Twin Paradox with a twist

  • #1
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Hi all,


I know the twin paradox has been discussed many times, so I hope you'll bear with me. My version has a slight twist.

Suppose twin's A and B start off in a "rest" frame in dead space, frame F, at x = 0. At t = 0, A moves in the direction x with velocity c/2, and B moves in direction -x with velocity c/2. The numbers are just to remove any ambiguity. At t1, both A and B reverse their directions and head back to x = 0. From A's point of view, B has taken a journey at a relativistic speed more than c/2 and less than c. Therefore, A should expect B to be younger than him after the journey. From B's point of view, A has gone on a "relativistic" journey, and expects that A is the younger.

If tpN is the time passed for N, then

According to A:

tpA > tpF > tpB

According to F:

tpA = tpB < tpB

According to B:

tpB > tpF > tpA


Intuitively, A and B should have aged similarly. So how is this paradox resolved?


thanks,
Aaron
 
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  • #2
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t1 in which frame?
Directly before B reverses, he'll think of A moving away at this point in time. Then he changes his direction - and suddenly the "simultaneous" point happens to be when A is returning already. If you just calculate the time A has on its clock, in the frame of B, you'll suddenly see a jump forwards when B reverses.
This is not a physical jump, of course, it is a consequence of a poor way of time-keeping if you accelerate.

A similar effect: The andromeda galaxy is about 2.5 million light years away. You see events "now" as they happened 2.5 million years ago (in the frame of earth). If you walk towards the galaxy, relativity tells you its distance became one day less. So you see events as they happened (2.5 million years minus one day) ago. You still see the same events as others on earth, of course, but the definition of "now" at that large distance changed significantly.
 
  • #3
Dale
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Intuitively, A and B should have aged similarly. So how is this paradox resolved?
They have indeed aged the same. You can calculate that in any inertial frame using the standard time dilation formula and you will get that answer.

A's frame and B's frame are non inertial so the standard time dilation formula doesn't apply.
 
  • #4
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Thanks for the replies.

Hi mfb, t1 refers to F. At t1 in F, both A and B reverse directions. I'm sorry, but I didn't quite get your point. It sounds like it has to do more with GR than SR, and unfortunately, I haven't reached that part in Einstein's book yet :D I'll come back to your explanation when I do.

Hi DaleSpam, so you're saying that in my example, I can only use the rest frame, F, for my calculations. Can I not simply transform between reference frames based on the instantaneous velocity? i.e. integrate the changes in spacetime?

Alternatively, suppose A and B only experience acceleration for a fraction of the journey. An example of a possible journey would look like this for A wrt F:

1) accelerate in +x direction for 0.1t
2) move at constant velocity, c/2 for 0.3t in +x direction.
3) decelerate for 0.1t, change directions and accelerate in -x direction for 0.1t
4) move at constant velocity c/2 for 0.3t in -x direction.
5) decelerate for 0.1t and stop.

For stages 2 and 4, both A and B are in inertial frames so I should be able to apply the standard time dilation formulas. Furthermore, as we already agreed, during stages 1, 3, and 5, both A and B cover similar distances and ages wrt F.


thanks,
Aaron
 
  • #5
Dale
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Hi DaleSpam, so you're saying that in my example, I can only use the rest frame, F, for my calculations. Can I not simply transform between reference frames based on the instantaneous velocity? i.e. integrate the changes in spacetime?
No, I said:
You can calculate that in any inertial frame
That means any inertial frame whatsoever. F was the only inertial frame that you identified, but there are an infinite number of other inertial frames, all of which would be valid.

I do however mean that you cannot use A's frame nor B's frame, at least not without deriving the correct time dilation formula in their frame. The reason is that those frames are non-inertial so the simplified inertial-frame result does not apply.

Can I not simply transform between reference frames based on the instantaneous velocity? i.e. integrate the changes in spacetime?
The usual approach of doing this runs quickly into some mathematical problems that render it an invalid way of defining a coordinate chart across all spacetime. Most discussions of the twin paradox on this forum contain a discussion of exactly this problem.
 
