Understanding Einstein's Twin Paradox, past the usual level?

[physicsdude30]

I heard some scientists say special relativity may not be relative to your frame of reference, but rather possibly distant galaxies or great sources of gravity?

I heard they sent a jet around the world with an atomic clock, and also decaying sub atomic particles down a tube, to test special relativity. Have they done any tests to see if it's really related to one's frame of reference, like the Twin Paradox tells us? Or could time/space rather be relative to distant galaxies or large sources of gravity?

Is anyone familar with this?

 

[Dale]

Have they done any tests to see if it's really related to one's frame of reference, like the Twin Paradox tells us?

Here are some http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#Twin_paradox"

 

[HallsofIvy]

I heard some scientists say special relativity may not be relative to your frame of reference, but rather possibly distant galaxies or great sources of gravity?

I've never heard or read of any scientists saying such a thing. In fact, it seems to contradict the very basis of relativity. Can you give a citation?

I heard they sent a jet around the world with an atomic clock, and also decaying sub atomic particles down a tube, to test special relativity. Have they done any tests to see if it's really related to one's frame of reference, like the Twin Paradox tells us? Or could time/space rather be relative to distant galaxies or large sources of gravity?

Is anyone familar with this?

I have no idea what being "relative to distant galaxies or large sources of gravity" could mean! Are you clear on what the word "relative" itself means?

 

[physicsdude30]

I've never heard or read of any scientists saying such a thing. In fact, it seems to contradict the very basis of relativity. Can you give a citation?


I have no idea what being "relative to distant galaxies or large sources of gravity" could mean! Are you clear on what the word "relative" itself means?

My source is from ScienceDaily


Professor Resolves Einstein's Twin Paradox
ScienceDaily (Feb. 15, 2007)
http://www.sciencedaily.com/releases/2007/02/070214220824.htm

The fact that time slows down on moving objects has been documented and verified over the years through repeated experimentation. But, in the previous scenario, the paradox is that the earthbound twin is the one who would be considered to be in motion -- in relation to the sibling -- and therefore should be the one aging more slowly. Einstein and other scientists have attempted to resolve this problem before, but none of the formulas they presented proved satisfactory. Kak's findings were published online in the International Journal of Theoretical Science, and will appear in the upcoming print version of the publication. "I solved the paradox by incorporating a new principle within the relativity framework that defines motion not in relation to individual objects, such as the two twins with respect to each other, but in relation to distant stars," said Kak. Using probabilistic relationships, Kak's solution assumes that the universe has the same general properties no matter where one might be within it.

So I'm curious if there's a way we could empirically test this relative to distant stars rather than individual bodies of matter by sending a super fast jet across the world (calculate special relativity after accounting for general relativity) similar to past experiments? The jet would be moving faster in frame of reference to distant stars compared to the Earth's surface (even if both are moving extremely fast in reference to the stars). So as a logical consequence, what if in addition to seeing what the jet's clock is to the one on the ground, could there be some way to have a researcher from another frame of reference check the clocks the other way around? Would there be a way to find calculations for that to make the idea proposed in that article falsifiable?

I think critical thinking with experiments is fun.

 

[PeterDonis]

This statement in the article:

Einstein and other scientists have attempted to resolve this problem before, but none of the formulas they presented proved satisfactory.

is not only false, it's egregiously false. As the Usenet Physics FAQ page linked to earlier shows, the Hafele-Keating experiment that tested the twin paradox directly, by flying atomic clocks around the world and then bringing them back together with clocks that had remained Earth-bound, was performed in 1972. And that experiment just confirmed what every sane physicist in the field expected to happen, and had expected for decades. As the http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html" states,

the "paradox" has been no more than an entertaining (and educational) exercise since it first saw the light of day.

I've read a few articles on Science Daily before and gotten a feeling that they weren't quite all there, without being able to pin it down. Now I *know* they're out to lunch.

 

[PeterDonis]

I just looked on arxiv.org and found http://arxiv.org/abs/physics/0605199" by Subhash Kak, the physicist referred to in the Science Daily article. I don't know if it's a preprint of the same paper the article refers to, but the subject seems similar. The abstract reads:

We show how the anisotropy resulting from the motion of an observer in an isotropic universe may be determined by measurements. This provides a means to identify inertial frames, yielding a simple resolution to the twins paradox of relativity theory. We propose that isotropy is a requirement for a frame to be inertial; this makes it possible to relate motion to the large scale structure of the universe.

 

[sylas]

Yes, I am familiar with this episode. I looked at in a bit of detail when it first came out. Most of this post is summarized from stuff I wrote at the time in another forum.

In brief, you're right PeterDonis. There's no "past the usual level" here; this is all no different from the errors of any beginner.

The twin "paradox" is a simple undergraduate level issue. It's a basic exercise that should be solved by a first year undergraduate at the start of the introductions to special relativity.

