Solving the Twin Paradox with Lorentz Transformation

[stevmg]

I think this is getting really complicated when it doesn't have to be so.

This post by JesseM explains the conceptual and simple mathematical approach to this problem

https://www.physicsforums.com/showpost.php?p=2610219&postcount=63

In essence we have twin A and B. If one looks at it from the point of view of twin A's frame of reference (FOR) B moves to the right, turns around and moves to the left. Time in A's FOR is proper time as he ain't movin'. Folks who are moving experience less time because of the motion (you know, Lorentz, et al.) Thus B is moving both away and back and experiences less time. JesseM gives a nice quick calculation.

The supposed symmetrical situation is to look from B's FOR. In this case A moves left - BUT never stops. Twin B starts moving to catch up with A and eventually does. When all the times are added up the elapsed time for B is the same this way as it was looking at it the first way in the above paragraph.

Guess what! This is NOT a symmetrical situation is it? In the first case one of the twins sits still (and gets older) while the other twin moves and gets older slower. The first twin never moves.

In the second case, BOTH twins move although one sits still for a while before mving.

These are NOT symmetrical approaches. There's no way to make them symmetrical. JesseM's calculations and working through the problem is self explanatory.

A symmetrical scenario would be to have both twin A and B depart the reference frame in opposite directions at the same speed for the same time and both turn around and come back to meet. In this case, they both would age at the same rate (though not as fast as their triplet brother who remained on Earth) and be the same age when they rejoined. Their triplet brother who remained on Earth would be older than both.

I am not going through the calculation looking at it from A's FOR or B's FOR but I guarantee you, it would work out. Who cares about Doppler, acceleration, deceleration and all that?

Don't make this more complicated than it is, which it isn't (really.)

 

[MikeLizzi]

I think this is getting really complicated when it doesn't have to be so.

This post by JesseM explains the conceptual and simple mathematical approach to this problem

https://www.physicsforums.com/showpost.php?p=2610219&postcount=63

In essence we have twin A and B. If one looks at it from the point of view of twin A's frame of reference (FOR) B moves to the right, turns around and moves to the left. Time in A's FOR is proper time as he ain't movin'. Folks who are moving experience less time because of the motion (you know, Lorentz, et al.) Thus B is moving both away and back and experiences less time. JesseM gives a nice quick calculation.

The supposed symmetrical situation is to look from B's FOR. In this case A moves left - BUT never stops. Twin B starts moving to catch up with A and eventually does.

"In this case A moves left - BUT never stops." ??

The Twins "paradox" involves observing and calculating aging from the point of view of each twin. That means when Twin A is the observer, all motion is described with respect to Twin A. (B goes out and back) And when twin B is the observer all motion is described with respect to twin B. (A goes out and back) That's the definition of the problem. Wether you are doing SR or Newtonian physics that's what happens from the point of view of each observer.

We are all free to define and solve any problems we want but we ought to give dfferent problems different names. The problem being solved in your reference is not the Twins Paradox.

 

[DrGreg]

I think this is getting really complicated when it doesn't have to be so.

This post by JesseM explains the conceptual and simple mathematical approach to this problem

https://www.physicsforums.com/showpost.php?p=2610219&postcount=63

In essence we have twin A and B. If one looks at it from the point of view of twin A's frame of reference (FOR) B moves to the right, turns around and moves to the left. Time in A's FOR is proper time as he ain't movin'. Folks who are moving experience less time because of the motion (you know, Lorentz, et al.) Thus B is moving both away and back and experiences less time. JesseM gives a nice quick calculation.

The supposed symmetrical situation is to look from B's FOR. In this case A moves left - BUT never stops. Twin B starts moving to catch up with A and eventually does.

"In this case A moves left - BUT never stops." ??

The Twins "paradox" involves observing and calculating aging from the point of view of each twin. That means when Twin A is the observer, all motion is described with respect to Twin A. (B goes out and back) And when twin B is the observer all motion is described with respect to twin B. (A goes out and back) That's the definition of the problem. Wether you are doing SR or Newtonian physics that's what happens from the point of view of each observer.

We are all free to define and solve any problems we want but we ought to give dfferent problems different names. The problem being solved in your reference is not the Twins Paradox.

If you read what stevemg read a little more carefully, it is the Twins Paradox. It's just that in the final paragraph quoted here, the phrase "B's FOR" is unclear. What he should have said was something like "the inertial frame of reference in which B is initially (i.e. for the "outward" journey) at rest", and then it all makes sense.

 

[Aaron_Shaw]

Look at this diagram:

The shows something that could be the two twins. Alice at home and Bob moving. It shows the situation of Alice's viewpoint. Her time and space axes are in white.
The diagram also shows Bob's time and space axes in bold blue. They are skewed, as expected, because he is moving relative to Alice.

