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A phone call at the speed of light?

  1. Apr 9, 2013 #1
    If time passes so much slower near the speed of light... What would happen if somone on Earth made a 10 minute phone call to somone traveling at the speed of light? In this case, the 10 minutes would be relative to a watch from the person on Earth and a watch from the person moving near light speed. So time in this case is not a perception by either person in the given scenario, it is defined by a static object that can only perceive time in one way and only one way.

    I'm sure this has quite a simple answer; I am new to understanding GR and quantum theories. Since this is a question I came up with myself, I'm hoping a solid answer will help define my sense of logic, propelling me further into such an interesting field of study.

    Also, I apologize in advance if this topic is misplaced or if similar questions have been recently answered.

    Thank you!
     
  2. jcsd
  3. Apr 9, 2013 #2

    phyzguy

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    You can't travel at the speed of light. Let's assume you mean near the speed of light.

    The two watches will not read the same. If the watch of the person on Earth says that the phone call takes 10 minutes, the watch of the person traveling near the speed of light will say the phone call takes much longer than 10 minutes.

     
  4. Apr 9, 2013 #3

    ghwellsjr

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    First off, as phyzguy pointed out, you can't travel at the speed of light so let's assume the traveler is going at 96% of the speed of light. I like that number because it allows us to get an exact solution instead of one with a lot of digits past the decimal.

    Secondly, you didn't specify which direction the traveler was moving with respect to the person on Earth but you did stipulate that the phone call will take ten minutes for both the Earth person and for the traveler as defined by their own watches.

    Thirdly, this problem has nothing to do with Time Dilation or with frames of reference and it is not even a problem that requires Special Relativity to solve, although we can use SR to help us solve it. Instead, it is a problem having to do with Relativistic Doppler and at 96%c the Doppler factor is exactly 7 or its reciprocal.

    Now let's see how we can set up a scenario to accomplish what you want. Let's suppose the traveler is far away from Earth and traveling almost directly towards Earth. He's going to fly right past Earth during the phone call and then be traveling away from Earth.

    While the traveler is approaching Earth at 96%c, the Relativistic Doppler shift is 7. That means that when he gets the phone call from Earth, he will hear the voice of the Earth person sped up 7 times faster than normal and taking 1/7 of the length of time. Clearly, if he was really far away, the ten minute call would only last for less than a minute and a half.

    But let's suppose that he has already passed Earth when the phone call is made. Now he will hear the Earth person speaking very slowly, 1/7th of normal and the phone call will take 70 minutes to happen according to his watch.

    So, in order to get this phone call to last ten minutes according to the traveler, we just have to solve a mathematical problem. Let t1 be the time according to the traveler's watch prior to him passing Earth and t2 be his time after passing Earth. We want t1+t2 to be equal to 10. But we also need for t1*7 + t2/7 to equal 10.

    t1+t2=10
    t1*7 + t2/7 = 10

    t1*49 + t2 = 70
    t2 = 10 - t1
    t1*49 - t1 + 10 = 70
    t1*48 = 70 -10 = 60
    t1 = 60/48 = 1.25
    t2 = 10 - 1.25 = 8.75

    So we just make sure that the traveler spends 1.25 minutes receiving the first part of the phone call at 7 times normal which means that the Earth guy will be talking for 8.75 minutes and then just when the traveler passes Earth, he spends 8.75 minutes talking to the Earth guy who will hear it come in at 1/7 of normal speed.

    So they both get to talk for 8.75 minutes and they listen for 1.25 minutes for a total time of ten minutes according to both of their watches.

    That was fun although I'm sure it isn't what you expected. Nevertheless, this is the sort of thing that happens when a scenario is ill-defined.
     
  5. Apr 9, 2013 #4

    phyzguy

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    Just to clarify, in my post I assumed that the traveler was moving directly away from the stationary person on Earth. As George pointed out, if the person is moving toward the Earth, he will see the phone call taking less time than the Earth observer sees. Sorry if this was confusing.
     
  6. Apr 9, 2013 #5

    HallsofIvy

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    No. The direction is not relevant- the time reduction depends upon speed not velocity. The person on earth will hear the person in the space ship talking very slowly, the person in the space ship will hear the person on earth talking very slowly.
     
  7. Apr 9, 2013 #6


    :confused:

    How do you suppose the phones communicate?
     
  8. Apr 9, 2013 #7

    Nugatory

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    Time dilation depends only on the relative speed of course, but unless the communication is instantaneous, we also have to consider Doppler - and that will depend on the direction as well as the speed.
     
  9. Apr 9, 2013 #8

    phyzguy

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    Not true. Re-read ghwellsjr's post, which is correct. Someone approaching the Earth at a high rate of speed will hear the conversation happening faster than the person on the Earth. Think of the twin paradox, and review the space time diagrams of a twin who travels out at a high rate of speed, then travels back at a high rate of speed. If he has a telescope pointed back at the stationary Earth, on the way out he will see his twin on Earth aging more slowly than he is, but on the way back, he will see his twin on Earth aging more quickly, such that when he arrives back on Earth, the stationary Earth twin will have aged more than the traveling twin.
     
  10. Apr 9, 2013 #9

    pervect

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    Note that you won't be having a 10 minute 2-way phone conversation with anyone unless they are within 10 light minutes of you.

    If you give more detals on the exact scneraio you have in mind, we can maybe answer better.

    The scenario I am thinking of, is that you talk for 10 minutes. Much much later, the signal arrives at the destination.

    Your 10 minute monologue will play out either longer or shorter than 10 minutes to the recipient, depending on their motion. It's basically just a refinement of doppler shift.

    They then record a 10 minute reply to you and send it off. IT will play out longer or shorter than you on actual receipt, longer if they're moving away, shorter if they're moving towards you.

    The idea of an "instantaenous" phone is mostly incompatible with relativity, it insists that phone calls occur at light speed.
     
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