TRAVELLING TWINS

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What happens if time dilation/contraction that takes place when the travelling twin (1)first accelerates (2)travels at constant speed for some time. (3)then decelerates and makes his speed zero (4)changes direction and accelerates till he gets the speed (5)travels back for some time towards the stationary twin (6)then decelerates in such a way so that he comes to rest at the same point where the stationary twin.
HAS ANY BODY ATTEMPTED TO COMPUTE IN THE ABOVE MANNER USING GENERAL THEORY OF RELATIVITY ALSO ? IF SO WHAT IS THE RESULT?

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Type: Question • Score: 7 • Views: 3,592 • Replies: 66

[+3] - rosborne979 - 04/28/2015Perhaps I misunderstood the question. But my main point was that changing direction and re-accelerating back where you came from isn't going to negate the effects of the time dilation. My apologies...

@CD MURTY,

I doubt whether "change in direction" has any significance, since either leg can be considered a separate event.

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@CD MURTY,

Speeding up and slowing down doesn't change the end result. Likewise, where the object ends up doesn't matter either. There is nothing relevant to calculate in the scenario you propose.

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@rosborne979,

Quote:

Speeding up and slowing down doesn't change the end result. Likewise, where the object ends up doesn't matter either. There is nothing relevant to calculate in the scenario you propose.

I agree with everything you said here, but this is not a novel sequence he's proposing. It is, in fact the standard "twin scenario."

He's asking how GR would treat this, that's all. The standard analysis is given for Minkowskian "flat" spacetime. I can't really answer the question, because I don't know enough about GR [although I understand that it adopts an "absolute" (as opposed to relative) approach to time dilation; that the speed of light is NOT constant in GR, and that there are other major differences between SR and GR].

That said, Einstein would never comment on the "twin paradox" until AFTER he had developed GR. When he did comment, he indicated that all the prior "resolutions" were unsatisfactory. He tried to explain it with GR by invoking "fictitious gravitational fields" which came and went in an implausible and arbitrary manner. His explanation is generally disregarded these days, from what I gather.

What follows are excerpts from commentary by a contempory physicist on Einstein's "equivalence principle analysis of the twin scenario:

Quote:

The Equivalence Principle analysis of the twin paradox simply views the scenario from the frame in which Stella is at rest the whole time. This is not an inertial frame; it's accelerated, so the mathematics is harder. But it can certainly be done. When the mathematics is described fully, what results is that we can treat a uniformly accelerated frame as if it were an inertial frame with the addition of a "uniform pseudo gravitational field". By a "pseudo gravitational field", we mean an apparent field (not a real gravitational field) that acts on all objects proportionately to their mass; by "uniform" we mean that the force felt by each object is independent of its position. This is the basic content of the Equivalence Principle.

The Equivalence Principle analysis of the twin paradox does not use any real gravity, and so does not use any General Relativity. (General Relativity is the study of real gravitational fields, not pseudo ones, so it has nothing to say about the twin paradox.) Nevertheless, what General Relativity does say about real gravitational fields does hold in a restricted sense for pseudo gravitational fields. The one thing we need here is that time runs slower as you descend into the potential well of a pseudo force field. We can use that fact to our advantage when analysing the twin paradox. But it needs to be emphasised that we are not using any actual General Relativity here, and no one ever needs to, to analyse the paradox. We are simply grabbing a result about real gravitational fields from General Relativity, because we know (from other work) that it does apply to a pseudo gravitational field.

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

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@CD MURTY,

CD MURTY wrote:

What happens if time dilation/contraction that takes place when the travelling twin (1)first accelerates (2)travels at constant speed for some time. (3)then decelerates and makes his speed zero (4)changes direction and accelerates till he gets the speed (5)travels back for some time towards the stationary twin (6)then decelerates in such a way so that he comes to rest at the same point where the stationary twin.

The stationary twin probably asks his sibling how he managed to do all that accelerating and **** and why he can't do it. Mother must have had her favourite after all.

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@layman,

Your question was:

Quote:

HAS ANY BODY ATTEMPTED TO COMPUTE IN THE ABOVE MANNER USING GENERAL THEORY OF RELATIVITY ALSO ? IF SO WHAT IS THE RESULT?

The quotation above seems to answer that question, more or less:

Quote:

General Relativity is the study of real gravitational fields, not pseudo ones, so it has nothing to say about the twin paradox.... it needs to be emphasised that we are not using any actual General Relativity here, and no one ever needs to, to analyse the paradox.

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@layman,

I find this concept a little difficult to swallow:

Quote:

The Equivalence Principle analysis of the twin paradox simply views the scenario from the frame in which Stella is at rest the whole time. This is not an inertial frame; it's accelerated...

How can a person be "at rest the whole time," while also being "accelerated?"

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@CD MURTY,

The answer is yes people have calculated this... in fact anyone with a Physics degree has calculated this. Any college student taking a course in Relativity makes exactly this calculation. The effect has also been measured in the laboratory (where there are two identical particles and one experiences more "time" than the other).

