Twin Paradox And Time Dilation

RajeshTrivedi · Jul 9, 2015

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But then who will 'Bells' the cat !!!

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brucep · Jul 9, 2015

RajeshTrivedi said: ↑

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But then who will 'Bells' the cat !!!
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You feel the need to start this thread with cryptic bullshit as the content? Quit trolling these threads with bullshit irrelevant nonsense. This is a good example why the moderation should include a review of initial thread content before it gets on the board.

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OnlyMe · Jul 10, 2015

brucep said: ↑

You feel the need to start this thread with cryptic bullshit as the content? Quit trolling these threads with bullshit irrelevant nonsense. This is a good example why the moderation should include a review of initial thread content before it gets on the board.
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Earlier today Bells posted the following in another area of the forum...!
http://www.sciforums.com/threads/ac...aradox-and-time-dilation.151804/#post-3314104

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RajeshTrivedi · Jul 10, 2015

Mods,

Please shift this thread to where Bells posted, that is at SF Open Govt......otherwise it may bring in some unwarranted steam.

Plazma Inferno! · Jul 20, 2015

*Administrator's Notice*

The discussion below is recovery of previously deleted "Twin Paradox and Time Dilation" thread.

I'll post all previous posts with quote references to original posters.

Job will be done during the next couple of days because the amount of work and my other duties.
Until then, thread stays locked for new posts.

Also, LaTex don't work this way, so if you'll have to send me the proper formatting for formulas.

Plazma Inferno! · Jul 20, 2015

RajeshTrivedi said: ↑

It is to do with Time Dilation in Special Theory of relativity. The details are available at...

https://en.wikipedia.org/wiki/Twin_paradox

The paradox, gets further compounded by bringing in another spaceship moving in opposite directions, there are few versions of this available on the web, which attempt to challenge the SR..

I feel there exists a simple resolution to this paradox, if we consider a Dynamic Hypothetical Frame of Reference as suggested below..

The frame itself is not at any spatial fixed point, and the same is hypothetical in a sense that it always aligns itself in the direction of the resultant motion of the observed particle.

To understand the same, consider a point source of light, situated far away (at infinity) from the observed objects, which is emitting light radially in all the spatial direction. Thus there shall be infinite hypothetical lines emitting out of this point source and travelling at a speed of light. Now if we wish to define the time aspect of a clock placed on an observer moving at some speed ‘v’ in any random direction, at any given instant there will be only one radial line from this point source of light lines which will be parallel to this direction of ‘v’ and moving in the same direction as the clock. So the apparent speed of light line with respect to this clock1 shall be c-v1, similarly for a clock2 moving with a speed v2 with respect to another parallel light line it will be c-v2.

So the effective Relative Speed between the two clocks shall be = (v2-v1). What is being done is that time is being calculated with respect to this third aligned reference frame, which does not distinguish between the direction of motion, it only looks after the speed magnitude in comparison with speed of light. Two spaceships moving at the same speed but in different directions are taken to be same with respect to this frame.

Example: If two spaceship are launched at a speed 0.2c from Earth in opposing direction, then the relative speed between Earth and Each spaceship will be 0.2 c (ignoring the Earth's own background resultant speed), and the relative speed between the spaceships shall be zero.....both spaceships are moving at (c-0.2c) with respect to their respective orientation light line.
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Plazma Inferno! · Jul 20, 2015

[URL='http://www.sciforums.com/members/schmelzer.282758/']Schmelzer[/URL] said:

First, the "twin paradox" is not paradoxical at all, it only shows that "time dilation" is a real effect of clocks: Moving clocks are going slower.

Of course, in relativity you have no way to identify what is the same time given this distortion of clocks. So, this slowing down of clocks can be established without problems of coordination between different clocks only if initially and finally the clocks are at the same place. This does not change the fact that moving clocks are going slower.

Your text seems to suggest a particular way to construct some system of coordinates. You are, of course, free to construct arbitrary systems of coordinates, but this does not modify anything in the thought experiment named "twin paradox". That it is not even a paradox, so that it cannot be solved even in principle, we can even ignore - even if there would be something paradoxical, yet another system of coordinates would not change anything.
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Plazma Inferno! · Jul 20, 2015

origin said:

I don't know why you insist on trying to push pseudoscience. What is the point? The only thing that matters for time dilation in SR is the relative velocity between the observer and the observed. It does not matter if there are 1500 space ships in different reference frames.

Anyway, like Schmelzer said it is not a paradox, SR resolves the apparent paradox.
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Plazma Inferno! · Jul 20, 2015

RajeshTrivedi said:

In reply to Schmelzer:

The one of the offshoot of original problem is as follows...

