Simultaneity in Special Relativity
- The term 'simultaneous' means to occur at the same time
- The relativity of simultaneity states that
Whether two spatially simultaneous events happen at the same time is not absolute, but depends on the observer's reference frame
- This means that in one reference frame, two events that occur at different points in space seem to happen at the same time, whilst in another reference frame moving relative to the first the events seem to happen one after another
- This was not the case in Galilean relativity, where simultaneity was absolute
- This is best shown in the following example
- Person B is in a train carriage moving to the right at constant velocity
- They switch on a lamp above them and they observe that the light from the lamp reaches the two ends of the carriage, points X and Y, at the same time
Person B sees the light from the lamp reach point X and Y at the same time
- Meanwhile, Person A is stationary on a platform and observes the train travel past
- Person A will still see the light from the lamp move to both ends of the carriage at the same speed (c)
- This is in line with Einstein's second postulate
- However, Person A will see the light reach point X before it reaches point Y
- This is because the whole carriage is moving to the right (relative to Person A), so the left side of the carriage is moving towards the light ray and the right side of the carriage is moving away from the light ray
- This means that Person A will see the light ray reach point Y slightly later
Person A sees the light from the lamp reach point X before point Y
- This image is exaggerated to show the point; the difference between the times will be very very small and is dependent upon the speed of the train carriage
- Simultaneity can be visualised using space-time diagrams