# Time Dilation According to Stationary Object [duplicate]

Hello I am learning time dilation and I'm getting confused with some concepts:

Consider the given scenario, in the frame of reference of the Earth an event takes 2 seconds to occur. In the frame of reference for a moving object moving away from Earth will this event appear to take longer or slower?

I was doing a problem that involved this type of thinking and the answer suggested that the observer on the rocket would perceive it as longer. They took 2 seconds as proper time for Earth and multiplied it by the Lorentz factor to get an even longer time than 2 seconds.

My confusion is that I had the preconception that if you are moving you should perceive time as slower and therefore the time experienced is less. So if time experienced is less than the time for the event in the rocket's perspective should be less than 2 seconds. However, this problem suggests to me that even if you are moving in an object such as a rocket you can experience more time than the stationary object. Is this true or am I misunderstanding time dilation?

I would appreciate some explanations to rethink time dilation. Thanks!

• I think you could very well check a book on Modern Physics, say Serway, Krane, Holbrow, etc. and a bit of reading will clarify the subject. Commented Nov 21, 2023 at 13:28
• I don't have access to these books. Not everyone has access to these books. Commented Nov 21, 2023 at 13:53

## 2 Answers

Usually in physics we talk about events as being instantaneous, so if you have an event in the everyday sense that takes 2 seconds we would treat that as an interval between a pair of events, namely a start event and an end event 2 seconds apart. Given that, the normal formula for time dilation, in SR, applies when you have a pair of events that occur in the same place in one frame, and in two places in another. In that situation, the interval between the two events is less in the frame in which they occur in the same place.

So, to return to your scenario, if you have a pair of events that occur in the same place on Earth, and are two seconds apart on Earth, the time between them will be longer in the frame of a spaceship. Conversely, if you have two events that occur in the same place on the spaceship, and are two seconds apart on the spaceship, then the time between them will be longer in the Earth frame.

Einstein's view of special relativity can lead to many paradoxes like this , the correct view of special relativity is the Minkwoski metric.It says that the spacetime interval is the same for all observers and it relates proper distance and time to coordinate distance and time.