The red dots are events of either light being transmitted, reflected, or recieved. You can tell from the arrows. What this diagram shows is that events that are simultaneous for bob (the four red dots along his space axis) are not simultaneous for Alice as they are at different time coordinates according to her time axis.Now I've edited this image:

I've added some thin red lines to emphasize the simultaneity lines according to Bob. I've also highlighted a section in green. Here you can see the simultaneity lines (thin red) which will show simultaneous events according to Bob with regard to Alice's clock time and his own clock time.

This represents Bob's outward journey. Now if we flip it over to represent the inbound journed we have this:

Note the change in orientation of the simultaneity lines. So now our diagram of simultaneity looks something like this:

Following these lines we can clearly see that Bob observes Alice's clock ticking lesson each leg of the round trip. That's where the apparent paradox comes into play because we would normally expect Bob to return younger, yet he sees Alice aging less the whole time.

The important part of the diagram is the lines of simultaneity around the turning point. Here you can see that the orientation of the lines shift dramatically at the turn around point. At this point Bob observes Alice's experiencing a short but dramatic increase in clock ticking rate. So much so that Alice ages enough to enable Bob to then continue observing her clock run more slowly for the remainder of the journey so that when the two are reunited Alice is infact older than Bob even though he saw her clock running more slowly.

 

[AJ Bentley]

Look at this diagram:
The important part of the diagram is the lines of simultaneity around the turning point.

At last! - absolutely spot on!

SR relates to inertial F.O.R. Whichever twin steps out of his inertial frame sees this sudden change in his perspective on simultaneity.

The Lorentz formulae allow you to put numbers to it - but this is the basic Physical understanding.

 

[Aaron_Shaw]

Following these lines we can clearly see that Bob observes Alice's clock ticking lesson each leg of the round trip.

Actually I'm not quite sure if I'm right here. I know it to be the case and i know that the changing orientation of the simultaneity lines "fixes" the "paradox". But I'm not sure if I'm correct in saying that the lines show the clock running slower. It doesn't matter. It's besides the point.

 

[AJ Bentley]

But I'm not sure if I'm correct in saying that the lines show the clock running slower. It doesn't matter. It's besides the point.

As you say, it doesn't matter, the point is the change of view when changing F.O.R.

I haven't ever bothered to think about the physical implication of details of the Minkowski diagram in this context - they have to accord with the reality they describe.
And the plain simple fact is that while the two are moving relative to each other, each sees the other as moving slower. (Of course the fact that light takes time to travel the intervening distance is a complication but again, that's irrelevant.)

Thanks for a very clear explanation.

 

[AJ Bentley]

so that when the two are reunited Alice is infact older than Bob even though he saw her clock running more slowly.

You'e missing out the point that Bob also has to stop at journey' end - creating a second realignment.
The trouble with this 'paradox' is that it creates a lot of complication by having two journeys involved.

I prefer to think of a single very short, very, very fast journey (say a foot or two!). Then you don't have the 'coming back' problem.

 

[stevmg]

If you read what stevemg read a little more carefully, it is the Twins Paradox. It's just that in the final paragraph quoted here, the phrase "B's FOR" is unclear. What he should have said was something like "the inertial frame of reference in which B is initially (i.e. for the "outward" journey) at rest", and then it all makes sense.

I couldn't have said it more eloquenlty, and I didn't. That's why you "tightened up" my phraseology.

Thank you, Dr. Greg.

Steve G

Melbourne, FL

 

[AJ Bentley]

There's nothing wrong with Stevemg's post. It too is correct, as far as it goes.

But the common misunderstanding in the paradox is not that the viewpoint is asymmetric - that's a given. It's the fact that the velocity difference causes a disparity in the view of what is and is not simultaneous, which is only resolved by matching velocities.

That resolution is what causes the age difference and most people have difficulty grasping how that comes about. The reason they have trouble is because they lose sight of the basic premise - that there is literally no meaning to the common word 'simultaneous'. (Or at most a very restricted one).

When I look at an explanation of the paradox, I simply look for the word - if it's not there, I know this answer doesn't help.

PS. Substitute 'Now' for Simultaneous' - possibly a bit clearer.

 

[MikeLizzi]

If you read what stevemg read a little more carefully, it is the Twins Paradox. It's just that in the final paragraph quoted here, the phrase "B's FOR" is unclear. What he should have said was something like "the inertial frame of reference in which B is initially (i.e. for the "outward" journey) at rest", and then it all makes sense.

No it is not Dr. Greg.
You don’t get it either. True, they are solving a problem about a round trip. The differential aging is solved for an observer who is always in one inertial reference frame (the initial inertial reference of the astronaut). I haven’t even checked if the calculations are correct because it doesn’t make any difference. Any calculation of differential aging made from one inertial reference frame will give the same results as the calculation made from earth. The paradox will not appear. The paradox appears when you calculate the different ages with the ASTRONAUT as the OBSERVER.

