Exploring Time Dilation: From Twin Paradox to Maximum Speed of Future Spaceships

[Tomahoc]

Has any experiments been done equal to this scenerio where the twin leaving Earth and seeing Earth time dilated.. but when the twin reverses and returns to earth, the Earth speeds up or go in fast motion? If time dilation is slowing down.. what is the term for time speeding up?


Also what is the realistic maximum speed of future spaceship... we know it can't reach 0.999c... so any arguments or theorem that real ship can go only certain top speed (for example 0.5c) which the fastest in any conceivable future?

 

[Vorde]

Has any experiments been done equal to this scenerio where the twin leaving Earth and seeing Earth time dilated.. but when the twin reverses and returns to earth, the Earth speeds up or go in fast motion? If time dilation is slowing down.. what is the term for time speeding up?

In special relativity, there is no 'speeding up of time'. That is: if Person 1 sees the time of person 2 going slow, then no matter what, Person 2 will see Person 1's time going slow too. This may seem counterintuitive and paradoxical, but it's what happens. It comes from the fact that since all inertial frames are equally valid, any 'motion' Frame 1 might see in Frame 2 is interpreted with equal validity as Frame 2 seeing motion in Frame 1.

In General Relativity though, there is a thing called Gravitational Time Dilation. This time dilation has to do either with being near a massive body or undergoing acceleration (the two are equivalent in General Relativity). Unlike Special Relativity's Time Dilation, where both Observers could claim the other Observer's time is moving slower than their own, with Gravitational Time Dilation one Observer would say the other observer's time is moving slower and the other observer would agree.

http://en.wikipedia.org/wiki/Gravitational_time_dilation

 

[Tomahoc]

In special relativity, there is no 'speeding up of time'. That is: if Person 1 sees the time of person 2 going slow, then no matter what, Person 2 will see Person 1's time going slow too. This may seem counterintuitive and paradoxical, but it's what happens. It comes from the fact that since all inertial frames are equally valid, any 'motion' Frame 1 might see in Frame 2 is interpreted with equal validity as Frame 2 seeing motion in Frame 1.

In General Relativity though, there is a thing called Gravitational Time Dilation. This time dilation has to do either with being near a massive body or undergoing acceleration (the two are equivalent in General Relativity). Unlike Special Relativity's Time Dilation, where both Observers could claim the other Observer's time is moving slower than their own, with Gravitational Time Dilation one Observer would say the other observer's time is moving slower and the other observer would agree.

http://en.wikipedia.org/wiki/Gravitational_time_dilation

Hmm.. have you forgotten that when the traveling twin returns to earth.. the Earth twin is older. I read somewhere that when the twin do a reverse and returns to earth.. that's when he would see the Earth twin speeding up. But then... if he would still see the Earth twin as time dilating even when returning. How come when he returns to earth, the Earth twin becomes much older?

 

[Vorde]

Because there is acceleration involved.

If the twin that is traveling away from the Earth turns around at any point then there has to be some acceleration involved and the symmetry of the time dilation is broken. Once the acceleration happens General Relativity's time dilations tell you one will age and one won't (Special Relativity can also tell you this, but in a more complex way).

 

[Tomahoc]

Because there is acceleration involved.

If the twin that is traveling away from the Earth turns around at any point then there has to be some acceleration involved and the symmetry of the time dilation is broken. Once the acceleration happens General Relativity's time dilations tell you one will age and one won't (Special Relativity can also tell you this, but in a more complex way).

So what would the traveling twin who turns around see on earth.. time dilating or speeding? If dilating.. you mean for every slow motion movement of the Earth twin, the Earth twin ages 2 years for example.. that is why when the traveling twin finally lands on earth.. the Earth twin is 50 years older?

 

[Vorde]

Well I could explain it to you, but I'd just say read this: http://en.wikipedia.org/wiki/Twin_paradox

If you have any questions after, feel free to ask.

 

[arindamsinha]

Has any experiments been done equal to this scenerio where the twin leaving Earth and seeing Earth time dilated.. but when the twin reverses and returns to earth, the Earth speeds up or go in fast motion?

