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History

Main articles: History of special relativity and History of general relativity

The history of special relativity consists of many theoretical results and empirical findings obtained by Albert Michelson, Hendrik Lorentz, Henri Poincaré and others. It culminated in the theory of special relativity proposed by Albert Einstein, and subsequent work of Max Planck, Hermann Minkowski and others.

General relativity (GR) is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915, with contributions by many others after 1915.

History

• Conceptual evolution from Gallileo
• Newton, the calculus, and mechanics

• Maxwell's equations
  • Wave equation with characteristic group velocity
  • Analogous to transverse mechanical oscillations propagating through physical medium (e.g. waves on pond surface)
    • Seemed a natural interpretation given the legacy of Newton
• luminiferous aether is medium of propogation
  • What is its nature? Is it in a state of "absolute rest"?

crisis in physics

• Question arose: "Is the Earth's surface moving relative to the aether?"
  • If not, there are two possibilities
    • The Earth is at rest with the aether.
      • Violates Copernican Principle
    • The aether is being locally dragged by the earth
      • Observations of aberration of starlight contradicted that assumption
  • Only remaining possibility is that the Earth's surface is moving relative to the aether
    • There must be an "aether wind" with measurable effects
      • M-M experiment unable to detect presence of aether wind.
  • Contradiction.
    • Perhaps there is no aether?
    • Fitzgerald-Lorentz contraction.
      • Fitzgerald (1889) and Lorentz (independently in 1892) propose that motion parallel to the aether makes objects contract.

Einstein in 1905

• Influences. SR developed from a decade of work by others.
  • E's 1905 paper mentions only Maxwell, Hertz, Lorentz. No References
  • Debate as to whether E knew of MM experiment.
    • Said aware of them through Lorentz's 1895 paper, but assumed there was no aether, regardless.
      • Mentions "the failed attempts to detect a motion of the earth relative to the 'light-medium'"
  • Only aware of Lorentz's work up to 1895
    • Did not know the Lorentz transforms. He derived them himself from his 2 postulates(!)
    • Aberration of light and Fizeau experiments were "enough"

Experimental evidence

A diagram of the Michelson-Morley experiment

Like all falsifiable scientific theories, relativity makes predictions that can be tested by experiment. In the case of special relativity, these include the principle of relativity, the constancy of the speed of light, and time dilation. The predictions of special relativity have been confirmed in numerous tests since Einstein published his paper in 1905, but three experiments conducted between 1881 and 1938 were critical to its validation. These are the Michelson–Morley experiment, the Ives–Stilwell experiment, and the the Kennedy–Thorndike experiment. Einstein derived the Lorentz transformations from first principles in 1905, but these three experiments allow the transformations to be induced from experimental evidence.

Maxwell's equations – the foundation of classical electromagnetism – describe light as a wave which moves with a characteristic velocity. Maxwell and his contemporaries were convinced that light waves propagated through a medium, analogous to sound propagating in air, and ripples propagating on the surface of a pond. This hypothetical medium was called the luminiferous aether, at rest relative to the "fixed stars" and through which the Earth moves. Fresnel's partial ether dragging hypothesis ruled out the measurement of first-order (v/c) effects, and although observations second-order effects (v²/c²) were possible in principle, Maxwell thought they might be too small to be detected with then-current technology.

The Michelson-Morley experiment was designed to detect second order effects of the "aether wind" – the motion of the aether relative to the earth. Michelson designed an instrument called the Michelson interferometer to accomplish this. It comprised a light source, two highly reflective mirrors, a half silvered mirror, and a detector. Light emitted by a sodium lamp was split by the half-silvered mirror and sent along two paths of equal length at right angles to each other. Light moving along these paths was reflected by the two mirrors multiple times, eventually traveling 22 m before returning to the half silvered mirror where they were recombined and sent to the detector. The detector measured the interference pattern which resulted from the recombined beams. If the aether existed, it's velocity relative to the earth should change with the time of day and the season, as earth rotated and orbited the sun. Consequently, the travel time for light along the direction of the aether wind should be different than that of light moving at right angles to the wind. Changes in the interference pattern, if observed, would be an indication of the relative difference in travel times. Michelson and Morley floated the interferometer on a pool of mercury and slowly rotated it while looking for changes in the interference patter, and repeated the procedure at thee-month intervals. The apparatus was more than accurate enough to detect the expected effects, but he obtained a null result when the first experiment was conducted in 1881, and again in 1887. Although the failure to detect an aether wind was a disappointment, the results were accepted by the scientific community. In an attempt to salvage the aether paradigm, Fitzgerald and Lorentz independently created an ad hoc hypothesis in which motion the length of material bodies changes according to their motion through the aether. This was the origin of Fitzgerald-Lorentz contraction, and their hypothesis had no theoretical basis. The interpretation of the null result of the Michelson-Morley experiment is that the round-trip travel time for light is isotropic (independent of direction), but the result alone is not enough to discount the theory of the aether or validate the predictions of special relativity.

