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# Henri Bergson: Half-relativity – Lorentz Equations (9) – How light has the same speed for all observers

posted in: Relativity

We have just looked for how light could have the same speed for the fixed observer and for the moving observer: the deepening of this point revealed to us that a system S’, resulting from the splitting of a system S and moving in a straight line with a speed v, underwent singular modifications. We would formulate them like this:

1° All the lengths of S’ have contracted in the direction of its movement. The new length is the old one in the ratio of √(1 – v2/c2) to unity.

2° The time of the system has expanded. The new second is the old one in the ratio of unit to √(1 – v2/c2)

3° What was simultaneity in system S has generally become succession in system S’. Only those events, contemporaneous in S, which are located in the same plane perpendicular to the direction of movement remain contemporaneous in S’. Any two other events, contemporary in S, are separated in S’ lv/c2 seconds of the system S’, if we designate by l their distance counted on the direction of movement of their system, that is to say the distance between the two planes, perpendicular to this direction, which pass through each of them respectively.

In short, the system S, considered in space and time, is a double of the system S which has contracted, as far as space is concerned, in the direction of its movement; which has dilated, as to time, each of its seconds; and which finally, in time, has successively dislocated all simultaneity between two events whose distance has shrunk in space. But these changes escape the observer who is part of the mobile system. Only the fixed observer notices it.

Source: Henri Bergson, Durée et simultanéité : à propos de la théorie d’Einstein, Deuxième édition, qugmentée, Paris, 1923. Translation and interpretation Nicolae Sfetcu. © 2024 MultiMedia Publishing

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