Suppose two spaceship cross each other from opposing direction at a constant speed v, with respect to that cross over point. Now the standard relative speed between them is 2v (say non relativistic)...so the point is which clock will move slower and why? Assume that Earth is that cross over point, and all the 3 clocks are synchronized at the time of cross.......Now as per SR calculations both the clocks on the spaceships will be slower with respect to Earth by the same time factor, implying that both the clocks with respect to each other will have no time variation despite having a relative speed 2v between them. Is there any catch in this ?
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Plazma Inferno! · Jul 20, 2015

origin said:

RajeshTrivedi said: said:

The one of the offshoot of original problem is as follows...
Suppose two spaceship cross each other from opposing direction at a constant speed v, with respect to that cross over point. Now the standard relative speed between them is 2v (say non relativistic)...so the point is which clock will move slower and why?
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The clocks of each ship will run slower relative to the other. The reason is the relative velocity between the ships.

RajeshTrivedi said: said:

Assume that Earth is that cross over point, and all the 3 clocks are synchronized at the time of cross.......Now as per SR calculations both the clocks on the spaceships will be slower with respect to Earth by the same time factor
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Correct.

RajeshTrivedi said: said:

implying that both the clocks with respect to each other will have no time variation despite having a relative speed 2v between them.
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No, that is not correct. The clocks on the ships will still run slower with respect to the other ships clocks because of the relative velocity. Remember it is only the relative velocity between the observer and the observed, it does not matter if there is another observer of you two that disagrees with you, it is that simple.
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Plazma Inferno! · Jul 20, 2015

Janus58 said:

RajeshTrivedi said:

The one of the offshoot of original problem is as follows...

Suppose two spaceship cross each other from opposing direction at a constant speed v, with respect to that cross over point. Now the standard relative speed between them is 2v (say non relativistic)...so the point is which clock will move slower and why? Assume that Earth is that cross over point, and all the 3 clocks are synchronized at the time of cross.......Now as per SR calculations both the clocks on the spaceships will be slower with respect to Earth by the same time factor, implying that both the clocks with respect to each other will have no time variation despite having a relative speed 2v between them. Is there any catch in this ?
Click to expand...

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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Plazma Inferno! · Jul 20, 2015

Schmelzer said:

RajeshTrivedi said:

Suppose two spaceship cross each other from opposing direction at a constant speed v, with respect to that cross over point. Now the standard relative speed between them is 2v (say non relativistic)...so the point is which clock will move slower and why? Assume that Earth is that cross over point, and all the 3 clocks are synchronized at the time of cross.......Now as per SR calculations both the clocks on the spaceships will be slower with respect to Earth by the same time factor, implying that both the clocks with respect to each other will have no time variation despite having a relative speed 2v between them. Is there any catch in this ?
Click to expand...

The answer which clock is slower depends on how you define time. Thus, if you use different time coordinates you obtain different answers. What is the problem?
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Plazma Inferno! · Jul 20, 2015

paddoboy said:

As others have said, the twin paradox is not really a paradox.
Basically the two FoRs are not equitable due to the fact that one needs to turn around and decelerate and accelerate again.
The following explains it nice and simply.
http://newt.phys.unsw.edu.au/einsteinlight/jw/module4_twin_paradox.htm

Although janus58 seems to have explained it beautifully.

I'll just add that while travelling at relativistic speeds is beyond us at this moment, it is routine procedure in particle accelerators that can reach 99.999% "c"
Results of course have always supported SR 100%
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Plazma Inferno! · Jul 20, 2015

danshawen said:

As has already been noted, not really a paradox, but there is one point that always seems to get lost in any twin 'paradox' discussion.

There might be 1500 different inertial reference frames. Getting from one to another requires acceleration, negative or positive. However, in so many choices of inertial reference frames, not all are equal.

Some of them will be closer to the speed of light (the absolute limit). Some of them will be further from the speed of light. If some of them are "at rest", it is because either they were not accelerated relative to the others, or else were accelerated in such a manner that they are traveling more slowly, RELATIVE TO THE SPEED OF LIGHT, than any of the others. The ones that have relative velocities closer to that of light will have the greatest measure of time dilation. The ones that have relative velocities closer to "at rest" with respect to the reference frame from which they all began, will have the smallest measure of time dilation.

A more paradoxical issue is that right now, we are moving away from cosmologically distant galaxies at relativistic rates (but not the speed of light). So, evidently, you could make time pass much more quickly for yourself simply by embarking on a relativistic voyage that is in the general direction of the midpoint between those distant galaxies and our own. Someone going on a voyage in the same direction our galaxy is going would push the effective velocity even closer to the speed of light than it presently is, slowing time down relative to the point from which the twins departed. In this manner, the general direction a relativistic voyage takes makes a big difference with respect to whether time ends up speeding up and slowing down.

Think more carefully about it. Is this what you were taught? Didn't think so.
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Plazma Inferno! · Jul 20, 2015

origin said:

danshawen said:

As has already been noted, not really a paradox, but there is one point that always seems to get lost in any twin 'paradox' discussion.