No experiment is needed. First of all, a traveling twin will anyway see this even in a Newtonian world. When he is traveling outward, any signals from the Earth-based twin will be red-shifted and give the impression that the Earth-based clock is slower. On return, the opposite Doppler effect will make the Earth clock appear faster. This has nothing to do with relativity.

I believe you are asking this question from the context of the 'twin paradox' resolution in SR.

This is not a correct interpretation/explanation of SR or the twin problem. In SR, the traveling twin is getting the 'relative time dilation' or 'differential aging' (aka time slowdown) throughout his/her journey relative to the stay-at-home twin. It is not as if there is no differential aging when the traveling twin is outbound, but it suddenly starts when he gets inbound. SR does not differentiate between inbound and outbound trajectories.

Instead of the above example, take the traveling twin's trajectory as a large circle starting and ending at Earth, at a constant velocity, with the stationary twin sitting as the diamond in the ring. The initial acceleration, the acceleration throughout the trajectory to maintain a circular path, and the final deceleration are of little importance in SR. Only the constant velocity throughtout the path is held responsible for the slower aging of the traveling twin.

In special relativity, there is no 'speeding up of time'...

That's a little subjective. The traveling twin in the twin paradox will vouch for the fact that Earth's time speeded up during his little space-cruise.

...I read somewhere that when the twin do a reverse and returns to earth.. that's when he would see the Earth twin speeding up...

'Seeing', as based on Doppler effect on signals being exchanged between the two, yes. As I mentioned above, this has nothing to do with relativity, and Newtonian mechanics will predict the same. Throughout the period of travel though, it is the traveling twin's clock which is 'actually' slowing down compared to the Earth based twin's clock, causing a real 'differential aging'. These two are often confused, because this type of argument is used to resolve the twin problem somewhat indiscriminately.

Because there is acceleration involved.

If the twin that is traveling away from the Earth turns around at any point then there has to be some acceleration involved and the symmetry of the time dilation is broken. Once the acceleration happens General Relativity's time dilations tell you one will age and one won't (Special Relativity can also tell you this, but in a more complex way).

The acceleration breaks the symmetry, that is correct. Why the traveling twin ages slower because of that is not really explained in SR. It is something that was only found out in experiments like Hafele-Keating, GPS satellites and confirmed by lab experiments like Bailey et. al.

GR has no role in this. It can perhaps say which of them will age faster or slower during the acceleration, but that period is negligible in this scenario. Why the faster or slower aging will continue after the acceleration is gone, GR does not say. We have to depend on SR and experimental findings for that.

So what would the traveling twin who turns around see on earth.. time dilating or speeding? If dilating.. you mean for every slow motion movement of the Earth twin, the Earth twin ages 2 years for example.. that is why when the traveling twin finally lands on earth.. the Earth twin is 50 years older?

He will 'see' the Earth clock speeding up based on Doppler effect. On the outward journey, he will similarly see the Earth clock slow down, though in fact his clock is actually running slower than the Earth clock. We need to distinguish between what is 'seen' based on signals at speed of light, as opposed to the differential aging that is really happening between the two clocks.

Well I could explain it to you, but I'd just say read this: http://en.wikipedia.org/wiki/Twin_paradox

In this, do not ignore the small section at the bottom on 'Explanation in terms of Mach's principle', just because it is a minority view. Minority views have been proven right at times.

This is not to say I am endorsing or supporting this particular minority view, but we should keep our minds open to the possibility that better explanations than the currently accepted ones may exist for situations like the 'twin paradox'.

 

[ghwellsjr]

Tomahoc, You've gotten a lot of help on this thread so far, but I thought it might also be helpful to you to see some diagrams that I made to illustrate how Time Dilation is different in different Inertial Reference Frames (IRF's) and yet the Relativistic Doppler, what each observer sees of the other ones clock, is the same in all IRF's.

Please see my diagrams on post #9 and on page 5 of this thread:
https://www.physicsforums.com/showthread.php?t=656922