The author of the paper cited here is not a professor of physics. He is Subhash Kak, a professor of Electrical Engineering, and also Asian Studies. He's best known for work in computer science, like quantum computing and cryptography, and has an interest in philosophy of science also; but he doesn't understand relativity.

He's actually managed to publish this tripe. There's a copy at arxiv: Moving Observers in an Isotropic Universe, and it got into International Journal of Theoretical Physics, vol. 46, pp. 1424-1430, (2007). This prompted the press release, which got picked up by sciencedaily.

The paper mangles basic first year level relativity, and the only real question is how on Earth it got past the first level of review. Bad papers do get published from time to time. This is one such time.

In the text, Kak cites Unnikrishnan, another obscure writer who makes the same errors. Unlike Kak, Unnikrishnan does appear to be a physicist. Curiously, his understanding of relativity is no better; and being more technical his paper contains even more blatant outright errors in the details, where Kak is more inclined simply to waffle. I'm not going to attempt a critique of Unnikrishnan here; but there is one additional point that leapt out at me as soon as I looked up these references.

Kak's claimed solution is pretty much a vaguer repetition of a solution previously suggested by Unnikrishnan a couple of years ago – which he does not cite! Kak only cites Unnikrishnan for defending the claim that perfectly conventional discussions of the twin paradox are "wrong", but gives him no credit whatever for having worked out the "solution" that Kak implicitly claims for himself.

The paper trail:

• Unnikrishnan, in 2004, wrote "Cosmic Relativity: The Fundamental Theory of Relativity, its Implications, and Experimental Tests", which can be found in the unreviewed arxiv archive as gr-qc/0406023. This error-riddled drek proposes that "all relativistic effects that are presently attributed to kinematics of relative motion in flat space-time are in fact gravitational effects of the nearly homogeneous and isotropic Universe. The correct theory of relativity is the one with a preferred cosmic rest frame."
• Unnikrishnan, in 2005, wrote "On Einstein’s resolution of the twin clock paradox", in which he claims that Einstein's own explanations are full of errors. In this paper, Unnikrishnan also describes briefly his proposed solution with reference to the frame in which the CMBR is isotropic.
• Kak, in 2007, publishes the paper that has been cited here. He cites the 2005 paper in support of the idea that prior resolutions of the "paradox" are in error; but fails to make any mention of the close similarity between his proposed solution and that given by Unnikrishnan.

In other words, as well as being drivel, Kak's paper is less original than he would like to imply; a crude derivative of work by a rather crankish Indian physicist.

Cheers -- sylas

PS. I agree with you about sciencedaily. They don't show a lot of discrimination and are inclined to publish pretty much anything. Can be handy sometimes, but they are highly unreliable on the significance or standing of what they report. Basically, they seem to be a convenient outlet for anyone who can get some kind of official press release from a usually credible source. In this case there was a university press release from Kak's university; and probably Kak wrote the main content release himself, as a working academic will often do. There's not a great deal of checking done at the level of a release. If a working professor has an article in a legitimate journal, then it's presumed the journal does the checking. In this case, they can't have!

 

[Dale]

The twin "paradox" is a simple undergraduate level issue. It's a basic exercise that should be solved by a first year undergraduate at the start of the introductions to special relativity.

I wonder in what other contexts a sophomore-level homework mistake gets the title of "paradox".

 

[physicsdude30]

Yes, I am familiar with this episode. I looked at in a bit of detail when it first came out. Most of this post is summarized from stuff I wrote at the time in another forum.

So what I'm trying to figure out, and what experiments may tell us: If a twin goes travels through the Universe at the speed of light for 10 years and the other twin stays on the planet Earth, we know from the Earth bound twin the twin in the rocket through space is younger since he's moving at the speed of light. However, what about the perspective for the twin in the rocket? From his perspective, is the twin on Earth younger or older than him? I know they've tested Special Relativity by sending decaying subatomic particles down a tube and jet airplanes around the world. However, have they tested it the other way around to see the effects from the other's perspective?

For example, having a researcher stay with a clock on the surface of the Earth while the jet flies around the world, then comparing the clocks (which I guess they've done). Then next have the researcher get in the jet with that other clock and then compare the clock on the surface of the Earth when he gets back?

Do you see what I'm trying to figure out about what's been empirically tested? I know Special Relativity has been tested, but am trying to figure out if it has from the other angle/perspective?

 

[JesseM]

So what I'm trying to figure out, and what experiments may tell us: If a twin goes travels through the Universe at the speed of light for 10 years and the other twin stays on the planet Earth, we know from the Earth bound twin the twin in the rocket through space is younger since he's moving at the speed of light.

