Twins Paradox: Symmetry & Acceleration

[matheinste]

Hello granpa.

This is the explanation i was referring to.

Quote originally posted by robphy in "Twin Paradox"

-----------Here is the spacetime-geometric interpretation of the situation... which hopefully amplifies the key points.

The elapsed-proper-time of an observer (as read off from his wristwatch) is the arc-length of his worldline in spacetime.

Fix once and for all event A (the separation event) and event B (the reunion event),
as if one marked two points on a piece of paper.

There are many ways to experience both A and B.
That is, there are many worldlines that pass through both A and B.

In Minkowski spacetime,...

- there is one inertial observer that can experience both A and B, and that observer records the longest elapsed proper-time (as read off from his wristwatch). That is, there is one geodesic (one straight worldline) that meets both A and B, and this worldline has the longest arc-length (using the Minkowski metric)

- every other observer experiencing both A and B will not be an inertial observer, and such an observer will record a shorter elapsed proper-time (as read off from his own wristwatch). That is, every other worldline meeting both A and B will not be a geodesic and will not be a straight worldline... and thus must have at least a portion that is curved (a smooth portion representing a finite acceleration, or a kink representing an impulsive acceleration).
--Note that a kink itself will not contribute any additional arc-length to the worldline.
(That is, the impulsive acceleration at an event (say, a turnaround event) will not change (i.e., "will not cause a jump in") the reading of that observer's wristwatch experiencing that event. [Slightly off topic... what will change are the sets of distant events that this observer will regard as simultaneous. Possibly interesting... but secondary... and often a distraction from the key point.])
--[He will be a non-inertial observer and will be able to detect this because an ice cube placed over a spot on his frictionless table will be displaced at some time during the trip from A to B.]

The supposed paradox is due to ignoring the distinction between the inertial and noninertial observer... and falsely thinking that it is sufficient to consider "being at rest (in your own reference frame)". Said another way... "being at rest (in your own reference frame)" does not make you an inertial observer... especially when an ice cube on your table suddenly gets displaced.


The symmetry break (between inertial and noninertial) is the "presence of an acceleration (worldline curvature) somewhere during the trip" for the noninertial observer. Neither are causes of the shorter-elapsed-proper-time from A to B... they are correlated with the shorter-elapsed-time because they indicate that a noninertial (i.e. nongeodesic) worldline was used to experience both A and B.--------------------

Many thanks to robphy for this enlightening explanation

Matheinste.

 

[granpa]

frankly it doesn't seem to 'explain' so much as 'describe' what is happening but you asked whether it is compatible with 'my' explanation so:well it assumes that the accelerating twin can be told apart from the stationary twin (which i also assume), it assumes that the nonaccelerating twin can be treated as stationary (which i also assume), and it assumes time dilation proportional to velocity (which i also assume) so the only question is how does it explain that to the moving twin, while he is moving with respect to the stationary twin, it seems as though it is the stationary twin that is aging more slowly?

http://upload.wikimedia.org/wikipedia/commons/6/6a/Twin_paradox_Minkowski_diagram.png

http://en.wikipedia.org/wiki/Twin_paradox#Resolution_of_the_paradox_in_special_relativity

and it isn't 'my' theory. as far as i can tell it is exactly what the textbooks say is the solution (from the point of view of special relativity. that is, without going into general relativity) with one trivial exception. i don't throw away the idea of absolute time and velocity (which does not contradict relativity at all, relativity only says you can't detect it, not that it doesn't exist, so its not really even an exception). so your confusion is actually quite hard to understand.

 

[granpa]

so you understand minkowski space but you can't understand my thought experiment? that's hard to figure. look all of relativity is based on one observation. that our measurement of the speed of light is contstant even though we know we are moving. to explain this it follows that moving objects must contract, become time dilated, and experience loss of simultaneity. now we create a thought experiment in which one twin is moving along a long line of synchronized clocks. we already know what the nonmoving twin will see. he will see that the moving twin will be length contracted and time dilated and things on board the ship will seem to be out of synch. so the q is what will the moving twin see. the clock outside his window will seem to be ticking at twice the rate of his own (just as we would expect) but due to loss of simultaneity he will perceive the line of clocks to be out of synch and therefore it will seem to him that the nonmoving twins clock is ticking at half his own rate. so both observers see the other as time dilated even though only one actually is. in the same way the moving twin will see the nonmoving twin as length contracted. (the length of an object is the distance between the front and back at one simultaneous moment).

this is as far as i know, the textbook explanation for relativity.

 

[granpa]

the clock outside his window will seem to be ticking at twice the rate of his own (just as we would expect)

i probably should have said:
the total elapsed time as told by whatever clock happens to be outside his window at that point will be passing at twice the rate of his own clock (which is exactly what we would expect since he is time dilated).

