context of newtonian kinematics: it is the time that clocks at rest in a frame moving through the ether would read if they were synchronized using light signals, without taking into account the motion of that frame. This was an important hint that the problems of the electrodynamics and optics of moving bodies were connected with the concept of time. But, as we shall see, it was Einstein who made the final break with the concept of absolute time, by asserting that the local time of any inertial frame is as physically meaningful as that of any other because there is no absolute time with which they can be compared. But by the time Lorentz’s theory was completed, it was in trouble. Albert Michelson, a physicist specializing in optical interferometry, performed an experiment to detect motion through the ether that was sensitive to order (v/c)2 and, according to Lorentz’s theory, this experiment should have succeeded. But it did not. So Lorentz was forced to start patching up his theory by introducing a transformation to new spatial coordinates in a moving inertial frame. (He was ultimately also forced to modify his definition of the local time, and it is this modified transformation law that agrees formally with Einstein’s time-transformation law.) For Lorentz’s spatial transformation to eliminate the predicted second-order effect, Lorentz interpreted it as corresponding
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year of physics commentary type of radiation that would be emitted by a perfectly absorbing, and hence black-appearing, body.) The total energy of the black-body radiation contained in a unit volume and its dependence on temperature could be explained by the laws of thermo-dynamics and electrodynamics, but the distribution of this radiant energy over different frequencies defied classical calculation. If such a calculation were attempted consistently, it gave the absurd result that the total energy in a unit volume must be infinite, no matter how low the temperature of the radiation. By the turn of the century, experiment had produced a wellbehaved frequency distribution formula for the energy radiated by a black body, in the form of Planck’s law. The challenge then was to explain Planck’s law theoretically. Planck provided such a derivation in 1900, but its physical significance for the structure of matter and radiation remained obscure.
Enter Einstein
to a real dynamical contraction of rigid bodies in the direction of their motion through the ether, owing to electromagnetic forces exerted on the particles composing the body. We now call this effect the Lorentz contraction, even though, thanks to Einstein, it is regarded as the purely kinematical effect of comparing lengths in two inertial frames, rather than a dynamical contraction due to motion through the ether.
The kinetic–molecular challenge In spite of the problems posed by electrodynamics, the mechanical picture of the world was far from exhausting its potential at the end of the nineteenth century. A series of brilliant theoretical studies by Maxwell, Rudolf Clausius and Ludwig Boltzmann began to show how the empirically established laws of thermodynamics could be explained in terms of kinetic–molecular models of matter, first for gases and later for liquids and solids. Many properties of materials, such as thermal conductivity and viscosity, could also be explained by such a model. But many aspects of this kinetic–molecular theory of heat remained obscure. For example, how could the time-reversible laws of mechanics governing the behaviour of material particles give rise to the time-irreversible behaviour of bulk matter, summarized in the second law of thermodynamics? The ‘energeticists’ — a group of physicists and especially physical chemists — challenged the entire kinetic–molecular theory of heat, demanding that all physics be based on the macroscopic concept of energy and casting doubt on the kinetic–molecular hypothesis itself. They held that the laws of thermodynamics were strictly correct. In kinetic–molecular theory, however, the laws give the extremely probable results of some averaging procedure over an immensely large number of molecules in bulk matter. Demonstrating microscopic violations of the laws of thermodynamics was thus a crucial challenge for the proponents of kinetic–molecular theory. The newly-developed laws governing the behaviour of electromagnetic radiation in thermal equilibrium also presented a challenge. (This electromagnetic radiation is called ‘cavity radiation’ or Hohlraumstrahlung in German because it is the state that such radiation would reach were it confined to a cavity with walls at a fixed temperature, and it is called ‘black-body radiation’ in English because it is the
