Special relativity is a physical theory that plays a fundamental role in the description of all physical phenomena, as long as gravitation is not significant. Many experiments played (and still play) an important role in its development and justification.
The strength of the theory lies in its unique ability to correctly predict to high precision the outcome of an extremely diverse range of experiments. Many of those experiments are still being conducted to steadily increase precision, with modern experiments focusing on effects such as at the Planck scale and in the neutrino sector. Their results are consistent with the predictions of special relativity. Collections of various tests were given by Jakob Laub, Zhang, Mattingly, Clifford Will, and Roberts/Schleif.
Special relativity is restricted to flat spacetime, i.e., to all phenomena without significant influence of gravitation. The latter lies in the domain of general relativity and the corresponding tests of general relativity must be considered.
Experiments paving the way to relativity
The predominant theory of light in the 19th century was that of the luminiferous aether, a stationary medium in which light propagates in a manner analogous to the way sound propagates through air. By analogy, it follows that the speed of light is constant in all directions in the aether and is independent of the velocity of the source. Thus an observer moving relative to the aether must measure some sort of "aether wind" even as an observer moving relative to air measures an apparent wind.
First-order experiments
Beginning with the work of François Arago (1810), a series of optical experiments had been conducted, which should have given a positive result for magnitudes of first order in (i.e., of ) and which thus should have demonstrated the relative motion of the aether. Yet the results were negative. An explanation was provided by Augustin Fresnel (1818) with the introduction of an auxiliary hypothesis, the so-called "dragging coefficient", that is, matter is dragging the aether to a small extent. This coefficient was directly demonstrated by the Fizeau experiment (1851). It was later shown that all first-order optical experiments must give a negative result due to this coefficient. In addition, some electrostatic first-order experiments were conducted, again having negative results. In general, Hendrik Lorentz (1892, 1895) introduced several new auxiliary variables for moving observers, demonstrating why all first-order optical and electrostatic experiments have produced null results. For example, Lorentz proposed a location variable by which electrostatic fields contract in the line of motion and another variable ("local time") by which the time coordinates for moving observers depend on their current location.
Second-order experiments
The stationary aether theory, however, would give positive results when the experiments are precise enough to measure magnitudes of second order in (i.e., of ). Albert A. Michelson conducted the first experiment of this kind in 1881, followed by the more sophisticated Michelson–Morley experiment in 1887. Two rays of light, traveling for some time in different directions were brought to interfere, so that different orientations relative to the aether wind should lead to a displacement of the interference fringes. But the result was negative again. The way out of this dilemma was the proposal by George Francis FitzGerald (1889) and Lorentz (1892) that matter is contracted in the line of motion with respect to the aether (length contraction). That is, the older hypothesis of a contraction of electrostatic fields was extended to intermolecular forces. However, since there was no theoretical reason for that, the contraction hypothesis was considered ad hoc.
Besides the optical Michelson–Morley experiment, its electrodynamic equivalent was also conducted, the Trouton–Noble experiment. By that it should be demonstrated that a moving condenser must be subjected to a torque. In addition, the Experiments of Rayleigh and Brace intended to measure some consequences of length contraction in the laboratory frame, for example the assumption that it would lead to birefringence. Though all of those experiments led to negative results. (The Trouton–Rankine experiment conducted in 1908 also gave a negative result when measuring the influence of length contraction on an electromagnetic coil.)
To explain all experiments conducted before 1904, Lorentz was forced to again expand his theory by introducing the complete Lorentz transformation. Henri Poincaré declared in 1905 that the impossibility of demonstrating absolute motion (principle of relativity) is apparently a law of nature.
Refutations of complete aether drag
The idea that the aether might be completely dragged within or in the vicinity of Earth, by which the negative aether drift experiments could be explained, was refuted by a variety of experiments. Oliver Lodge (1893) found that rapidly whirling steel disks above and below a sensitive common path interferometric arrangement failed to produce a measurable fringe shift. Gustaf Hammar (1935) failed to find any evidence for aether dragging using a common-path interferometer, one arm of which was enclosed by a thick-walled pipe plugged with lead, while the other arm was free. The Sagnac effect showed that aether wind caused by earth drag cannot be demonstrated. The existence of the aberration of light was inconsistent with aether drag hypothesis. The assumption that aether drag is proportional to mass and thus only occurs with respect to Earth as a whole was refuted by the Michelson–Gale–Pearson experiment, which demonstrated the Sagnac effect through Earth's motion.
Lodge expressed the paradoxical situation in which physicists found themselves as follows: "...at no practicable speed does ... matter [have] any appreciable viscous grip upon the ether. Atoms must be able to throw it into vibration, if they are oscillating or revolving at sufficient speed; otherwise they would not emit light or any kind of radiation; but in no case do they appear to drag it along, or to meet with resistance in any uniform motion through it."
