Simultaneity is doing something at the same time as someone else as viewed from your frame of reference.
Just before we begin, here is a Key Definition before you read on:
What is an inertial frame of reference? Any frame of reference in which Newton’s first law of motion (A body will maintain at rest or continue at constant velocity provided that no external forces act on it) holds. A frame of reference is how things ‘look’ from that point in space/ point of view.
The foundations of special relativity begin with something called Einstein’s postulates:
- First postulate (The principle of Relativity) –The laws of physics are the same in all inertial frames of reference.
- Second postulate – The speed of light in a vacuum is the same in all inertial frames of reference and is independent of the motion of the source. This means that the speed of light doesn’t change if you were to accelerate a frame of reference.
These two postulates are extremely important because of their implications – including time dilation (the length of one second changes) and length contraction (the distance of one meter changes). These effects all come from the idea that an observer cannot travel at or exceed the speed of light.
Time dilation and length contraction follow on from an idea of simultaneity. The best way to understand simultaneity is to use a thought experiment.
Lets imagine that due to extremely bad weather, lightning bolts start to occur. These two lightning bolts hit the side of the carriage that the passenger is in. This just so happens to be at the same time the train is aligned with the platform meaning that the person on the platform (observer) sees the bolts hit the train at the same time.
Now, from the point of view of the person in the carriage, the light from the bolt at the front of the carriage arrives at the passenger first, soon followed by the bolts from the back of the train. This happens because the train (frame of reference) is moving towards the bolt at the front of the train and away from the bolt that hit the back of the train. Kind of like the Doppler effect.
However for the person on the platform, they will say that the light from the lightning strikes reached them at the same time (since they were not moving compared to the lightning and also half way between the bolts).
This means that both observers saw the lightning strikes but they disagree on when they saw the bolts of lightning. However one is not more right than the other. When the light reached them depended completely on their inertial frame of reference.
Imagine a train is travelling at close to the speed of light and that there is a single passenger in the train. At the same time there is someone on the train platform observing this train as it whizzes past.
To get a mathematical representation of this please look at section on time dilation derivation.