A century of relativity Irwin I. Shapiro Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138 [S0034-6861(99)05302-7] CONTENTS A. Theory I. Introduction S41 Hendrik Lorentz regarded his 1904 set of transforma- II. Special Relativity S41 tions among space and time variables—the (homoge- A. Theory S41 neous) Lorentz transformation—as a mathematical de- B. Experiment S42 vice; he believed in the ether and also in the inability to C. Applications S42 observe any effects from the motion of light with respect III. General Relativity S43 A. Theory S43 to the ether, which he attributed to dynamical effects B. Experiment S44 caused by motion through the ether. 1. Principle of equivalence S44 Henri Poincare´ adopted the notion that no motion 2. Redshift of spectral lines S45 with respect to the ether was detectable. He also sug- 3. Deflection of light by solar gravity S45 gested in 1902 that the ether is a hypothesis that might 4. Time-delay by gravitational potential S45 someday be discarded as pointless; in fact, he gave a 5. ‘‘Anomalous’’ perihelion advance S47 physical interpretation of ‘‘frame time,’’ in terms of the 6. Possible variation of the gravitational constant S48 synchronization with light signals of clocks at rest in that 7. Frame dragging S48 frame, as distinct from ether-frame time. Poincare´ did 8. Gravitational radiation S49 not, however, develop a comprehensive theory that pos- C. Applications S49 tulated a new interpretation of space and time, and he 1. Cosmology S49 did not discard the concept of an ether. Those tasks 2. Black holes S50 were left to Einstein. 3. Gravitational lenses S51 The state of Einstein’s knowledge of these issues, both IV. Future S53 Acknowledgments S53 theoretical and experimental, and the thinking that un- dergirded his development of his special theory of rela- tivity in 1905, remain elusive; even historians have failed I. INTRODUCTION to reach a consensus. It is nonetheless clear that he was Except for quantum mechanics—a more than modest thinking seriously about these issues as early as 1899. He exception—relativity has been the most profound con- based his new kinematics of moving bodies on two now ceptual advance in 20th century physics. Both in devel- well-known principles: (1) the laws of nature are the oping special and general relativity, Albert Einstein’s same in all frames moving with constant velocity with hallmark was to anchor his theory on a few simple but respect to one another; and (2) the speed of light in profound principles. The results have provided endless vacuum is a constant, independent of the motion of the fascination and puzzlement to the general public, and light source. He used these postulates to define simulta- have had an enormous impact on our conceptual frame- neity for these (nonaccelerating) frames in a consistent work for understanding nature. way and to derive transformation equations identical to In this brief review, I note the rise and spread of spe- Lorentz’s, but following from quite different underlying cial and general relativity throughout physics and astro- reasoning. Einstein also derived a new composition law physics. This account is quasihistorical, first treating spe- for the ‘‘addition’’ of relative velocities and from it new cial and then general relativity. In each case, I consider formulas for the Doppler effect and for aberration. theory, experiment, and applications separately, al- Poincare´ in 1905 showed that the transformation though in many respects this separation is definitely not equations formed a group and named it the Lorentz ‘‘clean.’’ Responding to the request of the editors of this group.1 The extension of this group to the inhomoge- volume, I have included my personal research in matters neous group, which included spatial and temporal trans- relativistic. As a result, the recent is emphasized over lations as well, is now known as the Poincare´ group. the remote, with the coverage of the recent being rather slanted towards my involvement. II. SPECIAL RELATIVITY The roots of special relativity were formed in the 19th 1He did not mention Einstein’s paper and may not yet have century; we pick up the story near the beginning of this been aware of it; in any case, he seems never to have referred century. in print to Einstein’s work on special relativity. Reviews of Modern Physics, Vol. 71, No. 2, Centenary 1999 0034-6861/99/71(2)/41(13)/$17.60 ©1999 The American Physical Society S41 S42 Irwin I. Shapiro: A century of relativity Also in 1905, Einstein concluded that the inertial mass flown around the world from one remaining at ‘‘home,’’ is proportional to the energy content for all bodies and matched the observed difference to within the approxi- deduced perhaps the most famous equation in all of sci- mately 1% standard error of the comparison. ence: E5mc2. Although this type of relation had been Another of the many verifications, and one of the proposed somewhat earlier for a specific