 

[paw]

...with one trivial exception. i don't throw away the idea of absolute time and velocity (which does not contradict relativity at all, relativity only says you can't detect it, not that it doesn't exist, so its not really even an exception)...

If you allow the notion of absolute time and velocity you can obtain results completely at odds with SR.

If there is some form of absolute time and velocity you can define a frame of reference in which two events are absolutely simultaneous. Let's call this frame A. Now two lights, at rest in A, separated by 10ls flash simultaneously at t=0s. So an observer (O), in frame A, mid way between B and C, will see the flashes simultaneously at t=5s.

Another observer (O') is moving at 0.5c wrt A, on a line connecting B and C. The lights are timed to flash when O' passes O (ie: is midway between B and C). Observer O' sees C flash at 2.84s and B flash at 7.17s. O' does not agree with O that the flashes were simultaneous.

Since O' does not agree with O that the flashes were simutaneous the assumption of absolute simutaneity is falsified. Your assumption of absolute time and velocity are likewise falsified. The notion of absolute time and velocity does contradict SR.

 

[granpa]

when o' moves of course he experiences a loss of simultaneity. how does that contradict anything?

i have no idea what you are trying to say but i am sure its wrong. relativity says that any frame can be treated as being at absolute rest so it can't possibly be true that assuming that one frame really is at absolute rest leads to a contradiction with relativity.

you might want to look at this:
https://www.physicsforums.com/showthread.php?t=235661

 

[paw]

relativity says that any frame can be treated as being at absolute rest so it can't possibly be true that assuming that one frame really is at absolute rest leads to a contradiction with relativity.

Any frame can be treated as if it is at rest; sure. Not at absolute rest though. There is no such thing in SR as absolute rest. You should be more careful with your language.

i have no idea what you are trying to say but i am sure its wrong.

If you have no idea what I'm saying how can you possibly conclude that it's wrong. That's mighty conceited of you.

 

[granpa]

i have no idea what you are trying to say but i am sure its wrong because relativity says that any frame can be treated as being at absolute rest so it can't possibly be true that assuming that one frame really is at absolute rest leads to a contradiction with relativity.

there is no significant difference between being at rest and being at absolute rest.

 

[paw]

there is no significant difference between being at rest and being at absolute rest.

There is a huge difference between rest and absolute rest. Absolute rest implies there is a preferred frame of reference against which an observer could determine some universal 'truth' about what time an event happened, how fast they are moving, their length etc. This is simply not true according to SR and all the experiments that support it.

 

[granpa]

could determine some universal 'truth' about what time an event happened, how fast they are moving, their length etc.

not true at all. if a frame of absolute rest exists it does not follow that one can find it. relativity says that all observers see exactly the same thing that they would see if they were at rest so they can't determine whether they are moving or not. but it does not say that there is no frame of absolute rest. it just says that you can't find it. things don't cease to exist just because you can't see them.

i wish i had a nickel for every time i have had to say that.

 

[matheinste]

Hello granpa

Quote

-------there is no significant difference between being at rest and being at absolute rest.----------

This is just about the biggest mistake you can make in relativity.

Matheinste

 

[granpa]

relativity says that any frame can be treated as being at absolute rest. how then does introducing a frame of absolute rest result in a contradiction with relativity.

relativity doesn't say there is no frame of absolute rest it just says that you can't find it.

 

[matheinste]

Hello again

Quote

-------there is no significant difference between being at rest and being at absolute rest.----------

Whatever else you may say about relativity not denying that an undetectable absolute rest frame may exist the above statement quoted is completely against the idea of relativity. It is no use just repeating the same thing over and over again. The statement is wrong.

Matheinste.

 

[paw]

relativity says that any frame can be treated as being at absolute rest.

You need to provide a reliable source to support this quote or stop repeating it.

'There is no universal frame of reference pervading all of space, so there is no such thing as "absolute motion [rest]"' : Beiser, Arthur. Concepts of Modern Physics, p2.

relativity doesn't say there is no frame of absolute rest it just says that you can't find it.

Again, please cite a reliable reference or stop repeating this.

Saying you can't find an absolute frame is the same as saying it doesn't exist. To argue otherwise would be an article of faith not science.

 

[robphy]

relativity says that any frame can be treated as being at absolute rest. how then does introducing a frame of absolute rest result in a contradiction with relativity.

relativity doesn't say there is no frame of absolute rest it just says that you can't find it.

I haven't been following this thread... but let me offer two comments. (I saw an earlier post of mine quoted.. so I decided to pop in and see what is up.)

Issues regarding paradoxes in relativity are more likely about
the distinction between inertial and noninertial observers,
rather than about observers "at rest" and "in motion".