Einstein set about tackling all the problem areas mentioned above. Far from being an unqualified revolutionary, his first papers, during 1904, were concerned with the further development of classical mechanics. In particular, Einstein focused on thermodynamics and the kinetic–molecular theory of heat, and attempted to fill some gaps that he saw in the theory (although he later admitted that some of these gaps were in his knowledge of the existing literature). By 1905, Einstein was intent on demonstrating both the reality of molecules, by showing how their size could be estimated from the effect of a suspension of small particles in a fluid on the viscosity of that fluid, and the necessity of the kinetic–molecular theory, by showing that microscopic violations of the laws of thermodynamics do exist. He not only proved that fluctuation phenomena — inconsistent with purely macroscopic thermodynamics but easily explained by the kinetic–molecular theory of heat — exist, but also realized that they had been observed decades earlier as the brownian motion of pollen grains in water2. Einstein derived formulae for the change in viscosity of a solvent as a function of the fraction of solute present; for the diffusion coefficient of small particles suspended in a liquid; and for the variation of the mean free path of a brownian particle as a function of the time interval during which it is observed. For the change in solvent viscosity, the original calculation was wrong, proving that no one is perfect; only after discrepancies with experiment came to light did Einstein find the error and publish a corrected result in 1911. The last result, modelling brownian motion, is the first example of the successful theoretical treatment of a stochastic process. Because of their practical importance — in fields as varied as the study of aerosol particles, the properties of milk, and semiconductor physics — Einstein’s studies on molecular size5 and brownian motion2 are the most cited of his 1905 oeuvre. By this time, some physicists (such as Max Abraham) advocated abandoning the mechanical world-view in favour of an electromagnetic world-picture based on Maxwell’s theory; others (including Planck) wanted to tinker with classical mechanics and Maxwell’s theory — in particular, with the laws governing the exchange of energy between mechanical oscillators and the electromagnetic field. But Einstein’s profound concern with the nature of thermal radiation led him to the conclusion that neither classical mechanics nor Maxwell’s electrodynamics could survive intact. Both would have to be modified to take account of Planck’s discovery in 1900 of the quantum of action, h. To explain the laws of thermal radiation and the exchange of energy between matter and radiation, quantum theories of matter and radiation would be required. It was this aspect of his work that Einstein characterized as “very revolutionary”8. In his first published paper1 of 1905, Einstein suggested that electromagnetic radiation at high frequencies could be thought of as NATURE | VOL 433 | 20 JANUARY 2005 | www.nature.com/nature
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year of physics commentary composed of ‘light quanta’, and thereby founded the field of quantum optics; but this was a step considered so radical at the time that few followed him in taking it. Planck himself was not convinced and almost a decade later, when recommending Einstein for a position in the Prussian Academy of Sciences, he still felt it necessary to excuse Einstein for this apparent mistake. (It was only the discovery of the Compton effect in 1923 that made the photon concept respectable.) By 1907, Einstein had applied the quantum hypothesis to crystalline solids. By treating a crystal as an ensemble of particles oscillating about their equilibrium position with quantized energies, he was able to explain the anomalously low specific heat of such solids at low temperatures. In fact, it was the successful experimental verification of Einstein’s formula for specific heat that first brought the quantum theory to the attention of most physicists9.
replaced by a new special-relativistic mechanics for particles and continuous media (rigid bodies proved incompatible with the special theory), and this was developed by Einstein, Planck, Max Born, Max von Laue and others over the next decade. The new concepts of space and especially of time that were inherent in the new kinematics proved difficult for many physicists to assimilate — and indeed still are for many. Yet Einstein’s most revolutionary revision of these concepts still lay ahead, when he turned in 1907 to the problem of fitting gravitation into his new kinematic framework. He soon convinced himself — although, again, it was a long time before others were persuaded — that this could not be done within the bounds of the special theory of relativity, and he embarked on another decade-long odyssey that led him to the general theory. But that is a story for another occasion. ■
Classical physics completed
John Stachel is at the Department of Physics and Director of the Center for Einstein Studies, Boston University, Boston, Massachusetts 02215, USA e-mail:
[email protected] He is the editor of Einstein’s Miraculous Year: Five Papers That Changed the Face of Physics. A new edition will appear in May 2005.
