The shortest measurement for an event is always shortest for a stationary observer at the location of the event → Proper Time.
- Very related to Length Contraction
- 2 Trains on different routes, i.e. Northbound vs Southbound:
- the clock on the wall in your own cabin is always proper time because your clock is stationary from your reference point.
- Meanwhile, the clock in the train that is passing you is never proper time because it’s moving from your perspective and thus its time is dilated.
- From the perspective of a passenger on the other train, they view the situation reciprocally, where their clock is proper time and yours is dilated
- Neither observer’s frame is preferred and therefore both perspectives are different
- To be clear only relative velocity is important here
Why dilation?
is the stationary reference frame, while is the one is relative motion. We want the time from the moving observer in in terms of the Proper Time where
is the Proper Time of a stationary observer of position is the time measured by moving observers of position because the stationary observer is not moving. This results in being a dilated version of the proper time, as