How Does Time Dilation Work in Relativity?

[Master J]

Time Dilation...what it means

I am trying to get my head around some of the basics of relativity.

dt' = ydt

Where dt is the time between 2 events in frame S, and dt' is the time betwen the same events in frame S', that is moving witha constant velocity relative to S.

What exactly does this say? Does it mean that the observer in S' will measure a greater time interval than in S, or that the observer in S will see the time interval in S' as longer than his?

Like if it means that the observer in S' will measure a greater time interval, well howcome the observer in S doesn't, since one could equally say that he is moving relative to S'?

I hope you guys can sort this out, its just tricky to get the hang of.

 

[Ich]

Like if it means that the observer in S' will measure a greater time interval, well howcome the observer in S doesn't, since one could equally say that he is moving relative to S'?

The formula is valid only if the two events happen at the same place in S, not in S'. It says that in this case, S' measures a longer time between the events than S, since y>1. Generally, the observer for which the two events happen at the same place measures the shortest time.

 

[Entropia]

Time dilation is a concept in Einstein's theory of relativity that states that time is not absolute, but rather is dependent on the observer's frame of reference. This means that time can appear to pass at different rates for different observers depending on their relative velocities. The equation you mentioned, dt' = ydt, is known as the time dilation equation and it shows that the time interval measured by an observer in a moving frame (S') will be longer than the time interval measured by an observer in a stationary frame (S). In other words, the observer in S' will perceive time as passing slower than the observer in S. This is because as an object approaches the speed of light, time appears to slow down for that object from the perspective of an outside observer. This phenomenon has been proven through experiments and is a fundamental aspect of relativity. So to answer your question, it is not that the observer in S does not measure a longer time interval, but rather that the time interval appears longer to the observer in S' due to their relative velocities. I hope this helps clarify the concept of time dilation for you.