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Time dilation, reference frames

  1. Jun 4, 2013 #1
    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...
     
  2. jcsd
  3. Jun 4, 2013 #2

    ghwellsjr

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    You don't sound confused to me. You got everything correct.
     
  4. Jun 4, 2013 #3

    ghwellsjr

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    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:

    attachment.php?attachmentid=59288&stc=1&d=1370393992.png

    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:

    attachment.php?attachmentid=59289&stc=1&d=1370394201.png

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

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  5. Jun 4, 2013 #4
    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.
     
  6. Jun 4, 2013 #5

    ghwellsjr

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    You're welcome.
     
  7. Jun 4, 2013 #6
    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.
     
  8. Jun 5, 2013 #7
    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"?
     
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