  • #6
ghwellsjr
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Hi all,


I know the twin paradox has been discussed many times, so I hope you'll bare with me. My version has a slight twist.

Suppose twin's A and B start off in a "rest" frame in dead space, frame F, at x = 0. At t = 0, A moves in the direction x with velocity c/2, and B moves in direction -x with velocity c/2. The numbers are just to remove any ambiguity. At t1, both A and B reverse their directions and head back to x = 0.
As mfb asked, t1 in which frame? We could say it is the Coordinate Time in frame F and that is what I think you mean but A and B will not have any way of knowing when that time occurs. We could also say that they each individually turn around when their own clocks reach a certain Proper Time value which will be that same Coordinate Time for themselves in their individual rest frames up to the point of turn around but it won't be the same Coordinate Time for the other one. I'll show you some spacetime diagrams to illustrate these different times starting with frame F:

TwinsWithTwist1.PNG

A is shown in red, B in black and blue is an observer who remains at rest in F throughout the scenario. The dots represent one-year increments of time. So the Proper Time for A and B when they turn around is 7 in this example and they spend another 7 years getting back so their total age accumulation during their trips is 14 years and they get back to F when he has aged just over 16 years.

From A's point of view, B has taken a journey at a relativistic speed more than c/2 and less than c.
This is only partially true. In A's rest frame up to the point of turn around, B is traveling away from him at 0.8c but B doesn't turn around until some later at which point he comes to rest in that frame:

TwinsWithTwist2.PNG

If we look at A's rest frame after he turns around, we see that B is approaching him at 0.8c but B has already turned around much earlier:

TwinsWithTwist3.PNG

Therefore, A should expect B to be younger than him after the journey.
No, not if he is applying SR correctly. He should expect them to be the same age as we can see from any of the above three Inertial Reference Frames.

From B's point of view, A has gone on a "relativistic" journey, and expects that A is the younger.
B has the same issues that A has and should come to the same conclusions. You can just interchange the last two diagrams to apply everything to B.

If tpN is the time passed for N, then

According to A:

tpA > tpF > tpB
As I have pointed out, this statement is only partially true, that is, it is only true up to the point of A's turn around.

According to F:

tpA = tpB < tpB
I think you meant:

tpA = tpB < tpF

And this is a true statement.

According to B:

tpB > tpF > tpA
Again, this is only partially true, that is, up to the point of B's turn around.

Intuitively, A and B should have aged similarly. So how is this paradox resolved?


thanks,
Aaron
Hopefully, by now, the paradox has been resolved. If not, ask.
 
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  • #7
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Hi DaleSpam,

.
That means any inertial frame whatsoever.

thanks for the clarification, but I did understand what you meant, I was only referring to the reference frames pointed out in my example.

The usual approach of doing this runs quickly into some mathematical problems that render it an invalid way of defining a coordinate chart across all spacetime. Most discussions of the twin paradox on this forum contain a discussion of exactly this problem.

I see. I assume that you are referring to the sudden jump when A turns around and changes its reference frame. Just out of curiosity, has the problem been mathematically resolved?


Hi George,


thank you for taking the time to draw those very informative space-time diagrams. I can see how you worked it out. Based on the diagrams, just before the turn-around point of A (from A's frame), B appears to have a ways to go, but just after A turns around, he sees that not only has B turned around, but B has completed more than half of the return journey. This sudden jump must be what mfb was talking about. What I understood from DaleSpam's post is that trying to treat the problem in the usual way of finding change in x wrt t and then integrating leads to difficulties. So has the problem been resolved mathematically?


thanks,
Aaron
 
  • #8
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I see. I assume that you are referring to the sudden jump when A turns around and changes its reference frame. Just out of curiosity, has the problem been mathematically resolved?
There is no problem, at least not with physics or mathematics - nothing to solve.
It is just a problem of understanding the different reference frames and that things change if you change frames.
 
