Absolute Velocity?

[Deneb]

Isn't this just another formulation of the twin paradox?

If so, here is the resolution in SR: http://en.wikipedia.org/wiki/Twin_paradox#Resolution_of_the_paradox_in_special_relativity

And in GR: http://en.wikipedia.org/wiki/Twin_paradox#Resolution_of_the_paradox_in_general_relativity

 

[shadron]

Look at the voodoo approach you are taking? Its a total outright refutation with absolutely no comeback to it. And you jibber on about some unscientific notion like "verdicts of history". What next? You going to conduct polls?

Really good at dodging the main argument as well, I see.

 

[Tubbythin]

Well GMB, baring in mind that "our" theory can help explain among other things:
Why travelling muons have longer lifetimes than stationary muons.
Why particle physics experiments work (remember that each collision is essentially one experiment so this is literally trillions upon trillions of experiments).
Where the energy of the Sun comes from.
How nuclear power works.
Which nuclei are likely to decay and which are stable.
And many many many many many many many many many many many many many many many other experiments, whilst you have failed to offer an alternative, I think I'll keep hold of said theory. If its all the same to you.

 

[rjh01]

In case you missed it. Suspension Notice: gmb

GMB has been suspended for three days for repeated breaches of the Membership Agreement despite mod warnings.

 

[Perpetual Student]

A question for s. i.

If two individuals are moving in opposite directions and observe each other's clocks as slowing down, what happens if they make simultaneous u-turns and eventually come to rest next to each other? Would their clocks now be synchronized? If so, did each observer see the others clock speed up at some time during the acceleration needed for the turns? I am not aware of anything involving "time constriction" in SR. Does GR somehow handle this? If so, how did physicists handle this question during the time between the developement of SR and GR?

 

[RecoveringYuppy]

@PS

If both of those individuals experience the same accelarations along their journey they will arive with their clocks synchronized. If they observe each others clocks along the way they will see the others clocks as slowed when receding from each other and sped up when approaching each other.

On a space time diagram these two individuals would have identically shaped world lines. Their clocks would not be syncrhonized when they re-united after having taking different journeys involving different accelerations. The one who experiences more space experiences less time.

 

[RecoveringYuppy]

Went off to google "time constriction". Think you mean "time dilation"? The case you just outlined is covered by SR. And Lorentz worked on the problem as early as 1895. His transformation, incorporated in to Einstein's relativity, was worked out around that time.

 

[Thabiguy]

Although you said the question is for sol, I hope you won't mind me answering it. After all, sol can always provide a more sophisticated answer later.

If two individuals are moving in opposite directions and observe each other's clocks as slowing down, what happens if they make simultaneous u-turns and eventually come to rest next to each other? Would their clocks now be synchronized?

If they were synchronized to begin with, then yes, they'll be synchronized afterwards.

If so, did each observer see the others clock speed up at some time during the acceleration needed for the turns?

Yes, exactly. By making the turn, the observer made a change in frame of reference, which caused a shift in simultaneity - effectively setting the other observer's clock to a future date. When this happens over time, as in acceleration, the effect is that the other clock speeds up during this period for the observer.

But note that that is what the observer observes (i.e. concludes from observations), not what he sees. What he would see is that radio ticks from the other ship would start arriving at a quicker pace after he makes the turn, and after the tick with the timestamp of the scheduled turn arrives, they will start coming even faster. But that is Doppler effect, not time dilation.

I am not aware of anything involving "time constriction" in SR.

If you mean the opposite of time dilation, then change of simultaneity that happens over time can cause that - in other words, acceleration of the observer. It doesn't happen in inertial frames, though.

Does GR somehow handle this? If so, how did physicists handle this question during the time between the developement of SR and GR?

GR doesn't enter this, this is all SR. GR deals with curved spacetime, which is not relevant for this experiment.

 

[RecoveringYuppy]

If two individuals are moving in opposite directions and observe each other's clocks as slowing down, what happens if they make simultaneous u-turns and eventually come to rest next to each other?

There's a simpler and easier to understand answer to your question, but it's only simpler if you've already worked through the so-called "twin paradox".

You're basically have a triplet situation here. One guy stays home and his two siblings go off on identical trips, except in different directions. The directions don't matter so, yes, the two people who travelled come back with their clocks synchronized with each other. They both aged less than their stay at home brother and by the same amount.

 

[RecoveringYuppy]

But note that that is what the observer observes (i.e. concludes from observations), not what he sees. What he would see is that radio ticks from the other ship would start arriving at a quicker pace after he makes the turn, and after the tick with the timestamp of the scheduled turn arrives, they will start coming even faster. But that is Doppler effect, not time dilation.

To amplify your point: It's not necessary that they get back together to establish that their clocks are synchronized. Since they are taking identical trips, they will find that their clocks are always synchronized. But, when they are far apart it will take time for the evidence of this to reach them.

 

[Thabiguy]

To amplify your point: It's not necessary that they get back together to establish that their clocks are synchronized. Since they are taking identical trips, they will find that their clocks are always synchronized. But, when they are far apart it will take time for the evidence of this to reach them.

Hmm... I'm afraid that's not quite the case. They would find that their clocks are always synchronized in some reference frame (the "rest" frame, in which their journeys are symmetrical), but not in their frame.

