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Suppose that there are two points in an empty space A and B and observers at A and B having clocks:

  • If A were to be traveling near speed of light, when clock at A passes 1 hour, observer at A observes that clock at B passes more than 1 hour, say 5 hours.
  • If B were to be traveling near speed of light, then when clock at B passes 1 hour, observer at B observes that clock at A passes 5 hours.

Velocity is relative, however A or B can observe each others clock and can come to a conclusion whether they are the one traveling near speed of light?

Apparently I am confusing something here, can you point it out?

Qmechanic
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CuriousCrypto
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  • if A is traveling near speed of light wrt to B, then B is also traveling near the speed of light wrt A (in the other direction), so both of your statements will hold – Toyesh Jayaswal Feb 17 '24 at 01:04
  • @ToyeshJayaswal Does A see B's clock with 1:5 or 5:1 ratio with respect to his clock? – CuriousCrypto Feb 17 '24 at 01:15
  • Nobody thinks that they themselves are moving – RC_23 Feb 17 '24 at 02:14
  • Every clock ticks at least as fast in its own frame as in any other. – WillO Feb 17 '24 at 02:35
  • A would "see" B's clock read 1 hr when A's clock reads 5 hrs, and likewise B would "see" A's clock read 1 hr when B's clock reads 5 hrs (hopefully that's in the right order). I put see in quotes because it would take extra time for the light to actually reach the eyes, but when I say see, I mean what the equal time slices are in the spacetime diagram. – Toyesh Jayaswal Feb 17 '24 at 06:03

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You are overlooking the fact that speed is relative and time dilation is symmetric. When you say that A is travelling at near the speed of light- relative to what? Do you mean relative to B? If so, then B is travelling at near the speed of light relative to A. There is no difference between the two ways of describing the relative motion of A and B- you can say A is moving relative to B or B is moving relative to A- they both mean the same thing.

Marco Ocram
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  • So wait... at first, A and B have clocks showing the same time when they are stationary with respect to each other. B starts revolving around A near speed of light relative to A. After some time, B becomes stationary to A again and they observe each others clock. Now A observes that B's clock is behind his and B observes that A is ahead of his. However, since it is same to say A was the one traveling near speed of light B also observes that A is behind his? So both of them observe that each other's clock is behind their own? How is this possible? – CuriousCrypto Feb 17 '24 at 10:03
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    Referee!!!! You've changed the goalposts! Seriously, what I said in my answer applies to inertial motion- when you introduce rotation, that's a whole new ballgame. If you are moving inertially, the standard time dilation equation applies, and it is symmetrical, so if I am time dilated relative to you, you are time dilated relative to me... – Marco Ocram Feb 17 '24 at 11:12
  • So essentially, based on this and the comments to the posts, A or B sees themselves as 'unmoving' entities having zero velocity, and other as having velocity close to light., this is something I get. However, this means that A and B both observe 1 hour on other's clock when their clock passes 5 hours (as ToyeshJayaswal also points this out).

    I have somehow 'thought' if A observes 1:5 ratio to B's clock, this implies that B observes this ratio as 5:1 hence causing confusion. My stupidity seems to be trying to convince me this way I guess...

     – CuriousCrypto Feb 17 '24 at 12:15
  • There does not need to be rotation in my comment by the way, B can move away from A at near speed of light and come back to its original place and become stationary to A and they observe each others clock, isn't this motion relative as well? – CuriousCrypto Feb 17 '24 at 12:24
  • @CuriousCrypto Any time things are moving and are later stationary, you introduce acceleration, which involves non-inertial motion. The problem of the "twin paradox" is resolved because it is realized that the non-inertial effects make it clear that it is the twin on the ship whose clock moves slow and not that of the twin on the earth. – Albertus Magnus Feb 17 '24 at 13:27
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    Acceleration is absolute, unlike velocity, so you can have asymmetric effects. However, the key point in time dilation is that you never actually have two clocks ticking at different rates- they all tick off a second in a second. What it means is that time in one frame is systematically out of synch with time in another frame moving relative to the first, and that is what allows time dilation to be symmetric. It's too complicated to explain in a comment, but everyone is phased by it when they encounter relativity for the first time. – Marco Ocram Feb 17 '24 at 13:45
  • @AlbertusMagnus but then, doesn't it mean that now 5:1 ratio of clocks irrespective of we look from A or B's perspective does not hold? As if it were, wouldn't they see each other's clock as behind theirs when they become stationary to each other which is impossible? – CuriousCrypto Feb 17 '24 at 13:47
  • @CuriousCrypto Nope. The process of deceleration where each become stationary will destroy all of the symmetry. Only if the motion is inertial for the entire duration will the observers experience symmetric time dilation. – Albertus Magnus Feb 17 '24 at 14:12
  • @AlbertusMagnus hmm then if I were to start at stationary state (with respect to each other), and accelerate B up to near speed of light and leave it there. So now we have two inertial bodies, but A sees clock ratio as 5:1 to B's clock. Wait... so does it mean that we can figure out which body is actually accelerated by looking at this ratio of change of each others clock/time? – CuriousCrypto Feb 17 '24 at 14:57
  • @AlbertusMagnus ...also, since we can find out which one is accelerated this way, how can we talk about existance of such symmetric effect, since there are just accelerated, and not-accelerated bodies? – CuriousCrypto Feb 17 '24 at 15:02
  • Thats right, the acceleration introduces asymmetry. – Albertus Magnus Feb 17 '24 at 16:37