Understanding Einstein's Twin Paradox, past the usual level?

[sylas]

I only say they agree to use their own proper times for the acceleration/deceleration.

Here is the question again. This is an important question, and answering it will help sort out the situation.

Do you understand that as long as the period of coasting inertially is much longer than the period of accelerating, the actual length of the acceleration is basically irrelevant?

All that matters is the velocity at which the coasting occurs. If you agree with this, all the irrelevant stuff about accelerations can be dropped.

Cheers -- sylas

 

[JesseM]

I only say they agree to use their own proper times for the acceleration/deceleration.

The entire event causes an overall 0 acceleration for each "twin" but with relative velocity between the two for an extended period.

"0 overall acceleration" is misleading, it's a bit like saying a zig-zag path in 2D has "0 overall bending" because every zig in one direction is balanced by a zag in the other--it's still obviously true that a zig-zag path is different from a straight path (a zig-zag path between two points will have a greater length than a straight line between the same two points, for example). Anyway, if they both start out at rest in frame #1, then accelerate to different velocities relative to frame #1, coast inertially for significantly longer than the period of acceleration (so that as an approximation you can treat the acceleration as instantaneous), then both decelerate to being at rest in frame #1 again after the same amount of proper time has passed on each clock (assuming that's what you meant by 'they agree to use their own proper times for the acceleration/deceleration'), then whichever one had a larger velocity in frame #1 will take longer before it decelerates in frame #1 since it's been running slower since the initial acceleration. This means that after both come to rest in frame #1 again, the one that had a larger velocity will show an earlier time in frame #1 than the one that had a smaller velocity, because it decelerated later (and both showed the same proper time at the moment they decelerated).

 

[marxmarvelous]

"The twin "paradox" is a simple undergraduate level issue. It's a basic exercise that should be solved by a first year undergraduate at the start of the introductions to special relativity."

When I taught undergraduates at Hopkins in the '60s it was still a "paradox" and not interesting to the students or me cause it wouldn't appear on tests and that was what they and I were interested in.
Later when I went to a library just for fun, to just learn something I found a book in which Einstein specifically said that acceleration of one or both of the persons didn't "answer" the paradox.
Then I read where he accounted for the inability of Special Relativity to "answer" the paradox and this inability was one motive for the General theory. He even admitted that the Special theory was WRONG when applied to the twins. "a defect in epistomology" An error in the theory of knowledge.
l Later I found his book that just had his theories, nobody else's "simplifications. He included a page on Mach's recognition of the intuitive necessity for matter to "know" of all this other stuff out there that would in effect establish a preferred frame. To me the most important thing is that the media ignored Einstein and his admission of the inapplicability of SR to the twin paradox and ignored him also when he suggested that an international police force be established to ensure that no-one had the bomb. He was completely ignored from 1948 to his death in '55 when he reiterated his lifelong vie that immigrants to Palestine must get along with Palestinians.
He was also clear that infinities, anything divided by zero is not representative of a physical state. He knew that the Greek-Think(logos) method of mathematics and Science in which postulates are manipulated with a system of logic was not to be followed into physical non-sense just because a formula delivered that conclusion.
Postulates can't be proven; they are simply accepted in-the- beginning of a mathematical or scientific field. When they give "singularities, infinities, unmeasureable things we are not required to accept them as represetations of the physical.
As far as the Intelligence agents who flew the clocks from the Naval Observatory around the world both ways the experiment was faulted. I'd appreciate a physicist look at the revelation of the sloppy technique and straighten me out. I'll have to go find the site again. The main effect was the GR effect of altitude(proximity of Earth slowed clocks) The clocks weren't stable enough to give the result.

GPS satellite clocks are adjusted with the GR formulas applied to their orbit. Interesting also is the media protection of the reputation of the Boys with government airplane tickets and clocks.
Scientific American fumbled the Twin thing a few years ago. "Solved it" They did not reply to my note of the error they made in their explanation. If anyone will post it I'll point to their error again.

 

[sylas]

"The twin "paradox" is a simple undergraduate level issue. It's a basic exercise that should be solved by a first year undergraduate at the start of the introductions to special relativity."

When I taught undergraduates at Hopkins in the '60s it was still a "paradox" and not interesting to the students or me cause it wouldn't appear on tests and that was what they and I were interested in.
Later when I went to a library just for fun, to just learn something I found a book in which Einstein specifically said that acceleration of one or both of the persons didn't "answer" the paradox.
Then I read where he accounted for the inability of Special Relativity to "answer" the paradox and this inability was one motive for the General theory. He even admitted that the Special theory was WRONG when applied to the twins. "a defect in epistomology" An error in the theory of knowledge.

[...]

This is all incorrect. Einstein did answer the paradox just fine, using special relativity; and he never said the special theory was wrong applied to the twins. It isn't wrong at all -- and Einstein solved the problem just fine. Indeed it is not really about acceleration at all. It is about the proper time integrated over your world line. An accelerated observer always has more elapsed time than an inertial observer, when they return to a common point; but you still solve the problem by integrating proper time; and that is a function of velocity. You don't need to use acceleration.

Cheers -- sylas

 

[ernestpworrel]

No one should be debating this issue. The twin paradox is a paradox in every sense of the word. You would think that the rocketing twin would age faster, but in fact the opposite is true. This is easily understood when you account for the Lorentz contraction and you understand that time is relative to the motion of the frame in which it is measured. Anyone who has a clear understanding of SR should be able to figure this out. This is something that has been proven.

 

[ernestpworrel]

This is all incorrect. Einstein did answer the paradox just fine, using special relativity; and he never said the special theory was wrong applied to the twins. It isn't wrong at all -- and Einstein solved the problem just fine. Indeed it is not really about acceleration at all. It is about the proper time integrated over your world line. An accelerated observer always has more elapsed time than an inertial observer, when they return to a common point; but you still solve the problem by integrating proper time; and that is a function of velocity. You don't need to use acceleration.

Cheers -- sylas

Cheers, sylas. You're right again.

 

[Al68]

Then I read where he accounted for the inability of Special Relativity to "answer" the paradox and this inability was one motive for the General theory. He even admitted that the Special theory was WRONG when applied to the twins. "a defect in epistomology" An error in the theory of knowledge.

Did you read Einstein's own subsequent twin paradox resolution, then? Although he uses a different method to deal with the acceleration, the end result is the same as in the standard SR resolutions.

 

[Dale]

The twin paradox is a paradox in every sense of the word.

Not in the technical sense of the word. It is not a logical contradiction.

 

[marxmarvelous]

physicsdude30: Yes, GR is the correct transformation for time and space. The totality of matter in the universe enters those equations. If you would like to discuss this please reply. Jack and Jill needn't be consulted abut which formulas to trust. Ever see a picture of the two guys that the government bought tickets to go arond the world--both ways? And loaned them Naval Observatory clocks. There is a site that covers how they didn't properly consider the drift rate of the clocks.