Formulations of special relativity

The theory of special relativity was initially developed in 1905 by Albert Einstein. However, other interpretations of special relativity have been developed, some on the basis of different foundational axioms. While some are mathematically equivalent to Einstein's theory, others aim to revise or extend it.

Einstein's formulation was based on two postulates, as detailed below. Some formulations modify these postulates or attempt to derive the second postulate by deduction. Others differ in their approach to the geometry of spacetime and the linear transformations between frames of reference.

As formulated by Albert Einstein in 1905, the theory of special relativity was based on two main postulates:

Einstein developed the theory of special relativity based on these two postulates. This theory made many predictions which have been experimentally verified, including the relativity of simultaneity, length contraction, time dilation, the relativistic velocity addition formula, the relativistic Doppler effect, relativistic mass, a universal speed limit, mass–energy equivalence, the speed of causality and the Thomas precession.

Several physicists have derived a theory of special relativity from only the first postulate – the principle of relativity – without assuming the second postulate that the speed of light is constant. The term "single-postulate" is misleading because these formulations may rely on unsaid assumptions such as the cosmological principle, that is, the isotropy and homogeneity of space. As such, the term does not refer to the exact number of postulates, but is rather used to distinguish such approaches from the "two-postulate" formulation. Single postulate approaches generally deduce, rather than assume, that the speed of light is constant.

Without assuming the second postulate, the Lorentz transformations can be obtained. However, there is a free parameter k, which renders it incapable of making experimental predictions unless further assumptions are made. The case k = 0 is equivalent to Newtonian physics.

Hendrik Lorentz and Henri Poincaré developed their version of special relativity in a series of papers from about 1900 to 1905. They used Maxwell's equations and the principle of relativity to deduce a theory that is mathematically equivalent to the theory later developed by Einstein.

Taiji relativity is a formulation of special relativity developed by Jong-Ping Hsu and Leonardo Hsu. The name of the theory, Taiji, is a Chinese word which refers to ultimate principles which predate the existence of the world. Hsu and Hsu claimed that measuring time in units of distance allowed them to develop a theory of relativity without using the second postulate in their derivation.