It's impossible for an object with mass to move at the speed of light (light itself has no mass), but relativity says that clocks moving at significant fractions at the speed of light relative to a given observer will be measured to be running slow in that observer's inertial rest frame (inertial meaning it's a non-accelerating frame of reference). Note that there is no notion of absolute speed in relativity--if I am moving at 60% the speed of light (0.6c) in the inertial frame where you are at rest, then there will be another inertial frame where I am at rest and you are moving at 60% the speed of light. In either frame, the one who is moving at 0.6c is aging slower by a factor of 0.8 (in general, if a clock is moving at speed v in a given frame, then it is slowed down by a factor of $$\sqrt{1 - v^2/c^2}$$)

However, what about the perspective for the twin in the rocket? From his perspective, is the twin on Earth younger or older than him?

In any inertial frame, the twin that is moving faster is aging more slowly. So, for example, you can pick an inertial frame where the Earth is moving and the rocket is at rest during the outbound phase of the trip, and in this frame the Earth twin is aging more slowly. However, if the rocket turns around to return to Earth so the two twins can compare ages at a single location, then this means the rocket changes velocity (accelerates), so there is no inertial frame where the rocket is moving slower than the Earth during both phases of the trip before and after the turnaround, and thus it works out that all inertial frames agree that the rocket twin has aged less overall when they reunite (on the other hand, if the rocket twin continued to move at constant velocity while giant rockets were attached to the Earth so that it could accelerated and catch up with the rocket, then the Earth twin would have aged less when they reunite--the twin that moves inertially between the two meetings will always have aged more than the one that accelerated).

Different inertial frames always agree about localized events like two clocks meeting at a single point in spacetime and comparing readings there, but they can disagree about issues relating to "simultaneity" when it comes to events that happen far apart, meaning that two events that happened "at the same time" in one frame may have happened at "different times" in another. For example, if the rocket twin has been moving away from the Earth at a constant speed of 0.6c in the Earth frame, having departed from the Earth when both twins were aged 20, then in the Earth frame the event of the Earth twin's 30th birthday is simultaneous with the event of the rocket twin's 28th birthday (so the rocket twin has aged less in the Earth frame); but in the frame where the rocket is at rest and the Earth is moving at 0.6c, the event of the rocket twin's 28th birthday is simultaneous with the event of the Earth twin being 26.4 years old (so the Earth twin has aged less in the rocket frame).

For example, having a researcher stay with a clock on the surface of the Earth while the jet flies around the world, then comparing the clocks (which I guess they've done). Then next have the researcher get in the jet with that other clock and then compare the clock on the surface of the Earth when he gets back?

It's not like the jets were unmanned! Anyway, are you suggesting that the presence or absence of a human researcher next to a clock might somehow change which of two clocks has elapsed more time?

 

[Al68]

So what I'm trying to figure out, and what experiments may tell us: If a twin goes travels through the Universe at the speed of light for 10 years and the other twin stays on the planet Earth, we know from the Earth bound twin the twin in the rocket through space is younger since he's moving at the speed of light. However, what about the perspective for the twin in the rocket? From his perspective, is the twin on Earth younger or older than him?

Older. The answer is the same for either perspective, although the perspectives obviously are different.

Do you see what I'm trying to figure out about what's been empirically tested? I know Special Relativity has been tested, but am trying to figure out if it has from the other angle/perspective?

Yes. Each experiment's results apply to both perspectives.

The clock that was flown in a jet and compared to a clock left on Earth showed that the jet clock had less elapsed time than the Earth clock. This result logically can't be different according to those on the jet than for those on the ground.

 

[physicsdude30]

Older. The answer is the same for either perspective, although the perspectives obviously are different.Yes. Each experiment's results apply to both perspectives.

The clock that was flown in a jet and compared to a clock left on Earth showed that the jet clock had less elapsed time than the Earth clock. This result logically can't be different according to those on the jet than for those on the ground.

So if I'm understanding correctly, from the Earth twin's perspective, the one in the rocket is younger? From the rocket twin's perspective, the one on Earth is older? And this has been resolved, meaning you can't say speed is subjective to what frame of reference you're in in determining time dilation/length contraction?

 

[JesseM]

So if I'm understanding correctly, from the Earth twin's perspective, the one in the rocket is younger? From the rocket twin's perspective, the one on Earth is older? And this has been resolved, meaning you can't say speed is subjective to what frame of reference you're in in determining time dilation/length contraction?

If you pick an inertial frame, then at a point on one twin's worldline when he's far away from the other twin, different frames can disagree on whether the other twin is older or younger (If the rocket twin is moving away from the Earth at constant velocity, then in the Earth's inertial rest frame the rocket twin is aging slower, but in the rocket's inertial rest frame the Earth twin is aging slower). However, if one twin accelerates to turn around after the two twins have been moving apart for a while, so that the two twins can reunite and compare clocks at the same location (not far apart), then all inertial frames agree that whichever twin accelerated will be younger when they reunite.