case, Einstein most important, was of the equivalence of mass and en- was apparently the first to assert its universality. ergy. A quantitative check was first made in 1932 via a nuclear reaction by John Cockcroft and Ernest Walton. B. Experiment C. Applications Special relativity has among its roots the famous 2 Michelson-Morley experiment. This experiment, based After the invention of quantum mechanics, the need on clever use of optical interferometry, found no evi- to make it consistent with special relativity led Paul dence, at the few percent level, for the effect expected Dirac to create the relativistic wave equation for the were the Earth moving through a (‘‘stationary’’) ether. electron in 1928. This equation eventually led Dirac to The round-trip average—both group and phase—speed propose that its negative-energy solutions describe a of light in vacuum has been demonstrated in many ex- particle with the same mass as the electron, but with periments this past century to be independent of direc- opposite charge. The discovery of the positron shortly tion and of the motion of the source. In addition, just thereafter in 1932 ranks as one of the major discoveries recently, analysis of the radio signals from the Global in 20th century physics. Dirac’s equation was soon incor- Positioning System (GPS) satellites—all of whose clocks porated into the developing formulation of quantum were, in effect, governed by a single atomic standard— field theory. yielded a verification of the independence of direction of Before and after Dirac’s work on the relativistic wave the one-way speed of light, at the level of about 3 parts equation, relativistic treatments and their refinements 9 in 10 . were developed for a wide variety of domains such as The first experimental tests of special relativity veri- classical electrodynamics, thermodynamics, and statisti- fied the velocity-momentum relation for electrons pro- cal mechanics, while Newtonian gravitation was re- duced in beta decay. During the 1909–1919 decade a placed by an entirely new relativistic theory: general sequence of experiments resulted in verification reach- 3 relativity. ing the 1% level. On the experimental side, special relativity has also The time dilation effect for moving clocks is a major left indelible marks, as witnessed by its important appli- prediction of special relativity. Its experimental verifica- cation in the design of high-energy particle accelerators. tion had to await the discovery of unstable elementary The equivalence of mass and energy, coupled with de- particles, e.g., mesons, whose measured lifetimes when velopments in nuclear physics, formed the basis for the in motion could be compared to the corresponding mea- solution of the previously perplexing problem of the surements with the particles at rest (or nearly so). First, generation of energy by stars. This work reached an in the late 1930s this predicted effect of special relativity apex with Hans Bethe’s development and detailed was used by Bruno Rossi and his colleagues to infer the analysis of the carbon-nitrogen cycle of nuclear burning. at-rest lifetime of mesons from cosmic-ray observations, A striking contribution of special relativity to the following a 1938 suggestion by Homi Bhabha. flowering of astrophysics in the 1970s was discovered Another effect—the so-called ‘‘twin paradox’’—gave serendipitously: ‘‘superluminal’’ expansion. My group rise to a huge literature over a period of over two de- and I used very-long-baseline (radio) interferometry cades, before the ‘‘opponents,’’ like old generals, just (VLBI) in October 1970 to observe two powerful ex- faded away: If twin member B leaves twin member A, tragalactic radio sources, 3C279 (z'0.5)4 and 3C273 who is in an inertial frame, and moves along another (z'0.2), to measure the deflection of light by solar world line and returns to rest at the location of A, B will gravity (see below). To our surprise, we noticed that the have aged less than A in the interim. Such an effect has time variation of the 3C279 fringe pattern with the diur- been demonstrated experimentally to modest accuracy: nally changing resolution of our two-element, crosscon- the predicted difference in clock readings of a clock tinental interferometer, matched very well that for a model of two equally bright point sources. Comparison observations taken four months later, in 2 Although the extent to which this experiment influenced February 1971, showed an even more dramatic result: Einstein’s development of special relativity is not clear, it is these two bright pointlike sources had moved apart at an clear that he knew of its existence: A paper by Wien, men- apparent speed of about 10 c. I developed a simple tioned by Einstein in an early letter to Mileva Maric, referred model of this behavior that showed that if a radio-bright to this experiment, allowing one to conclude with high reliabil- ity that Einstein was aware of it.