I Does the "space twin" benefit from length contraction?

[laymanB]

@nomadreid , as you can see from reading through this thread and the reply posts above, acceleration is not needed to explain the differential aging. The important thing to remember is that any proper analysis will come up with the same results. With that being said, personally I think some ways are simpler than others to analyze the problem, based on how it is presented. With the standard twin paradox problem setup, the easiest way for me to analyze it is to say that the space twin is the only one of the two twins to feel an acceleration, therefore we know that his worldline is not a straight line in flat spacetime between the two events. And because a straight worldline between two events in flat spacetime has the longest proper time, ergo; the Earth twin will have aged more. But if you present the solution like that then people come away thinking that the acceleration is necessary to explain the differential aging.

Don't worry if you still don't have a rock solid intuition about the asymmetry, you are in good company. I have read through many forums where people seem to know GR very well, claim that it requires acceleration and GR, work out the equations, and still come to the faulty conclusion that the problem is symmetric without someone experiencing acceleration.

 

[Herman Trivilino]

@nomadreidAnd because a straight worldline between two events in flat spacetime has the longest proper time, ergo; the Earth twin will have aged more. But if you present the solution like that then people come away thinking that the acceleration is necessary to explain the differential aging.

The acceleration is necessary, and it does explain the asymmetry, but it is not the cause of the difference in the ages of the twins.

If you're hit by a drunk driver your presence at the collision is necessary to explain the collision. But your presence is not the cause of the collision.

 

[laymanB]

The acceleration is necessary, and it does explain the asymmetry, but it is not the cause of the difference in the ages of the twins.

If you're hit by a drunk driver your presence at the collision is necessary to explain the collision. But your presence is not the cause of the collision.

Good point. In the standard twin paradox setup acceleration is a necessary condition for the twins to reunite. Acceleration in this setup is a necessary but not sufficient condition for differential aging.

I should have been more precise: In any generalized setup of the twin paradox, with or without acceleration, acceleration is not a necessary condition to explain the asymmetry of the problem.

 

[hutchphd]

So, it's really the word "cause" that is the issue. The acceleration cannot be seen as a direct cause of differential ageing.

I think the semantics get very slippery here. If we lock Homer and Romer in the usual opaque elevators at birth then the only measurable difference in their experiences is the acceleration. So will they agree that that is causal? I also note that Romer (or Homer!) needs only the measured time course of his acceleration to completely characterize his path..

In other words, you can have the very same amount of acceleration in each case with very different outcomes. So it cannot be that the acceleration accounts for the difference in ages.

The fact that the total amount of acceleration is the same does not mean the acceleration is exactly the same. If I know only the measured acceleration profiles (and the initial conditions), I can characterize each twin completely and uniquely determine outcome. So you can't say "cannot be causal". Does this make it a "cause"?? "direct cause?? It is manifestly sufficient, yes?

 

[PeroK]

I think the semantics get very slippery here. If we lock Homer and Romer in the usual opaque elevators at birth then the only measurable difference in their experiences is the acceleration. So will they agree that that is causal? I also note that Romer (or Homer!) needs only the measured time course of his acceleration to completely characterize his path..

The fact that the total amount of acceleration is the same does not mean the acceleration is exactly the same. If I know only the measured acceleration profiles (and the initial conditions), I can characterize each twin completely and uniquely determine outcome. So you can't say "cannot be causal". Does this make it a "cause"?? "direct cause?? It is manifestly sufficient, yes?

I don't disagree with any of that. When I was learning SR, I quite quickly gave up all talk of twins and various other devices that seemed to me only to cloud the issue. I started to think in terms of clocks. Clocks can be reset and used to measure proper time along a worldline without worrying about their experience from birth!

For example, in this case you could have two stop-clocks on board Rover's ship, one of which you pause for the acceleration phases. That would give you the proper time for the entire trip on one clock and the proper time for the inertial phases only on the second clock.

That then gets to the heart of the matter, where thinking about twins is too inflexible.

 

[Herman Trivilino]

If we lock Homer and Romer in the usual opaque elevators at birth then the only measurable difference in their experiences is the acceleration.

They can also measure the amount of time they spend not accelerating.

I also note that Romer (or Homer!) needs only the measured time course of his acceleration to completely characterize his path..

They also need the amounts of time they spend not accelerating.