  • #9
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There is no problem, at least not with physics or mathematics - nothing to solve.
It is just a problem of understanding the different reference frames and that things change if you change frames.

thanks for the reply. What I mean is that if you were to take a gradual deceleration instead of an instantaneous reversal of velocity could you avoid this jump in the reference frames, and has anybody got a simple example of how this is solved mathematically?

Aaron
 
  • #10
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You could record a very fast "advance of the clock of A", but that is an artifact of your calculation that constantly changes inertial frames.
For every point within the acceleration procedure, you can check the spacetime diagram and draw the line of constant time. You can also calculate it, of course. I don't think the result is so interesting.
 
  • #11
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For every point within the acceleration procedure, you can check the spacetime diagram and draw the line of constant time. You can also calculate it, of course. I don't think the result is so interesting.

I understand your point, thanks. My curiosity comes from DaleSpam's comment,

The usual approach of doing this runs quickly into some mathematical problems that render it an invalid way of defining a coordinate chart across all spacetime. Most discussions of the twin paradox on this forum contain a discussion of exactly this problem.

regards,
Aaron
 
  • #12
Dale
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I see. I assume that you are referring to the sudden jump when A turns around and changes its reference frame. Just out of curiosity, has the problem been mathematically resolved?
There are many valid mathematical solutions for defining the reference frame of a non inertial object. The problems with the naive approach do not mean that there is no valid solution. Just that specific approach is flawed.

The other problem is that there is no one standard convention. So saying "the reference frame of X" is ambiguous when X is non inertial. You could mean any one of an infinite number of possible coordinate systems.
 
  • #13
Nugatory
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thanks for the reply. What I mean is that if you were to take a gradual deceleration instead of an instantaneous reversal of velocity could you avoid this jump in the reference frames

No. Either way, there is no inertial frame in which you are at rest during the turnaround.
 
  • #14
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The problems with the naive approach do not mean that there is no valid solution.

Sure, I agree with that. By the naive approach, I assume you mean the approach that most people would initially attempt, and that pointed out by mfb:

For every point within the acceleration procedure, you can check the spacetime diagram and draw the line of constant time.

You could mean any one of an infinite number of possible coordinate systems.

Well, I don't really know what you mean here. I figure that once you define the deceleration in the "rest" frame, then what A sees (i.e. from his frame of reference) is defined, and has only one possibility. I will try the "naive" approach and maybe I'll understand what you mean.

No. Either way, there is no inertial frame in which you are at rest during the turnaround.

Did I understand you correctly and you're saying that, "no, there is no way to avoid the jump in reference frames". So if I were person A, then as I turn around, I would suddenly see B "jump", which implies that for that instant, he would be travelling faster than the speed of light (in my point of view, which I understand is not an inertial frame)? It sounds like there's a lot of information behind your statement which I'm not familiar with, so I'll have to do some more reading.


thanks for the help,
Aaron
 
  • #15
Fredrik
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Well, I don't really know what you mean here. I figure that once you define the deceleration in the "rest" frame, then what A sees (i.e. from his frame of reference) is defined, and has only one possibility.
There's no obviously correct definition of "his frame of reference". If what you mean is a different inertial coordinate system (the momentarily comoving one) at each point on his world line, then what he "sees" as he turns around is that the other guy starts moving and aging much faster than before. This happens because these comoving inertial systems have very different simultaneity lines. In fact, if the turnaround is near instantaneous, the other guy's age will make a huge jump, because A just before the turnaround considers himself simultaneous with an event where the other guy recently left the starting point, and A just after the turnaround considers himself simultaneous with an event where the other guy is soon going to be back to the starting point.

Note that the word "sees" is sometimes used very loosely in these discussions. What an observer "sees" may have nothing to do with the light that hits his eyes, and everything to do with the numbers assigned by the coordinate system(s) that we have chosen to think of as describing his "point of view". For example, when we say that he "sees" two events as simultaneous, it means that the coordinate system that we're associating with his motion at a certain event assigns the same time coordinate to those two events.

Edit: A better option than using the word "see" in this counterintuitive way is to avoid it entirely in these discussions.

