History
In 1892 and 1895, Hendrik Lorentz used a mathematical tool called "local time" t' = t – v x/c2 for explaining the negative aether drift experiments. However, Lorentz gave no physical explanation of this effect. This was done by Henri Poincaré who already in 1898 emphasized the conventional nature of simultaneity and who argued that it is convenient to postulate the constancy of the speed of light in all directions. However, this paper does not contain any discussion of Lorentz's theory or the possible difference in defining simultaneity for observers in different states of motion. This was done in 1900, when he derived local time by assuming that within the aether the speed of light is invariant. Due to the "Principle of relative motion" also moving observers within the aether assume that they are at rest and that the speed of light is constant in all directions (only to first order in v/c). So if they synchronize their clocks by using light signals, they will only consider the transit time for the signals, but not their motion in respect to the aether. So the moving clocks are not synchronous and do not indicate the "true" time. Poincaré calculated that this synchronization error corresponds to Lorentz's local time. Also in 1904 Poincaré emphasized the connection between the principle of relativity, "local time", and light speed invariance, however, the reasoning in that paper was presented in a qualitative and conjectural manner.
Albert Einstein in 1905 used a similar method to derive the time transformation for all orders in v/c, i.e. the complete Lorentz transformation (also Poincaré got the full transformation in 1905 but in those papers he did not mention his synchronization procedure). This derivation was completely based on light speed invariance and the relativity principle, so Einstein noted that for the electrodynamics of moving bodies the aether is superfluous. Thus the separation into "true" and "local" times of Lorentz and Poincaré vanishes – all times are equally valid and therefore the relativity of length and time is a natural consequence.
In 1908 Herman Minkowski introduced the concept of a world line of a particle in his model of the cosmos called Minkowski space. The mathematical model of spacetime is an affine geometry equipped with a quadratic form that measures intervals between events. (When the events are connected by light, the interval is zero). In Minkowski's system there is a simultaneous hyperplane determined by the quadratic form at each event along a world line. This simultaneous hyperplane depends on the velocity of the particle, and thus is relative to velocity.
Read more about this topic: Relativity Of Simultaneity
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