*Reference: **Einstein’s 1920 Book*

*This paper presents Part 1, Chapter 9 from the book **RELATIVITY: THE SPECIAL AND GENERAL
THEORY by A. EINSTEIN.
The contents are from the original publication of this book by Henry
Holt and Company, New York (1920).*

*The paragraphs of the original
material (in black) are accompanied by brief comments (in color) based on the present
understanding. Feedback on these comments is appreciated.*

*The heading below is linked to
the original materials.*

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## The Relativity of Simultaneity

Up to now our considerations have been referred to a particular body of reference, which we have styled a “railway embankment.” We suppose a very long train travelling along the rails with the constant velocity ** v** and in the direction indicated in Fig. 1. People travelling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. Then every event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment. As a natural consequence, however, the following question arises:

Are
two events (*e.g.* the two strokes of
lightning ** A** and

**) which are simultaneous**

*B**with reference to the railway embankment also simultaneous relatively to the train?*We shall show directly that the answer must be in the negative.

When
we say that the lightning strokes ** A** and

**are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places**

*B***and**

*A***, where the lightning occurs, meet each other at the mid-point**

*B***of the length**

*M***of the embankment. But the events**

*A —> B***and**

*A***also correspond to positions**

*B***and**

*A***on the train. Let**

*B***be the mid-point of the distance**

*M’***on the travelling train. Just when the flashes**

*A —> B*^{1}of lightning occur, this point

**naturally coincides with the point**

*M’***, but it moves towards the right in the diagram with the velocity**

*M***of the train. If an observer sitting in the position**

*v***in the train did not possess this velocity, then he would remain permanently at**

*M’***, and the light rays emitted by the flashes of lightning**

*M***and**

*A***would reach him simultaneously,**

*B**i.e.*they would meet just where he is situated. Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from

**, whilst he is riding on ahead of the beam of light coming from**

*B***. Hence the observer will see the beam of light emitted from**

*A***earlier than he will see that emitted from**

*B***. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash**

*A***took place earlier than the lightning flash**

*B***. We thus arrive at the important result:**

*A*^{1} As judged from the embankment.

Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and *vice versa* (relativity of simultaneity). Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.

*Events that are simultaneous with reference to one body of reference are not simultaneous with respect to another body of reference. Therefore, every body of reference has its own particular time, just like it has its own particular space.*

Now before the advent of the theory of relativity it had always tacitly been assumed in physics that the statement of time had an absolute significance, *i.e.* that it is independent of the state of motion of the body of reference. But we have just seen that this assumption is incompatible with the most natural definition of simultaneity; if we discard this assumption, then the conflict between the law of the propagation of light *in vacuo* and the principle of relativity (developed in Section 7) disappears.

*Before relativity time was considered uniform for all locations in space. If the characteristics of time is variable with locations in space then the contradiction between the law of propagation of light and the principle of relativity disappears.*

We were led to that conflict by the considerations of Section 6, which are now no longer tenable. In that section we concluded that the man in the carriage, who traverses the distance *w** per second* relative to the carriage, traverses the same distance also with respect to the embankment *in each second* of time. But, according to the foregoing considerations, the time required by a particular occurrence with respect to the carriage must not be considered equal to the duration of the same occurrence as judged from the embankment (as reference-body). Hence it cannot be contended that the man in walking travels the distance ** w** relative to the railway line in a time which is equal to one second as judged from the embankment.

*The time required by a particular occurrence with respect to the carriage must not be considered equal to the duration of the same occurrence as judged from the embankment.*

Moreover, the considerations of Section 6 are based on yet a second assumption, which, in the light of a strict consideration, appears to be arbitrary, although it was always tacitly made even before the introduction of the theory of relativity.

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## FINAL COMMENTS

*The “relativity of simultaneity” as demonstrated by Einstein in this chapter allows him to conclude that the characteristics of both distance and time change with velocity. Therefore, each inertial system can have its distance and time characteristics, such that, relative to it the velocity of light will have the same value. Einstein’s theory is basically saying that the ratio of space to time is constant. This appears as the velocity of light. *

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