 

[Fredrik]

This statement in the article:
...
is not only false, it's egregiously false.
...
I've read a few articles on Science Daily before and gotten a feeling that they weren't quite all there, without being able to pin it down. Now I *know* they're out to lunch.

I think you're much too kind to it. I'm having a hard time finding strong enough words to express how bad that Science Daily article is. I'm just sitting here with my jaw dropped, shaking my head in disbelief. It was obviously written by someone who doesn't understand anything at all about relativity, someone who doesn't even understand the difference between time dilation and the twin "paradox".

 

[sylas]

I think you're much too kind to it. I'm having a hard time finding strong enough words to express how bad that Science Daily article is. I'm just sitting here with my jaw dropped, shaking my head in disbelief. It was obviously written by someone who doesn't understand anything at all about relativity, someone who doesn't even understand the difference between time dilation and the twin "paradox".

Remember: science daily is pretty much just repeating a university press release. The release itself was probably written by Kak himself or someone at the LSU press office, with Kak's help. The release was also picked up spaceref.com, and at physorg.com, and at eurekalert, and various other such outlets for press releases.

Here is a link to the http://appl003.lsu.edu/unv002.nsf/9faf000d8eb58d4986256abe00720a51/d9d322b95c639fac86257282007a0845?OpenDocument .

What really leaves me gobsmacked is that the paper was actually published, in "International Journal of Theoretical Physics". This is what prompted the release, and no doubt encouraged the uncritical acceptance of such nonsense. People normally trust a journal to have at least a basic level of review.

I've got a bit of an interest in how such material gets into a real journal (albeit a low impact journal). It happens from time to time, in various fields; and I'd like to see journals do better at publicly recognizing such a conspicuous failure of their own procedures for maintaining basic quality when it occurs.

Cheers -- sylas

 

[physicsdude30]

It's not like the jets were unmanned! Anyway, are you suggesting that the presence or absence of a human researcher next to a clock might somehow change which of two clocks has elapsed more time?

Hmmm, okay sorry for the confusion. Maybe this slight modification of the Twin Paradox will help you understand what I'm trying to figure out about actual empirical experimentation?

Hypothetically, let's say we have a researcher named Jill. For the first round, Jill stays on Earth for 5 years with the Earthbound twin while the rocket twin goes out. Then Jill writes down in her notebook that the returning rocket twin is younger than the Earthbound Twin. Then for the second round, Jill instead goes up in the rocket with that twin and carries her notebook with her previous notes. The rocket twin and Jill fly into space for five years and return. Obviously her notebook will still say for round one that the rocket twin lost time. However, if motion is relative to individual objects in determining time, Jill's notes will take a spin and say the Earthbound twin had slower time the second round even if the first round had faster time. If motion is relative to something else for determining time then it would seem Jill's notes will still say the rocket twin had slower time when she was with him the second round. If we had a researcher stay on Earth with an Earthbound atomic clock as the jet goes around the world, then the same researcher goes with the jet and jet's atomic clock the second time around, that could rule out if motion is due to individual objects for determining time, or if it really is that way? Does that make sense how I'm suggesting making what ScienceDaily possible to falsify with experiments? No matter how bad an idea may be, I like to think of ways to make it falsifiable.

Did the Twin Paradox get resolved with General Relativity, or was it resolved another time, or what happened? Sorry if I'm a little confused here, I'm just trying to develop an analytic conceptual understanding.

 

[JesseM]

Hypothetically, let's say we have a researcher named Jill. For the first round, Jill stays on Earth for 5 years with the Earthbound twin while the rocket twin goes out. Then Jill writes down in her notebook that the returning rocket twin is younger than the Earthbound Twin. Then for the second round, Jill instead goes up in the rocket with that twin and carries her notebook with her previous notes. The rocket twin and Jill fly into space for five years and return. Obviously her notebook will still say for round one that the rocket twin lost time. However, if motion is relative to individual objects in determining time,

As I explained before, the time dilation equation is not meant to be used relative to arbitrary objects, it only works in the frame of inertial observers (observers who do not accelerate, and thus feel no G-forces). Jill has to accelerate to turn around, so she changes velocity in all inertial frames, while the Earth maintains a constant velocity in all inertial frames. Thus although some inertial frames will say that Jill initially had a lower speed than the Earth during the outbound leg of her trip and was thus aging faster during that leg, in these frames she will have had a higher speed than the Earth during the inbound leg of the trip so that she can catch up with it, and all inertial frames end up agreeing that by the time Jill reunites with the Earth twin, she has aged less in total.

Jill's notes will take a spin and say the Earthbound twin had slower time the second round even if the first round had faster time.