Did I understand you correctly and you're saying that, "no, there is no way to avoid the jump in reference frames". So if I were person A, then as I turn around, I would suddenly see B "jump", which implies that for that instant, he would be travelling faster than the speed of light (in my point of view, which I understand is not an inertial frame)? It sounds like there's a lot of information behind your statement which I'm not familiar with, so I'll have to do some more reading.
The concept you need to understand is simultaneity lines in spacetime diagrams.

My favorite introduction to SR is the one in chapters 1-2 in "A first course in general relativity", by Schutz.
 
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  • #16
Nugatory
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then what A sees (i.e. from his frame of reference) is defined, and has only one possibility. I will try the "naive" approach and maybe I'll understand what you mean.
What A sees is always clearly defined and is the same no matter what reference frame you or he choose to use. He's seeing light hitting the retina of his eye, he's seeing the position of the hands of his clocks and the readings on dials of his lab equipment. All of these phenomena are local. The reference frame is just a convention for assigning times to non-local events; for example if light from an event three light-seconds away reaches my eyes at noon, it is natural to say that it happened three seconds ago at 11:59:57 AM. But I didn't actually see it happen at 11:59:57; I received a light signal at noon and assigned the label "11:59:57" to the emission event. An observer moving at a different speed might assign a different label to that event; or he and I could standardize on my labeling scheme (agree to use the frame in which I am at rest and he is not); or we could standardize on his labeling scheme (agree to use the frame on which he is at rest and I am not).

Did I understand you correctly and you're saying that, "no, there is no way to avoid the jump in reference frames".
No. An easy way to avoid the jump is to just use one inertial reference frame throughout the entire thought experiment. Of course the traveller won't be always be at rest in that frame, but that's to be expected because the traveller is changing speed.
So if I were person A, then as I turn around, I would suddenly see B "jump", which implies that for that instant, he would be travelling faster than the speed of light (in my point of view, which I understand is not an inertial frame)?
No, you do not see B jump. What you will see is explained here: http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_doppler.html and it is the same no matter what reference frame (convention for assigning time labels to distant events) you use.
 
  • #17
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Hi all,


thank you both for your patience. I understand the confusion I created by using the word "see". What I meant was what Nugatory explained about assigning a time to a non-local event. I will go ahead and use the word "measure" for this, and the measurement de-embeds the time it takes for light to reach the observers eyes.

If what you mean is a different inertial coordinate system (the momentarily comoving one) at each point on his world line, then what he "sees" as he turns around is that the other guy starts moving and aging much faster than before. This happens because these comoving inertial systems have very different simultaneity lines. In fact, if the turnaround is near instantaneous, the other guy's age will make a huge jump, because A just before the turnaround considers himself simultaneous with an event where the other guy recently left the starting point, and A just after the turnaround considers himself simultaneous with an event where the other guy is soon going to be back to the starting point.

Yes, this is what I meant. So A would "measure" that B has essentially jumped through space-time. This is allowed because A is in a non-inertial frame, and is basically experiencing the shift in his reference frame. i.e. he is not an observer who could believe himself to be in a "rest" frame.

My favorite introduction to SR is the one in chapters 1-2 in "A first course in general relativity", by Schutz.

thank you for the reference.

No. An easy way to avoid the jump is to just use one inertial reference frame throughout the entire thought experiment. Of course the traveller won't be always be at rest in that frame, but that's to be expected because the traveller is changing speed.

I understand that, but I am more interested in observer A's "measurements". I guess the crux of the matter is that being in a non-inertial frame allows A to observe B jumping through space-time. Thanks for the link on the doppler effect.


best regards,
Aaron
 
  • #18
Nugatory
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I understand that, but I am more interested in observer A's "measurements". I guess the crux of the matter is that being in a non-inertial frame allows A to observe B jumping through space-time.

That's still not quite right. What A observes and measures is completely independent of any reference frame, and doesn't lead to B "jumping through space-time" - B is moving through space-time on whatever path he is following and that's unaffected by anything that A does or observes. All that A's acceleration does is make the times that he assigned to events back on earth before he accelerated not match up properly with the times that he assigned to events back on earth after he he accelerates.

