I'm having a hard time figuring out in problems which is proper time and which is just time, and I think it follows from my misunderstanding of time dilation. I've read my book and looked over my notes but I can't seem to figure it out. Here's an example: A person in frame S' moves with a speed of .95c along the positive x axis relative to a person in frame S. If the time interval between two events is 20 s according to a clock in S' what would the person in frame S measure for this time interval? So what I'm thinking is (because I already know the answer) tp=20s [itex]\gamma[/itex]=3.2 and therefore frame S measures 64s. This is easy but what if the question was backwards and frame S measured the time between events to be 64s and it wanted to know what would the person in frame S' measure. tp would be 64 and [itex]\gamma[/itex] would be 3.2 right? This means frame S measures 204s which HAS to be wrong because we already know it was 20s. What am I doing wrong? Please and Thank you!