Nope, there is no version of relativity where this would be true (unless the rocket moved inertially the whole time and the Earth was somehow accelerated to catch up with it), and this doesn't even make sense as a hypothesis--how can the presence of a note-taker somehow change the readings on the two clocks when they are brought to the same location and compared? That sounds more like magic than physics!

Did the Twin Paradox get resolved with General Relativity, or was it resolved another time, or what happened?

It was never a genuine "paradox" at all in the sense of an unsolved problem, it was just meant to illustrate a common misconception about relativity. If you understand the fact that the time dilation equation only works in inertial frames in SR, then you've already solved it, and there was never a time when physicists didn't understand this.

 

[Mentz114]

physicsdude,

Did the Twin Paradox get resolved with General Relativity, or was it resolved another time, or what happened? Sorry if I'm a little confused here, I'm just trying to develop an analytic conceptual understanding.

Listen to what you're being told. There never was a paradox to be resolved, and your question indicates you haven't got to grips with this.

When we travel, we don't just move through space, in SR there is a 4 dimensional continuum, so we move through space and time. Just as we can define a distance through space, so in SR we define a 'distance' through spacetime. It's called 'proper length', 'proper time' or even 'the proper interval'. There is a straightforward formula for computing this distance. In the twin or travellers situation, where two clocks start at the same place and then one or both go on a journey and meet up again, the elapsed time on their clocks is just the proper interval. Which one has the most time on it depends only on the proper length of the journey.

So, far from being a paradox, there is a simple way to predict what the clocks will say when the travellers meet. All inertial frames in the universe agree on this, otherwise there really would be a paradox.

 

[JesseM]

When we travel, we don't just move through space, in SR there is a 4 dimensional continuum, so we move through space and time. Just as we can define a distance through space, so in SR we define a 'distance' through spacetime. It's called 'proper length', 'proper time' or even 'the proper interval'. There is a straightforward formula for computing this distance. In the twin or travellers situation, where two clocks start at the same place and then one or both go on a journey and meet up again, the elapsed time on their clocks is just the proper interval. Which one has the most time on it depends only on the proper length of the journey.

For more on the analogy between path length in space and "proper time" in spacetime, physicsdude might want to read my post #9 on this thread.

 

[matheinste]

This extract is from page 45 of Wolfgang Rindler's book Essential Relativity--Special, General and Cosmological--.

"Like length contraction, so also time dilation can lead to an apparent paradox when viewed by two different observers. In fact, this paradox, the so-called twin or clock paradox (or paradox of Langevin), is the oldest of all the relativistic paradoxes. It is quite easily resolved, but its extraordinary emotional appeal keeps debate alive as generation after generation goes through the cycle of first being perplexed, then elated at understanding (sometimes mistakenly), and then immediately rushing into print as though no one had understood before. The articles that have been published on this one topic are practically uncountable, while their useful common denominator would fill a few pages at most. But while no one can get very excited about pushing long poles into short garages and the like, the prospect of going on a fast trip through space and coming back a few years later to find the Earth aged by a few thousand years--this modern elixir vitae--keeps stirring the imagination."

Matheinste.

 

[wxyz]

How about if the question is asked this way.

Assume you have 2 spaceships in the same inertial frame.
They both both synchronize their clocks with Einstein's clock synchronization method.

They both agree to quickly accelerate in opposite linear directions one for some small time period ta and one for time period tb, tb != ta.

They both agree after some other long time period the one that accelerated longer will decelerate to force the two back into the same inertial frame and then they will perform Einstein's clock synchronization method.

To put in words, at first they are in the same frame, 0 relative motion.

They both accelerate for different time periods to create relative motion for a long time period.

One decelerates to force the two back into the same inertial frame.

They then test their clocks at the end of this.

What will be the result.

 

[JesseM]

How about if the question is asked this way.

Assume you have 2 spaceships in the same inertial frame.
They both both synchronize their clocks with Einstein's clock synchronization method.

They both agree to quickly accelerate in opposite linear directions one for some small time period ta and one for time period tb, tb != ta.

They both agree after some other long time period the one that accelerated longer will decelerate to force the two back into the same inertial frame and then they will perform Einstein's clock synchronization method.

To put in words, at first they are in the same frame, 0 relative motion.

They both accelerate for different time periods to create relative motion for a long time period.

One decelerates to force the two back into the same inertial frame.

They then test their clocks at the end of this.

What will be the result.

Assuming the times spent accelerating are very small compared to the time spent moving inertially, the problem can be simplified by just assuming the acceleration is instantaneous, so they both suddenly change velocity with one achieving a greater speed relative to their initial rest frame than the other (call the one with the greater speed after acceleration A, and the one with the smaller speed after acceleration B). There will be no set answer to your question without filling in details, like whether it's A or B who accelerates a second time so that they come to rest relative to one another again, how much proper time elapses between accelerations for the one who accelerates twice, and what the change in velocity is with each acceleration. By changing the answers to these questions, I'm pretty sure (based on imagining various spacetime diagrams) that one could change the answer to whose clock has elapsed more time after they've come to rest relative to another again.

