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, s… - Hans Reichenbach

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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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About Hans Reichenbach

Hans Reichenbach (26 September 1891 – 9 April 1953) was a leading philosopher of science, educator and proponent of logical positivism.

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If E<sub>1</sub> is the cause of E<sub>2</sub>, then a small variation (a mark) in E<sub>1</sub> is associated with a small variation in E<sub>2</sub>, whereas small variations in E<sub>2</sub> are not associated with variations in E<sub>1</sub>. If we wish to express even more clearly that this concept does not contain the concept of temporal order, we can express it in the following form, where events that show a slight variation are designated E*: E<sub>1</sub>E<sub>2</sub>, E<sub>1</sub>*E<sub>2</sub>*, E<sub>1</sub>E<sub>2</sub>* and never the combination E<sub>1</sub>*E<sub>2</sub>.

...introduce the auxiliary concept of first-signal...defined as the fastest message carrier between any two points in space. We now send a first-signal from P, calling the event of departure E<sub>1</sub>... The event of its arrival at P' is called E'. Simultaneously with the arrival of this signal, another first signal is sent from P'. The arrival of this signal at P is the event E<sub>2</sub>. ...the time interval between E<sub>1</sub> and E<sub>2</sub> is coordinated to the event E', [E<sub>1</sub> is earlier than E' and E<sub>2</sub> is later than E'] and every event of this time interval except for the endpoints is inderterminate as to the time order relative to E'.

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