Twin Paradox And Time Dilation

Plazma Inferno! · Jul 20, 2015

origin said:

RajeshTrivedi said:

Two of the triplets on two different spaceships, when they return to Earth, have aged identically...despite relative speed.....You cannot wriggle out from this by mere statements. Where is the catch ? I could not fine one yet.
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There is nothing to wriggle out of. If the 2 ships accelerate at the same rate, to the same speed (same inertial frame) and then decelerate at the same speed to the original frame they will be exactly the same age, even though if they were somehow able to view each others clocks they would each say that the others is running slower. Both of the moving triplets will be younger than the triplet that remained in the original frame.

I think the easiest way to look at this is imagine 2 triplets are on earth and the other is (somehow) on Alpha Centuri and they somehow all synchronize their clocks. Both Sol and Alpha Centuri are essentially in the same reference frame so it will work. 1 triplet leaves from AC and one triplet leaves from sol and they pass each other in transit. Both the moving triplets will age the same and both will be younger than the stay at home triplet AND both of the moving triplets will say the other clock is running slower as they pass.
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Plazma Inferno! · Jul 20, 2015

RajeshTrivedi said:

origin said:

There is nothing to wriggle out of. If the 2 ships accelerate at the same rate, to the same speed (same inertial frame) and then decelerate at the same speed to the original frame they will be exactly the same age, even though if they were somehow able to view each others clocks they would each say that the others is running slower. Both of the moving triplets will be younger than the triplet that remained in the original frame.
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So, we are attributing the dilation, not to the relative speed, but to the acceleration / deceleration....which could have an equivalent math in GR.........the invoking of acceleration / deceleration to resolve this can be thwarted as there are many other offshoots of the paradox which remove this aspect.

This is well stated in the OP that both the triplets on the spaceships will be younger to the one who remained on the Earth (Original Frame), but there should be time dilation between the two as well, as they also had relative speed for the entire motion.
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Plazma Inferno! · Jul 20, 2015

Schmelzer said:

RajeshTrivedi said:

Between the two on the spaceships when they arrived at the Earth, despite relative speed...
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As I have explained you, relative speed of different clocks does not matter at all. What matters is what appears in the formula τ=∫γηmndγmdγn−−−−−−−−−√. It is only one clock, only its trajectory γm(t), which matters.

RajeshTrivedi said:

The Lorentz Transformation factor is non linear with respect to relative speed between two frames...So if there are 3 (or more) frame of references moving with velocities say, v1, v2 and stationery.Then the time dilation figures can give problematic values at least between some pairs, as given by this example, which you have called 'constructed exception'. I am sorry it is not.
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Note that a single frame is sufficient to compute all the clock times for all the clocks. All you need is the trajectories of all clocks γm(t) in a fixed system of coordinates xm. You can, of course, repeat the same computations in another system of coordinates, but it will give you the same numbers if you do all this correctly.
No such animal as a "Lorentz transformation factor" between different frames is, therefore, necessary. One frame is sufficient.

If you want to consider a second frame, this may be useful as an independent check that you obtain the same results with a different way to compute all this - a consistency check. That's all. To consider three or more frames is already simply a loss of time.
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Plazma Inferno! · Jul 20, 2015

origin said:

RajeshTrivedi said:

So, we are attributing the dilation, not to the relative speed, but to the acceleration / deceleration....which could have an equivalent math in GR.........the invoking of acceleration / deceleration to resolve this can be thwarted as there are many other offshoots of the paradox which remove this aspect.
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No, that is not what we are doing. You can assume that the acceleration and deceleration were instantaneous and the analysis stays the same.

RajeshTrivedi said:

This is well stated in the OP that both the triplets on the spaceships will be younger to the one who remained on the Earth (Original Frame), but there should be time dilation between the two as well, as they also had relative speed for the entire motion.
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As I have pointed out each moving triplet will see the others clock as time dilated, but if they both return to the original frame at the same time they will have aged exactly the same amount.