Perhaps the most intuitive way of seeing this is to imagine that instead of turning his spaceship around, the traveller grabs his notebook and jumps from his outbound ship onto a ship that conveniently just happens to be travelling in the opposite (inbound) direction at the appropriate speed. When he compares his notes with the logbooks of the second ship and discusses his and his twin's past history with the crew of the second ship, he will find a completely consistent story in which he was ageing less quickly than the stay-at-home twin the whole time. The fact that the traveller's diary doesn't line up well with the ship's logbook just tells us that the two logs were maintained using a different standard of time.
 
  • #19
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B is moving through space-time on whatever path he is following and that's unaffected by anything that A does or observes. All that A's acceleration does is make the times that he assigned to events back on earth before he accelerated not match up properly with the times that he assigned to events back on earth after he he accelerates.

The fact that the traveller's diary doesn't line up well with the ship's logbook just tells us that the two logs were maintained using a different standard of time.



Hi Nugatory,


thank you for the clarification. I do understand of course that B from his own perspective has not leaped through time, however, I don't see exactly where my thinking was wrong. From A's perspective, he really does appear to measure B leap through space-time, however, having experienced acceleration/deceleration, he is aware that there will be an inconsistency in his result. Of course, as you say, when they meet-up back on Earth, they will be able to resolve the puzzle into a consistent story. Feel free to correct me if I have misunderstood the situation.


regards,
Aaron
 
  • #20
Dale
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What I meant was what Nugatory explained about assigning a time to a non-local event.
This is precisely the process that is not uniquely defined for a non inertial observer.

One approach is to take the momentarily co moving inertial frame and use that to assign the time to a non local event. This has several problems, the least of which is the "jump forward" of the home twin's clock.

But that is not the only possibility. Any smooth one to one mapping will work. Here is another common approach. http://arxiv.org/abs/gr-qc/0104077
 
  • #21
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Hi DaleSpam,


so if I understand you correctly, the manner of how to transform coordinate systems in a non-inertial frame of reference can be approached in more than one way, and a general consensus in the scientific community has not yet been reached on which method is best. I'm not sure that I have the mathematical fortitude to follow that paper, but anyway thanks. In fact, some nice person just messaged me a link to a different possible transformation method.


Thank you for your time ( :P ),
Aaron
 
  • #22
Dale
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the manner of how to transform coordinate systems in a non-inertial frame of reference can be approached in more than one way, and a general consensus in the scientific community has not yet been reached on which method is best
Yes, that is essentially correct.
some nice person just messaged me a link to a different possible transformation method.
And there are an infinite number of possible other possible transformation methods besides that and the two I mentioned.
 
  • #23
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This is allowed because A is in a non-inertial frame, and is basically experiencing the shift in his reference frame. i.e. he is not an observer who could believe himself to be in a "rest" frame.
It bothered Einstein that special relativity distinguished between an inertial frame and others. He objected to any effort to "grant a kind of absolute physical reality to non-uniform motion". It's one of the motivations he had for his work in general relativity. He refers to the rotating bucket of water and his dislike of having to say that the bucket is rotating and forcing the water toward the sides, whereas others might say that the bucket is stationary and the universe is spinning around it. With general relativity, we can assume that the universe is spinning around a stationary bucket and pulling the water to the sides. A simplified model of a spinning universe has given surprisingly close results. Likewise, he would say that either twin should be able to consider his reference frame as stationary and the other twin is accelerating, even if that means the entire universe is accelerating with the other twin. With general relativity, the answers are the same assuming either reference frame is "stationary" and there is no conflict at all. Just as a rotating universe would pull water to the sides of a stationary bucket, an accelerating universe with the other twin would cause the "stationary" twin to age slower.
 
  • #24
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It bothered Einstein that special relativity distinguished between an inertial frame and others. With general relativity, the answers are the same assuming either reference frame is "stationary" and there is no conflict at all.

