Twin paradox and time dilation.

anonymoussome

When we read that two twins would age differently when one moves with relativistic speeds.
i.e. When one twin travels at speed near to speed of light then the twin on earth would see that time for the travelling twin has slowed down. Thats what we say time Dilation.
Similar is the case with the other twin. He may also say on returning back that time had slowed for the twin on earth. But his claim is refused because he was initially and finally in a non inertial frame. But what about the time when he was moving with constant velocity. At that time he was moving in an inertial frame. Why does it happen then that what he sees is false and the OP is true??

JesseM

If he continued moving inertially, then what he measures in his frame (which is different from what he see--look at this thread if the distinction isn't clear to you) is just as valid as what is measured in any other frame. But as long as you stick to a single inertial frame for the entire problem you'll conclude the traveling twin ages less in total (the laws of physics work the same in every inertial frame, but they don't work the same way in non-inertial frames). For example, you could take the perspective of the frame where the traveling twin was at rest during the first phase of the journey while the Earth is flying away, and in this frame, he will age more than the Earth prior to the turnaround, but after the turnaround he'll be moving at an even greater speed than the Earth, and so be aging slower. It'll work out that when you add how much he ages in both the outbound stage and the inbound stage, and compare it to how much the Earth ages from start to end, the traveling twin still ages less, by exactly the same amount as if you had used the rest frame of the Earth.

MeJennifer

After accelerating away from the twin on earth his clock is going to accumulate less time compared to his twin on earth until he reverses the direction of acceleration. Then after he accelerates toward his twin on earth his clock again will accumulate less time compared to his twin on earth until also that acceleration is reversed. At that time he is together with his twin on earth again.

JesseM

Note that this is only true in certain inertial frames, like the rest frame of the Earth. As I said above, you can also pick an inertial frame where the twin accumulates more time than the Earth twin between leaving Earth and turning around, but then less time between turning around and reaching Earth again; in this frame the total time accumulated by the traveling twin between leaving and reuniting will still be less than the time accumulated by the Earth twin, by exactly the same amount that's predicted by any other inertial frame.

MeJennifer

Not sure what you mean here, could you please provide an example where the accelerating twin's clock, accumulates more time than the twin's clock on earth until the point he accelerates to turn around.

JesseM

Sure, just analyze the situation from the point of view of an inertial frame where the accelerating twin's speed during the inertial phase between leaving Earth and turning around is smaller than the Earth's speed in this frame. Naturally if the Earth's speed is greater during this interval, its clock is ticking slower during this interval.

For a numerical example, consider the same situation first viewed from the rest frame of the inertial stay-at-home twin (call this frame A), next viewed from the inertial frame where the traveling twin is at rest between leaving Earth and turning around (call this frame B). If both twins are exactly 30 when the traveling twin departs the stay-at-home twin, and in the stay-at-home twin's frame A, the traveling twin moves away for 10 years at 0.6c before instantaneously accelerating to come to rest relative to the stay-at-home twin, then in frame A the stay-at-home twin turning 40 will happen simultaneously with the traveling twin accelerating while turning 38. But in the frame B of an inertial observer who sees the traveling twin at rest until accelerating, the stay-at-home twin is moving away at 0.6c for 8 years before the traveling twin accelerates (again at age 38) to match speeds with him, and at the moment of acceleration the stay-at-home twin is 36.4 years old. This is just an example of the relativity of simultaneity. Both frames agree the traveling twin is turning 38 at the moment of acceleration, but in the first frame A this event is simultaneous with the stay-at-home twin turning 40, while in the second frame B this event is simultaneous with the stay-at-home twin turning 36.4.

If you doubt these numbers are correct, I can show that they are by using the Lorentz transformation, if you wish.

MeJennifer

Perhaps I misunderstand you but, if we have:

1. Twin A and B on planet P and point X, a fixed distance away from planet P.
2. A accelerates away from P towards X.
3. A accelerates towards P to stop at X.
4. A records the total elapsed time since 2.
5. A accelerates away from X towards P.
6. A accelerates towards X to stop at P.
7. A records the total elapsed time since 5.

Then all observers must agree on both recorded proper times recorded in step 4 and 7.

JesseM

Yes, I agree. I was talking about comparing how much A had aged at step 4 with how much B had aged "at the same moment", which of course is frame-dependent since different frames disagree on simultaneity. In some frames B has aged more than A at the moment A stops at position X, while in other frames B has aged less than A at the moment A stops at position X. In a frame where B (the twin on planet P, which we can think of as earth) has aged less at the moment A stops/turns around, then I would interpret that as contradicting your statement that "After accelerating away from the twin on earth his clock is going to accumulate less time compared to his twin on earth until he reverses the direction of acceleration."

MeJennifer

Ok, I agree with that notion.

cybersurf88

Interesting is that screenwriters for Flash Gordon in 1950's (West Berlin production) had "Flash" testing a machine which would theoretically allow Flash to travel faster than the speed of light. Dale quips,(summary) "...you'll be travelling so fast that you'll be arriving before leaving."
What physics principle were the screenwriters incorporating in that segment?
Thank you.
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JesseM

See this thread for a discussion of why, in relativity, faster-than-light travel opens up the possibility of sending information backwards in time (although it does not mean that the FTL object itself is going back in time in any absolute sense).

Fredrik

...or this thread.