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Relativity of Simultaneity

We will now consider two observers A and B making observations of two events. Think of the term "event" as meaning something which takes a very short time. In other words, an event defines a very precise point in space and time or a point in space-time as Einstein would have said. The events will be the arrival of two flashes of light at two mirrors.

Observer A has a long support on which are mounted two mirrors, p and q, as shown below. The two mirrors are equidistant from A.

A sends a flash of light towards each mirror (flashes sent at the same time).

The light flashes are reflected and arrive back at A at the same time.

A must therefore conclude that the two events, light hitting mirror p and light hitting mirror q, were simultaneous.

Now we will consider another observerís view of the same situation.

B is very close to A.

B has his/her own ruler and watch (the diagram shows Bís ruler).

We will first assume that A and B have zero relative speed. It is hoped that the reader will agree that if the experiment is repeated, B will also conclude that the two events occurred simultaneously.

We will now consider that A and B have a very large relative speed. Again, we will imagine that at the instant the flashes are sent, A and B are very close to each other.

A short time later, the situation, as seen by B, might be something like that shown in the following diagram.

As B sees things, mirror p is moving towards the light source and mirror q is moving away from the light source. In Bís frame of reference, therefore, the light going towards mirror p will have a shorter distance to travel before it reaches the mirror than the light going the other way.

Remembering that the speed of light is the same for all inertial observers, we can see that B will consider that the light hits p before it hits q.

B must therefore conclude that the two events, light hitting mirror p and light hitting mirror q, were NOT simultaneous.

A and B are both right; simultaneity is relative.

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