An Illustrated Guide to Relativity by Tatsu Takeuchi

Author:Tatsu Takeuchi [Takeuchi, Tatsu]
Language: eng
Format: azw3, pdf
Publisher: Cambridge University Press
Published: 2010-09-09T04:00:00+00:00

6.3 What time dilation DOES NOT mean

Now, time dilation is often misunderstood to mean that time itself is flowing at a slower rate in a moving frame compared to a frame at rest. And consequently, time intervals measured by the moving clock will always be shorter than those measured by the stationary clock.

This is not true at all.

First, the relationship between the stationary and moving frames is completely symmetrical. After all, which frame we consider to be moving is a matter of choice. So if time is flowing at a slower rate in the moving frame than the stationary frame, then time has to be flowing at a slower rate in the stationary frame than the moving frame. This is a clear contradiction.

Second, as we have seen, when the two observers are comparing the readings of their clocks, they are not measuring the chronological separation of the same events at all. They are always measuring events along the worldline of the other clock.

If the two observers actually measure the time interval between the same events on the spacetime diagram, then there is no rule that says that one observer will obtain a shorter time than the other. For instance, take the four points A, B, C, and D shown here. The chronological separation between A and B is measured to be shorter in the ground-frame than in the car-frame. However, the time interval between B and C are measured to be the same in both frames, while the time interval between C and D is longer in the ground-frame than in the car-frame.

Time dilation is a phenomenon caused by the relativity of simultaneity, and has nothing to do with how fast time is flowing.

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