A resolution in the "rest" vs "absolute rest" debate could arise if one had
mathematical formulation of those concepts rather than just a reliance on imprecise words.

 

[paw]

A resolution in the "rest" vs "absolute rest" debate could arise if one had mathematical formulation of those concepts rather than just a reliance on imprecise words.

I agree with you on the above but I submit that most people reading 'absolute rest' would take that to mean there exists some preferred frame. I think you'd agree that there is no preferred frame in SR. It's very misleading to use the term 'absolute'.

 

[robphy]

I agree with you on the above but I submit that most people reading 'absolute rest' would take that to mean there exists some preferred frame. I think you'd agree that there is no preferred frame in SR. It's very misleading to use the term 'absolute'.

So, here is how I use the word "absolute"... i.e., my definition for "absolute".

But first...
if there is a transformation that let's a certain direction (observer worldline)
in a space[time] diagram be the "vertical axis" (the "observer at rest"),
then there is a choice of axes (frame of reference) where that direction is vertical (that observer is at rest).
[Maybe a little redundant and imprecise, but should be clear enough.]

Now.. "absolute".

In a Euclidean rotation, there are no eigenvectors (i.e. directions left unchanged ["invariant"] by the rotation). So, there are no "absolute directions" in the plane.

In a Galilean boost, there are no [timelike] eigenvectors (i.e. [non-infinite] velocities left unchanged by the boost). This says that there are no preferred timelike observers. Note that there are eigenvectors which could correspond to "absolute velocities"...those which are infinite. In addition, the notions of "absolute time", "absolute simultaneity", and "absolute length of an object" can be used in this context.

In a Lorentz boost, there are again no [timelike] eigenvectors (i.e. [non-lightspeed] velocities left unchanged by the boost). This says that there are also no preferred timelike observers. Note, however, that there are eigenvectors which could correspond to "absolute velocities"... those which are lightspeed velocities.

If in the relativity cases, there were a timelike eigenvector (and it could be transformed to vertical), then I would regard that as the "observer at absolute rest".

So, for me, "absolute"-ness about the eigenvectors of the transformation.
It seems that if you want "absolute rest", one way is to only have the "identity transformation"... i.e. practically no transformation at all... like the so-called Aristotelian spacetime. One could also dream up a more complicated transformation law to have a timelike eigenvector... but it would probably be accompanied by some possibly-unappealing properties [including disagreement with experiments].

 

[paw]

So, for me, "absolute"-ness about the eigenvectors of the transformation.
It seems that if you want "absolute rest", one way is to only have the "identity transformation"... i.e. practically no transformation at all... like the so-called Aristotelian spacetime. One could also dream up a more complicated transformation law to have a timelike eigenvector... but it would probably be accompanied by some possibly-unappealing properties [including disagreement with experiments].

If I remember the identity transformation is the trivial one that give you back the original matrix right?

Anyway, you don't seem to be saying anything that disagrees in any substantial way with the quote from Beiser above that there is no 'absolute motion [rest]'. If there were it would qualify as a preferred frame and the way I understand that it would imply a positive result for MM type experiments.

I think that for introducing SR or for casual discussions the statement that there is no preferred frame should be sufficient, no?

 

[robphy]

If I remember the identity transformation is the trivial one that give you back the original matrix right?

Anyway, you don't seem to be saying anything that disagrees in any substantial way with the quote from Beiser above that there is no 'absolute motion [rest]'. If there were it would qualify as a preferred frame and the way I understand that it would imply a positive result for MM type experiments.

I think that for introducing SR or for casual discussions the statement that there is no preferred frame should be sufficient, no?

Yes, the identity transformation gives you back the original matrix.

I don't think what I have said is at odds with any relativity text...
What it does, I hope, is to clarify physical concepts with some specific definitions and appropriate mathematical formulations which hopefully capture the essence of these physical concepts. Then, any debates in terminology can shift to a discussion in the context of the mathematical formulation.

 

[granpa]

Saying you can't find an absolute frame is the same as saying it doesn't exist. To argue otherwise would be an article of faith not science.

so if you can't see it then it doesn't exist and to say otherwise is unscientific? ok. fine. it doesn't exist then.

Whatever else you may say about relativity not denying that an undetectable absolute rest frame may exist the above statement quoted is completely against the idea of relativity.

as i pointed out relativity says that any frame may be considered to be at absolute rest. please explain therefore how considering one frame to be at absolute rest leads to a contradiction with relativity.

I agree with you on the above but I submit that most people reading 'absolute rest' would take that to mean there exists some preferred frame.

preferred for what?

 

[RandallB]

relativity doesn't say there is no frame of absolute rest it just says that you can't find it.

