Time Dilation: Triplet Paradox makes no sense

[Seminole Boy]

Triplets, three boys.

Assume all this happens on the same day and at the same time.

Boy A: leaves Earth in vessel going .9c in zig-zag directions for thirty days. Returns to earth.
Boy B: leaves Earth in vessel going .9c but goes in straight line (15 days), turns around and returns to Earth after 15 days in that direction. (Returns to Earth same moment as Boy A.)
Boy C: stays on earth

From my understanding of spacetime, Boys A and B should be the exact same age (younger than Boy C) because they moved through spacetime at the same speeds relative to light speed. Direction shouldn't, if my understanding of moving through spacetime is correct, matter in determining the ages of the boys. It should simply concern the speeds at which they moved through spacetime.

What am I missing?

 

[bug_man_russ]

I don't quite think so. Relative to boy c. Both A and B should be younger. Between A nd B that's more difficult. As they move away from each other at the same speed they should age the same. However Boy A is going to zig zag and by this will change velocities by perception to Boy b. Simply put it he wil appear (or really willdependding on direction changed) to accelerate and decelerate relative to B. Time or the appearance of time between each will not be constant. I would expect at the end of your experiment boy B will be "younger".

 

[Seminole Boy]

Mr. Russ:

Thanks for your insight. However, I don't believe Boy B should be younger. If space "coats" matter as I understand it does, direction is meaningless. All that "matters'', in terms of time (or aging), is the speed (relative to light) at which matter moves through space(time). The continuum seems not to care about direction.

 

[PeterDonis]

From my understanding of spacetime, Boys A and B should be the exact same age (younger than Boy C)

Yes, this is correct.

because they moved through spacetime at the same speeds relative to light speed.

No, this is not correct. The key is that boys A and B both moved at the same speed relative to boy C, who remained at rest the whole time at the spatial location that both boy A and boy B returned to. The bolded part is key; as long as it's true, then yes, the direction doesn't matter (nor does the fact that boy B changed direction a lot more than boy A); A's and B's speed relative to C is the only relevant factor.

Direction shouldn't, if my understanding of moving through spacetime is correct, in determining the ages of the boys. It should simply concern the speeds at which they moved through spacetime.

The result you've arrived at is correct, but as above, it isn't because of "speed through spacetime". A's and B's speed relative to C is *not* the same as their "speed through spacetime". In so far as that phrase has any meaning at all (which depends on how you feel about the particular interpretation of SR that it's based on--I don't use it much myself), *all three* of A, B, and C are "moving through spacetime" at c the whole time, so their "speed through spacetime" is irrelevant to determining their relative aging.

 

[PeterDonis]

If space "coats" matter as I understand it does

What do you mean by this? It's not part of any interpretation of SR that I'm aware of.

 

[Simon Bridge]

Welcome to PF folks;

Boy A: leaves Earth in vessel going .9c in zig-zag directions for thirty days. Returns to earth.

... how do you mean "zig-zg patterns"?

Assume all this happens on the same day and at the same time.

The most common stumbling block in trying to understand relativity is in not being careful with how you say things. "Simultaneous" is one of those common everyday concepts that makes little sense in relativity. Are you sure you are not accidentally trying to think classically here?

Have a look through:
http://www.physicsguy.com/ftl/html/FTL_intro.html
... to where they talk about the twin's paradox. See how they explain it - and try to draw the space-time diagram for each of the triplets in your situation.

If space "coats" matter as I understand it does,

... I'm with PeterDonis on this one. Are you sure your understanding is not in error?

 

[Seminole Boy]

I'm using "coats" very loosely. Don't dig too deep into that. I'm basically saying motion and space are very connected. Space coats matter. Matter makes sense of space--give us space.

I'm enjoying the responses. You guys (and maybe girls) are very smart.

 

[Seminole Boy]

You guys are smart, so I'm trying to match you.

There seems not to be any absolute direction in the cosmos (or space, or outer-space, or whatever you label it). Direction is a human-constructed concept. North is equivalent to south, as is east and west.

If we--and by this I mean all forms of condensed matter--are moving through a spacetime continuum, as Einstein suggests, how does anything outside of (relative) speed affect or influence our aging process? I'm simply saying different bodies of matter are moving at the same speed (Boys A and B), so how can their so-called directional behavior create some state of inequality with regard to their aging process, if moving through spacetime in "this direction" is the same as moving through it in "that direction"?