Thanks for the input. I think distinguishing between inertial frames and others would bother anybody who is really thinking about it. I'm only just starting to read about general relativity, but hopefully the answers are there as you say.


best regards,
Aaron
 
  • #25
Fredrik
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You don't need general relativity for this. You just need to consider a larger class of coordinate systems.
 
  • #26
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You don't need general relativity for this. You just need to consider a larger class of coordinate systems.
Without the universe as a reference frame to identify one of the Twins as "accelerating", there is complete symmetry of the twins and they must remain the same age. General relativity is necessary to explain why one Twin should age differently from the other, regardless of which Twin is identified as "accelerating".
 
  • #27
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It bothered Einstein that special relativity distinguished between an inertial frame and others. He objected to any effort to "grant a kind of absolute physical reality to non-uniform motion". It's one of the motivations he had for his work in general relativity. He refers to the rotating bucket of water and his dislike of having to say that the bucket is rotating and forcing the water toward the sides, whereas others might say that the bucket is stationary and the universe is spinning around it. With general relativity, we can assume that the universe is spinning around a stationary bucket and pulling the water to the sides. A simplified model of a spinning universe has given surprisingly close results. Likewise, he would say that either twin should be able to consider his reference frame as stationary and the other twin is accelerating, even if that means the entire universe is accelerating with the other twin. With general relativity, the answers are the same assuming either reference frame is "stationary" and there is no conflict at all. Just as a rotating universe would pull water to the sides of a stationary bucket, an accelerating universe with the other twin would cause the "stationary" twin to age slower.
Einstein's general relativity of motion is nowadays not much supported*, and one reason may be that if taken seriously, it does lead to conflict. See my discussion in an earlier thread on this topic:
https://www.physicsforums.com/threa...paradox-as-paradox.780185/page-7#post-4921049

* See the terms "pseudo" and "not real" as well as "nothing to say about the twin paradox" (contrary to Einstein and your remark), and also the section "What is General Relativity?" in http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_gr.html
 
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  • #28
Dale
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Without the universe as a reference frame to identify one of the Twins as "accelerating", there is complete symmetry of the twins and they must remain the same age. General relativity is necessary to explain why one Twin should age differently from the other, regardless of which Twin is identified as "accelerating".
This is not correct and not consistent with mainstream physics. Regardless of the rest of the universe, the different accelerometer readings make them not symmetric. GR is not necessary to explain this.
 
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  • #29
WannabeNewton
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It bothered Einstein that special relativity distinguished between an inertial frame and others.

Regardless of what Einstein thought, SR distinguishes between inertial frames and accelerating frames to the same extent that GR distinguishes between locally inertial frames and accelerated frames. There are no preferred frames in SR. One can use accelerated frames throughout their study of SR if they wished.

It's one of the motivations he had for his work in general relativity.

In GR accelerated and rotational motions are absolute so that wasn't so much achieved.

With general relativity, we can assume that the universe is spinning around a stationary bucket and pulling the water to the sides.

In SR/GR you can have spinning bodies in flat space-time wherein there is no matter content at all. As there is no matter content at all available to constitute a rotating universe in which the bucket is stationary, the Machian interpretation you refer to fails in GR. GR is for the most part non-Machian so you have a misconception of the theory.


A simplified model of a spinning universe has given surprisingly close results.

Reference?

Also this is highly off-topic as I see nothing in your post that even remotely addresses the OP's concerns. This is just the same old song of "GR is needed to explain the twin paradox" which is wrong as others have pointed out. Many SR textbooks address this problem.
 
  • #30
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Thanks for the input. I think distinguishing between inertial frames and others would bother anybody who is really thinking about it. I'm only just starting to read about general relativity, but hopefully the answers are there as you say.
Don't get me wrong. Although general relativity is necessary for understanding the difference between inertial and non-inertial reference frames, it is completely impractical for getting answers to problems like the Twins Paradox. It is more practical to use the methods that everyone is describing here. Einstein's book "Relativity, The Special and the General Theory" is a good description of what he was thinking, what motivated his work, and why he worked so long and hard on the general theory.
 