When the astronaut is the observer, the Earth goes away and comes back. The challenge is to correctly calculate the difference in elapsed time between the astronaut and Earth for that observer. That's what the Twins Paradox is about. The solution attempted above does not address that paradox.

 

[Dale]

When the astronaut is the observer, the Earth goes away and comes back. The challenge is to correctly calculate the difference in elapsed time between the astronaut and Earth for that observer. That's what the Twins Paradox is about. The solution attempted above does not address that paradox.

Yes, it does address the paradox because the value calculated is frame invariant. It is the same in ALL frames, inertial or non-inertial.

 

[stevmg]

No it is not Dr. Greg.
You don’t get it either. True, they are solving a problem about a round trip. The differential aging is solved for an observer who is always in one inertial reference frame (the initial inertial reference of the astronaut). I haven’t even checked if the calculations are correct because it doesn’t make any difference. Any calculation of differential aging made from one inertial reference frame will give the same results as the calculation made from earth. The paradox will not appear. The paradox appears when you calculate the different ages with the ASTRONAUT as the OBSERVER.

When the astronaut is the observer, the Earth goes away and comes back. The challenge is to correctly calculate the difference in elapsed time between the astronaut and Earth for that observer. That's what the Twins Paradox is about. The solution attempted above does not address that paradox.

Hey, Paesano -

No, no, no... "When the astronaut is the observer, the Earth goes away and comes back." That ain't true. The Earth does NOT go away and come back. The Earth goes away and keeps on going. The astronaut stays put and then chases the Earth. The way you are looking at it the frame of reference shifts direction, which is not "allowed." The astronaut can himself/herself shift direction but not his/her original frame of reference.

Garramone siempre ha ragione

(By the way, that's what my great great great grandfather said in his defense in Potenza, Lucania Province when he was being sentenced to hanging for stealing horses.)

Sort of like Robin Hood - he didn't steal from the rich and give to the poor... He stole from everybody and kept everything.

 

[DrGreg]

Any calculation of differential aging made from one inertial reference frame will give the same results as the calculation made from earth.

Well that is what the example demonstrates, and you only get an apparent contradiction if you mistakenly treat a non-inertial observer as if they were an inertial observer. So I don't really see what you are objecting to.

 

[AJ Bentley]

Gentlemen, Please!

Humour me, have a go at this restatement of the paradox in a different form.

********************************
Observer Alice, says to Bob ,who is just passing by at nearly the speed of light 'My Granny on Proxima Centauri is just sitting down to kippers for her tea'

Alice knows that because she has an Ansible (which allows her to see what Granny is doing right now without having to wait for the light to arrive)

Bob, who also has an Ansible, takes a quick look and says 'No she isn't, your Granny had her kippers for tea three days ago'

Explain.

You might like to show how Bob's Ansible allows him to travel back in time and re-experience events that have already happened.
What would Alice need to do to 'freeze' her Granny in time so that she is always having tea?
How long can she hold Granny frozen?

 

[stevmg]

LAck of simultaneity

It is 4 AM and I just got up and I can't describe it in detail but Einstein does in his book on Relativity in which he explains that events which are simultaneous from observation in one frame of reference are not when observed from a different frame of reference. His is the example of the lightning strikes on a moving train. Simultaneous when observed by a ground observer, not simultaneous when observed from a train traveler.

Steve Garramone

 

[AJ Bentley]

LAck of simultaneity

That's part way to an answer, but it's basically a mantra.
I'm not asking for a restatement of the principle, or a math derivation of the L transform.

In fact I've deliberately introduced the Ansible so that the standard arguments about L transforms and the speed of light signals don't come into it.

I've fixed the space/time position too, to a single event at the origin with both Bob and Alice in the Here/Now position. The signals from Granny's tea event travel instantaneously to both Bob and Alice so there is no time delay there either, no Doppler shift.

Yet, They can't agree about what Granny is doing right now. Why not?

I'm looking for a simple, common-sense answer. No math, no sound bytes.

 

[MikeLizzi]

Well that is what the example demonstrates, and you only get an apparent contradiction if you mistakenly treat a non-inertial observer as if they were an inertial observer. So I don't really see what you are objecting to.

What I am objecting to is the presentation of solutions as resolutions. If I were given a homework problem to calculate the difference in ages of the twins, I might copy any of a dozen posting in this thread. If I were given the problem of explaining why two different solutions give contradictory results, the only postings worth copying are those like your last one.

Maybe I am being overly sensitive to this issue. This is after all a forum where people are invited to offer opinions and engage in dialogs. But I have had some very negative experiences regarding the Twins Paradox.

 

[Fredrik]

Yet, They can't agree about what Granny is doing right now. Why not?