 

[1977ub]

A & B both experience acceleration before they come back to join C. This acceleration, this change-in-inertial-frames is what leads to an objective slowing of A & B that they can all agree on when they all come back together to compare timepieces.

 

[ghwellsjr]

A & B both experience acceleration before they come back to join C. This acceleration, this change-in-inertial-frames is what leads to an objective slowing of A & B that they can all agree on when they all come back together to compare timepieces.

That's just one of many "explanations" but it is a very complicated way to show that A & B are the same age when they come back together, don't you think? It's far easier to explain using C's single Inertial Reference Frame and to say that A & B are always at the same speed during their trips and so their clocks remain in sync.

Your explanation, or something like it, is what it seems to me led bug_man_russ astray in post #2:

I don't quite think so. Relative to boy c. Both A and B should be younger. Between A nd B that's more difficult. As they move away from each other at the same speed they should age the same. However Boy A is going to zig zag and by this will change velocities by perception to Boy b. Simply put it he wil appear (or really willdependding on direction changed) to accelerate and decelerate relative to B. Time or the appearance of time between each will not be constant. I would expect at the end of your experiment boy B will be "younger".

His reasoning is correct but without working through the details, it's not obvious how things will come out.

 

[Alain2.7183]

It's far easier to explain using C's single Inertial Reference Frame and to say that A & B are always at the same speed during their trips and so their clocks remain in sync.

A and B will always be in sync according to C, but not according to each other (except at the end of the trip, of course). The zig-zagger in particular will say that the other traveler's age is varying wildly during the trip.

 

[PeterDonis]

If we--and by this I mean all forms of condensed matter--are moving through a spacetime continuum, as Einstein suggests, how does anything outside of (relative) speed affect or influence our aging process? I'm simply saying different bodies of matter are moving at the same speed (Boys A and B), so how can their so-called directional behavior create some state of inequality with regard to their aging process, if moving through spacetime in "this direction" is the same as moving through it in "that direction"?

Um, did you see where I said you were correct that A and B age the same? They do. Since they both meet up with C at the end, the only thing that matters is their speed relative to C. Their "directional behavior" does *not* create any "inequality" between A and B in this case.

 

[PeterDonis]

His reasoning is correct but without working through the details, it's not obvious how things will come out.

In general you're right, but in this particular case we can see easily how things will come out, because of the particular facts about this particular scenario that I pointed out in post #4.

 

[Seminole Boy]

Mr. Donis:

How am I misunderstanding spacetime? I'm regarding space as a property through which we (forms of matter) travel, which gives us (matter) the idea of relative motion and relative time (and all kinds of other relative concepts).

 

[PeterDonis]

How am I misunderstanding spacetime?

Did I say you were?

I'm regarding space as a property through which we (forms of matter) travel, which gives us (matter) the idea of relative motion and relative time (and all kinds of other relative concepts).

This is not wrong, exactly, but I would put it differently, because the word "spacetime" as opposed to "space" is key. Space and time are not separate, and "motion through space" is not what gives us the idea of relative motion and time. Space, time, and relative motion are all built into spacetime on the same fundamental footing.

 

[Seminole Boy]

So you're saying--and I'm drawing on a previous post of yours--that we're all moving through spacetime at the speed of light? I can accept this, but how does variation in relative motion, which seems to stem from speed, which would imply that matter through the spacetime continuum is deviating from c, get factored into your contention? In other words, if everything is going through the continuum at c, and that number is constant and cannot vary, how is it possible for the time dilation idea to make sense? It seems Einstein is suggesting that matter can manipulate its relative speed through spacetime, whereas you are saying everything is going through spacetime at C.

 

[PeterDonis]

So you're saying--and I'm drawing on a previous post of yours--that we're all moving through spacetime at the speed of light?

I said that's one particular interpretation of the math of special relativity. It's not the only one, and as I said, it's not one I use much myself, because it tends to lead to incorrect inferences, such as the ones you draw. The key thing is that this interpretation talks about speed through spacetime, which is *not* the same as either relative speed *or* speed through space.

but how does variation in relative motion, which seems to stem from speed

It stems from *relative* speed; it does *not* stem from any variation in "speed through spacetime". In terms of the "speed through spacetime" interpretation, what is different about two objects in relative motion is that they are moving in different "directions" in spacetime; and their relative velocity is the "spacetime angle" between the directions in spacetime in which they are moving.