The Kennedy-Thorndike experiment shown with interference fringes.

While the Michelson-Morley experiment showed that the velocity of light is isotropic, it said nothing about how the magnitude of the velocity changed (if at all) in different inertial frames. The Kennedy–Thorndike experiment was designed to do that, and was first performed in 1932 by Roy Kennedy and Edward Thorndike. They used an interferometer similar to the one used by Michelson and Morley, except the arms were about 16 cm different in length. They used a mercury lamp for a light source, and took great pains to ensure the stability of the detector: The interferometer was mounted on a plate of quartz, which has a very low coefficient of thermal expansion, and was enclosed in a vacuum chamber. The vacuum chamber was surrounded by a water jacket whose temperature was maintained within ±0.001 °C. The water jacket was enclosed in two nested darkrooms whose temperatures were also very precisely maintained. As in the Michelson-Morley experiment, the interferometer produced a pattern of bright and dark fringes at the detector. Changes in the fringe pattern (a phase shift) would indicate changes in the travel time for light along the arms in different inertial frames as as Earth orbits the sun. In order to carry out the experiment, Kennedy and Thorndike would have had to run the apparatus continually for six months, but this was not feasible at the time. Instead, they ran the machine at intervals ranging from eight days to one month, with separations of three months between successive runs. They obtained a null result, and concluded that "there is no effect ... unless the velocity of the solar system in space is no more than about half that of the earth in its orbit", or in other words, unless the Sun is at rest relative to the aether. That possibility was thought to be too outrageous to provide an acceptable explanation, so from the null result of their experiment it was concluded that the round-trip time for light is the same in all inertial reference frames.

The Ives-Stillwell experiment was carried out by Herbert Ives and G.R. Stillwell first in 1938 and with better accuracy in 1941. It was designed to test the transverse Doppler effect – the redshift of light from a moving source in a direction perpendicular to its velocity – which had been predicted by Einstein in 1905. This effect is extremely difficult to directly detect and interpret, so Ives and Stillwell measured the longitudinal Doppler effect and looked for discrepancies between what was predicted by classical theory and special relativity. Specifically, they measured the blueshift and redshift of light emitted by canal rays – beams of positive ions – as they moved past a detector. According to classical electromagnetism, the difference in the observed redshift and blueshift frequences should be inversely proportional to the difference between the speed of light and the speed of the light source. According to special relativity, there should be a slight redshift correction to both of those frequencies. The strategy of the Ives-Stillwell experiment was to average the observed red and blue-shits, and look for a Lorentz factor correction. Such a correction was observed, from which was concluded that the frequency of a moving atomic clock is altered according to special relativity.

The conclusions of these three optical experiments – that the round-trip time of light is isotropic in all inertial frames(TW 86), the round-trip time is independent of the the inertial reference frame, and the clock speed of a moving source changes according to the Lorentz factor – provide an experimental ground from which we can induce the Lorentz Transformations.

Special relativity

• Testable predictions of SR
  • Principle of relativity
  • Constancy of the speed of light
  • Time dilation
• Three crucial tests; results can be used to derive the Lorentz transforms.
  • Ives–Stilwell experiment 1938, 1941. Transverse Doppler effect. Described by Einstein in 1905 paper.
  • Michelson–Morley experiment. 1881. 1887.
    • Experiments in the 19t century (Fizeau experiment, Aberration of light) suggested an (almost) stationary either, i.e. not dragged by Earth
    • Fresnel's partial ether dragging hypothesis ruled out measuring first-order (v/c) effects. Observations second-order effects (v^2/C^2) could be used to incestigate ether, though. Pointed out by Maxwell.
    • Ether should be moving in different directions depending on time of day and time of year
    • Interferometer floating on pool of mercury. Looking for change in interference fringes. Null result.
  • Kennedy–Thorndike experiment. Modified MM experiment. Time dilation. 1932.
    • MM showed speed of light independent of oriantation, KT showed c independent of velocity of the apparatus.
    • Similar to MM, but one arm shorter than the other.
    • Indirect test of time dilation. While an ad hoc length contraction could be used to explain MM, time dilation was also required to explain KT.
    • Fringe shifts should occur because of changes in Earth's velocity, unless frequency of light changed according to SR. Exp done over period of many months.
• Rossi-Hall experiment. Muon decay. 1940. Time dilation.
• De_Sitter_double_star_experiment Emission theory. 1913. Light velocity not dependent on moving source.
• Relativistic energy and momentum are verified constantly in accelerators, and SR is necessary to our understanding of cyclotrons and synchrotrons.
• Current experiments looking for Lorentz symmetry violation.

General relativity

• Einstein proposed three tests in 1916.
  • the perihelion precession of Mercury's orbit
  • the deflection of light by the Sun
  • the gravitational redshift of light

• Hafele–Keating_experiment Twin paradox. 1971. Time dilation.