Because they're using their own motion and a synchronization convention to define what "right now" means. This is what makes the simultaneity lines in Aaron_Shaw's post on the page before this one look the way they do.

In fact I've deliberately introduced the Ansible so that the standard arguments about L transforms and the speed of light signals don't come into it.

Unfortunately an "ansible" can only exist in Galilean spacetime. It can't exist in Minkowski spacetime. It would make SR logically inconsistent (link), so there's no point asking what SR says about anything after you've introduced it.

 

[AJ Bentley]

Because they're using their own motion and a synchronization convention to define what "right now" means.

That's more-or-less correct, but isn't it easier to simply say that the word 'now' has absolultely no meaning (outside of your own narrow world view)?

Unfortunately an "ansible" would make special relativity logically inconsistent, so there's no point asking what SR says about anything after you've introduced it.

Not so. the Ansible merely removes obfuscating factors. It prevents you applying the Lorentz Transform or Doppler shift. Each person carries around their own personal Anisble anyway - it's called 'imagination'.
When we think of Now, we have a very clear image of what that means. In doing so, we Ansible-up our own universe.

The twin paradox comes about because the paradoxee is constantly thinking 'Now Alice is 25 as far as Bob (Now age 35) is concerned' and ' Now Bob is 25 as far as Alice (Now age 35) is concerned.

Remove 'Now' and the paradox is gone with it.

Until the Twins meet up again at journey's end, their ages have no meaning except to themselves. It's very similar to the idea of a quantum state and it's resolution (Don't leap on that observation, it's merely a comparison)

 

[Aaron_Shaw]

Gentlemen, Please!

Humour me, have a go at this restatement of the paradox in a different form.

********************************
Observer Alice, says to Bob ,who is just passing by at nearly the speed of light 'My Granny on Proxima Centauri is just sitting down to kippers for her tea'

Alice knows that because she has an Ansible (which allows her to see what Granny is doing right now without having to wait for the light to arrive)

Bob, who also has an Ansible, takes a quick look and says 'No she isn't, your Granny had her kippers for tea three days ago'

Explain.

You might like to show how Bob's Ansible allows him to travel back in time and re-experience events that have already happened.
What would Alice need to do to 'freeze' her Granny in time so that she is always having tea?
How long can she hold Granny frozen?

That's the old alien invasion from alpha centauri "paradox"?

Lack of simultaneity is the reason of course, but i think that the main cause of "concern" regarding this scenario is implications regarding determinism, fate, free will, and all that stuff.

 

[Austin0]

That's part way to an answer, but it's basically a mantra.
I'm not asking for a restatement of the principle, or a math derivation of the L transform.

In fact I've deliberately introduced the Ansible so that the standard arguments about L transforms and the speed of light signals don't come into it.

I've fixed the space/time position too, to a single event at the origin with both Bob and Alice in the Here/Now position. The signals from Granny's tea event travel instantaneously to both Bob and Alice so there is no time delay there either, no Doppler shift.

Yet, They can't agree about what Granny is doing right now. Why not?

I'm looking for a simple, common-sense answer. No math, no sound bytes.

Hi AJ

Given your imaginary premise of the Ansible then it would seem there would be two possible eventualites:

1) They would not agree.
In this case it might be inferred that relative simultaneity was an actual temporal dislocation. As you put it actually in the past or future.

2) They would agree.

It would seem to follow that this would mean that relative simultaneity would not apply between spatially separated points
but only to observers in the respective frames that were colocated with granny at the time of Ansible observation.

I posted a similar thread a while ago approaching the same question with EPR transmission.

The premise was rejected on the grounds that can be no instantaneous information transmission with EPR due to the neccessity of statisical comparison between the two sites to give meaning to the observations.
At the time I accepted this as a valid criticism but later realized that this was not really the case.
It is not relevant to have real time confirmation of reception. As long as later analysis can confirm reception then their logs give the proper time of reception.
By the time i realized this I was off onto other things and forgot about the problem. Thanks to you I may give it another shot with EPR

 

[matheinste]

If you allow instantaneous transmission of information you do not remove the now but make possible to define the same for everyone, or make time absolute, as in a Galillean or Newtonian universe. If everyone has the same now at every instant then there would be no differential proper times, the now at every spatial location would be the same foer all observers.

I also think that giving objects special properties denied to others is a recipe for many more contradictions somewhere along the line.

Matheinste.

 

[Austin0]

That's the old alien invasion from alpha centauri "paradox"?

Lack of simultaneity is the reason of course, but i think that the main cause of "concern" regarding this scenario is implications regarding determinism, fate, free will, and all that stuff.

If we're on the same page; Penrose looked at the divergent lines of simultaneity as indicating that the observers had an actual relationship with the Alpha C worldline at widely separated points.

