New understanding of relativity - twin paradox resolved.

Chumly wrote:

Can both twins discover that B has aged more than A if the speed differential is only 100 MPH?

Not likely, but please answer my question regarding relativistic speeds.

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I'm probably somewhat confused on this!

What you're saying is that unless or until the speed deferential becomes non-relativistic, both twins would perceive the other to have slowed down in time?

I don't know why the TT would be the odd man out except that he is returning to the non-relativistic world, and the other twin never left it?

So if the earth sped up to catch up with the TT, as opposed to the TT slowing down to meet the TOE, then there would be no relativistic time dilation within the confines of the earth and the TT?

What happens to the time dilation effect if both the TOE and TT are traveling at 75% C in opposite directions (besides red shift)?

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Chumly wrote:

Can both twins discover that B has aged more than A if the speed differential is only 100 MPH?

Yes. The important point is that traveller `feels' acceleration or gravity acting on his mass (both of which is the same according to the general theory of relativity). The speed isn't important. You can think of a clock on Earth and another one on a space station outside the Earth's gravity field. Although both clocks are resting, the clock on Earth runs slower because it, unlike the one in space, `feels' the Earth's gravity acting on it.

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Chumly wrote:

I'm probably somewhat confused on this!

What you're saying is that unless or until the speed deferential becomes non-relativistic, both twins would perceive the other to have slowed down in time?

I don't know why the TT would be the odd man out except that he is returning to the non-relativistic world, and the other twin never left it?

So if the earth sped up to catch up with the TT, as opposed to the TT slowing down to meet the TOE, then there would be no relativistic time dilation within the confines of the earth and the TT?

Each twin obeserves the other to have a clock running slowly, and each is equally correct, but the reason why the final result is not symmetrical, why it's twin A and not twin B who ages less, has to do with the fact that twin A is in non-inertial reference frames when he turns around to come back (undergoes accelerated motion).

Chumly wrote:

What happens to the time dilation effect if both the TOE and TT are traveling at 75% C in opposite directions (besides red shift)?

Let me re-state your question slightly. Some third observer who does not undergo accelerated motion, perhaps a planet bound one, observes two twins to enter space ships and travel in opposite directions - each at 75% the speed of light. According to this third observer, their relative speed is 150% of the speed of light (by definition). But each twin observes the other twin to separate from him at 96% of the speed of light. If both travel away from the Earth for the same amount of time, and then turn around and come back in about the same manner, they will both have aged the same amount, which will be less than the third observer.

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Thomas wrote:

Chumly wrote:
Can both twins discover that B has aged more than A if the speed differential is only 100 MPH?

Yes. The important point is that traveller `feels' acceleration or gravity acting on his mass (both of which is the same according to the general theory of relativity). The speed isn't important. You can think of a clock on Earth and another one on a space station outside the Earth's gravity field. Although both clocks are resting, the clock on Earth runs slower because it, unlike the one in space, `feels' the Earth's gravity acting on it.

Sorry, but no. In the twin paradox, the time dilation effect is a result of the motion, not the relatively mild gravitational field difference. Particles in an accelerator on Earth also experience considerable time dilation despite the fact that they are remaining in the Earth's gravitational field. Einstein described the effect of motion on time in his special theory of relativity. He described the effect of gravity on time in his general theory of relativity.

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Brandon9000 wrote:

Sorry, but no. In the twin paradox, the time dilation effect is a result of the motion, not the relatively mild gravitational field difference.

We have no disagreement. I wasn't directly talking about the twin paradox in the part you are criticizing. Instead, I was presenting the clock-on-Earth-vs-clock-in-Space case as an analogy to the twin paradox. In both cases, the clock runs slower where it feels a force -- gravity or acceleration -- acting on its mass.

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Brandon9000 wrote:

Chumly wrote:
What happens to the time dilation effect if both the TOE and TT are traveling at 75% C in opposite directions (besides red shift)?
Let me re-state your question slightly. Some third observer who does not undergo accelerated motion, perhaps a planet bound one, observes two twins to enter space ships and travel in opposite directions - each at 75% the speed of light. According to this third observer, their relative speed is 150% of the speed of light (by definition). But each twin observes the other twin to separate from him at 96% of the speed of light. If both travel away from the Earth for the same amount of time, and then turn around and come back in about the same manner, they will both have aged the same amount, which will be less than the third observer.

Why 96%?

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Chumly wrote:

Brandon9000 wrote:
Chumly wrote:
What happens to the time dilation effect if both the TOE and TT are traveling at 75% C in opposite directions (besides red shift)?
Let me re-state your question slightly. Some third observer who does not undergo accelerated motion, perhaps a planet bound one, observes two twins to enter space ships and travel in opposite directions - each at 75% the speed of light. According to this third observer, their relative speed is 150% of the speed of light (by definition). But each twin observes the other twin to separate from him at 96% of the speed of light. If both travel away from the Earth for the same amount of time, and then turn around and come back in about the same manner, they will both have aged the same amount, which will be less than the third observer.
Why 96%?

I used the relativistic velocity addition formula.

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OK, thanks guys!

http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html

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Brandon9000 wrote:

Why do both twins discover that B has aged more than A? Since "travelling at a high speed" is relative, and the twin who remains at home could be equally accused of "travelling at a high speed," what is it that determines which twin will ultimately be observed to have aged less, and which to have aged more?

While the "felt an acceleration" explanation of B's greater aging is valid, it is certainly not the simplest choice for understanding the paradox. There are a number of approaches but I like THIS mercifully-brief explanation the best. It resolves the twin paradox without the need for accelerations at all ..and it doesn't resort to complex math or General Relativity. It uses only the simplest most basic Lorentz Transformation to arrive at resolution.

The thing that everyone habitually overlooks is that time dilation and length contraction are merely two of the three distortions attendant to Special Relativity. The overlooked 3rd factor is the UNsimultaneity of spatially-separated clocks along an observed moving frame. Once this gets figured in, clarity dawns -- hopefully.

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New understanding of relativity - twin paradox resolved.

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