special relativity

The Relativity of Simultaneity

Now is not absolute

introduction

Events are points in space and time. Two events that are synchronized in the spacecraft will not be synchronized when the spacecraft is moving.

animation

In the animation many events are created by photons hitting mirrors. In each spacecraft there are 3 photons reflecting off 6 mirror surfaces. See the illustration below.

Here is a listing of the mirrors.

  • a mirror attached to the right clock.
  • a mirror attached to the left clock.
  • a mirror at the top of the spacecraft.
  • 3 mirrors at the center of the spacecraft.

The 3 photons are created so they hit the central mirrors all at the same time. They each then travel away from the center to a mirror that reflects them back to the center. All the photons travel the same distance to arrive simultaneously at the centre.

events

With each reflection an event is created. Each reflection has a position in time and space.

In this animation we will consider the central mirrors to be very small. All the photons arrive at the central mirrors are the same time. Since the mirrors are small we shall consider this meeting of all three photon at the center of the spacecraft to be one location and so be one event.

The photons leave the central mirrors and radiate out and hit the three outer mirrors. When the spacecraft is stationary the distance to all these mirrors is the same so the events created by hitting these outer mirrors all happen at the same time. These three events are synchronized.

maintaining events

When you select a velocity other than zero all the events mentioned above must still happen.

Be mindful of

  • the speed of each photon is c. The speed of the spacecraft has no effect on the speed of the photons.
  • to maintain the single central event, the length of the spacecraft must contract. The top view in the animation is incorrect.
  • the events at the outer mirrors are no longer synchronized.
  • the left clock ticks before the right clock. Or compared to the direction of travel the back clock ticks first.

interpretation

Our concept of the word "now" can be measured by recording all the events about us that have the same time at the moment we say now. All the events in that moment "now" are synchronized. The animation illustrates that that concept of now is relative. A moment in time in the spacecraft is no longer made up of synchronized events when the spacecraft is moving.

When the spacecraft is moving we observe the back of the spacecraft in the future compared to the front of the spacecraft. The clock at the back ticks first and so we are experiencing it in the future compared to the front clock. Since we experience the back in the future and the spacecraft is moving you can imagine the back has caught up to the front a little and results in the spacecraft contracting.