How is twin paradox resolved in case of no/zero acceleration?

[lovetruth]

Clearly. But why do they BOTH subtend smaller angles? How come one doesn't subtend a smaller angle and the other subtend a larger angle? The answer, unsurprisingly, is symmetry.

Symmetry is more general than that. Mathematically and physically symmetry means that something does not change under some specific transformation. For instance, an equilateral triangle is symmetric under 120º rotations about its center because it is unchanged by that transformation.

In the case of the example above with distant objects, A and B, looking at each other the angle subtended is determined by Euclidean geometry which is unchanged by rotations and translations. Since A and B are related to each other via a rotation and a translation they are symmetric, meaning that the geometry is also unchanged by transformation of swapping A with B. Therefore, if the angle subtended by A decreases for B then by symmetry we can swap A and B and state that the angle subtended by B decreases for A.

In the case of relativity (either Galileo's or Einstein's) it is a fundamental postulate of the theory that the laws of physics are unchanged by boosts. So if A and B are related to each other via a boost then they are symmetric and in any statement you can swap A and B and have an equally valid statement. So if A's clock is slow according to B then by symmetry B's clock is slow according to A.

Do you feel like you understand the important role of symmetry a little better now?

You are right that both twins will observe Time Dilation according to SR. No doubt.

But you can not see the PARADOX. A twin will see that other twin is younger than him. So both the twin will see different reality or things.
Twin A will see that he is older than B. Twin B will see that he is older than A.
But reality is unique and can not be relative otherwise, the concept of "personal reality" should be there which is absurd.

 

[lovetruth]

Yes, and a moving clock going slower is also just an optical illusion …

do you really think that a moving (non-accelerating) clock is actually going slower? ​

btw, the Lorentz-Fitzerald contraction is an optical illusion too …

do you really think that a moving train actually changes shape? ​

Time dilation & length contraction are real not illusion.

Yes the train length will shorten really.

 

[HallsofIvy]

You are right that both twins will observe Time Dilation according to SR. No doubt.

But you can not see the PARADOX. A twin will see that other twin is younger than him. So both the twin will see different reality or things.
Twin A will see that he is older than B. Twin B will see that he is older than A.
But reality is unique and can not be relative otherwise, the concept of "personal reality" should be there which is absurd.

No, it's not. Each twin will see the other as younger and that is reality. As long as the two twins never get back together, at the same place with 0 relative speed, there is no paradox.

 

[Dale]

You are right that both twins will observe Time Dilation according to SR. No doubt.

But you can not see the PARADOX. A twin will see that other twin is younger than him. So both the twin will see different reality or things.
Twin A will see that he is older than B. Twin B will see that he is older than A.
But reality is unique and can not be relative otherwise, the concept of "personal reality" should be there which is absurd.

In this case which twin is older is a matter of perspective (I.e. Coordinate dependent), and does not have anything to do with the uniqueness of "reality".

If there were two fans watching a race from opposite sides of the road and one saw that the racers went left while the other saw that the racers went right, would you complain about PARADOX and "personal reality", or would you simply recognize that the direction the racers ran is coordinate dependent?

 

[lovetruth]

No, it's not. Each twin will see the other as younger and that is reality. As long as the two twins never get back together, at the same place with 0 relative speed, there is no paradox.

In this case which twin is older is a matter of perspective (I.e. Coordinate dependent), and does not have anything to do with the uniqueness of "reality".

If there were two fans watching a race from opposite sides of the road and one saw that the racers went left while the other saw that the racers went right, would you complain about PARADOX and "personal reality", or would you simply recognize that the direction the racers ran is coordinate dependent?

So you both are suggesting that reality is frame dependent.
Is it not equivalent to multiverse. Every observer living in his own world different from that of another.
Consider this: You see that a man has died but the man sees that he is alive. Is this not a paradox.

I think there is only one universe and a single reality. Everyone sees the same.

 

[Aimless]

So you both are suggesting that reality is frame dependent.
Is it not equivalent to multiverse. Every observer living in his own world different from that of another.
Consider this: You see that a man has died but the man sees that he is alive. Is this not a paradox.

I think there is only one universe and a single reality. Everyone sees the same.

