“If the definition of simultaneity is given from a moving system, the spherical surface will result when Einstein's definition with є = 1/2 is used, since it is this definition which makes the velocity of light equal in all directions.”

— Hans Reichenbach

The Philosophy of Space and Time (1928, tr. 1957)

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Hans Reichenbach 41

American philosopher 1891–1953

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“…the famous assertion by Einstein that the length of a rod depends on its velocity and on the chosen definition of simultaneity. …is based on the fact that we do not measure the length of the rod, but its projection on a system at rest. How the length of the projection depends on the choice of simultaneity can be illustrated by reference to a photograph taken through a focal-plane shutter. Such a shutter… consists of a wide band with a horizontal slit, which slides down vertically. Different bands are photographed successively on the film. Moving objects are therefore strangely distorted; the wheels of a rapidly moving car for instance, appear to be slanted. The shape of the objects in the picture will evidently depend on the speed of the shutter. Similarly, the length of the moving segment depends on the definition of simultaneity. One definition of simultaneity differs from another because events that are simultaneous for one definition occur successively for another. What may be a simultaneity projection of a moving segment for one definition is a "focal-plane shutter photograph" for another.”

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“According to the Special Theory of Relativity, the velocity of a moving body is always less than the velocity of light. Since the energy of motion of a body depends on its inertial mass and its velocity, it follows that if the energy of a body is increased indefinitely by the continual application of a force, the inertial mass of the body must be increased too; for, if not, the velocity would ultimately increase indefinitely and exceed the velocity of light. Einstein found that, corresponding to any increase in the energy content of a body, there is an equivalent increase in its inertial mass. Mass and energy thus appeared to be different names for the same thing, the energy associated with a mass M being Mc2, where c is the velocity of light; and the mass M of a body moving with velocity v he found to be given by the following formulaM = \frac {m}{\sqrt{(1 - \frac {v^2}{c^2}}}</center”

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“If the definition of simultaneity is given from a moving system, the spherical surface will result when Einstein's definition with є = 1/2 is used, since it is this definition which makes the velocity of light equal in all directions.”

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Hans Reichenbach 41

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