 

[hutchphd]

They can also measure the amount of time they spend not accelerating.
They also need the amounts of time they spend not accelerating.

Measurement of the acceleration certainly includes zero as a possible measurement...(semantic issue).

 

[hutchphd]

I don't disagree with any of that. When I was learning SR, I quite quickly gave up all talk of twins and various other devices that seemed to me only to cloud the issue. I started to think in terms of clocks. Clocks can be reset and used to measure proper time along a worldline without worrying about their experience from birth!

For example, in this case you could have two stop-clocks on board Rover's ship, one of which you pause for the acceleration phases. That would give you the proper time for the entire trip on one clock and the proper time for the inertial phases only on the second clock.

That then gets to the heart of the matter, where thinking about twins is too inflexible.

For me the opposite is true. In particular thinking about Rover seeing the dephasing of the clocks in his frame as he decelerates to turn around is what makes the whole thing make sense to me. Thinking only about proper time is too inflexible!

 

[Nugatory]

Rover seeing the dephasing of the clocks in his frame as he decelerates to turn around

But now how do you explain the acceleration-free but otherwise equivalent case in which Rover turns around by executing a tight hyperbolic orbit around some mass conveniently placed at the the turnaround point?

 

[PeroK]

For me the opposite is true. In particular thinking about Rover seeing the dephasing of the clocks in his frame as he decelerates to turn around is what makes the whole thing make sense to me. Thinking only about proper time is too inflexible!

The proper time along a worldline is the physics. SR is about the nature of space and time. You don't gain anything by considering a pair of twins as your clocks other than confusion and obfuscation - which this thread proves.

Considering clocks allows you to see the physics, rather than getting bogged down in misconceptions.

Finally, you know, SR and GR are far more than simply the twin paradox. Your thinking about SR in terms of acceleration cannot be extended to GR, where you must focus on the geometry of spacetime intervals.

There is, thankfully, no popular extension of the twin paradox to GR.

 

[hutchphd]

But now how do you explain the acceleration-free but otherwise equivalent case in which Rover turns around by executing a tight hyperbolic orbit around some mass conveniently placed at the the turnaround point?

If we limit ourselves to the "full" paradox sequence: birth, traveling interval, meet again, there is no acceleration--free case is there?? If rover is unaware of the existence of the mass he will be surprised that he has returned to his twin but the initial and final perceived acceleration will still be necessary (but no longer sufficient) to achieve this path. I believe there is no nontrivial closed (complete) trajectory that does not require a perceived acceleration.for Romer. (?)

 

[jbriggs444]

If we limit ourselves to the "full" paradox sequence: birth, traveling interval, meet again, there is no acceleration--free case is there?? If rover is unaware of the existence of the mass he will be surprised that he has returned to his twin but the initial and final perceived acceleration will still be necessary (but no longer sufficient) to achieve this path. I believe there is no nontrivial closed (complete) trajectory that does not require a perceived acceleration.for Romer. (?)

There is no requirement that the twins begin or end at rest with respect to one another. That dispenses with the need for an initial or a final acceleration.

However, inclusion of a mass and a hyperbolic swing-by makes this a problem for general relativity. It goes beyond the flat space-time background normally assumed for the classical twin paradox.

 

[hutchphd]

The proper time along a worldline is the physics. SR is about the nature of space and time. You don't gain anything by considering a pair of twins as your clocks other than confusion and obfuscation - which this thread proves.

For me the point is to imagine that I am Romer. This is easier than imagining I am a clock!

 

[jbriggs444]

For me the point is to imagine that I am Romer. This is easier than imagining I am a clock!

So put a watch on your wrist. That's easier than measuring your hair length, waistline or secondary sexual characteristics.

 

[hutchphd]

So put a watch on your wrist. That's easier than measuring your hair length, waistline or secondary sexual characteristics.

And of course it would be silly to try to imagine riding along with, say, an electromagnetic wave...what a useless enterprise!

 

[jbriggs444]

And of course it would be silly to try to imagine riding along with, say, an electromagnetic wave...what a useless enterprise!

Yes. An electromagnetic wave would out-pace you. So yes, that would be silly unless you contrived to have it bounce back and forth in some kind of light clock.

[Sarcasm really does not work well in an electronic medium. Please try to say what you mean simply and directly]

 

[PeroK]

And of course it would be silly to try to imagine riding along with, say, an electromagnetic wave...what a useless enterprise!