Reality is not frame dependent. Observations of reality are frame dependent. Fortunately, we happen to know how to transform observations from one frame to another.

 

[GrayGhost]

Consider this: You see that a man has died but the man sees that he is alive. Is this not a paradox.

Depends on if the man sees himself still alive "when and where" you see him dead. That would be a parodox. IOWs, you see the man die when the man's own wristwatch read 7/21/11 12:00pm. If the man "holds himself alive" when his own wristwatch read 7/21/11 12:01pm, that would be a parodox. On the other hand, if the man holds himself alive when his own wristwatch read 7/20/11 3:01am, then no parodox, no problem.

Per STR, the man can be reported by others as both dead and alive, but not by any single observer. If you and I execute a flyby, with you at rest with the man and I at luminal speed wrt the man, ... then upon our flyby event, you can later prove he was deceased per you (his clock may have read 7/21/11 12:01pm) and I can later prove he was still alive per me (his clock may have read 7/20/11 3:01am). When we are momentarily colocated, I see the man as 9 hr younger than the dead man you see, but the same man none the less. I will also be able to prove that "later", when the man's clock read 7/21/11 12:01pm per ME, he had just died. This would be consistent with what you saw, and consistent with a single reality.

I think there is only one universe and a single reality. Everyone sees the same.

That's what STR suggests as well. One reality, differing points of view.

GrayGhost

 

[lovetruth]

Reality is not frame dependent. Observations of reality are frame dependent. Fortunately, we happen to know how to transform observations from one frame to another.

As I have discussed in the previous posts that Twins with no acceleration will see that they are older than their counterpart.
The views of both the Twins will not be consistent. They will not agree on who is more older. This means they are living in different realities or world or universe(interchangeable terms). Their observations are not same. Thus a concept of reality as unique or observe-independent is shattered.

Consider this paradoxial situation: Twin A sees that he is an old man while twin B is still a baby. Twin B sees that he is an old man while twin A is still a baby.

 

[Aimless]

Consider this paradoxial situation: Twin A sees that he is an old man while twin B is still a baby. Twin B sees that he is an old man while twin A is still a baby.

There is no paradox. By transforming the observations from the frame of Twin A into the frame of Twin B, we find that both observations are consistent. Which is what I said to begin with. Observations are frame dependent. QED

 

[pervect]

As I have discussed in the previous posts that Twins with no acceleration will see that they are older than their counterpart.
The views of both the Twins will not be consistent. They will not agree on who is more older. This means they are living in different realities or world or universe(interchangeable terms). Their observations are not same. Thus a concept of reality as unique or observe-independent is shattered.

Consider this paradoxial situation: Twin A sees that he is an old man while twin B is still a baby. Twin B sees that he is an old man while twin A is still a baby.

I haven't read the previous posts in depth, and you failed to provide a link to which post in this long thread you're referring to. But if you think there is some inconsistency here, you're sill wrong, whether or not you've previously posted the wrongness. But it's a bit hard to tell exactly where y you're going wrong if you're just saying that "I still say that", repeating some previous incorrect conclusion, rather than providing the details. But this leads to another meta-issue.

You don't give the impression of to be actually trying to understand what's going on, (as per your remarks about "I've said this wrong thing before", as if it proved something), you seem intent on reiterating your wrong views rather than learning something.

As far as what you did say, it wouldn't be paradoxical for twin A to conclude that he was old and B was a baby, and vica-versa, if they are spatially separated and using different definitions of how to compare there ages.

For instance see https://www.physicsforums.com/attachment.php?attachmentid=37080&stc=1&d=1310342900

One twin uses the red lines to compare simultaneous events, another the green lines. So each can say that they are younger than the other, according to their method of comparison.


And there isn't a case where an actual pair of real observers (and not some composite created from the view of multiple real different observers, said composite being generated using additional assumptions that need to be gone into) that actually observes what you describe. So the case you describe would be a paradoxical, however it doesn't actually happen that way (unless you count the case I mentioned above, where one twin uses the red lines and the other the green lines). Which is most likely what people have been trying to tell you all along, and I'm guessing from your remarks about having "posted this all before' that they've tried to correct you before.

 

[GrayGhost]

As I have discussed in the previous posts that Twins with no acceleration will see that they are older than their counterpart. The views of both the Twins will not be consistent. They will not agree on who is more older.