A resolution in the "rest" vs "absolute rest" debate could arise if one had mathematical formulation of those concepts rather than just a reliance on imprecise words.

But there is a “mathematical formulation” for it. The The Science of Astrophysics as we know it could not exist without it.

What does not exist is a theoretical basis for establishing a preferred frame of reference to identify something to use as a frame of “absolute rest” when restricted to Special Relativity, but the science of Astrophysics is not limited to SR it uses GR and real world observations.

The idea that there is no “Preferred Frame” to use as a reference for “at rest” only applies when limited to SR alone.

 

[paw]

But there is a “mathematical formulation” for it. The The Science of Astrophysics as we know it could not exist without it.

What does not exist is a theoretical basis for establishing a preferred frame of reference to identify something to use as a frame of “absolute rest” when restricted to Special Relativity, but the science of Astrophysics is not limited to SR it uses GR and real world observations.

The idea that there is no “Preferred Frame” to use as a reference for “at rest” only applies when limited to SR alone.

I'm not disagreeing with you but I thought the discussion was about Special Relativity. In that context I believe I'm correct in my assertion that there is no preferred, or absolute, frame of reference.

I have much less experience with GR although I must say I have never seen a claim that a preferred or absolute frame should exist in GR either. Please correct me if I'm wrong.

 

[paw]

Whatever else you may say about relativity not denying that an undetectable absolute rest frame may exist the above statement quoted is completely against the idea of relativity.

On the contrary. The lack of a frame at absolute rest is fundamental to SR. If such a frame existed and two non-local events in that frame were simultaneous then all other frames would have to also agree that they were simultaneous. But we already know that any frame in motion relative to the absolute frame will not agree they are simultaneous.

as i pointed out relativity says that any frame may be considered to be at absolute rest. please explain therefore how considering one frame to be at absolute rest leads to a contradiction with relativity.

SR says any frame may be considered to be at rest not at absolute rest. There is a difference. If you are confusing rest with absolute rest then Ok but if you are insisting on absolute rest then I ask again; please provide a citation to support your claim.

preferred for what?

In this context a preferred frame is one with the property of absolute rest. That is, one in which 'motion' is absolute. The idea of an ether (aether if you prefer) is a preferred frame. A frame of reference can be defined in which the ether is at rest.

As for your stated notion that an 'absolute frame exists but it can't be detected' I won't go as far as to say that's nonsense but I will say as a working hypothesis it's useless. You might as well argue fairies exist but you can't detect them. If your 'undetectable' frame has no effect on physical reality then you might as well abandon the idea. If it does affect reality then it is detectable in principle.

 

[matheinste]

Hello paw.

Please look at post #43 and you will see that your first quote is what i said in response to granpa saying that there is no significant difference between a rest frame and an absolute rest frame. My words agree with your view.

Matheinste.

 

[paw]

Hello paw.

Please look at post #43 and you will see that your first quote is what i said in response to granpa saying that there is no significant difference between a rest frame and an absolute rest frame. My words agree with your view.

Matheinste.

I already saw it and agree. I was just having one more try to get the point across to granpa. I'm un-likely to succeed I know but what the heck...

 

[granpa]

i refer you to the last paragraph of the op of this thread:

https://www.physicsforums.com/showthread.php?t=236978

that is my final word on aether. agree or disagree as you like.

 

[paw]

i refer you to the last paragraph of the op of this thread:

https://www.physicsforums.com/showthread.php?t=236978

that is my final word on aether. agree or disagree as you like.

Quoting yourself is hardly authoritative support for your own argument. However, after reading your lengthy and convoluted post I see you aren't disagreeing with SR, rather, you are adding an unsupported, unnecessary and confusing layer of complexity to it. I think it would be better to drop the idea of a preferred frame entirely instead of saying one may exist but can't be detected. It's just simpler all around.

 

[granpa]

where do you read anything about a preferred frame??

i have dropped the whole issue of an aether altogether. that post was supposed to be plain and simple special relativity. did you not read the part about 'there is no absolute velocity'? it sounds like you just want to argue to me.

and i wasnt quoting myself. i was answering your question. why are you being so argumentative? chill out.

 

[paw]

where do you read anything about a preferred frame??

i have dropped the whole issue of an aether altogether. that post was supposed to be plain and simple special relativity. did you not read the part about 'there is no absolute velocity'? it sounds like you just want to argue to me.

and i wasnt quoting myself. i was answering your question. why are you being so argumentative? chill out.

Geez, you didn't read my post too carefully. I said your link showed you weren't disagreeing with SR. We agree that there 'is no absolute velocity'. I'm glad that's finally clear. It was the point I was making all along.

 

[granpa]

there is nothing in that thread about a preferred frame. and every word of it is entirely supported mathematically.