Einstein never regarded his work on resolving the apparent conflict between classical mechanics and electrodynamics3,4 — which led to what we now call the special theory of relativity — as revolutionary in the same sense as his work on the quantum hypothesis. He saw it rather as the culmination and completion of classical physics. His decade-long confrontation with the problems of the electrodynamics of moving bodies finally led to a breakthrough in 1905. Einstein realized that, at the classical (non-quantum) level, all the contradictions between mechanics and electrodynamics could be removed by recognizing the need for — and the feasibility of — a radical modification of the newtonian concept of absolute time. This modification led to a new kinematical foundation for all of physics. Einstein based this modification on a new interpretation of the Lorentz–Poincaré local time. Instead of regarding this as an ‘apparent but false’ time for each inertial frame, as compared to the one true, absolute and universal time of Newton, Einstein saw it as a possible definition of time that could be introduced in each inertial frame, in such a way that the vacuum speed of light is the same in every inertial frame (he dropped all reference to the privileged ether frame). Note the subtle but crucial difference. Poincaré had interpreted the local time as that given by clocks at rest in a frame moving through the ether when synchronized as if — contrary to the basic assumptions of newtonian kinematics — the speed of light were the same in all inertial frames. Einstein dropped the ether and the ‘as if ’: one simply synchronized clocks by the Poincaré convention in each inertial frame and accepted that the speed of light really is the same in all inertial frames when measured with clocks so synchronized. Of course, the galileian law of addition of velocities can no longer hold, so a new kinematics was required. Einstein showed how to set up such a kinematics, which we now call special-relativistic. The principle of relativity (that is, the democracy of all inertial frames), which in newtonian theory held only for mechanical phenomena, now holds for all phenomena, in particular for all optical and electromagnetic phenomena. So negative results, such as that of Michelson, do not call for a dynamical explanation (as they did in Lorentz’s version of Maxwell’s theory). They are simply a consequence of the universal validity of the principle of relativity as an empirical generalization; just as the impossibility of all perpetual motion machines follows from the laws of thermo-dynamics. The theoretical reason for the earlier problems in reconciling mechanics and electrodynamics became clear. Maxwell’s laws of electrodynamics are invariant under the space-time transformations of the new kinematics, now called the Lorentz transformations; the laws of mechanics were invariant under the spacetime transformations of the old kinematics, usually called Galilei transformations. So classical mechanics had to be
1. 2. 3. 4. 5. 6.
Einstein, A. Ann. Phys. (Leipz.) 17, 132–148 (1905). Einstein, A. Ann. Phys. (Leipz.) 17, 549–560 (1905). Einstein, A. Ann. Phys. (Leipz.) 17, 891–921 (1905). Einstein, A. Ann. Phys. (Leipz.) 18, 639–641 (1905). Einstein, A. Ann. Phys. (Leipz.) 19, 289–306 (1906). Einstein, A. in The Collected Papers of Albert Einstein Volume 1: The Early Years, 1879–1901 (eds Stachel, J. et al.) (Princeton Univ. Press, Princeton, 1987). 7. Stachel, J. Fresnel’s (Dragging) Coefficient as a Challenge to 19th Century Optics of Moving Bodies (preprint 283, Max-Planck-Institut für Wissenschaftsgeschichte, Berlin 2004). 8. Einstein, A. in The Collected Papers of Albert Einstein Volume 1: The Early Years, 1879–1901 (eds Stachel, J. et al.) 31–32 (Princeton Univ. Press, Princeton, 1993). 9. Kuhn, T. S. Black-Body Theory and the Quantum Discontinuity, 1894–1912 Ch. 9 (Oxford Univ. Press, Oxford, 1978).
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