It appears that you are stuck on the assumption that there is some absolute time to compare your time to, but in reality there isn't.
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Plazma Inferno! · Jul 21, 2015

Schmelzer said:

origin said:

It appears that you are stuck on the assumption that there is some absolute time to compare your time to, but in reality there isn't.
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It is IMHO his relativism - the idea that the relative velocity somehow causes time dilation - which is confusing him.

The formula for proper time works connects the clock time with the time coordinate of some fixed system of coordinates. If this coordinate time is interpreted as some absolute time or not is irrelevant - this is nothing one could even identify by looking at the formula. If it would be interpreted as absolute - what would be the problem?
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Plazma Inferno! · Jul 21, 2015

danshawen said:

RajeshTrivedi said:

Your related post in the other thread is quite interesting where you raised the issue with respect to calculus. Yes if 'dt' varies spatially either due to Gravity or even due to relative speed, then only explanation is Physics becomes frame specific which is incorrect....So there has to be something else....may be digging more into coordinate time and proper time will resolve....but then again the Biology is the problem as suggested in my post # 14. I was wondering and attempting too, that this Galaxy Speed Distribution and spacetime expansion appear to be the outcome of time dilation in true sense, not necessarily time dilation as arrived from Lorentz Transformation and SR, a real variable aspect of flow rate of time....only thoughts as on date and some slippery maths.
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There is still a problem with calculus, Rajesh. Euclidean space is simply not compatible with relativistic space. Minkowski knew this too, but bringing imaginary time as a dimension and Pythagorus into the mix is not a solution. If it was, his math could be used to easily resolve things like the twin paradox. By using the relativity of simultenaety as an excuse for doing so, he eliminated any possibility of us ever understanding the real physics underlying either entanglement or inertia.

Not only is time a dimension; it is EVERY dimension. There is only energy and time.

The twin paradox isn't a paradox, really, as has already been said.

About 13. 7 billion years ago, the Milky Way and its twin or the parts out of which both would eventually form left a region of space in which they were both originally at rest. Over aeons, both were so slowly accelerated that only now are the respective time dilation factors appreciable. If both of those galaxies were miraculously returned to that intermediate space at some time in the distant future, the galaxies and everything in them would be very close to the same respective ages.

The accelerations were likely quite low, but acted for a very long time to make their respective velocities relativistic with respect to each other. But it doesn't matter. Whether they accelerated fast or slow, over a long time or a short one, the twin paradox works the same in every direction, and only local relative time dilation is needed to explain the twin paradox.

If only one of those galaxies accelerated, the situation would be temporally assymmetrical, but that would also have required the action of a very large (understatement) unbalanced force, which is unlikely in the extreme.

I seem to recall, most of my physics instructors were somehow uncomfortable explaining the twin paradox in this much detail. Now I can understand why. It is easy to get lost when the math you must use to analyze it makes something as concrete as time imaginary.
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Plazma Inferno! · Jul 21, 2015

Schmelzer said:

Sorry, but the twin paradox, which is pure SR, has nothing to do with the expansion or acceleration of the expansion of the universe, which is pure GR.
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Plazma Inferno! · Jul 21, 2015

origin said:

Schmelzer said:

It is IMHO his relativism - the idea that the relative velocity somehow causes time dilation - which is confusing him.

The formula for proper time works connects the clock time with the time coordinate of some fixed system of coordinates. If this coordinate time is interpreted as some absolute time or not is irrelevant - this is nothing one could even identify by looking at the formula. If it would be interpreted as absolute - what would be the problem?
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That is true, my understanding is that frame S by convention is the 'nonmoving' frame and S' is the moving frame. Of course either frame can actually be thought of as the moving frame.
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Plazma Inferno! · Jul 21, 2015

danshawen said:

Schmelzer said:

Sorry, but the twin paradox, which is pure SR, has nothing to do with the expansion or acceleration of the expansion of the universe, which is pure GR.
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I wasn't trying to suggest that the expansion of the universe was analogous to the twin paradox in any manner other than acceleration (fast or slow) as a means of changing reference frames
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Plazma Inferno! · Jul 21, 2015

danshawen said:

There is only time, energy, and two quantum fields; one at rest, one in motion at c in every direction and mode in which energy is capable of propagating. Space is simply related to the propagation of energy or bound energy which is matter. Any space in between particles are just so much light travel time. At least, Minkowski got this much right. Time has an origin (instant of 'now') anchored in the stationary quantum field, runs at different rates anywhere anything moves or is influenced by a gravitational field.

