Time dilation, reference frames

[casualreader]

Hi,
Basic question.
I'm confused by a time dilation example (37.3 in Young and Freedman 11th ed.). Mavis is moving at .600c relative to earth-bound Stanley, and at the instant she passes, both start timers. Part b asks "At the instant when Mavis reads .400 s on her timer, what does Stanley read on his?" The answer they get is .320 s.

My question is, doesn't this depend on what reference frame you're in? I think for the .320 s answer you'd need to assume we're in Mavis' frame. (Somehow the textbook's reasoning is not transparent to me.)

Thanks in advance...

 

[ghwellsjr]

Hi,
Basic question.
I'm confused by a time dilation example (37.3 in Young and Freedman 11th ed.). Mavis is moving at .600c relative to earth-bound Stanley, and at the instant she passes, both start timers. Part b asks "At the instant when Mavis reads .400 s on her timer, what does Stanley read on his?" The answer they get is .320 s.

My question is, doesn't this depend on what reference frame you're in? I think for the .320 s answer you'd need to assume we're in Mavis' frame. (Somehow the textbook's reasoning is not transparent to me.)

Thanks in advance...

You don't sound confused to me. You got everything correct.

 

[ghwellsjr]

Here's a couple spacetime diagrams depicting the scenario from the two Inertial Reference Frames (IRF's) under consideration. First is Stanley's Earth frame. Stanley is shown in blue with dots every tenth of a second of his Proper Time and Mavis is shown in red with similar dots:

You can see that when Mavis's red clock is at 0.4 seconds, Stanley's blue clock would be at 0.5 seconds (but I didn't drawn that in).

Now for Mavis's rest frame:

Now you can see that when Mavis's red clock is at 0.4 seconds, Stanley's blue clock is at 0.32 seconds.

 

[casualreader]

Thanks a bunch, ghwellsjr, much appreciated. I wasn't sure if I was going to be reassured or if I was somehow wrong. Definitely reassured.

 

[ghwellsjr]

You're welcome.

 

[bobc2]

Hi,
Basic question.
I'm confused by a time dilation example (37.3 in Young and Freedman 11th ed.). Mavis is moving at .600c relative to earth-bound Stanley, and at the instant she passes, both start timers. Part b asks "At the instant when Mavis reads .400 s on her timer, what does Stanley read on his?" The answer they get is .320 s.

My question is, doesn't this depend on what reference frame you're in? I think for the .320 s answer you'd need to assume we're in Mavis' frame. (Somehow the textbook's reasoning is not transparent to me.)

Thanks in advance...

I thought the wording implied that the author was talking about Mavis's instant of time (Mavis's simultaneous space), which means at Mavis's instant of time and in her instantaneous 3-D world, Stanley was seeing 0.320 s on his clock. I don't see how you could interpret this as Stanley's instant.

 

[casualreader]

Okay, thanks for the input bobc2. Well I didn't see that the wording specified either Mavis's or Stanley's frame. Is it because the question starts with Mavis?; so would "What does Stanley read on his timer at the instant when Mavis reads .400s on her timer?" be the way of implying "in Stanley's frame"?