Given that the slope of Line's of S in Minkowski spacetime is merely a graphical convention
that represents rulers with clocks [and observers ,real or virtual] that are congruent with and extended along the vector of motion , an alternative view is possible.
Any given event on the AC worldline would also find colocated observers from the respective frames who would disagree on the date.

Does this have any more significance than the difference in respective time [simultaneity]
between the train and track observers?

Isn't it exactly the same situation , just a very long train and tracks?

So if you are going to assume any temporal meaning in one case [which Penrose seemed to do] then to be consistent you should make the same assumption in the other , no?

Not that I have any objection to doing this, in fact consider this question extremely valid and germaine.
I don't see how determinism ,fate or free will is affected in either case??
Just thoughts.

 

[Austin0]

If you allow instantaneous transmission of information you do not remove the now but make possible to define the same for everyone, or make time absolute, as in a Galillean or Newtonian universe. If everyone has the same now at every instant then there would be no differential proper times, the now at every spatial location would be the same foer all observers.

I also think that giving objects special properties denied to others is a recipe for many more contradictions somewhere along the line.

Matheinste.

Would it give everyone the same now or just a standard of evaluation??

A means to determine the difference in "now" at disparate locations?

SR would still apply exactly as it does currently and for the same reasons.
Setting all the clocks to a universal now would make them inoperable for physics or or an invariant measurement of c.

We could right now institute a universal terran time standard but clocks in different parts of the world would be completely out of phase with the sun etc except for a very small region. IMO

thanks

 

[Aaron_Shaw]

I don't see how determinism ,fate or free will is affected in either case??

I think the idea is that one person can see the invading fleet deliberating a potential invasion. He's watching; waiting to discover his fate.
Meanwhile some other bloke moving relatively has already seen the aliens decide on war and launch the fleet.

The first guy is deciding what course of action to take, depending on the outcome of the aliens deliberations which, according to the second guy, is pointless because they've already made their decision.

I think it's just an illusion as the first guy can't have any influence on that outcome at that point anyway due to information transfer speed limit. But i can't find the original problem to refresh my memory.

 

[AJ Bentley]

I thought we were having a sensible discussion. What's all this 'aliens' nonsense?

 

[AJ Bentley]

it would seem there would be two possible eventualites:

1) They would not agree.
In this case it might be inferred that relative simultaneity was an actual temporal dislocation. As you put it actually in the past or future.

2) They would agree.

Case 2 of course means that they are in the same inertial frame and is therefore simply a special case of 1).

The lack of simultaneity isn't exactly a dislocation because it's a continuous function, but it'll do.

I would not say that the events for the observers are 'actually in the past or future' - at least, not without specifying who's past/future - but, yes, you get the idea.

I would say that there is no such thing as past or future in any absolute sense as I did for the word 'now'. (Now is just a point in past and future.) These concepts apply to the world view of an individual world line. They have no absolute meaning.
Each F.O.R. sees a different set of events as past/future, depending on the position of those events and his velocity with respect to any opposing view.

In some frames of reference. The birth of christ has not yet happened. (Not that the light hasn't got there yet - I mean literally not happened as viewable by Ansible).

In the same way, in others, you and I are long gone to dust.

Yes. It plays merry havoc with free will - but I don't see that as my problem.

PS That raises the interesting thought of just how far away and how fast moving you would need to be to to be contemporary with JC. (It may be outside the observable universe...)

 

[Fredrik]

That's more-or-less correct, but isn't it easier to simply say that the word 'now' has absolultely no meaning (outside of your own narrow world view)?

You could say that it has no absolute meaning, but maybe that's what you meant. If we want to explain why the incorrect calculation of the stay-at-home twin's age is incorrect, we need to understand the procedures that we use to associate a coordinate system with an observer's world line.

Not so. the Ansible merely removes obfuscating factors.

This is definitely incorrect. As I said, an "ansible" would make SR inconsistent (I included a link to a proof), or simply replace Minkowski spacetime with Galilean spacetime.

It prevents you applying the Lorentz Transform or Doppler shift. Each person carries around their own personal Anisble anyway - it's called 'imagination'.
When we think of Now, we have a very clear image of what that means. In doing so, we Ansible-up our own universe.

Unfortunately one of the "obfuscating factors" you removed is special relativity.

The twin paradox comes about because the paradoxee is constantly thinking 'Now Alice is 25 as far as Bob (Now age 35) is concerned' and ' Now Bob is 25 as far as Alice (Now age 35) is concerned.

Remove 'Now' and the paradox is gone with it.

That's also not correct, because the paradox isn't about what they would be saying before they meet again. It's about two calculations of their ages at the event where they meet when the astronaut twin comes back.

 

[AJ Bentley]

an "ansible" would make SR inconsistent (I included a link to a proof),

The link simply proves the impossibility of such a device - which I freely admit.

