History of special relativity

The history of special relativity consists of many theoretical results and empirical findings obtained by Albert A. Michelson, Hendrik Lorentz, Henri Poincaré and others.

Although Isaac Newton based his physics on absolute time and space, he also adhered to the principle of relativity of Galileo Galilei restating it precisely for mechanical systems.

According to Maxwell's theory, all optical and electrical phenomena propagate through that medium, which suggested that it should be possible to experimentally determine motion relative to the aether.

Following the work of Thomas Young (1804) and Augustin-Jean Fresnel (1816), it was believed that light propagates as a transverse wave within an elastic medium called luminiferous aether.

However, Maxwell's theory was unsatisfactory regarding the optics of moving bodies, and while he was able to present a complete mathematical model, he was not able to provide a coherent mechanical description of the aether.

However, this now famous Michelson–Morley experiment again yielded a negative result, i.e., no motion of the apparatus through the aether was detected (although the Earth's velocity is 60 km/s different in the northern winter than summer).

For example, Emil Cohn (1900, 1901) created an alternative electrodynamics in which he, as one of the first, discarded the existence of the aether (at least in the previous form) and would use, like Ernst Mach, the fixed stars as a reference frame instead.

He also rejected any connection with the existing constructions of n-dimensional spaces and non-Euclidean geometry, so his philosophical model bears only little resemblance with spacetime physics, as it was later developed by Minkowski.

[47] In his paper Electromagnetic phenomena in a system moving with any velocity smaller than that of light, Lorentz (1904) was following the suggestion of Poincaré and attempted to create a formulation of electrodynamics, which explains the failure of all known aether drift experiments, i.e. the validity of the relativity principle.

And using the electromagnetic momentum, he could explain the negative result of the Trouton–Noble experiment, in which a charged parallel-plate capacitor moving through the aether should orient itself perpendicular to the motion.

Abraham showed, that both assumptions were incompatible, because in Lorentz's theory of the contracted electrons, non-electric forces were needed in order to guarantee the stability of matter.

He illustrated (like Joseph Larmor in the same year) this transformation by using rods and clocks: If they are at rest in the aether, they indicate the true length and time, and if they are moving, they indicate contracted and dilated values.

He wrote that the discovery of magneto-cathode rays by Paul Ulrich Villard (1904) seemed to threaten the entire theory of Lorentz, but this problem was quickly solved.

[54] However, although in his philosophical writings Poincaré rejected the ideas of absolute space and time, in his physical papers he continued to refer to an (undetectable) aether.

This method was criticized by many scholars, since the assumption of a conspiracy of effects which completely prevent the discovery of the aether drift is considered to be very improbable, and it would violate Occam's razor as well.

Einstein discovered that light can also be described (at least heuristically) as a kind of particle, so the aether as the medium for electromagnetic "waves" (which was highly important for Lorentz and Poincaré) no longer fitted into his conceptual scheme.

[..] The new feature of it was the realization of the fact 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 was for me of particular importance because I had already previously found that Maxwell's theory did not account for the micro-structure of radiation and could therefore have no general validity.Already in §10 of his paper on electrodynamics, Einstein used the formula for the kinetic energy of an electron.

[77] Following Planck, other German physicists quickly became interested in relativity, including Arnold Sommerfeld, Wilhelm Wien, Max Born, Paul Ehrenfest, and Alfred Bucherer.

[78] Kaufmann (1903) presented results of his experiments on the charge-to-mass ratio of beta rays from a radium source, showing the dependence of the velocity on mass.

[84] As was explained above, already in 1895 Lorentz succeeded in deriving Fresnel's dragging coefficient (to first order of v/c) and the Fizeau experiment by using the electromagnetic theory and the concept of local time.

Poincaré's attempt of a four-dimensional reformulation of the new mechanics was not continued by himself,[54] so it was Hermann Minkowski (1907), who worked out the consequences of that notion (other contributions were made by Roberto Marcolongo (1906) and Richard Hargreaves (1908)[88]).

[90][91] In 1908, Einstein and Laub rejected the four-dimensional electrodynamics of Minkowski as overly complicated "learned superfluousness" and published a "more elementary", non-four-dimensional derivation of the basic equations for moving bodies.

There were no textbooks on linear algebra as modern vector space and transformation theory, and the matrix notation of Arthur Cayley (that unifies the subject) had not yet come into widespread use.

Subsequent writers,[100] principally Varićak, dispensed with the imaginary time coordinate, and wrote in explicitly non-Euclidean (i.e. Lobachevskian) form reformulating relativity using the concept of rapidity previously introduced by Alfred Robb (1911); Edwin Bidwell Wilson and Gilbert N. Lewis (1912) introduced a vector notation for spacetime; Émile Borel (1913) showed how parallel transport in non-Euclidean space provides the kinematic basis of Thomas precession twelve years before its experimental discovery by Thomas; Felix Klein (1910) and Ludwik Silberstein (1914) employed such methods as well.

One historian argues that the non-Euclidean style had little to show "in the way of creative power of discovery", but it offered notational advantages in some cases, particularly in the law of velocity addition.

[101] (So in the years before World War I, the acceptance of the non-Euclidean style was approximately equal to that of the initial spacetime formalism, and it continued to be employed in relativity textbooks of the 20th century.

[103] Laue was also the first to analyze the situation based on Minkowski's spacetime model for special relativity – showing how the world lines of inertially moving bodies maximize the proper time elapsed between two events.

As a consequence, the notion of a complete "special relativistic" theory of gravitation had to be given up, as in general relativity the constancy of light speed (and Lorentz covariance) is only locally valid.

This surprising gap in the experimental record was quickly closed in the ensuing years, by experiments by Fox, and by Alvager et al., which used gamma rays sourced from high energy mesons.