 

[matheinste]

How about if the question is asked this way.

Assume you have 2 spaceships in the same inertial frame.
They both both synchronize their clocks with Einstein's clock synchronization method.

They both agree to quickly accelerate in opposite linear directions one for some small time period ta and one for time period tb, tb != ta.

They both agree after some other long time period the one that accelerated longer will decelerate to force the two back into the same inertial frame and then they will perform Einstein's clock synchronization method.

To put in words, at first they are in the same frame, 0 relative motion.

They both accelerate for different time periods to create relative motion for a long time period.

One decelerates to force the two back into the same inertial frame.

They then test their clocks at the end of this.

What will be the result.

However you care to pose the problem the answer will always be that the ship that travels the greatest "spacetime distance" will have accumulated the least proper time, or, if you like, aged the least.

Matheinste.

 

[wxyz]

Assuming the times spent accelerating are very small compared to the time spent moving inertially, the problem can be simplified by just assuming the acceleration is instantaneous, so they both suddenly change velocity with one achieving a greater speed relative to their initial rest frame than the other (call the one with the greater speed after acceleration A, and the one with the smaller speed after acceleration B). There will be no set answer to your question without filling in details, like whether it's A or B who accelerates a second time so that they come to rest relative to one another again, how much proper time elapses between accelerations for the one who accelerates twice, and what the change in velocity is with each acceleration. By changing the answers to these questions, I'm pretty sure (based on imagining various spacetime diagrams) that one could change the answer to whose clock has elapsed more time after they've come to rest relative to another again.

Yes, I did not word it well.

My intention was to cause an instananeous constant acceleration for both initially with one being longer. Then, the observer that accelerated longer would declerate such that the overall acceleration for both is equal.

 

[wxyz]

However you care to pose the problem the answer will always be that the ship that travels the greatest "spacetime distance" will have accumulated the least proper time, or, if you like, aged the least.

Matheinste.

The overall acceleration for both is equal.

This wording of the paradox removes the turn around and acceleration differential allowing us to focus completely on time dilation and SR between two frames.

Then, Einstein's clock sych procedure is applied which is allowed.

I am simply unable to come up with any answer that makes sense when viewed this way.

 

[JesseM]

Yes, I did not word it well.

My intention was to cause an instananeous constant acceleration for both initially with one being longer. Then, the observer that accelerated longer would declerate such that the overall acceleration for both is equal.

When I said "instantaneous acceleration", I meant that the period of the acceleration itself is treated as instantaneous, so the ship's velocity just changes abruptly from one value to another at a single moment in time. As I said, as long as the period of acceleration in your scenario (where the acceleration is not instantaneous in this sense) is very brief compared to the time spent moving inertially between accelerations, the difference between your scenario and my scenario with instantaneous acceleration should be negligible. If you think the overall period of time spent accelerating has anything to do with the time elapsed on each clock, you're misunderstanding something--the rate a clock is ticking at any given moment in some frame depends only on its velocity at that moment, not its acceleration. Please read my geometric analogy in post #9 of this thread and see if it helps (note that in the analogy, the greater length of the bent path is mostly accumulated on the straight segments of the path with are analogous to constant velocity motion in spacetime, the length of the curved segment is not the deciding factor, and in fact you could make the bent path have an instantaneous change in slope like the tip of a triangle and it would have little effect on the overall length of the bent path).

 

[sylas]

The overall acceleration for both is equal.

What is "overall acceleration"?

Note that acceleration is not what matters, but velocity.

Your problem says that they accelerate in opposite directions, and then after a time one accelerates to make them both in the same frame. That would mean they are both now moving in the same direction again, or (equivalently) they are not moving at all relative to each other. (But why opposite directions?)

Let's just say that A accelerates almost instantaneously to velocity v, and B accelerates almost instantaneously to velocity u. Then, at a time t, B accelerates again to be at velocity v, the same as A. Assume everything is along one dimension for simplicity, with the direction being given with the sign of velocity.

All variables are defined in the frame where A and B are initially at rest, and synchronized.

Which has the greater elapsed time on their clock? Well, this actually depends on who is measuring it, because A and B are separated in space, and therefore simultaneity is relative.

In the frame where A and B were initially at rest; the frame in which A has velocity v and B has velocity u, the one that shows the greatest elapsed time is the one with the smaller magnitude of velocity.

In the frame of A, A is at rest and B is moving, and then decelerates to come to rest. In this frame, A has the greatest elapsed time.

These are two different frames, and in general they give different results for the time difference between A and B, because they use different notions of being at the "same time" for A and B. Hence there's no paradox.

