question re Einsteins theory of relativity

[nicktallguy]

I'm a non science graduate and trying to understand Einstein's theories as a beginner.

In the relativity theory, as I understand it, if a person went on a trip to space in a rocket that travelled close to the speed of light, when they returned to earth they would appear younger in relation to any observers, who in turn would have aged more. But what I don't get, is that you could look at it as though the earth was moving away from the space traveller at the same speed (relative velocities) - so who is really moving away from whom, and why does the space traveller age slower and not the observers in earth ?

[mathematic]

The basic explanation is that the rocket ship traveler had to stop and turn around to get back to earth. The situation is not symmetric.

[Janus]

This is a common question from people first learning about the theory. The trick is that in order for the two people to separate and then come back together, at least one of them has to accelerate at the point of their maximum separation in order to bring them back together again. In the example you give, it is the person in rocket who does this so they can meet up again, and this is what decides who ends up being older than who when they meet up again. There is a lot more going on as far as our Friend in the Rocket is concerned than just the fact that Earth is moving relative to him and thus its clock should run slow.

 

For one thing, he measures the distance of maximum separation at the point of turn around as being less than the person on the Earth does. So for example, if the distance is 1 light year as measured by the Earth, and he is moving at 0.8c relative to the Earth, then he measures the distance as being only 0.6 light years. Thus for the Earth his round trip takes 2/0.8 = 2.5 years and for him it only takes 1.2/0.8 = 1.5 years. There is another effect known as the Relativity of Simultaneity that helps to explain why he agrees that 2.5 years has passed on the Earth (even though, for parts of the trip, he concludes that the Earth clock ran slow compared to his).

[Tim88]

[..] what I don't get, is that you could look at it as though the earth was moving away from the space traveller at the same speed (relative velocities) - so who is really moving away from whom, and why does the space traveller age slower and not the observers in earth ?

 

Elaborating on the asymmetry: physically it is not the same if the traveler turns around, or if the Earth turns around. That explains that the situation is not symmetrical.

For the standard Lorentz equations to be valid, one must relate them to a reference system that does not change velocity, a so-called "inertial reference system" as also used for classical physics. Then it's the other system that will clock "less time"; simply put, it has been "more in motion" according to all inertial reference systems.

 

Of course, that explanation suffices for the calculation but does not explain the deeper "why", as in "what is really going on". For our intellectual satisfaction and in order to make sense of it, one can imagine models for what may be going on "under the hood". Historically there have been two models that explained the deeper "why" (thus going "beyond" the experimental physics), as discussed in detail in the appropriate forum.

PS welcome to the forum nicktallguy

[AbstractDreamer]

What if the rocket trip is circular with most of the trip over flat Euclidean space.

And the Earth is instead an observer just outside the event horizon of a relatively small black hole subject to huge gravitational time dilation?

[Sriman Dutta]

This is a common question from people first learning about the theory. The trick is that in order for the two people to separate and then come back together, at least one of them has to accelerate at the point of their maximum separation in order to bring them back together again. In the example you give, it is the person in rocket who does this so they can meet up again, and this is what decides who ends up being older than who when they meet up again. There is a lot more going on as far as our Friend in the Rocket is concerned than just the fact that Earth is moving relative to him and thus its clock should run slow.

 

For one thing, he measures the distance of maximum separation at the point of turn around as being less than the person on the Earth does. So for example, if the distance is 1 light year as measured by the Earth, and he is moving at 0.8c relative to the Earth, then he measures the distance as being only 0.6 light years. Thus for the Earth his round trip takes 2/0.8 = 2.5 years and for him it only takes 1.2/0.8 = 1.5 years. There is another effect known as the Relativity of Simultaneity that helps to explain why he agrees that 2.5 years has passed on the Earth (even though, for parts of the trip, he concludes that the Earth clock ran slow compared to his).

 

Hi Janus, as far as I can interpret your calculations, it is based on the formula-

[math] d' = d\gamma [/math]

where d' is the distance measured by the spaceman ans d is the distance measured by the earth-man and [math]\gamma[/math] is the Lorentz factor.

Edited December 9, 2016 by Sriman Dutta

[Mordred]

Up to a point, those transforms you posted are no longer accurate when Janus described any dynamic where it is an acceleration. Which includes change in magnitude and direction. Once you undergo acceleration you must reestablish simultaneity under a different transform (synchronization) which will follow a hypola curve. The twin that undergoes (rapidity=acceleration) is the inertial twin (not at rest).