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Consider a hypothetical situation: In which a time traveler travels in a spaceplane at close to speed of light circling the earth and I get a live telecast of inside of that plane to my television. How time dilation will effect him and what will I observe sitting next to the tv seeing him live. Considering time runs slower at speed of light, will he be looking like a slow motion video? (Or let he also watching live streaming of us at earth, what it will look to him) P.S. I'm not sure if it even makes some sense but if it does kindly explain in logical details. Sorry for the the bad english, I'm not a native speaker.

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  • $\begingroup$ One must remember that even while the video is being recorded at regular speed for the astronaut, the light waves from him will be affected by the Doppler effect. This means that if he was travelling away from us, the signal broadcasting the livestream would be stretched out, making it appear as if he is in slow motion. $\endgroup$
    – Tweej
    Apr 24, 2016 at 7:50
  • $\begingroup$ @Tweej: relativity is not about delays due to the finite speed of light, because this fact is compatible with classical mechanics and can easily be compensated for (Doppler effect changes the frequency of the signal but not the information it carries). Relativity is about the independence of $c$ from the frame of reference. $\endgroup$
    – L. Levrel
    Apr 24, 2016 at 9:24
  • $\begingroup$ What effort have you made to find the answer to this question elsewhere? There are dozens of websites that discuss the Twins Paradox. $\endgroup$ Apr 24, 2016 at 14:06
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    $\begingroup$ Yep, but all of them explain what would happen and I'm asking how will it happen, how the passage of time will look like to the observer and to the traveler, what changes actually occur as a result of time dilation, does our metabolism start working slow etc. If you still think this is just another twin paradox question kindly give me the link which answers these question. $\endgroup$
    – Asker
    Apr 24, 2016 at 14:35

3 Answers 3

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Since the traveller is circling Earth, he/she is actually accelerated. So his/her frame of reference is not inertial (if we take that of the beholder to be inertial). The two points of views are then not equivalent, unlike those in the twins paradox.

If I'm not mistaken, one may show that the beholder will "see" the traveller be slower, and the traveller will "see" the beholder be faster. I put double quotes because this is not mere appearance: time does pass slower for the traveller than for the beholder. Given they remain close to each other, they can easily meet (the traveller just has to land) to compare their watches.

If the traveller were moving in a straight line at constant speed (simple Lorentz transform, both persons are in an inertial frame), both would see the other one be slower. This is only an apparent paradox, because in such a situation they won't meet again. If the traveller were then to come back to Earth, during his/her U-turn he/she would see the beholder become very fast, so that when they meet again there is indeed asymmetry between them, and the traveller is younger (this is called Langevin's twins paradox).

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    $\begingroup$ Assuming you (the recipient of the signal) are at the center of the earth --- or that the radius of the orbit is large enough so that we can treat the earth as a point --- general relativity has nothing to do with it. All of the travelers' light signals are subject to the same gravitational time dilation, so that dilation has no effect on the speed of the streamed video. There is just the special relativisitic effect that slows down the video by a factor $\sqrt{1-v^2}$. $\endgroup$
    – WillO
    Apr 24, 2016 at 14:31
  • $\begingroup$ Alright for the traveller seen by the beholder. But what about the other way round? The traveller is not in an inertial frame, how would you apply SR to what he/she sees? $\endgroup$
    – L. Levrel
    Apr 24, 2016 at 14:36
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    $\begingroup$ You can integrate the spacetime interval along the traveler's path to see what his clock shows at any given event on his worldline. You can also identify the light ray from earth that passes through that event, and calculate what earthclocks were showing at the event when that lightray left earth. Do this for two different points on the traveler's journey and you can compute the ratio between time passed on the traveler's own clock and time passed on the clock on the traveler's video screen. Still no need for GR. $\endgroup$
    – WillO
    Apr 24, 2016 at 15:06
  • $\begingroup$ Thanks a lot @WillO! I rewrote the first two paragraphs, would you be so kind as to check the new phrasing? $\endgroup$
    – L. Levrel
    Apr 24, 2016 at 17:27
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    $\begingroup$ I believe what you've written in your new second paragraph is correct. Here is the key: Alice (on earth) and Bob (on the ship) have to agree on what Bob's clock says after exactly one rotation. If Alice says that one rotation took five minutes and that Bob's clock moved only four minutes in that time, then Bob has to agree that his clock moved only four minutes in that time. So if Alice sends out five equally spaced signals during her five minutes, Bob must receive those five equally spaced signals during his four minutes --- so he sees her video as speeded up. $\endgroup$
    – WillO
    Apr 25, 2016 at 0:20
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I am adding this answer to respond to your last followup comment on L.Levrel's answer.

Point One: Alice and Bob have to agree on how many times Alice's clock ticks per rotation, and they have to agree on how many times Bob's clock ticks per rotation. Therefore, if Alice says Bob's clock is slow, Bob must say Alice's clock is fast, and vice versa.

Point Two: Alice is an inertial observer. Bob is in motion with respect to Alice, so Alice must say that Bob's clock is slow. Between this and Point One, we can conclude that Bob must conclude Alice's clock runs fast, i.e. he sees the video she transmits as speeded up.

Point Three: At any given instant, Alice is in motion with respect to Bob, causing Bob to say her clock runs slow. You seem to be worried that this contradicts Point Two. But it's also true that any given instant, Bob is accelerating toward Alice, which causes him to see her clock jumping ahead in that instant, and this more than counteracts the effect of the time dilation we've already acknowledged.

To see the effect of Bob's acceleration (which is indeed directed toward Alice, since he's orbiting her), draw a spacetime diagram in which Alice's worldline is vertical, and Bob's, initially tilted toward Alice (so that he's moving toward her), tilts a bit more in the same direction. Then his line of simultaneity also tilts, so as to hit Alice's worldline at a later time on Alice's clock. That is, Bob's acceleration causes him to see Alice's clock move forward.

So: Bob's velocity with respect to Alice (which of course he thinks of Alice's velocity with respect to Bob) makes him say that her clock is running slow, but at the same time his acceleration makes him say that her clock is running fast. If you carefully calculate the two effects (over a given infinitesimal time increment) and add them together, you should get exactly the speed-up factor promised in Point Two. I confess that I have not done this calculation, but it should be easy and I am confident of how it would come out.

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I dont think it's a problem, that the satellite is accelerating. Locally the time will nevertheless run slower.

If the camera is directed onto a watch, you would see it ticking more slowly.

If the webcam is directed on the outside, you will see the normal speed of happenings, e.g. it would show you the same number of rounds as you have seen by looking at the vehicle. Only it would have to be a very fast camera, otherwise you would see less frames per second.

And it probably would have to be a magical webcam, since the usual connection to a WLAN would probably not work. But I'm not sure about the engineering details. (Well, I'm sure it would break from the acceleration, so it has to be magical anyways)

Well, and besides, you would see the world distorted, everything shifted to the forward direction, and brighter there and less bright backwards. Just like the pictures you find on the internet, e.g. here

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