Cheers -- sylas

 

[wxyz]

What is "overall acceleration"?

Note that acceleration is not what matters, but velocity.

Your problem says that they accelerate in opposite directions, and then after a time one accelerates to make them both in the same frame. That would mean they are both now moving in the same direction again, or (equivalently) they are not moving at all relative to each other. (But why opposite directions?)

Let's just say that A accelerates almost instantaneously to velocity v, and B accelerates almost instantaneously to velocity u. Then, at a time t, B accelerates again to be at velocity v, the same as A. Assume everything is along one dimension for simplicity, with the direction being given with the sign of velocity.

All variables are defined in the frame where A and B are initially at rest, and synchronized.

Which has the greater elapsed time on their clock? Well, this actually depends on who is measuring it, because A and B are separated in space, and therefore simultaneity is relative.

In the frame where A and B were initially at rest; the frame in which A has velocity v and B has velocity u, the one that shows the greatest elapsed time is the one with the smaller magnitude of velocity.

In the frame of A, A is at rest and B is moving, and then decelerates to come to rest. In this frame, A has the greatest elapsed time.

These are two different frames, and in general they give different results for the time difference between A and B, because they use different notions of being at the "same time" for A and B. Hence there's no paradox.

Cheers -- sylas

Thank you. I agree.


Now I know how to word it properly as my example before is wrong.


O and O' are in the same inertial frame.

O applies a constant acceleration and so does O'. but for different time periods such that their relative motion is v.

O apples the acceleration for the longer period.

They agree to proceed with this relative v for a long period of agreed upon time.

Then O applies a constant acceleration in the opposite direction of the prior acceleration for the shorter time period.

O' applies a constant acceleration in the opposite direction of the prior acceleration for the longer time period such that they are forced back to the original inertial frame but at a much greater distance.

Now, they apply the Einstein's clock synchronization procedure.

What will be the result?

 

[JesseM]

Thank you. I agree.Now I know how to word it properly as my example before is wrong.O and O' are in the same inertial frame.

O applies a constant acceleration and so does O'. but for different time periods such that their relative motion is v.

O apples the acceleration for the longer period.

They agree to proceed with this relative v for a long period of agreed upon time.

Then O applies a constant acceleration in the opposite direction of the prior acceleration for the shorter time period.

O' applies a constant acceleration in the opposite direction of the prior acceleration for the longer time period such that they are forced back to the original inertial frame but at a much greater distance.

Now, they apply the Einstein's clock synchronization procedure.

What will be the result?

Do you understand that as long as the period of coasting inertially is much longer than the period of accelerating, the actual length of the acceleration is basically irrelevant? In other words, instead of saying that O applies an acceleration for a longer period, you could just say that both O and O' instantaneously change velocities, but the velocity of O changes by a larger amount than the velocity of O'.

Also, do you understand about the relativity of simultaneity? Presumably the first acceleration of O and the first acceleration of O' are meant to happen simultaneously in their original rest frame prior to acceleration, but if you then want them both to accelerate again at a later time so they come to rest relative to one another, if these second accelerations are supposed to be "simultaneous" in some frame, you need to specify which frame that is--is it the same frame as before, the one they were originally at rest in? Or is it the rest frame of either O or O' immediately before the second acceleration?

 

[wxyz]

Do you understand that as long as the period of coasting inertially is much longer than the period of accelerating, the actual length of the acceleration is basically irrelevant? In other words, instead of saying that O applies an acceleration for a longer period, you could just say that both O and O' instantaneously change velocities, but the velocity of O changes by a larger amount than the velocity of O'.

Also, do you understand about the relativity of simultaneity? Presumably the first acceleration of O and the first acceleration of O' are meant to happen simultaneously in their original rest frame prior to acceleration, but if you then want them both to accelerate again at a later time so they come to rest relative to one another, if these second accelerations are supposed to be "simultaneous" in some frame, you need to specify which frame that is--is it the same frame as before, the one they were originally at rest in? Or is it the rest frame of either O or O' immediately before the second acceleration?

I only say they agree to use their own proper times for the acceleration/deceleration.

The entire event causes an overall 0 acceleration for each "twin" but with relative velocity between the two for an extended period.

 

[sylas]

I only say they agree to use their own proper times for the acceleration/deceleration.

Here is the question again. This is an important question, and answering it will help sort out the situation.

Do you understand that as long as the period of coasting inertially is much longer than the period of accelerating, the actual length of the acceleration is basically irrelevant?

All that matters is the velocity at which the coasting occurs. If you agree with this, all the irrelevant stuff about accelerations can be dropped.

Cheers -- sylas

 

[JesseM]

I only say they agree to use their own proper times for the acceleration/deceleration.

The entire event causes an overall 0 acceleration for each "twin" but with relative velocity between the two for an extended period.