Special relativity
Overview Eventually, Albert Einstein (1905) drew the conclusion that established theories and facts known at that time only form a logical coherent system when the concepts of space and time are subjected to a fundamental revision. For instance:
Maxwell-Lorentz's electrodynamics (independence of the speed of light from the speed of the source), the negative aether drift experiments (no preferred reference frame), Moving magnet and conductor problem (only relative motion is relevant), the Fizeau experiment and the aberration of light (both implying modified velocity addition and no complete aether drag).
The result is special relativity theory, which is based on the constancy of the speed of light in all inertial frames of reference and the principle of relativity. Here, the Lorentz transformation is no longer a mere collection of auxiliary hypotheses but reflects a fundamental Lorentz symmetry and forms the basis of successful theories such as Quantum electrodynamics. There is a large number of possible tests of the predictions and the second postulate:
Principle of relativityConstancy of the speed of lightTime dilationAny uniformly moving observer in an inertial frame cannot determine his "absolute" state of motion by a co-moving experimental arrangement.In all inertial frames the measured speed of light is equal in all directions (isotropy), independent of the speed of the source, and cannot be reached by massive bodies.The rate of a clock C (= any periodic process) traveling between two synchronized clocks A and B at rest in an inertial frame is retarded with respect to the two clocks.Also other relativistic effects such as length contraction, Doppler effect, aberration and the experimental predictions of relativistic theories such as the Standard Model can be measured.
Fundamental experiments
The effects of special relativity can phenomenologically be derived from the following three fundamental experiments:
Michelson–Morley experiment, by which the dependence of the speed of light on the direction of the measuring device can be tested. It establishes the relation between longitudinal and transverse lengths of moving bodies. Kennedy–Thorndike experiment, by which the dependence of the speed of light on the velocity of the measuring device can be tested. It establishes the relation between longitudinal lengths and the duration of time of moving bodies. Ives–Stilwell experiment, by which time dilation can be directly tested.
From these three experiments and by using the Poincaré-Einstein synchronization, the complete Lorentz transformation follows, with being the Lorentz factor:
Besides the derivation of the Lorentz transformation, the combination of these experiments is also important because they can be interpreted in different ways when viewed individually. For example, isotropy experiments such as Michelson-Morley can be seen as a simple consequence of the relativity principle, according to which any inertially moving observer can consider himself as at rest. Therefore, by itself, the MM experiment is compatible to Galilean-invariant theories like emission theory or the complete aether drag hypothesis, which also contain some sort of relativity principle. However, when other experiments that exclude the Galilean-invariant theories are considered (i.e. the Ives–Stilwell experiment, various refutations of emission theories and refutations of complete aether dragging), Lorentz-invariant theories and thus special relativity are the only theories that remain viable.
Constancy of the speed of light
Interferometers, resonators
Modern variants of Michelson-Morley and Kennedy–Thorndike experiments have been conducted in order to test the isotropy of the speed of light. Contrary to Michelson-Morley, the Kennedy-Thorndike experiments employ different arm lengths, and the evaluations last several months. In that way, the influence of different velocities during Earth's orbit around the Sun can be observed. Laser, maser and optical resonators are used, reducing the possibility of any anisotropy of the speed of light to the 10−17 level. In addition to terrestrial tests, Lunar Laser Ranging Experiments have also been conducted as a variation of the Kennedy-Thorndike-experiment.
Another type of isotropy experiments are the Mössbauer rotor experiments in the 1960s, by which the anisotropy of the Doppler effect on a rotating disc can be observed by using the Mössbauer effect (those experiments can also be utilized to measure time dilation, see below).
No dependence on source velocity or energy
Emission theories, according to which the speed of light depends on the velocity of the source, can conceivably explain the negative outcome of aether drift experiments. It was not until the mid-1960s that the constancy of the speed of light was definitively shown by experiment, since in 1965, J. G. Fox showed that the effects of the extinction theorem rendered the results of all experiments previous to that time inconclusive, and therefore compatible with both special relativity and emission theory. More recent experiments have definitely ruled out the emission model: the earliest were those of Filippas and Fox (1964), using moving sources of gamma rays, and Alväger et al. (1964), which demonstrated that photons did not acquire the speed of the high speed decaying mesons which were their source. In addition, the de Sitter double star experiment (1913) was repeated by Brecher (1977) under consideration of the extinction theorem, ruling out a source dependence as well.
Observations of Gamma-ray bursts also demonstrated that the speed of light is independent of the frequency and energy of the light rays.
One-way speed of light