There might be 1500 different inertial reference frames. Getting from one to another requires acceleration, negative or positive. However, in so many choices of inertial reference frames, not all are equal.
Click to expand...

All frames are equal there is no preferred frame!

danshawen said:

Some of them will be closer to the speed of light (the absolute limit). Some of them will be further from the speed of light. If some of them are "at rest", it is because either they were not accelerated relative to the others, or else were accelerated in such a manner that they are traveling more slowly, RELATIVE TO THE SPEED OF LIGHT, than any of the others. The ones that have relative velocities closer to that of light will have the greatest measure of time dilation. The ones that have relative velocities closer to "at rest" with respect to the reference frame from which they all began, will have the smallest measure of time dilation.
Click to expand...

This shows a real confusion about Special Relativity. The time dilation depends only on the relative speed between the observer and the observed. The line "Some of them will be closer to the speed of light (the absolute limit)" is basically meaningless.
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Plazma Inferno! · Jul 20, 2015

danshawen said:

You are right.
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Plazma Inferno! · Jul 20, 2015

RajeshTrivedi said:

origin said:

The clocks of each ship will run slower relative to the other. The reason is the relative velocity between the ships.

Correct.

No, that is not correct. The clocks on the ships will still run slower with respect to the other ships clocks because of the relative velocity. Remember it is only the relative velocity between the observer and the observed, it does not matter if there is another observer of you two that disagrees with you, it is that simple.
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I think your 'correct' and 'not correct' is not based on logical approach...

Statement
Assume that Earth is that cross over point, and all the 3 clocks are synchronized at the time of cross.......Now as per SR calculations both the clocks on the spaceships will be slower with respect to Earth by the same time factor

Deduction
implying that both the clocks with respect to each other will have no time variation despite having a relative speed 2v between them.

You agree to the statement, but disagree to the deduction. How is that possible ? The deduction appears to be the most logical inference from the statement. Where is the catch ?
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Plazma Inferno! · Jul 20, 2015

RajeshTrivedi said:

Schmelzer said:

The answer which clock is slower depends on how you define time. Thus, if you use different time coordinates you obtain different answers. What is the problem?
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You hit it right, but...
The Biology is the problem.

1. A spaceship speed profile is programmed in such a manner that when it returns to Earth the time dilation is 4 years...that means if the person on the Earth has grown old by 10 years, then the person on the spaceship has grown old just by 6 years.

2. Now take triplets, and dispatch two spaceships in different directions with the same speed profile to enable them return to earth at the same time after the time dilation of 4 years.

3. Now suppose there is a biological gland, which triggers exactly when the person gets 18 years old. Now the experiment started when all the triplets were 8 years old...when the spaceships returned (10 years of Earth time), the triplet on the Earth is 18 and his biological gland triggered, but the fellows on spaceship are just 8 + 6 = 14 years. Will their Gland also trigger or now on Earth they will have to wait for 4 more years ? This explains the other related problem of no time dilation in both travelling spaceships with each other despite having relative speeds.
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Plazma Inferno! · Jul 20, 2015

RajeshTrivedi said:

Janus58 said:

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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Thanks for the detailed post, but the colored line is quite intriguing. You mean to say that Twin on spaceship, when it returns to the Earth, will be of the same age with the twin on the Earth....
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Plazma Inferno! · Jul 20, 2015

RajeshTrivedi said:

danshawen said:

As has already been noted, not really a paradox, but there is one point that always seems to get lost in any twin 'paradox' discussion.

There might be 1500 different inertial reference frames. Getting from one to another requires acceleration, negative or positive. However, in so many choices of inertial reference frames, not all are equal.

Some of them will be closer to the speed of light (the absolute limit). Some of them will be further from the speed of light. If some of them are "at rest", it is because either they were not accelerated relative to the others, or else were accelerated in such a manner that they are traveling more slowly, RELATIVE TO THE SPEED OF LIGHT, than any of the others. The ones that have relative velocities closer to that of light will have the greatest measure of time dilation. The ones that have relative velocities closer to "at rest" with respect to the reference frame from which they all began, will have the smallest measure of time dilation.

A more paradoxical issue is that right now, we are moving away from cosmologically distant galaxies at relativistic rates (but not the speed of light). So, evidently, you could make time pass much more quickly for yourself simply by embarking on a relativistic voyage that is in the general direction of the midpoint between those distant galaxies and our own. Someone going on a voyage in the same direction our galaxy is going would push the effective velocity even closer to the speed of light than it presently is, slowing time down relative to the point from which the twins departed. In this manner, the general direction a relativistic voyage takes makes a big difference with respect to whether time ends up speeding up and slowing down.

Think more carefully about it. Is this what you were taught? Didn't think so.
Click to expand...

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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