Actually, here is my alternative twin paradox. Owing to a) the boredom of the space flight; b) the lack of fresh air and exercise; c) the deleterious effects of cosmic radiation: Rover actually looks and feels much older than Homer upon his return. Thus confirming that Homer is the "younger" twin.

 

[hutchphd]

Yes. An electromagnetic wave would out-pace you. So yes, that would be silly unless you contrived to have it bounce back and forth in some kind of light clock.

[Sarcasm really does not work well in an electronic medium. Please try to say what you mean simply and directly]

The point is that measurement means something very specific and it involves "being there". Quantum mechanics indicates this in a surprising way. I have always found that reducing problems to real human beings making simple real measurements eliminates the chance of making some very subtle errors. This is my method...you are free to have your own but not to disparage mine.
The light beam comment was of course an homage to the 16 yr old Albert wrestling with Maxwell's equations

 

[jbriggs444]

The point is that measurement means something very specific and it involves "being there".

The point is that in order to measure time, one needs a clock. The human body is a remarkably poor one.

 

[nitsuj]

When I was learning SR, I quite quickly gave up all talk of twins and various other devices that seemed to me only to cloud the issue. I started to think in terms of clocks. Clocks can be reset and used to measure proper time along a worldline without worrying about their experience from birth!

For example, in this case you could have two stop-clocks on board Rover's ship, one of which you pause for the acceleration phases. That would give you the proper time for the entire trip on one clock and the proper time for the inertial phases only on the second clock.

Well said!

 

[nitsuj]

one needs a clock. The human body is a remarkably poor one.

bah, we make and read em.

 

[hutchphd]

If you're hit by a drunk driver your presence at the collision is necessary to explain the collision. But your presence is not the cause of the collision.

But if you were present at all drunk driver collisions wouldn't somebody get suspicious?

 

[laymanB]

For me the point is to imagine that I am Romer. This is easier than imagining I am a clock!

You and Homer can put on identical wrist watches that are guaranteed accurate. You and Homer will synchronize your watches before each run of the experiment (space trip). Do each run of the experiment using different acceleration profiles for the turnaround section, maintaining the same average relative velocity for each leg of the trip, and traveling the same proper length each time, as computed by Homer. Assume that there is a flag floating in the vacuum of space (marking the turnaround point) that is at rest relative to Homer, which he has bounced radio waves off of to determine proper length. Notice that during the accelerations phases, you do not notice anything "strange" happening to your wrist watch that would key you into something "weird" happening. At the end of each trip, you and Homer compare the time elapsed on your wrist watches (each person's proper time). Ask Homer if he noticed anything "weird" happen to his wrist watch at any point when you were gone. Notice that the results are the same every time and therefore the acceleration can not be the cause of the differential aging (difference in proper times).

If that doesn't convince you, go on several more trips, but this time make the proper length 1/2 the original proper length. Use the same average relative velocity and the same acceleration profiles for the turnaround as for the first set of experiments. Compare watch readings after these experiments and see that the results are 1/2 the difference in proper times compared the first set of experiments.

If that doesn't convince you, read through @PeroK post #45 a few times to see that the clock's proper time traced out the path through spacetime without acceleration on any physical object. The same path you would have made with an instantaneous turnaround neglecting acceleration. And then conclude that acceleration is not necessary to explain the results.

 

[Herman Trivilino]

But if you were present at all drunk driver collisions wouldn't somebody get suspicious?

The point is that someone must be, and just because they are doesn't mean they're the cause.

Acceleration may be present, that doesn't mean it's the cause. Even if acceleration were always present in every version in which there's a difference in ages, that doesn't mean it's the cause. That's true regardless of your suspicions.

 

[laymanB]

This reminds me of the old story where the farmer noticed that every time his rooster crowed the sun came up, which woke him up because of the bright light. Wanting to be able to sleep in, he decided to kill his rooster.

Correlation does not prove causation.