For each observer, the other observer's clock will only be synchronized at three times: at the beginning of the journey, in the middle of the turn, and at the end of the journey.

During the outward leg, the other observer's clock will be behind and slower (thus getting increasingly more behind). During the return leg, the other observer's clock will be ahead and slower (getting increasingly less ahead, until they meet, at which point the clocks will be synchronized again).

 

[RecoveringYuppy]

Agree with your first paragraph. What do you mean by "will be ahead"?

 

[Thabiguy]

What do you mean by "will be ahead"?

The opposite of behind. In A's reference frame, when A's clock shows 12:00, B's clock shows 12:05. A's clock is behind B's, and B's clock is ahead of A's.

 

[RecoveringYuppy]

When you say A's (or B's) reference frame, do you mean a frame at rest compared to them at the time of measurement? So you're explaining it from five different "points of view"? (which might be convenient if you're are trying to explain what they experience along the way, but doesn't have to be done to resolve the end result).

 

[Thabiguy]

When you say A's (or B's) reference frame, do you mean a frame at rest compared to them at the time of measurement?

Yes, that's what I mean. The frame is of course not inertial due to the A's acceleration, and specifically, the inertial frame coinciding with his frame during the outward leg is not the same as the inertial frame coinciding with his frame during the return leg.

So you're explaining it from five different "points of view"? (which might be convenient if you're are trying to explain what they experience along the way, but doesn't have to be done to resolve the end result).

I'm explaining it from a single point of view - A's. This is a point of view of a non-inertial observer. During various parts of the journey, it coincides with points of view of various (hypothetical) inertial observers - infinitely many during the acceleration, actually.

You're of course right that this doesn't have to be done to resolve the end result. I've explained A's point of view because that's what Perpetual Student asked about ("did each observer see the others clock speed up at some time during the acceleration needed for the turns?").

 

[RecoveringYuppy]

I'll think on this a while and come back (when hopefully the forum software/server is a bit more stable) but still having trouble with "In A's reference frame, when A's clock shows 12:00, B's clock shows 12:05.".

 

[Perpetual Student]

OK, let me clarify a few points. First by "time constriction" – my choice of term -- I did mean the opposite of time dilation. As far as I know, the Lorenz transformation only accounts for time and space dilation. How do the clocks in my example speed up? Is there an inverse gamma function? In my view, none of the above responses come close to answering this question.

I will rephrase and recast my question:

Two observers with synchronized clocks take off in opposite directions (both accelerate by equal amounts). They observe each others clocks slowing down. The relationship for this is dt* = dt(gamma) for both observers. They then simultaneously turn around and come together. In the end, if their clocks are again synchronized, then each observer saw the others clock speed up (constrict). How did that happen? Is there an inverse Lorenz transformation for this result? Does this come about because of the acceleration? If so, what is that transformation equation? Since it involves acceleration, is GR involved?

 

[Thabiguy]

I'll think on this a while and come back (when hopefully the forum software/server is a bit more stable) but still having trouble with "In A's reference frame, when A's clock shows 12:00, B's clock shows 12:05.".

Okay, think about it. But there's nothing unusual about that, it's just a consequence of time dilation. When B moves relative to A (say at 0.866c), his clock will tick slower in A's frame. So if A's and B's clock both show 10:00 when they pass, then in A's frame, B's clock shows 10:05 when A's clock shows 10:10 (B's clock is behind), and it shows 9:55 when A's clock shows 9:50 (B's clock is ahead).

 

[Thabiguy]

OK, let me clarify a few points. First by "time constriction" – my choice of term -- I did mean the opposite of time dilation. As far as I know, the Lorenz transformation only accounts for time and space dilation. How do the clocks in my example speed up? Is there an inverse gamma function? In my view, none of the above responses come close to answering this question.

I fully answered your question. Maybe I wasn't clear enough. I'll try again.

Two observers with synchronized clocks take off in opposite directions (both accelerate by equal amounts). They observe each others clocks slowing down. The relationship for this is dt* = dt(gamma) for both observers.

Yes.

They then simultaneously turn around and come together. In the end, if their clocks are again synchronized, then each observer saw the others clock speed up (constrict).

You can call it that.

How did that happen?

It happened when the observer changed his reference frame by accelerating.

Does this come about because of the acceleration?

Yes. This caused a change of reference frame, thus a change in simultaneity. When this change happens over some timespan (as is the case in acceleration), the effect can be that the other clock "speeds up".

If so, what is that transformation equation?

You can find it here, but I would recommend you to read the whole article.

Since it involves acceleration, is GR involved?

No. SR if perfectly sufficient for all of this. The notion that "GR is required for things involving acceleration" is unfortunately a common misconception.

 

[RecoveringYuppy]

Okay, think about it. But there's nothing unusual about that, it's just a consequence of time dilation. When B moves relative to A (say at 0.866c), his clock will tick slower in A's frame. So if A's and B's clock both show 10:00 when they pass, then in A's frame, B's clock shows 10:05 when A's clock shows 10:10 (B's clock is behind), and it shows 9:55 when A's clock shows 9:50 (B's clock is ahead).

Yes, but that's a statement about the events as measured against a reference frame. Earlier I thought you were making statements about what A "would see" as in "experience for himself". And I think that is what PS is asking about.