Their view will be inconsistent only if they do not consider the Lorentz transformations as the relationship wrt space and time between themselves.

This means they are living in different realities or world or universe(interchangeable terms). Their observations are not same. Thus a concept of reality as unique or observe-independent is shattered.

Yes, I can remember long ago when I thought the exact same thing. It's very difficult to de-cling oneself from ancient beliefs. Took me awhile before I accepted the meaning of relativity. Folks simply have to prove it to themselves, and everyone takes the time they themselves need. I've seen many give up.

Consider this paradoxial situation: Twin A sees that he is an old man while twin B is still a baby. Twin B sees that he is an old man while twin A is still a baby.

They always agree on their disagreements, per the LTs. When they ever reunite, they agree on their age differential per clock comparison, which abides by the LTs applied over the roundtrip.

GrayGhost

 

[Dale]

So you both are suggesting that reality is frame dependent.

I never suggested any such thing. This is a complete mischaracterization of what I actually said. Please re- read what I posted.

Everyone sees the same.

This is clearly false.

 

[lovetruth]

They always agree on their disagreements, per the LTs. When they ever reunite, they agree on their age differential per clock comparison, which abides by the LTs applied over the roundtrip.

GrayGhost

If the twins disagree on their age difference then, observations should depend on perspective. So there is no absolute fact on which all observers agree as observations are relative.

 

[lovetruth]

I haven't read the previous posts in depth, and you failed to provide a link to which post in this long thread you're referring to. But if you think there is some inconsistency here, you're sill wrong, whether or not you've previously posted the wrongness. But it's a bit hard to tell exactly where y you're going wrong if you're just saying that "I still say that", repeating some previous incorrect conclusion, rather than providing the details. But this leads to another meta-issue.

You don't give the impression of to be actually trying to understand what's going on, (as per your remarks about "I've said this wrong thing before", as if it proved something), you seem intent on reiterating your wrong views rather than learning something.

As far as what you did say, it wouldn't be paradoxical for twin A to conclude that he was old and B was a baby, and vica-versa, if they are spatially separated and using different definitions of how to compare there ages.

For instance see https://www.physicsforums.com/attachment.php?attachmentid=37080&stc=1&d=1310342900

One twin uses the red lines to compare simultaneous events, another the green lines. So each can say that they are younger than the other, according to their method of comparison.


And there isn't a case where an actual pair of real observers (and not some composite created from the view of multiple real different observers, said composite being generated using additional assumptions that need to be gone into) that actually observes what you describe. So the case you describe would be a paradoxical, however it doesn't actually happen that way (unless you count the case I mentioned above, where one twin uses the red lines and the other the green lines). Which is most likely what people have been trying to tell you all along, and I'm guessing from your remarks about having "posted this all before' that they've tried to correct you before.

You are trying too hard to make a point that I am wrong. You have unnecessarily overstressed on my phrase 'As i have posted before'.

The only thing that I find paradoxial or counterintuitive is the fact that Observers or Twins should disagree on any subject or matter. It may be my experience bias and this may not be a paradox at all.
But even if I accept that Twins will disagree on their age, how can twins are seeing the same reality?

 

[tiny-tim]

But even if I accept that Twins will disagree on their age, how can twins are seeing the same reality?

they don't disagree on their age, they disagree on their rate of ageing

(they don't disagree on their age because they can't make measurements at what they both agree is at the same time)

the whole point of the twin paradox (or clock paradox) thought-experiments is that they incorporate a comparison of age …

and they agree on which one is older (at the same time)​

leave out the comparison of age, and all you have left is the standard comparison of ageing which is no more surprising than perspective​

 

[lovetruth]

There is no paradox. By transforming the observations from the frame of Twin A into the frame of Twin B, we find that both observations are consistent. Which is what I said to begin with. Observations are frame dependent. QED

Since seeing is believing, observations and reality must be synonymous. If observations are frame dependent then so should reality be. Everything depends on perspective.

A twin will see that he is not only older but also fatter than his counterpart.
Now I like to believe that reality is rigid, absolute, frame-independent and objective. Every observer must agree on what other see. If a kid sees that he is younger than his parents then, parents should see that they are older than their kid.
To say that observations are relative is equivalent to saying that reality is subjective and a matter of perspective.