My point is that the horizontal axis in the Minkowski diagram is an 'ansible' line - it is a line of instant communication.
I am simply pointing out the significance of that line in terms that anyone can understand.


IMO No absolute meaning is not strong enough. I prefer to say absolutely no meaning and add the rider -except for one very special case. The point needs to be hammered home.

Throughout all of this I am only telling you what I see when I look at a Minkowski diagram. If that isn't SR - then what is?

the paradox isn't about what they would be saying before they meet again. It's about two calculations of their ages at the event where they meet when the astronaut twin comes back

.

The final calculation is simply a bit of kindergarten maths.
MikeLizzi said it:-
"What I am objecting to is the presentation of solutions as resolutions. If I were given a homework problem to calculate the difference in ages of the twins, I might copy any of a dozen posting in this thread".

 

[yossell]

My point is that the horizontal axis in the Minkowski diagram is an 'ansible' line - it is a line of instant communication.

You might like to rethink this. The horizontal line represents a frame's line of simultaneity, the events that are judged simultaneous in that frame, but that doesn't meant that there can be instantaneous signals and communication along these lines.

 

[AJ Bentley]

that doesn't meant that there can be instantaneous signals and communication along these lines.

Did I not just say in words of one syllable that such a device is impossible?

 

[yossell]

uhhh...so it's not a line of instant communication.

 

[AJ Bentley]

uhhh...so it's not a line of instant communication.

Just in case this is a genuine response, and not a wind-up - and in case anyone else has the same problem with what I said:-

'A line of instant communication' does not imply that it can be used in practice for the purposes of instant communication.
It is simply a line on the Minkowski diagram that such signals would travel if it were possible.

 

[Fredrik]

My point is that the horizontal axis in the Minkowski diagram is an 'ansible' line - it is a line of instant communication.

It's an "ansible" line (why not call it a simultaneity line like everyone else?) only for an observer whose world line is a vertical line in the diagram.

IMO No absolute meaning is not strong enough. I prefer to say absolutely no meaning and add the rider -except for one very special case. The point needs to be hammered home.

I can't agree with that. Every coordinate system gives meaning to the concept of simultaneity. You could argue that it's not "natural" enough, but the standard synchronization procedure is definitely natural enough. It just isn't absolute.

Throughout all of this I am only telling you what I see when I look at a Minkowski diagram. If that isn't SR - then what is?

You can't tell just by looking at the diagram if it's a diagram of something moving in Galilean spacetime (the one used in pre-relativistic theories) or of something moving in Minkowski spacetime.

The final calculation is simply a bit of kindergarten maths.

Yes, it's not hard to calculate the final age. But to resolve the paradox, you need to explain what's wrong with the incorrect calculation that just uses the time dilation formula twice.

Just in case this is a genuine response, and not a wind-up - and in case anyone else has the same problem with what I said:-

'A line of instant communication' does not imply that it can be used in practice for the purposes of instant communication.
It is simply a line on the Minkowski diagram that such signals would travel if it were possible.

It was very easy to misunderstand you because you defined an "ansible" to be a machine that does instantaneous communication and called these lines "ansible lines". Everyone else calls them simultaneity lines.

 

[AJ Bentley]

To save laying out a lot of quotes Fredrik, your points in order.

1/ I'm using the word Ansible to make people think 'what does he mean?' rather than assuming they know what it means because they've seen the phrase before. In the context, I was pointing out that line as an example - there are of course an infinite number of such lines - each point on the diagram has an infinite number of them passing through it. Each corresponding to a different 'now'. Each is no more important than the other.

2/ The resolution of the paradox hinges on knocking down the concept of simultaneity - why do you keep trying to prop it up?

3/http://en.wikipedia.org/wiki/Minkowski_diagram"

4/ What can I tell you? It's a conceptual device - a thought tool - something to use in a thought experiment. You actually want me to build one for you?

 

[yossell]

It's not possible to combine Minksowski space-time with the possibility of instant communication. The two aren't compatible, so I don't understand how you're combining them when `a line on the Minkowski diagram that such signals would travel if it were possible'

I agree that sometimes we can define things in terms of counterfactuals - the path an object would travel if it were unacted on by forces; the force a unit charge would feel if it were at a certain point - even if it's practically impossible to get a unit charge to that point. But in this case, instant communication and Minkowski spacetime are incompatible with each other, so I think it's incoherent to talk of a line in a *Minkowski* space that a signal would travel were it possible.

 

[AJ Bentley]

OK, that's enough.
This thread has become virtually a monologue, My bad.

Anyone wants to PM me on the subject is welcome.

Over and out.

 

[Fredrik]

2/ The resolution of the paradox hinges on knocking down the concept of simultaneity - why do you keep trying to prop it up?

No, to resolve the paradox, you have to explain what's wrong with the incorrect calculation, and to do that you need to understand the precise nature of relative simultaneity. It's not sufficient to just "knock down" absolute simultaneity.