"0 overall acceleration" is misleading, it's a bit like saying a zig-zag path in 2D has "0 overall bending" because every zig in one direction is balanced by a zag in the other--it's still obviously true that a zig-zag path is different from a straight path (a zig-zag path between two points will have a greater length than a straight line between the same two points, for example). Anyway, if they both start out at rest in frame #1, then accelerate to different velocities relative to frame #1, coast inertially for significantly longer than the period of acceleration (so that as an approximation you can treat the acceleration as instantaneous), then both decelerate to being at rest in frame #1 again after the same amount of proper time has passed on each clock (assuming that's what you meant by 'they agree to use their own proper times for the acceleration/deceleration'), then whichever one had a larger velocity in frame #1 will take longer before it decelerates in frame #1 since it's been running slower since the initial acceleration. This means that after both come to rest in frame #1 again, the one that had a larger velocity will show an earlier time in frame #1 than the one that had a smaller velocity, because it decelerated later (and both showed the same proper time at the moment they decelerated).

 

[marxmarvelous]

"The twin "paradox" is a simple undergraduate level issue. It's a basic exercise that should be solved by a first year undergraduate at the start of the introductions to special relativity."

When I taught undergraduates at Hopkins in the '60s it was still a "paradox" and not interesting to the students or me cause it wouldn't appear on tests and that was what they and I were interested in.
Later when I went to a library just for fun, to just learn something I found a book in which Einstein specifically said that acceleration of one or both of the persons didn't "answer" the paradox.
Then I read where he accounted for the inability of Special Relativity to "answer" the paradox and this inability was one motive for the General theory. He even admitted that the Special theory was WRONG when applied to the twins. "a defect in epistomology" An error in the theory of knowledge.
l Later I found his book that just had his theories, nobody else's "simplifications. He included a page on Mach's recognition of the intuitive necessity for matter to "know" of all this other stuff out there that would in effect establish a preferred frame. To me the most important thing is that the media ignored Einstein and his admission of the inapplicability of SR to the twin paradox and ignored him also when he suggested that an international police force be established to ensure that no-one had the bomb. He was completely ignored from 1948 to his death in '55 when he reiterated his lifelong vie that immigrants to Palestine must get along with Palestinians.
He was also clear that infinities, anything divided by zero is not representative of a physical state. He knew that the Greek-Think(logos) method of mathematics and Science in which postulates are manipulated with a system of logic was not to be followed into physical non-sense just because a formula delivered that conclusion.
Postulates can't be proven; they are simply accepted in-the- beginning of a mathematical or scientific field. When they give "singularities, infinities, unmeasureable things we are not required to accept them as represetations of the physical.
As far as the Intelligence agents who flew the clocks from the Naval Observatory around the world both ways the experiment was faulted. I'd appreciate a physicist look at the revelation of the sloppy technique and straighten me out. I'll have to go find the site again. The main effect was the GR effect of altitude(proximity of Earth slowed clocks) The clocks weren't stable enough to give the result.

GPS satellite clocks are adjusted with the GR formulas applied to their orbit. Interesting also is the media protection of the reputation of the Boys with government airplane tickets and clocks.
Scientific American fumbled the Twin thing a few years ago. "Solved it" They did not reply to my note of the error they made in their explanation. If anyone will post it I'll point to their error again.

 

[sylas]

"The twin "paradox" is a simple undergraduate level issue. It's a basic exercise that should be solved by a first year undergraduate at the start of the introductions to special relativity."

When I taught undergraduates at Hopkins in the '60s it was still a "paradox" and not interesting to the students or me cause it wouldn't appear on tests and that was what they and I were interested in.
Later when I went to a library just for fun, to just learn something I found a book in which Einstein specifically said that acceleration of one or both of the persons didn't "answer" the paradox.
Then I read where he accounted for the inability of Special Relativity to "answer" the paradox and this inability was one motive for the General theory. He even admitted that the Special theory was WRONG when applied to the twins. "a defect in epistomology" An error in the theory of knowledge.

[...]

This is all incorrect. Einstein did answer the paradox just fine, using special relativity; and he never said the special theory was wrong applied to the twins. It isn't wrong at all -- and Einstein solved the problem just fine. Indeed it is not really about acceleration at all. It is about the proper time integrated over your world line. An accelerated observer always has more elapsed time than an inertial observer, when they return to a common point; but you still solve the problem by integrating proper time; and that is a function of velocity. You don't need to use acceleration.

Cheers -- sylas

 

[ernestpworrel]

No one should be debating this issue. The twin paradox is a paradox in every sense of the word. You would think that the rocketing twin would age faster, but in fact the opposite is true. This is easily understood when you account for the Lorentz contraction and you understand that time is relative to the motion of the frame in which it is measured. Anyone who has a clear understanding of SR should be able to figure this out. This is something that has been proven.