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I Is my thought right or wrong? Light and a moving observer

  1. Nov 17, 2017 #1
    I would like to know whether my thought is right or wrong about time dilation example.

    Let's say,

    A person is standing at a starting point so his velocity is 0 ms'1.
    A car runs from that point in the velocity of 3 ms'1.
    A photon from a light source at that point is also emitted at the same time. Let the velocity of photon be 5ms'1.( Yeah I know the real velocity of photon)

    Relative velocity of the photon is 5ms'1 for both standing person and car.

    For the standing person at the starting point, the photon is at 50 meters ahead of that point after 10 seconds.
    For the car, the photon is at 50 meters ahead of it after 10 seconds. At that time, the car is at 30 meters ahead of the starting point and so the photon is at 80 meters from that point.

    That means, for the standing person, it takes 16 seconds to find the photon reach 80 meters away from the standing point. Yet, for the car, it takes just 10 seconds to find the photon reach 80 meters away from that point. When the person looks at the clock of the car, the clock motion of the car is running slower than his.
     
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  3. Nov 17, 2017 #2

    Nugatory

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    You can make the problem a bit easier by stating the distances on light-seconds instead of meters: the speed of light is one light-second per second.
     
  4. Nov 17, 2017 #3

    PeterDonis

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    His velocity in the frame in which the starting point is at rest is 0. When you give positions, velocities, and times, you need to specify a frame; otherwise they are meaningless. One of the most common errors in relativity is to fail to do that, and then not notice that you are switching frames implicitly. As you will see, you yourself have made that mistake.

    Velocity in the frame in which the starting point is at rest.

    Or just 5, without units. That way you don't have to pretend the speed of light is something other than it is.

    Or we could just make the photon's velocity 1 and the car's velocity 3/5. (Units in which the speed of light is 1 are very common and useful in relativity.)

    Yes (with the caveat I gave above about velocity units). But these velocities are expressed in different frames--one in the rest frame of the starting point, one in the rest frame of the car.

    In the frame in which the starting point is at rest.

    In the frame in which the car is at rest.

    No. You just switched frames implicitly (between the two sentences quoted just above) and didn't notice it, which is the error I said above was very common. Can you see how?

    (If you can't, consider the following questions: In what frame is the car 30 meters ahead of the starting point in 10 seconds? In what frame is the photon 50 meters ahead of the car in 10 seconds? Hint: they are not the same frame. So you can't add the distances, because you're adding distances relative to different frames, which is meaningless.)

    In the frame in which the starting point is at rest, yes.

    No. See above.
     
  5. Nov 18, 2017 #4
    Then, how many meters away from the starting point will the photon be after 10 seconds in the car's clock, Sir ? not 80 meters ?
     
  6. Nov 18, 2017 #5

    Ibix

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    How are you defining the start point? Is there a marker there? Is that marker at rest with respect to the ground or the car?
     
  7. Nov 18, 2017 #6

    PeterDonis

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    In which frame? The car's frame?
     
  8. Nov 18, 2017 #7

    PeroK

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    Yes, 80m, in the car's frame of reference. The kinematics are relatively simple.

    To the person at the starting point, the car is moving away at 3m/s and the light at 5m/s.

    To the person in the car, the light is moving at 5m/s ahead and the starting point is moving at 3m/s behind him.

    Both can carry out normal kinematic calculations on that basis.
     
  9. Nov 18, 2017 #8
    Yes, Sir, Then am I right ?
     
  10. Nov 18, 2017 #9
    Then, doesn't it mean the clock of the standing person ticks 16 times when that of the car ticks 10 times, Sir ?
     
  11. Nov 18, 2017 #10

    PeroK

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    All such questions are frame dependent. In the frame of the person at the start the car clock ticks slower. But, in the car frame tge starting clock runs slower.
     
  12. Nov 18, 2017 #11

    Ibix

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    Unfortunately, simultaneity is also frame dependent. So what's happening at the same time as the car clock ticking 10 depends on which frame you use, because they have different definitions of "at the same time" for things that don't also happen in the same place.
     
