B Is Time Dilation Explained by Special Relativity, General Relativity, or Both?

[vanhees71]

Sorry, but I don't know the math and can't follow it. So, at this point I'm trying only to understand the concept, not the mathematical formulas used to derive precise predictable quantities.
The muons in above example are accelerating (exposed to g force). So their dilation is due to time dilation as described by GR.

That's the wrong approach. You have to learn the math first. You cannot even talk about physics without this math. Of course, muons are accelerated due to gravity of the Earth, but you can safely neglect the effects of gravity of the Earth in HEP physics. It's way too weak to have an important impact on the particles.

Of course, there are exceptions to this rule, as the beautiful example of the measurement of the energy levels of neutrons in the gravitational potential of the Earth (note that this is in the Newtonian approximation) above a reflecting surface, but that's of course physics of ultra-low energetic neutrons. Here is a diploma thesis on the subject:

http://www.pi.uni-hd.de/Publications/dipl_krantz.pdf

 

[Dale]

The odometer analogy doesn't work for me, it introduces a measurement of distance not time.

That is precisely the point. A measurement of time is a measurement of a kind of distance in spacetime, called the spacetime interval. Distance in normal Euclidean space is $ds^2=dx^2+dy^2+dz^2$ and the spacetime interval is $ds^2=-dt^2+dx^2+dy^2+dz^2$ so it is a distance in a spacetime with one timelike dimension and three spacelike dimensions.

The odometer analogy is intended to help you understand geometry in spacetime using mental experiences that you already have with geometry in space. You do yourself a great disservice by skipping it. It is one of the most powerful mental tools you have available.

 

[Dale]

assume that the size of the universe is small and has periodic boundaries

Note that this assumption violates the principle of relativity. The geometry is called a four-torus. A four-torus may be locally flat, but there exists a preferred reference frame globally.

 

[1977ub]

No, it can't be explained without acceleration/deceleration because they can't separate or meet again without acceleration/deceleration.

If a twin can be understood to be an AI and its history can be transferred electronically between closely passing ships, then the outgoing twin has his history transferred to an incoming ship without deceleration per se. Then when the incoming ship returns home, his history is transferred to a computer at home without deceleration per se.

 

[PeroK]

If a twin can be understood to be an AI and its history can be transferred electronically between closely passing ships, then the outgoing twin has his history transferred to an incoming ship without deceleration per se. Then when the incoming ship returns home, his history is transferred to a computer at home without deceleration per se.

That's a neat idea. Slightly less fancifully you could transfer the clock reading to an identical clock moving in the opposite direction and thus measure the proper time of the out and return journeys without a physical turn around.

 

[russ_watters]

If a twin can be understood to be an AI and its history can be transferred electronically between closely passing ships, then the outgoing twin has his history transferred to an incoming ship without deceleration per se. Then when the incoming ship returns home, his history is transferred to a computer at home without deceleration per se.

How did the "outgoing" twin come be "outgoing"?

 

[1977ub]

How did the "outgoing" twin come be "outgoing"?

The initial outgoing ship was accelerated to speed before t=0 and then the AI was transferred from home to the passing ship at t=0

 

[Arkalius]

If a twin can be understood to be an AI and its history can be transferred electronically between closely passing ships, then the outgoing twin has his history transferred to an incoming ship without deceleration per se. Then when the incoming ship returns home, his history is transferred to a computer at home without deceleration per se.

I like this way of subverting the acceleration requirement, but everything still works out. The AI "twin" that arrives on Earth still did not occupy a single inertial reference frame, whereas the one on Earth did. This is actually a good way of illustrating why the acceleration itself is not what is important, but the fact that one twin did not occupy a single inertial reference frame while the other did.

 

[PAllen]

I like this way of subverting the acceleration requirement, but everything still works out. The AI "twin" that arrives on Earth still did not occupy a single inertial reference frame, whereas the one on Earth did. This is actually a good way of illustrating why the acceleration itself is not what is important, but the fact that one twin did not occupy a single inertial reference frame while the other did.

Or even more simply, that time was not accumulated over a single inertial path; this statement does not even need to mention frames.