In terms of your scenario, C is moving through spacetime in the same "direction" the whole time. A starts out moving in a different spacetime direction at some angle to C corresponding to a relative velocity of 0.9c; then halfway through he switches to moving at an angle to C of the same magnitude but with the opposite sign, i.e., the same relative speed but in the opposite direction. B keeps switching signs of his angle with C much more than A, but he always keeps the magnitude of his angle with C the same until the end.

which would imply that matter through the spacetime continuum is deviating from c

No, it doesn't. See above.

 

[Simon Bridge]

we're all moving through spacetime at the speed of light? I can accept this

It is true though ... time and space are tied up together in such a way that the magnitude of the 4-velocity is always c. This is what allows things like time dilation happen. You can do the math yourself.

http://en.wikipedia.org/wiki/Four-velocity

 

[1977ub]

this: http://www.relativity.li/en/epstein2/read/c0_en/c2_en/

 

[ghwellsjr]

It's far easier to explain using C's single Inertial Reference Frame and to say that A & B are always at the same speed during their trips and so their clocks remain in sync.

A and B will always be in sync according to C, but not according to each other (except at the end of the trip, of course). The zig-zagger in particular will say that the other traveler's age is varying wildly during the trip.

The zig-zagger can say that the other traveler's age is varying wildly during the trip, if he chooses to use a particular analysis that leads to that conclusion, but he doesn't have to. He can use other analyses that show a smooth increase in the other traveler's age, including C's rest frame. My comment was directed at 1977ub, who implied that C's rest frame was not adequate to explain the final ages of the triplets.

A & B both experience acceleration before they come back to join C. This acceleration, this change-in-inertial-frames is what leads to an objective slowing of A & B that they can all agree on when they all come back together to compare timepieces.

And so my comment applies to you and I further want to make the comment that even more complicated analyses don't change what any observer actually sees and observes. A & B will not see the other traveler's age varying wildly, they will see a steady increase in the other ones age throughout the trip.

 

[ghwellsjr]

His reasoning is correct but without working through the details, it's not obvious how things will come out.

In general you're right, but in this particular case we can see easily how things will come out, because of the particular facts about this particular scenario that I pointed out in post #4.

Yes, in post #4 you said:

The key is that boys A and B both moved at the same speed relative to boy C, who remained at rest the whole time at the spatial location that both boy A and boy B returned to. The bolded part is key; as long as it's true, then yes, the direction doesn't matter (nor does the fact that boy B changed direction a lot more than boy A); A's and B's speed relative to C is the only relevant factor.

And how is that any different than what I said earlier in the post you quoted above:

That's just one of many "explanations" but it is a very complicated way to show that A & B are the same age when they come back together, don't you think? It's far easier to explain using C's single Inertial Reference Frame and to say that A & B are always at the same speed during their trips and so their clocks remain in sync.

I don't understand why you saw fit to comment on my post. What am I missing?

 

[Simon Bridge]

I don't understand why you saw fit to comment on my post. What am I missing?

For that matter (and leaving PeterDonis to answer the question...)

Time Dilation: Triplet Paradox makes no sense

... I'm not sure you told us what it was about the triplet paradox that you felt made no sense.

If we are talking past each other, even a little bit, it is hardly surprising. Perhaps you breifly outline your current understanding of the situation, understanding will dawn?

 

[PeterDonis]

And how is that any different than what I said earlier in the post you quoted above:

I don't think it's different from your earlier statement; but your earlier statement, like my post #4, explains why you *don't* need to work out any details to know how it comes out, in that particular case. So I wasn't sure why you said later in your post that one would need to work out the details to see how it comes out.

 

[ghwellsjr]

I don't think it's different from your earlier statement; but your earlier statement, like my post #4, explains why you *don't* need to work out any details to know how it comes out, in that particular case. So I wasn't sure why you said later in your post that one would need to work out the details to see how it comes out.

One needs to work out the details if they ignore the easy, obvious solution that you explained using C's single inertial rest frame and instead choose one of the accelerating triplet's multiple inertial frames like 1977ub implied was necessary in post #9. And then I said I thought maybe that is what bug_man_russ felt compelled to do in post #2 and since he didn't work out the details, he came to the wrong expectation that B would be younger than A.

I wish people like 1977ub, Alain2.7183 and bug_man_russ would actually work out the details and show us how to come to the correct conclusions instead of just making statements about accelerating observers jumping inertial frames.

 

[PeterDonis]

One needs to work out the details if they ignore the easy, obvious solution that you explained using C's single inertial rest frame and instead choose one of the accelerating triplet's multiple inertial frames like 1977ub implied was necessary in post #9.

Ah, ok, that makes sense. Sorry for the confusion on my part.