 

[Dale]

Since seeing is believing, observations and reality must be synonymous. If observations are frame dependent then so should reality be. Everything depends on perspective.

lovetruth, please answer the following question:

If there were two fans watching a race from opposite sides of the road and one observed that the racers went left while the other observed that the racers went right, would you say that therefore reality is frame dependent?

 

[lovetruth]

lovetruth, please answer the following question:

If there were two fans watching a race from opposite sides of the road and one observed that the racers went left while the other observed that the racers went right, would you say that therefore reality is frame dependent?

Left and right are just personal convention, they do not have meaning by themselves. They mean what the observer want it to mean. We can call the north as south and south as north and still there will be no major difference if all people will follow this convention. But an apple falling down on Earth is a fact, it should be observed by all observers. Ofcourse, people can call apple by any name in their own language but none can deny that it is falling towards the earth.

 

[harrylin]

So you both are suggesting that reality is frame dependent.
Is it not equivalent to multiverse. Every observer living in his own world different from that of another.
Consider this: You see that a man has died but the man sees that he is alive. Is this not a paradox.

I think there is only one universe and a single reality. Everyone sees the same.

Hi lovetruth, I agree that there is but a single reality. However, everyone has a different perspective of reality. And with relativity theory, it has become clear that some things that in Newtonian physics were assumed to be agreed upon by all, such as our concepts of "space" and "time", are also a matter of perspective.

See for one of the first lengthy, but interesting discourses on that topic (incl. the "twin paradox"):

http://en.wikisource.org/wiki/The_Evolution_of_Space_and_Time

Cheers,
Harald

 

[Dale]

Left and right are just personal convention, they do not have meaning by themselves.

Same with the rate of a clock, including biological clocks like ageing. The idea of frame-variant quantities is not particularly new, and relativity simply expands the class of quantities that are frame variant.

 

[harrylin]

Same with the rate of a clock, including biological clocks like ageing. The idea of frame-variant quantities is not particularly new, and relativity simply expands the class of quantities that are frame variant.

Yes indeed. Expanding on that, to make it less abstract: already in Newton's physics, a bullet may have for example a momentum of 1 kgm/s in one reference system, while the same bullet has a momentum of 0 kgm/s in a co-moving reference system.

Harald

 

[lovetruth]

Same with the rate of a clock, including biological clocks like ageing. The idea of frame-variant quantities is not particularly new, and relativity simply expands the class of quantities that are frame variant.

You have mixed up the idea of 'naming convention' and 'physical phenomena'. If A is older than B is a physical fact then it must be observed by all. There must be agreement among observers otherwise everyone sees differently and no absolute fact can exist as everything is relative. If this is true then everyone is living in his own world.

 

[lovetruth]

Yes indeed. Expanding on that, to make it less abstract: already in Newton's physics, a bullet may have for example a momentum of 1 kgm/s in one reference system, while the same bullet has a momentum of 0 kgm/s in a co-moving reference system.

Harald

Momentum is frame dependent but the application of Newtons law give same results in all frames. If bullet with 1 kgm/s will kill a person in one frame then, bullet with 0 kgm/s will kill the same person in another frame. All frames give same result.

But time dilation gives different result of a physical phenomena like ageing. The observation is affected by the choice of frame.

 

[Dale]

If A is older than B is a physical fact then it must be observed by all.

No, it is not. No more than if the racer is going left or right.

 

[Doc Al]

If A is older than B is a physical fact then it must be observed by all.

If they are side by side, then that's certainly true. But if they are a distance apart, then there is ambiguity. At what time are you measuring their age? Supposedly, 'at the same time'. But realize that observers in relative motion will measure simultaneity differently.

There must be agreement among observers otherwise everyone sees differently and no absolute fact can exist as everything is relative.

Despite the fact that measurements of time and space are frame dependent, there is agreement among observers: While they may measure different lengths and times, those in one frame can easily 'convert' their measurements to determine what observers in relative motion would measure. Some things that we once thought of as 'facts' turned out to depend on one's state of relative motion; that just led us to a deeper understanding of how the world is structured.