Time intervals are infinitely subdivisible, and this is something that throws mathematicians into fits trying to model. If time were not infinitely subdivisible, instant entanglement would not work, and it most certainly does, at a minimum of 10K x the speed of light.

In some areas, and the Standard Model is one of these, mathematicians simply gave up trying to use time on quantum scales, because it produced too many infinities. Yet today physicists routinely monitor processes on a quantum scale that require only a zeptosecond to complete. The propagation of light in a vacuum is not the "fastest" process in the universe by a long shot. This is chiefly why time is more fundamental than the propagation of a energy at the speed of light. This is also why relativity must be extended to the level of quantum fields. If they move, it must be relative to something. If they don't move, same idea.

Perhaps a model in some mathematician's head isn't the thing we should be concerned about, at least not until we have one that actually fits the observations.
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Plazma Inferno! · Jul 21, 2015

RajeshTrivedi said:

Schmelzer said:

As I have explained you, relative speed of different clocks does not matter at all. What matters is what appears in the formula τ=∫γηmndγmdγn−−−−−−−−−√. It is only one clock, only its trajectory γm(t), which matters.
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Are you sure with the color quote ? This is against the basic statement of SR with respect to 'context time dilation' and also against the stand of almost all the participants in this thread.

Although I am not a fan of Time Dilation as it is, but is the above line as per mainstream SR, or your alternative proposal ? Without claiming the knowledge of the proof of complex formula τ=∫γηmndγmdγn−−−−−−−−−√, I can say for sure that it cannot be derived from SR itself unless and until you bring in the spacetime, which is not an SR construct (although appears to use the gamma).

Your steadfast refusal to accept the time dilation between two spaceships despite their being relative velocities, suggests that you have something else in mind.

PS: I did some historical check, and found that indeed its a paradox, which was even acknowledged by the Einstein himself, he had to invoke GR to resolve this, that acceleration and Gravity aspect, but the issue remained unresolved due to many offshoots of this. Of course your 'ether' can solve this and I feel your above response is not based on SR, but based on your ether proposition only. [ you should have issued disclaimer.....not that I am opposing.]
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Plazma Inferno! · Jul 21, 2015

RajeshTrivedi said:

origin said:

That is true, my understanding is that frame S by convention is the 'nonmoving' frame and S' is the moving frame. Of course either frame can actually be thought of as the moving frame.
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You in your post # 44 seem to be agreeing with Schmelzer, his views relative speed of different clocks does not matter at all, is in direct contrast with your opening and early stand on this thread.
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Plazma Inferno! · Jul 21, 2015

danshawen said:

If the only tools a calculus instructor has to describe physical phenomena are calculus, Euclidean or Riemann geometry, finite math, complex numbers, linear algebra, probability and statistics, and optionally something like quaternions, you can rely on them trying to do exactly that with the available tools.

Just as it may be possible to build something like a functional clock or even a NAND gate (the most basic fundamental building block of digital computers) using only toy Lego blocks. Possible? Yes. Practical to use one as a wristwatch or a functional interface to the Internet? Probably not as easy as starting out using more suitable ideas, materials and specialized tools to build what you really needed from scratch.