  • #31
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This is not correct and not consistent with mainstream physics. Regardless of the rest of the universe, the different accelerometer readings make them not symmetric. GR is not necessary to explain this.
That surprises me. Without using objects external to a reference frame, how does one define acceleration of the entire reference frame? Isn't acceleration, velocity, and position all relative to something else? Then, without referring to the universe, how can inertia and the forces due to acceleration be explained? In other words, I don't see how to explain accelerometer readings other than by saying that an object is accelerating relative to the universe. I do know that there have been calculations done where the universe (a simplified model) was assumed to be spinning around a stationary bucket and the GR calculations said that the water would be pulled outward with the (approximately) correct force. Should I start a different thread for this? I don't want to hijack the thread.
 
  • #32
Fredrik
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general relativity is necessary for understanding the difference between inertial and non-inertial reference frames,
I disagree. The difference between SR and GR is that the metric in GR is a solution to Einstein's equation, and the metric in SR is the Minkowski metric, regardless of the matter content of spacetime.

Without using objects external to a reference frame, how does one define acceleration of the entire reference frame? Isn't acceleration, velocity, and position all relative to something else?
In the purely mathematical part of the theory, proper acceleration is defined as a measure of how much the world line deviates from being a geodesic. The physics is however in the correspondence rules, which tell us how to interpret the mathematics as predictions about results of experiments. They tell us in particular that the motion of an accelerometer that doesn't detect any acceleration is represented by a timelike geodesic.

Then, without referring to the universe, how can inertia and the forces due to acceleration be explained? In other words, I don't see how to explain accelerometer readings other than by saying that an object is accelerating relative to the universe.
It's quite possible that if the universe had been empty except for one accelerometer, that accelerometer would have to detect zero acceleration. But this is philosophical speculation of little value. It seems especially wrong to use it to argue against using SR in a scenario in which there are rockets, which by definition utilize the law of inertia to accelerate.
 
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  • #33
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Regardless of what Einstein thought, SR distinguishes between inertial frames and accelerating frames to the same extent that GR distinguishes between locally inertial frames and accelerated frames. There are no preferred frames in SR. One can use accelerated frames throughout their study of SR if they wished.
It seems that it's not so much a question of distinguishing between inertial and accelerated frames as it is a question of objectively identifying which is which. How can that be done without referring to the universe and the associated space? SR takes that for granted and assumes that it is obvious which twin is accelerating. GR explains why the twin which is stationary wrt the universe is not the same as the twin that accelerates wrt the universe. Without that, the Twins are perfectly symmetric.
Reference?
(regarding the calculations of centrifugal force in a stationary bucket with a spinning universe): I read it several years ago and do not remember where.
Also this is highly off-topic as I see nothing in your post that even remotely addresses the OP's concerns.
He liked my reply. That's all I know.
This is just the same old song of "GR is needed to explain the twin paradox" which is wrong as others have pointed out. Many SR textbooks address this problem.
Do they answer the question of what causes one twin to feel acceleration and to be considered the accelerating twin? That seems like a GR subject. Without that, the Twins are symmetric.
 
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It seems that it's not so much a question of distinguishing between inertial and accelerated frames as it is a question of objectively identifying which is which. How can that be done without referring to the universe and the associated space? SR takes that for granted and assumes that it is obvious which twin is accelerating.
SR relies on accelerometers, just like GR.

Do they answer the question of what causes one twin to feel acceleration and to be considered the accelerating twin? That seems like a GR subject. Without that, the Twins are symmetric.
A theory doesn't have to explain everything to be applicable. It just has to make some relevant predictions.

(I have to get some sleep, so I won't be able to discuss any of this further right now).
 
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Although general relativity is necessary for understanding the difference between inertial and non-inertial reference frames....

That is just plain wrong. Special relativity works fine for both inertial and non-inertial reference frames (as it must, because the one is merely a coordinate transform away from the other) in the absence of gravity. General relativity works for this case and also for the more general case in which gravity is present.
 

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