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show that the example of the two electrons with velocities 0.9c one to the left and...

show that the example of the two electrons with velocities 0.9c one to the left and the other one to the right, gives the same result for the observed velocity of the left electron as viewed from the right

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Answer #1

The velocity of the electron moving to the right is (choose right side to be + X axis)

The velocity of the electron moving to the left is (choose left side to be -X axis)

The observed velocity of the left electron as viewed from the right is

The speed (magnitude of v) is

The velocity is negative because the electron is moving to the left as observed from the right.

The observed velocity of the right electron as viewed from the left is

Thus we see that the observed speed of the left electron as viewed from the right is the same as the speed of the right electron as viewed from the left. The signs of relative velocities are opposite because they are moving in opposite directions.

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