Here is a little refresher on some definitions that we will be using:
Simultaneity – ‘Simultaneity is the relation between two events assumed to be happening at the same time in a given frame of reference. According to Einstein’s theory of relativity, simultaneity is not an absolute relation between events; what is simultaneous in one frame of reference will not necessarily be simultaneous in another’
Time Dilation – ‘According to the theory of relativity, time dilation is a difference in the elapsed time measured by two observers, either due to a velocity difference relative to each other’. This means that the value of one second, for example, changes between different frames of reference.
Much like simultaneity and many other concepts in special relativity, things are made easier when we use a thought experiment to think them through. So, that is exactly how we are going to help you to understand time dilation.
- Imagine there is a passenger on a train (travelling close to the speed of light) with a light box. The light box emits a light pulse from the bottom of the box and the passenger on the train measures the time it takes for the light pulse to go on its journey to the ceiling of the box and then reflected back to the source.
- As expected, the passenger on the train finds that the time measured for the light pulse to go on this journey is twice the height of the box divided by the speed of light (speed = d/v).
- Whilst the passenger on the train does this, there is also happens to be a person on a train platform (stationary compared to the train) watching this experiment on the train from outside. They are also timing the light pulse.
- To the person on the platform, the path of the light is not just up and then down, but since the train is moving forward compared to them, the light also moves horizontally. This means that it takes longer for the light to travel up to the ceiling then back to the base of the box since it is traveling a further distance. This is time dilation.
Remember one time measured is not more right than the other – it simply depends on their inertial frame of reference. However we can work out what each of the time they would have individually measured would have been. To see this derivation please refer to the page on time dilation derivation.