 

[GrayGhost]

If the twins disagree on their age difference then, observations should depend on perspective. So there is no absolute fact on which all observers agree as observations are relative.

Wrt 1st sentence ... observations do depend on perspective. Observations cannot disagree with reality, even though observers can disagree on the measure of space and time (and what are simultaneous events).

Wrt 2nd sentence ... incorrect. While the twins are separated, they disagree on where and when remotely located luminally moving others are per their own measurements of distance and duration. Per the LTs they agree they should disagree, and they can predict precisely what the other would then hold. Let's say some remotely located luminal fellow does a flyby of 5 bouys along his way over a defined interval. Even though observers have their disagreements, they can never disagree on what the moving fellow's clock read on each bouy flyby. All agree on that, including said fellow. Therefore, reality is rock solid and the same for all. When the twins arrive back on Earth for clock comparison and find twin B younger than twin A, all in the cosmos expected just that (again, 1 reality, no disagreement) assuming their predictions stemmed from application of the LTs.

The problem many folks have, is that they cling to the old notion that time's rate must pass unequivocally the same for all everywhere all the time, ie Newton's belief. Hence, they have difficulty accepting that the relative rate of time between luminally moving observers can vary with their relative motion. I must admit, it was not easy for me either :)

It seems that your primary concern comes from what's called "cooridnate measurements", which can disagree between observers because they are based on each one's own sense of NOW (ie sense of simultaneity cosmos wide) which are rotated wrt one another in space and time. Yet, even though this is true, 1 single sole reality is upheld, because no observers can ever disagree on what a clock reads AT any event in spacetime, ever. An event might be 2 clocks momentarily passing one another. It may be 2 twins sitting down at lunch for clock comparison after B returns from his roundtrip. It might by a single clock passing a bouy in free space. Might be the time a clock read while orbiting a star that went supernova. Etc. It's when 2 bodies (eg clocks) are in-the-same-place-at-the-same-time. All in the cosmos agree. I agree that the meaning of "coordinate time differentials" is a more difficult concept to grasp in STR. That seems to be the primary problem you are having from what I read.

GrayGhost

 

[tiny-tim]

But time dilation gives different result of a physical phenomena like ageing. The observation is affected by the choice of frame.

no they don't!

as GrayGhost says …

Let's say some remotely located luminal fellow does a flyby of 5 bouys along his way over a defined interval. Even though observers have their disagreements, they can never disagree on what the moving fellow's clock read on each bouy flyby …

… if one observer goes on a journey from A to B, then all observers agree on how much he aged between A and B …

the different observers time dilations are different, but they give the same result on physical phenomena like ageing …

do you really disagree with that? ​

 

[lovetruth]

If they are side by side, then that's certainly true. But if they are a distance apart, then there is ambiguity. At what time are you measuring their age? Supposedly, 'at the same time'. But realize that observers in relative motion will measure simultaneity differently.

Despite the fact that measurements of time and space are frame dependent, there is agreement among observers: While they may measure different lengths and times, those in one frame can easily 'convert' their measurements to determine what observers in relative motion would measure. Some things that we once thought of as 'facts' turned out to depend on one's state of relative motion; that just led us to a deeper understanding of how the world is structured.

The question at what time does not really matter because the twins are seeing themselves older than their counterpart all the time each in its own frame.

I am just suggesting that if twins disagree on who is older then they can also disagree on what is true.

 

[Doc Al]

The question at what time does not really matter because the twins are seeing themselves older than their counterpart all the time each in its own frame.

And you seem to have a problem with that. The question of 'at what time' is crucial to understanding how it can possibly be that each can see the other as 'younger'. Despite all your postings and obvious interest in relativity, you still haven't buckled down to learn these basics.

I am just suggesting that if twins disagree on who is older then they can also disagree on what is true.

Why do you think that?

 

[lovetruth]

Per the LTs they agree they should disagree, and they can predict precisely what the other would then hold.

You are using clever statement to hide the disagreement between the observers.[They agree to disagree]. So you do accept there can be diagreements among observers.

Here is a tale which will put the matters to rest.
In A's frame, he sees that he is 50 while B is 25. A in his own frame kills B.
Q: In B's frame, at what age does B die and how old was A when he killed B