If the only tool you have available to you is a hammer, every problem may resemble a nail. A large bag of assorted size hammers is probably not the ideal practical toolkit for most activities. Even if you may think they allow you to describe how gravity and impulses work in wonderful detail. Hammers are in some ways smarter than we are. They have no difficulty finding the exact geometrical direction to the center of the Earth, and they can do it without a compass, a straight edge, or the help of a long dead greek mathematician.
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Plazma Inferno! · Jul 21, 2015

origin said:

RajeshTrivedi said:

You in your post # 44 seem to be agreeing with Schmelzer, his views relative speed of different clocks does not matter at all, is in direct contrast with your opening and early stand on this thread.
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I was agreeing with the second part, I should not have had both sections there. Time dilation can be seen with relative velocity.
T′=T1−v2c2√
You will not see the aging difference with just relative velocity one of the twins must move to the reference frame of the other to see that.
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Plazma Inferno! · Jul 21, 2015

danshawen said:

Yes. A twin must accelerate, leave on a straight line or rounded trajectory, or else stop, turn around, re-accelerate, rejoin the twin that remained at rest. Then you will see a difference in aging. So walking, running, driving or flying can shave nanoseconds off your chronological age.

This does not mean you can accomplish more; you just age more slowly.
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Plazma Inferno! · Jul 21, 2015

Schmelzer said:

RajeshTrivedi said:

Are you sure with the color quote ? This is against the basic statement of SR with respect to 'context time dilation' and also against the stand of almost all the participants in this thread.
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First of all, I think it is clear enough that I do not care at all about majorities, not even in physics (else, I would be a string theorist), and even less in this forum.

Then, SR does not define any method to compute time dilation of clocks which are far away from each other. What would be necessary for this would be an absolute, objective notion of contemporaneity, which would allow such a comparison. It does not exist in the spacetime interpretation of SR at all, and even in the Lorentz interpretation it is unobservable.

RajeshTrivedi said:

Without claiming the knowledge of the proof of complex formula τ=∫γηmndγmdγn−−−−−−−−−√, I can say for sure that it cannot be derived from SR itself unless and until you bring in the spacetime, which is not an SR construct (although appears to use the gamma).
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The formula itself is far away from being complex, it is completely analogical to the formula τ=∫γδmndγmdγn−−−−−−−−−√ which described the length of a curve in Euclidean space. It is also an elementary consequence of the distortion of the clock time in the Lorentz ether, and does not require any spacetime interpretation.

RajeshTrivedi said:

Your steadfast refusal to accept the time dilation between two spaceships despite their being relative velocities, suggests that you have something else in mind.
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There is nothing I have to have in mind here, there is full agreement about the fact that there is no such animal as a "twin paradox" nor in SR, nor in the Lorentz ether. Of course, it is IMHO easier to understand this point based on the Lorentz ether, but the result is the same.

RajeshTrivedi said:

PS: I did some historical check, and found that indeed its a paradox, which was even acknowledged by the Einstein himself, he had to invoke GR to resolve this, that acceleration and Gravity aspect, but the issue remained unresolved due to many offshoots of this. Of course your 'ether' can solve this and I feel your above response is not based on SR, but based on your ether proposition only. [ you should have issued disclaimer.....not that I am opposing.]
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Nonsense. It seems you read wikipedia about this, there was such a nonsensical reference to Einstein there.
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Plazma Inferno! · Jul 21, 2015

paddoboy said:

RajeshTrivedi said:

PS : In Fact it is a good idea to create such sub forum, although dirty work, but Mods can shift the entire trash/abusive/plain-non-sense posts from each thread to such sub forum, just making the topic more readable...and if there are more than 10 such trashes in less than say 10 days, the member gets banned for 3 days. I stand to get banned as on date from this.
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What you suggest is already accepted procedure, just as posting alternative hypothesis under the guise of "questions" in science instead of the alternative section are, then when obvious removed to their proper place, as your past threads have.

RajeshTrivedi said:

As per SR/Lorentz Transformation math this Time Dilation does not seem to be about change in real time, this is just about observation time of an event in any frame, which would be of course frame specific once the observation is linked to light speed.
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All frames of references are as valid as each other, and that includes any time dilation effects. This is a postulate of relativity.