 

[hutchphd]

I am reminded that George Gamow long ago in "Mr Tompkins in Wonderland" fingered the brakeman:

“Yes, of course,” thought he, “if all were relative,the traveler would appear to his relatives
as a very old man, and they would appear very old to him, although both sides might in fact
be fairly young. But what I am saying now is definitely nonsense: One could not have relative whiskers!
So he decided to make a last attempt to find out how things really are, and turned to a solitary
man in railway uniform sitting in the buffet.
“Will you be so kind, sir, ” he began, “will you be good enough to tell me who is responsible
for the fact that the passengers in the train grow old so much more slowly than the people
staying at one place? ”
“I am responsible for it ”, said the man, very simply.
“Oh! ”exclaimed Mr Tompkins, “So you have solved the problem of the Philosopher's Stone
of the ancient alchemists. You should be quite a famous man in the medical world. Do you
occupy the chair of medicine here? ”
“No,” answered the man, being quite taken aback by this, "I am just a brakeman on this
railway. ”
“Brakeman! You mean a brake man . . .” exclaimed Mr Tompkins, losing ground beneath him
“You mean you just apply the brakes when the train comes to the station? ”
“Yup, that's all I do, and every time the train gets slowed down, the passengers gain in their
ages relative to other people… Of course, the engine driver who accelerates the train does his
part too.”

The "learned professor" discusses it further later with Mr Tompkins but you are invited to read (or re-read) this lovely book.

 

[Wes Tausend]

Time must never be thought of as preexisting in any sense; it is a manufactured quantity. --Hermann Bondi

 

[Nugatory]

The "learned professor" discusses it further later with Mr Tompkins but you are invited to read (or re-read) this lovely book.

Popularizations, even when written by well-regarded professionals like Gamow, should be approached with great caution. They belong to a different genre and are written for different purposes than serious presentations of the actual physics.

 

[hutchphd]

Popularizations, even when written by well-regarded professionals like Gamow, should be approached with great caution. They belong to a different genre and are written for different purposes than serious presentations of the actual physics.

I certainly agree, but the good popularizers (Sagan, Feynman, Gamow, Asimov...) are very careful not to say things that are incorrect just to make it "simple".
Thanks largely to your clarity of explanation, I believe the remaining disagreements here are semantic. The "common man" definition of the twin problem requires both the existence of time dilation (fully calculable using Special Relativity alone!) and an acceleration (to differentiate the younger twin). Choice of only one of them to be "the cause" is a semantic issue.

 

[Ibix]

Choice of only one of them to be "the cause" is a semantic issue.

But you can easily construct experiments with the same outcome that have no acceleration. So "it's a semantic issue", if true at all, could only be true about this version of the experiment, and not a general truth about physics

 

[hutchphd]

But you can easily construct experiments with the same outcome that have no acceleration. So "it's a semantic issue", if true at all, could only be true about this version of the experiment, and not a general truth about physics

What do you mean "same outcome"?? Please construct for me a complete experiment involving the birth of twins and the later meeting (for handshake) of same twins that does not include perceptible acceleration of the apparently younger twin.

 

[Ibix]

The three clocks experiment that has been discussed several times produces the exact same difference in accumulated time. The twins and the handshake aren't the important part of the experiment - for the purposes of the paradox they are just clocks and can be replaced by any other clock.

 

[hutchphd]

It is a simple request. You said it was easy...I think it is not.

 

[Ibix]

It is a simple request. You said it was easy...I think it is not.

I've already done so, and so has PeroK. See #22, the second half of #45, and #51 for example.

 

[PeroK]

It is a simple request. You said it was easy...I think it is not.

Instead of transferring clock readings, you could (theoretically at least) replicate one twin on a moving space ship. A la the transporter on Star Trek.

That would obviate the need for acceleration.

And, if you quibble about this, remember that we are not a fixed set of atoms from birth.

 

[hutchphd]

Instead of transferring clock readings, you could (theoretically at least) replicate one twin on a moving space ship. A la the transporter on Star Trek.

That would obviate the need for acceleration.

And, if you quibble about this, remember that we are not a fixed set of atoms from birth.

I
I was making a serious request.. .

 

[PeterDonis]

Please construct for me a complete experiment involving the birth of twins and the later meeting (for handshake) of same twins that does not include perceptible acceleration of the apparently younger twin.

In flat spacetime, you can't. So what? You can construct a thought experiment in which exactly the same worldlines--curves in spacetime--are involved, without any observer feeling any perceptible acceleration. You are singling out the acceleration by singling out the condition that a single twin has to follow the "traveling" worldlines--out and then back in. But that is not at all necessary to the key purpose of the thought experiment, which is to demonstrate that different paths through spacetime between the same two events can have different lengths. It's just the way the thought experiment happened to be originally formulated.

At this point nothing useful is being added to the discussion. Thread closed.