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I am currently reading Einstein's relativity book and trying to wrap my head around the time dilation.

I know about some implications of the twin paradox and wanted to ask a few questions that don't make any sense in my mind, obviously because of the ignorance. Please explain.

So let's assume, that we have two people. One is inertial at a certain point in space, not affected by any massive objects. Let that point be A. The second person is moving from this point A at 99.999999999% of speed of light, assume no acceleration. The trip one-way destination is 4 light-years away and let's say that's point B.

Now we know that the $t_{moving} = \frac{t_{standing}}{\gamma}$. So the time for stationary person will go slower. Time dilation in effect.

The moving person travels from A to B and back to A. Classic problem. Comes back. In his reference $t$ is 8yrs. For a stationary person $8*\gamma$ years. The moving person factually traveled to the future and came younger.

But my problem is that the only way the stationary person observed time dilation is if for her either the moving person's speed was slower or the overall distance was larger. We know that for inertial observers the speed of light will always be constant. So it has to be the distance that becomes larger and larger for the moving person with the speed approaching to the speed of light. Which doesn't make any sence.

The $D = 8yrs * c$. If nobody is moving. For the moving person it stays the same since their clock is at 8yrs precisely when they hit the A on the way back. However, for the stationary person the distance would have to be $D = 8yrs * \gamma *c$ or the c should be smaller, which is impossible.

Please help me out.

BioPhysicist
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Johnny smith
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  • The trip one-way destination is 4 light-years away and let's say that's point B. In which frame? Also, "stationary" and "moving" are meaningless in relativity. You need to specify with respect to which frame. – BioPhysicist Mar 03 '20 at 04:56
  • You came to the conclusion that the distance the traveller observes is shorter than what the person staying home observes. This is called length contraction and is explained by special relativity, so why do you think it is impossible? I think your calculations are correct, but there is no contradiction. – Azzinoth Mar 03 '20 at 05:08
  • Congratulations, you appear to have derived length contraction. – probably_someone Mar 03 '20 at 05:55
  • Well length contraction is related to the body itself not the overall distance. Or am I wrong? So let’s assume that the length of the ship is 10m. Now if the ship travels at light speed it’s length will become 0 meters. – Johnny smith Mar 03 '20 at 11:07
  • Aaron Stevens, fair enough. I am talking about a classic twin paradox. One is moving with the reference to another. So person 2 is moving with the reference to person 1 and person 1 is stationary with respect to person 2. I understand the math behind it and understand why time is shorter. What I don’t understand is that in order for time to be slower for person 1 either the speed of person 2 should be smaller or the overall distance should be larger. In the example you sent me, it turns out that the distance becomes larger (curve) which does not make any sense to me. – Johnny smith Mar 03 '20 at 11:13
  • You write "person 2 is moving with the reference to person 1 and person 1 is stationary with respect to person 2." This is impossible. If you are moving forward with respect to me, then I am moving backward with respect to you. It might seem like I am nitpicking, but understanding this is ESSENTIAL to understanding relativity. – Marius Ladegård Meyer Mar 03 '20 at 13:18
  • That I understand Marius. I said impossible about making the speed of light smaller. The only notion I am struggling with is the equation $D = t * c$, which becomes $D = t\gammac$ for a stationary observer. As c stays constant no matter what, then in order for time to be larger, the D has to be larger. So in the eyes of the stationary person, the moving person will warp space on a weird curvy trajectory and the distance will become larger. And it doesn't make sense that the distance would become larger. I just trying to wrap my head around that. – Johnny smith Mar 03 '20 at 13:40
  • It's kinda what they depict in the movies, when the ship goes to the light speed, the stars and the ship prolongate. https://www.youtube.com/watch?v=G-1kkB_qF28 For example in this clip in the beginning you clearly see that the start ship's trajectory wildly prolongates, so technically for an outside observer the distance that the ship travels is becoming larger. – Johnny smith Mar 03 '20 at 13:46
  • "Well length contraction is related to the body itself not the overall distance." No, it is related to all distances. " So in the eyes of the stationary person, the moving person will warp space on a weird curvy trajectory and the distance will become larger." No, the space is contracted for the traveller, so he observes a shorter distance than the stationary observer. This does not imply a curved trajectory. Also the distance doesn't "become" larger or smaller, if A and B are not moving relative to each other. The distance is constant in each inertial reference frame, but different. – Azzinoth Mar 03 '20 at 14:06

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