RajeshTrivedi said:

So, in my opinion
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Your opinion is just that. your opinion. It does not hold in the world of science in general, where SR/GR are overwhelmingly supported and align with all observations and experiments.

RajeshTrivedi said:

Although I am not a fan of Time Dilation as it is,
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Time dilation is an accepted part of the Universe we inhabit, and is evidenced every day.

RajeshTrivedi said:

Your steadfast refusal to accept the time dilation between two spaceships despite their being relative velocities, suggests that you have something else in mind.
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I'm sure Schmelzer does, and just as obviously so do you.....hence this thread in the guise of a question to push your anti SR religion.

RajeshTrivedi said:

PS: I did some historical check, and found that indeed its a paradox, which was even acknowledged by the Einstein himself, he had to invoke GR to resolve this, that acceleration and Gravity aspect, but the issue remained unresolved due to many offshoots of this. Of course your 'ether' can solve this and I feel your above response is not based on SR, but based on your ether proposition only. [ you should have issued disclaimer.....not that I am opposing.]
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Do you have a reference for that claim?
Obviously your claim is false and your reference [if you have one] is wrong.

Schmelzer said:

Nonsense. It seems you read wikipedia about this, there was such a nonsensical reference to Einstein there.
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Ahaa, So you got it from WIKI. WIKI in general serves a purpose rajesh, but there are other more reputable references from learned institutions and such that are more reliable.
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Plazma Inferno! · Jul 21, 2015

brucep said:

Janus58 said:

The two spaceships will measure a time difference between each others clocks. If the two ships are moving at 0.5c relative to the Earth, the Earth will measure their clocks as moving at a rate of 0.866 compared to the Earth clock and the ship will measure each others clocks as running at a rate of 0.6 compared to their own.

This is not contradictory, as with this scenario as with all others dealing with SR, you have to take all the effects of SR into account to get the complete picture and can't just isolate one like time dilation.

Here is a pair of space-time diagrams to illustrate.

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The left diagram are events according to the Earth. (the red line). Two either side at a distance of 1 light hr are two clocks which are synchronized to the Earth clock in the rest frame of the Earth. The numbers on the lines indicate clock readings 1 hr apart.

The two ships with their own clocks leave these two clocks when all clocks read zero. They meet at Earth when its clock reads 2 hrs and the ship clocks read 1.732 hours. They then continue until they reach the opposite clock when that clock reads 4 hrs and the ship clock read 3.464 hrs.

The right diagram shows events according to the ship that leaves the right clock (this ship is the light blue line. It leaves the right clock when both it and the right clock reads zero. However, according to this ship both the Earth clock and the opposite clock have already been running for sometime when his own ship starts off, and even though both clocks run slower than his,( by a factor of 0.866) the Earth clock already reads a bit less than 1/2 hr and the opposite clock reads 1 hr before the ship even leaves. And since the other ship left its clock when that clock read 0, it is already on its way before the right ship even starts. This means that the other ship's clock also started running before his.
What this means is that even though the other ship's clock is running slow by a rate of 0.6, its "head start" makes it so that when the two ships meet at Earth the right ship will agree that both ship's clocks read the same time. (1.732 hrs), also the Earth clock running at 0.866 speed, with its head start will read 2 hrs. The ships continue on. Our ship still measures the other ship as running slow, but now its lost its head start and starts to fall behind. But this ship (traveling at 0.8c away from me as measured by me is chasing after the clock I left which is moving away at 0.5c. Meanwhile the clock I am heading for is moving towards me at 0.5 c. I will reach my clock before he reach his. so when I reach my clock when it reads 4 hrs and mine reads 3.464 hrs, he hasn't reached his clock yet. He will continue on until he catches it when it read 4 hrs and his own clock reads 3.464 hrs.

