Is Proper Time Relative in Special Relativity?

[JesseM]

I'm not arguing that the concept of "proper time" is NEVER useful, or that it WASN'T the original subject of this thread. But when Shark_774 said:

"Ok but here's where I am getting stuck: 5 seconds pass for Bob, he calculates that only 2.18 seconds pass for Tim. Tim observes Bob to be moving past him and therefore calculates that it takes Bob 2.18/2.29 = 0.95 seconds. Obviously I am doing something totally wrong, as this can't be right.",

he was describing a calculation that he was doing, which is actually about the relativity of simultaneity, and has nothing to do with "proper time". My goal was to get him on track to an understanding of the relativity of simultaneity, and I felt his possible misunderstanding of the concept of proper time was interfering with his ability to understand the relativity of simultaneity.

Well, I agree the calculation is correct from the perspective of each observer's inertial frame, I shouldn't have said you were "trying to promote a particular coordinate-dependent notion of simultaneity here" since your comment didn't really require the use of your CADO, just the common notion that we take it for granted that each inertial observer calculates things from the perspective of their inertial rest frame unless explicitly stated otherwise. But I don't think ignoring proper time altogether is a good way of addressing the question since Shark emphasized confusion about the meaning of "proper time" in the question, I think it's better to discuss how simultaneity and proper time relate to one another as in my last comment to ghwellsjr:

'If we consider the events of John leaving Earth and arriving at NEC, his time between the events is 0.87 years, and if we consider the event E1 on Ann's worldline that's simultaneous in Ann's frame with John arriving at NEC, the time for Ann between John leaving and E1 is 2 years, whereas if we consider the event E2 on Ann's worldline that's simultaneous in John's frame with John arriving at NEC, the time for Ann between John leaving and E2 is 0.34 years. That's why I emphasized the relativity of simultaneity and being careful to keep track of what specific events you want to calculate proper time between, that way you can see how both "Ann experiences 2 years" and "Ann experiences 0.34 years" are correct in different senses.'

 

[Shark 774]

To add to what I said above, let me pick some specific pairs of events here. Suppose we have the events of Tim passing one object A and then the event of Tim passing another object B, and in Bob's frame this takes 5 seconds. So, he calculates that Tim will experience 2.18 seconds between the event of passing A and the event of passing B, which is the objective proper time for Tim between these events. Now Tim picks the event E1 on Bob's worldline that is simultaneous in Tim's frame with the event of Tim passing A, and the event E2 on Bob's worldline that is simultaneous in Tim's frame with the event of Tim passing B. Naturally in Tim's frame the time between E1 and E2 is 2.18 seconds, so he calculates that that Bob will experience 0.95 seconds of time between E1 and E2, and this is indeed the objective proper time for Bob between those events. However, in Bob's frame E1 is not simultaneous with the event of Tim passing A, and E2 is not simultaneous with the event of Tim passing B, for Bob these are just two meaningless events on his worldline where nothing of significance happened.

This is exactly what I needed to know. I'm no longer confused. Thanks a lot to everybody, this has really helped me a lot in trying to learn Special Relativity in high school without a teacher! Thanks again everybody.