The answer is fairly straightforward. The wikipedia article does a pretty good job providing a layman's explanation. Because one particle undergoes acceleration and the other one doesn't we are talking about more than one inertial frame. There is no symmetry.

There is no contradiction here. The math works and laboratory experiments with particles confirm that it is correct.

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@maxdancona,

To answer a couple of the responses here... yes the twin paradox can not happen without acceleration. A change in direction is an acceleration. The change in direction is relevant, especially since it brings the twins together again so they can be compared with being separated by long distances.

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@maxdancona,

Quote:

There is no contradiction here

No contradiction between what and what else? What "contradiction" would you even be talking about?

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@maxdancona,

Rosborne said:

Quote:

Speeding up and slowing down doesn't change the end result.

He's right about this. If you doubt it, look up the "clock hypothesis," at wiki.

You say:

Quote:

The change in direction is relevant

In what way is it relevant?

Rosborne said:

Quote:

Likewise, where the object ends up doesn't matter either.

You say:

Quote:

since it brings the twins together again so they can be compared with being separated by long distances

.

In what way is any aspect of SR, and the predictions it makes, dependent upon comparing clocks side by side? Does SR hold that predictions it makes regarding time dilation are accurate if, AND ONLY IF, two clocks can be directly compared?

I don't think so. I agree with Rosborne.

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@layman,

Did you notice that I said that this is a calculation done by college students?

There is reason I pointed it out. The calculations are all in the open, you go step by step... but you need a certain level of proficiency in math before you can do the math for special relativity. I first studied this in my third year of university after having studied linear algebra and partial differential equations.

You can sit and make uneducated guesses when you don't know what you are talking about, but your guesses are just guesses.

You are criticizing something that you haven't taken the time to learn about. That is just nonsense.

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@maxdancona,

Heh, Max, quite typical of your inability to answer simple questions.

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@layman,

$http://upload.wikimedia.org/math/e/b/0/eb0b3c344785188dd653604826382950.png$

http://simple.wikipedia.org/wiki/Lorentz_factor

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Perhaps I misunderstood the question. But my main point was that changing direction and re-accelerating back where you came from isn't going to negate the effects of the time dilation. My apologies if that wasn't what was implied in the original question.

Likewise, nothing is going to change simply by recalculating with GR instead of SR because GR is just a special case of SR, so they are going to produce the same result unless there is an underlying error in the math (which nobody has ever found). I'm sure students have recalculated using GR instead of SR, but that's the epitome of an academic exercise.

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A quick question. How many people on this thread have taken at least one college level course on relativity?

Education is a good thing. You really can't understand relativity without it. You can listen to people describe it in layman's terms, and you can try to understand what they are saying... but without learning and doing the math for yourself, you don't have a chance of having a true understanding.

This knowledge is accessible everyone... if they are willing to do the work to gain it.

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@maxdancona,

I haven't had even a shred of professional instruction in this area, so my understanding could be (and probably is) inaccurate to some degree.

But I'm open to adjusting my understanding if things can be explained without requiring me to take too much time out of my day (still need to work to pay the bills).

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@maxdancona,

Quote:

...but without learning and doing the math for yourself, you don't have a chance of having a true understanding

.

"True understanding?" Heh, that's truly laughable. You think that mechanically running formulas through your calculator gives you a "true understanding?" You have previously demonstrated that you have virtually no understanding of the CONCEPTS which underlie SR. Math can tell you NOTHING about those, I'm afraid. Perhaps you should take a class or two in the philosophy of science and get some inkling of just how much you don't know.

The whole "twin paradox" issue, for example, has nothing at all to do with the math, per se. You can't even answer a simple question about what "contradiction" you even think you are referring to when you announce that "there is no contradiction." Here's a hint, though: It has nothing to do with any claimed mathematical contradiction.

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@layman,

Quote:

You think that mechanically running formulas through your calculator gives you a "true understanding?"

No. I think that taking the time to get an education, to study to gain understanding gives an understanding.

You want to be a physicist without doing any of hard work or training it requires to be a physicist. Do you do this with any other fields? Do you have any comments on how Yo Yo Ma plays the cello all wrong in spite of the fact that he has done a lot more work learning the cello than you? Do you think you should be able to step into the ring with Mayweather on Saturday even though it is Pacquiao who has done the hard work and training to earn that right?

The idea that you can become an expert without any training or study is ridiculous. I am sorry that you feel offended by that.

You doing physics is like me standing behind center to lead a scoring drive in the NFL. I have no problem admitting that I completely unprepared for that.... I don't have the skill or the training. Tom Brady has done a lot more work than I have to be an expert quarterback. I have no problem admitting that if I tried to be a quarterback, I would just make a complete fool of myself.

If you want to understand physics, take the time and effort required to gain an understanding of physics. Pretending to understand physics without having put in the effort is just foolish.

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@CD MURTY,

There can be no such thing as a stationary twin, for a start. The best you could get in relativity is a twin that's not accelerated. E.g. if that twin remains on planet earth, as one would expect, how would he be stationary??? The earth is not stationary.

Long story short, what you describe can be calculated or rather estimated with general relativity equations, if the twins' respective trajectories are simple enough.

1 Reply

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