If I switched views to the ship moving from the left to right, it would be a mirror image of the above description. The right ship will have left first and arrived last. The the reading on the clocks of all involved when clock are at the same point in space will all agree. And that's the main point. Everyone will agree what clocks at the same point in space read, even though they won't agree as to what clocks separated from each other read. It doesn't matter that according to ship 1 ship 2's clock runs slow while according to ship 2 it's ship 2's clock that runs slow, or that according to ship 1, ship 2 started first while according to ship 2 it is the other way around, while according to the Earth they started at the same time and their clocks ticked at the same rate, just as long as these effect combine to assure that when the clocks meet, everyone agrees on their respective readings. And that is the whole point behind SR to ensure that all these clock do agree when they meet while at the same time maintaining the invariance of the speed of light.
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Nice discussion. Thanks.
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Plazma Inferno! · Jul 21, 2015

danshawen said:

I second the motion. Of all the discussions of time dilation I have ever read on any forum or text, this one is by far the most thorough and satisfying, even including ones I paid for in college. I lost a misconception or two here to boot. Thanks, everyone.

Everyone here seems to agree that time dilation is different everywhere (other than "at rest" in the same frame) depending on both relative motion and gravity.

Even "at rest" is a dynamic state in matter, and time dilation happens within atomic structure as well. The decay of atomic nuclei is an example. Models exist that can be used to calculate a lifetime of 10^18 years for the decay rate for a free photon. Bound as energy in an electron, a photon need never decay, so time dilation is a concept that easily applies in the quantum domain, even if its direct application is limited by the uncertainty principle.

Little Bang has pointed out that it would useful to know whether time dilation is infinite in the case of electrons, some of which are entangled as well.

Bound electrons routinely change quantum energy states by means of exchanging photons. This suggests that time dilation would also need to be infinite for electrons as it is for photons in order for bound electrons to capture the energy of photons prior to a change of state.

Can anyone answer LB's follow-up time dilation question?
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Plazma Inferno! · Jul 21, 2015

RajeshTrivedi said:

Schmelzer said:

First of all, I think it is clear enough that I do not care at all about majorities, not even in physics (else, I would be a string theorist), and even less in this forum.
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It is ok to follow the rational majority view, the problem and dissent comes only when the majority view is irrational. The problem comes who decides what is rational and what is irrational.

Coming back to OP, the majority view (SR) view is that the time dilation in the context is an outcome of relative motion between the frames, but it appears you have taken a contrary view on the cause, so please clarify your position.

Schmelzer said:

There is nothing I have to have in mind here, there is full agreement about the fact that there is no such animal as a "twin paradox" nor in SR, nor in the Lorentz ether. Of course, it is IMHO easier to understand this point based on the Lorentz ether, but the result is the same.

Nonsense. It seems you read wikipedia about this, there was such a nonsensical reference to Einstein there.
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You are not clear, here. if you are saying that as such there is no paradox, and it is just the construction of those who want to question SR, then thats the relativists point of view. Fair enough. But if you are refusing to accept the argument, that the SR statement itself which is thrown by many on this thread, is a paradox in itself, then you have to do some explaining. The statement which is found paradoxical is "That the SR only knows the relative speed between two frames (ignore the acceleration for time being), it does not know the individual speed, so both the frames will see the time dilation in other, but in reality it can happen to only one." Thats the paradox.

And as far as history of the same is concerned, do a small google search, you will get hundreds of papers on this paradox. Einstein kept his silence for quite some time despite Langevin (1911) pushed the same. Einstein attempted to provide a solution in 1918 based on GR (acceleration and turn around), but the same also was questioned later on.

So your adamant approach that it is not a Paradox, is not clear.

"Einstein wrote the paper after he created the General Theory of Relativity. He therefore emphasized that he was discussing the special principle of relativity and not the general principle of relativity. This was important, because the twin paradox was also explained within the scope of General Relativity, but in this 1918 paper Einstein supplied only the special relativistic explanation."

Lot of reference is there about this paper of Einstein (1918) wherein he attempted to resolve the issue.

Some, may refer to the link below, this is a good read, the example of locomotive and grass/landscape is a good attempt to differentiate between what is moving and what is not....(The above italics para is also taken from below)
http://arxiv.org/ftp/arxiv/papers/1205/1205.0922.pdf
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