3/http://en.wikipedia.org/wiki/Minkowski_diagram"

Is that supposed to refute what I said? It doesn't. You can draw spacetime diagrams for Galilean spacetime too. I don't like the term "Minkowski diagram" for precisely this reason.

4/ What can I tell you? It's a conceptual device - a thought tool - something to use in a thought experiment. You actually want me to build one for you?

I was just explaining to you why it was your fault that yossell misunderstood you. I have no idea why you're saying the things you're saying now. They seem completely unrelated to what we were talking about.

 

[MikeLizzi]

Yes, it does address the paradox because the value calculated is frame invariant. It is the same in ALL frames, inertial or non-inertial.

No it doesn’t address the problem. And now we are getting close to the source of your misunderstanding.

You wrote: “Because the value calculated is frame invariant”

So why calculate the value at all? We already know the value of the difference in ages by calculation from the point of view of earth. So what is the point of your exercise?

The point of the paradox is that a superficial calculation made with the astronaut as the observer gives a contradictory answer. The only way you resolve that problem is by providing the correct calculation, or at least explaining the correct calculation, with the ASTRONAUT as the OBSERVER.

You have not done that. You have not resolved the paradox.

 

[Al68]

The point of the paradox is that a superficial calculation made with the astronaut as the observer gives a contradictory answer. The only way you resolve that problem is by providing the correct calculation, or at least explaining the correct calculation, with the ASTRONAUT as the OBSERVER.

I've mentioned before that Einstein's 1918 resolution addresses it from the non-inertial frame of the ship. I know most consider the standard resolutions adequate because they provide the correct answer, but Einstein realized full well that a 100% correct resolution isn't necessarily a satisfactory one.

Basically, you can break the period of acceleration into as many segments as you want, and calculate Earth time for each one in the ship's (co-moving inertial) frame. Or just use the equivalent of an infinite series of co-moving inertial frames: gravitational time dilation.

Einstein's resolution just uses the simple gravitational time dilation equation for linear acceleration to calculate elapsed time on Earth's clock in the ship's frame during acceleration. And, unsurprisingly, gets the same answer as the standard resolutions.

 

[Dale]

The only way you resolve that problem is by providing the correct calcultion, or at least explaining the correct calculation, with the ASTRONAUT as the OBSERVER.

You have not done that. You have not resolved the paradox.

Pointing out the frame-invariant geometry of the problem (longest interval is a straight line) is a perfect resolution. It gives the student a new way to think about relativistic physics that both clearly demonstrates the mistake in the paradox and helps the student learn more advanced physics.

 

[Austin0]

=Al68;2794254]I've mentioned before that Einstein's 1918 resolution addresses it from the non-inertial frame of the ship. I know most consider the standard resolutions adequate because they provide the correct answer, but Einstein realized full well that a 100% correct resolution isn't necessarily a satisfactory one.

Hi Al68
I don't even remember if I ever read that paper let alone the contents but I have some questions on principle:

1) As I understand it G time dilation in an accelerating frame only has an effect within
the frame itself . A relative dilation between differnt locations in the frame.
It does not have any effect relative to inertial frames {clock hypothesis]

The relationship with other frames is simply derived from the instantaneous relative velocity. As per your statement below ((2))

2) Even in a round trip with only a relatively short acceleration phase compared to total trip length;- m the overall trip time the cumulative diilation is based on both accel. ICMF velocity and inertial velocity
but the inertial phase dilation (from velocity), which would normally be reciprocal [relative] has now become real , actual.
{Catalytic effect}

3) There is no corralation between the relative percentage of the trip that is accelerated and the end result . Quite unusual for a physical phenomenon wouldn't you say?
For a relevant parameter to vary with no consequence to the end result??

IMO The reason many people are unsatisfied with the resolution is:

It seems like you should be able to analyse the picture from either frame in an identical manner. Assume the accelerating frame as at rest and the Earth is accelerating etc.

Draw an Earth worldline that is curved in areas and straight while inertial and apply all the relevant math on that basis. This of course can be easily calculated and in actuality wouldn't the calculations also be identical,?

Then there would be symmetrical Minkowski diagrams [reciprocal mirrow images] and all the analysis that is commonly used in resolutions would be identical.

But this is not allowed. It is denied on the basis of somewhat ad hoc pricipals

a) Acceleration is real as opposed to inertial motion which is purely relative [unreal]

b) Because of a) only inertial frames are considered valid.

c) Because a world line which changes direction makes it longer and accelerated . ANother version of
a) and b)

Regarding :
a) It is true that there are measurable differences between accelerated and inertial motion.

Unquestionable.

But does there simply being a difference mean there must be a specific effect attributable to that difference?