  13. Nov 18, 2017 #12
    Sir, what I would like to know in my layman sense is whether the clock of standing person ticks 16 times when the clock of car ticks 10 times or not. That's why in the frame of standing person, the clock of car is running slow.
     
  14. Nov 18, 2017 #13
    I understand " In the frame of the person at the start the car clock ticks slower"

    But, I don't understand " But, in the car frame tge starting clock runs slower" , should it have not been faster, sir ?
     
  15. Nov 18, 2017 #14
    The basic description of time dilation is that moving clocks tick more slowly. But motion is relative, so no clock can be said to be absolutely moving. If I'm in a ship flying away from you at some speed, for you, my clock is ticking more slowly. But for me, you're the one who's moving, so your clock is ticking more slowly. This may seem contradictory until you incorporate the relativity of simultaneity. At some given moment X for you, my clock says Y. But for me, when my clock says Y, your clock says Z. We don't share the same concept of "now" due to being in motion relative to each other.
     
  16. Nov 18, 2017 #15

    PeterDonis

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    Ah, yes, you're right.

    However, that still doesn't quite address the question about time dilation. I'll address that in response to @thatoekhant below.

    You are right about the 80m in the car's frame, yes; I was mistaken about that. However, that still doesn't mean you can make the comparison you make here:

    To really understand what's going on, you need to first label all the events of interest in one frame (say the frame in which the starting point is at rest) and give them their proper coordinates in that frame. That means you need to identify what those events are. For example, there is an event at which the photon is 80 meters from the starting point in the rest frame of the starting point. There is also an event at which the photon is 80 meters from the starting point in the rest frame of the car. Question: are these the same event? (Hint: the answer is no. There are two separate events, each of which has its own distinct coordinates. So the comparison you make in the quote above is still comparing quantities that can't be directly compared.)

    Once you have coordinates for all events of interest in one frame, you then Lorentz transform all of those coordinates into the other frame (the frame in which the car is at rest). That tells you how things look from the car's point of view.

    Once you have described things in both frames, you can then look at what "time dilation" means in each frame. In the starting point rest frame, the car's clock appears to run slow; but in the car rest frame, the starting point's clock appears to run slow. That means the two comparisons must be comparing different things (similar to the way there were two events involving the photon above, not one). What are those different things?
     
  17. Nov 18, 2017 #16

    PeterDonis

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    No. Do the math as I described in my previous post and see.
     
  18. Nov 18, 2017 #17

    Ibix

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    There isn't a consistent answer in these terms. A major consequence of relativity is that time doesn't work the way we naively think about it.

    Both observers regard the other's clock as ticking slowly. This might appear inconsistent, but that's because youare thinking of "at the same time" as an absolute statement. It's not. It's like saying "straight in front of me". What that statement means depends on which way I'm facing, and means something different when soneone else says it. In relativity, "at the same time" turns out to depend on who says it and their state of motion. So "what happens at the same time as the car clock ticks 10?" can only be answered if you decide whose "same time" you mean.

    If you use the car's definition of "the same time" then the ground clock shows 8.125s when the car clock reads 10. If you use the ground's definition of "the same time" then the ground clock reads 12.5s when the car clock reads 10s.

    Note that we are correcting for light travel time here. If we don't correct for that, both frames will agree what time the car observer sees on the ground clock, so there is no contradiction inactual measurements. They also agree that what they see is not what's happening "now" because of the finite speed of light. But they don't agree on how to correct for the speed of light because they don't agree what "not moving" means, so they can't agree what "now" means.

    Einstein's train thought experiment is the usual illustration of this.
     
  19. Nov 18, 2017 #18
    Yeah, I think I understand what that means, Sir.
     
  20. Nov 18, 2017 #19

    Ibix

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  21. Nov 18, 2017 #20

    Mister T

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    Let's say the 16-tick period of time starts at the same time as the 10-tick period of the other clock. The only way we can establish that as an absolute fact is if the clocks share the same location. It's tempting now to say that the 16-tick period ends at the same time as the 10-tick period, but no such claim can be made absolutely because the clocks are in same place only that one time.
     
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