There is no physics principle or concept suggesting that acceleration would result in real dilation or how it might catalytically turn relative dilation into real or explaining how it possibly could effectuate this result.

So it is not because there aren't valid resoluions to the "paradox" that there remains the dissatisfaction [if anything there are too many]

it is because some seemingly valid ways of looking at it are negated on grounds that are themselves not completely satisfactory or consistent.

Basically, ((2)) you can break the period of acceleration into as many segments as you want, and calculate Earth time for each one in the ship's (co-moving inertial) frame. Or just use the equivalent of an infinite series of co-moving inertial frames: gravitational time dilation.

((1))

Einstein's resolution just uses the simple gravitational time dilation equation for linear acceleration to calculate elapsed time on Earth's clock in the ship's frame during acceleration. And, unsurprisingly, gets the same answer as the standard resolutions

I am going to have to read the 1918 paper (again?)
Judging by this it seems to indicate that G-dilation is exactly equivalent to velocity dilation [ICMF's etc.]
COnsistent with clock hypothesis
But this seems strange if G-dilation is constant but instantaneous velocities are varied.
ANy ideas ?
Thanks

 

[AJ Bentley]

You have not done that. You have not resolved the paradox.

IMO, the basic problem, and the reason for the astonishing clamour in this thread is that no-one seems to agree on what a 'resolution' is.

Certainly I personally can't agree that simply calculating the ages of the twins correctly is enough. Simply calculating the values correctly gives one an impression of having 'solved it' without striking to the heart of the paradox.

The paradox is deeper than that and for me it hinges on the question of what happens during a velocity change. Not in the sense of how acceleration affect time (General Theory), but what happens to the geometry of space time at that point.

 

[matheinste]

IMO, the basic problem, and the reason for the astonishing clamour in this thread is that no-one seems to agree on what a 'resolution' is.

Certainly I personally can't agree that simply calculating the ages of the twins correctly is enough. Simply calculating the values correctly gives one an impression of having 'solved it' without striking to the heart of the paradox.

The paradox is deeper than that and for me it hinges on the question of what happens during a velocity change. Not in the sense of how acceleration affect time (General Theory), but what happens to the geometry of space time at that point.

As Dalespam pointed out earlier, differing path lengths is the simplest answer. The path length (proper time) is frame independent, that is, everyone agrees upon it. The main problem is that because of the strangeness of the result the problem is introduced to whet the readers appetite for relativity before the reader is equipped with the tools to resolve it. Once the concept of proper time is understood the problem goes away. The twins scenario is no "deeper" than anything else in SR.

Matheinste.

 

[Austin0]

IMO, the basic problem, and the reason for the astonishing clamour in this thread is that no-one seems to agree on what a 'resolution' is.

Certainly I personally can't agree that simply calculating the ages of the twins correctly is enough. Simply calculating the values correctly gives one an impression of having 'solved it' without striking to the heart of the paradox.

The paradox is deeper than that and for me it hinges on the question of what happens during a velocity change. Not in the sense of how acceleration affect time (General Theory), but what happens to the geometry of space time at that point.

I agree the paradox is deeper and has nothing to do with the twins final ages really.

There are deeper questions intrinsic to the problem.

It involves the meaning of simultaneity. And the relationship between simultaneity and time dilation.

The meaning and reality of acceleration.

Certain inconsistencies between different valid methods of resolution which derive the same results.

On the GR and how acceleration effects the geometry of space ; from what I have gathered SR says there is no change in the geometry but GR and Rindler coordinates seem to imply there would be. My study of bGR and Rindler is just beginning so I would like to know the answer my self.

 

[AJ Bentley]

I agree the paradox is deeper and has nothing to do with the twins final ages really.

There are deeper questions intrinsic to the problem.

It involves the meaning of simultaneity. And the relationship between simultaneity and time dilation.

The meaning and reality of acceleration.

Certain inconsistencies between different valid methods of resolution which derive the same results.

On the GR and how acceleration effects the geometry of space ; from what I have gathered SR says there is no change in the geometry but GR and Rindler coordinates seem to imply there would be. My study of bGR and Rindler is just beginning so I would like to know the answer my self.

My point exactly.

I 'solved' this problem decades ago. Then suddenly realized much later that what I had wasn't a resolution at all - just a maths question with a textbook solution.

 

[matheinste]

I agree the paradox is deeper and has nothing to do with the twins final ages really.

No. The differeing ages of the twins is put forward as the paradox.

Matheinste

 

[AJ Bentley]

No. The differeing ages of the twins is put forward as the paradox.

Matheinste

Hmm... not a very good rolleyes smilie is it?

 

[matheinste]

As far as a "deeper" meaning goes; Differential ageing is a direct logical consequence of the axioms of SR. That is where any deeper meaning lies and when we find that deeper meaning we can start looking for a still deeper one.

Matheinste.