Unraveling the Twins Paradox: Examining the Actual Solution

[pervect]

So - am I correct in concluding that the physical reason why the two clocks disagree is because, after synchronization in a first frame J, one clock traveled a distance relative to frame J and the other clock remained at rest in frame J?

That's a good way of looking at it.

 

[yogi]

So you would say the physics (of age difference) is intrinsic to the geometry of the spacetime path - no further principles such as changing energy relationships are involved?

If so - would you also agree that a physical time difference is an unavoidable consequence of any motion of one of two Einstein synchronized clocks when the moved clock is returned to the original frame of synchronization, but to a remote spatial point (e.g., the turn around point of the proverbeal twin?

 

[TheAntiRelative]

Janus: you hit upon what my misunderstanding was. For some reason I was not considering direction of acceleration. Towards speeds it up and away slows it down...

Okay, now I'm going to go away and rethink this.

I'm trying to determine a way to create a computer model that can do the following:
1) Allow two different users to connect to it as two different twins.
2) Show the exact experience of each twin in each twins interface.

I was thinking of doing this by representing each user to the other as clocks in space colored yellow with a distance meter also available. The traveling twin would have a control for accelerating. I'll have to model this in a 3d game environment so that the users can see the other clocks get further away/closer and change color.

I just have to nail down when what happens and I'm going to be doing a total wave count as an accuracy check.

 

[pervect]

If you mean to accurately model the relativistic effects of arbitrary acceleration, you're in for a lot more trouble than you think :-(. We haven't even started to cover the math you'd need for the Rindler horizon - and there are other fun effects, like Thomas precession.

 

[TheAntiRelative]

No. For the Earth twin, the difference accumlates during the whole of of the trip due to his twin's clock running slow.
For the "traveling" twin, the age difference is due to the fact that the Earth clock ran slow during the inbound and outbound trips, and briefly runs fast during the turnaround phase.

Hmm, I'm missing something...
It sounds like you are saying here that the Earth twin would not calculate changes to the traveling twins clocks for acceleration.

Isn't that like saying GPS clocks would not calculate Earth's clocks to be running slower?

With the equivelence of acceleration and gravity I can't see there not being some sort of absolute reciprocating event here. We measure GPS to be fast and GPS measures us to be slow.

I guess I'm wondering where the gravitational and kinematic time shifts link together. Because of GPS I can understand a clock undergoing an amount of time change that is relative to the intesity of the acceleration/gravity * outside time (as measured from isome other frame like Earth's).

I can also understand that the acceleration portions of the trip would cause his times to run slower if he accelerated greater than G. During those portions of the trip I could easily calculate how long he would have to accelerate & how much because of the known difference between local G the GPS orbital G. Eventually I could extrapolate just about any figure I wanted from all those variables given an amount of time change amount of acceleration. How long he accelerated, the intesity etc etc.

What I don't understand is why the kinematic shift gets tossed into the calculation right along with the gravitational. They are completely opposite. As a matter of fact, if the acceleration phases were done at exactly 1 G at all times, though it might take a while, acceleration is no longer a consideration at all for time difference. Only Kinematic differences arise. (well I guess a little would be needed for escape velocity but that could be factored out)

I have to ask again. When do I see the clocks change, when does time rush forward on the Earth twins clock? Only during the acceleration phases? The whole time? Why?

If not only during the acceleration phases then how is the paradox resolved?

I'm still pretty confused actually...
Come to think of it I'm not getting the one detail that makes including acceleration into the mix fix the twins paradox. If you say that accelerating makes you the one moving then what if that acceleration is actually the decelleration needed to make you the one that is actually still and it's been the Earth that was accelerated at the big bang and you're finally the one that is still now on your seeming outbound trip. Being in motion at all wrt each other must cause Kinematic shift but only one can be right. Everything is being accelerated all the time so how on Earth can we say that "the one that accelerated moved" The Earth twin is being accelerated the entire trip. Why isn't he the one that moved?

It seems like the traveling twin should be the old one because he wasn't sitting in a gravitational field the whole time getting accelerated...

What am I missing?

I'm sure you've explained this all a hundred times before, sorry if I'm asking the same old crap. I just haven't been able to get it all settled in my head from other publications etc. I usually understand better by getting answers to direct questions.

 

[TheAntiRelative]

oops forgot to ask the question I actually came here for today:

Okay, I'm trying to get things down to their grade-school complexity level to make them easily modeled in the mind. This is just for the Earth observers perspective.

1) If I have a light source traveling toward me at sqrt(3)C/2, its time is running at 50% of mine correct? If not then please tell me the correct speed to get 50% time and assume that answer for the following questions.

2) When an object is traveling toward me at that same speed what is the percentage of the original signal that the relativistic doppler equation settles out to?

3) What does it become for an object moving away at that speed when represented as a percentage of the original?

 

[learningphysics]

oops forgot to ask the question I actually came here for today:

Okay, I'm trying to get things down to their grade-school complexity level to make them easily modeled in the mind. This is just for the Earth observers perspective.

1) If I have a light source traveling toward me at sqrt(3)C/2, its time is running at 50% of mine correct? If not then please tell me the correct speed to get 50% time and assume that answer for the following questions.

Yes, that's right.

2) When an object is traveling toward me at that same speed what is the percentage of the original signal that the relativistic doppler equation settles out to?

The ratio is sqrt[(1+v/c)/(1-v/c)] = 3.73 so the frequency the Earth observer sees is 3.73 times the source frequency.

3) What does it become for an object moving away at that speed when represented as a percentage of the original?

Same as above but switch v to -v... we get 1/3.73 = 0.268. So the observed frequency is 0.268 times the source frequency.

 

[TheAntiRelative]

So at extremely low speeds, the relativistic doppler effect and the typical doppler for sound etc are extremely similar but the relativistic calculation, unlike the classical one, is non linear so at higher speeds a greater effect is observed?

 

[Janus]

Hmm, I'm missing something...
It sounds like you are saying here that the Earth twin would not calculate changes to the traveling twins clocks for acceleration.

That's right.

Isn't that like saying GPS clocks would not calculate Earth's clocks to be running slower?

With the equivelence of acceleration and gravity I can't see there not being some sort of absolute reciprocating event here. We measure GPS to be fast and GPS measures us to be slow.

No it is not the same. With GPS satellites both the the observer on the surface and the satellite agree that they are in a gravitational field and that the satellite is a a higher potential in the field.
In the Twin paradox, the "equivalent gravitational field" only exists for the accelerating twin so he is the only one who would measure any effect from it.

I guess I'm wondering where the gravitational and kinematic time shifts link together. Because of GPS I can understand a clock undergoing an amount of time change that is relative to the intesity of the acceleration/gravity * outside time (as measured from isome other frame like Earth's).

Gravitational time dilation is not due to relative intensity of gravity, but to difference in potential. Example: Imagine a uniform gravity field of 1g, IOW, a field which does not change in intensity over space. Place one clock higher than the other in that field and even though both clocks experience the same force of 1g The higher clock will be seen as running faster than the lower clock.

I can also understand that the acceleration portions of the trip would cause his times to run slower if he accelerated greater than G.

The acceleration does not cause his clock to run slower. The acceleration causes the accelerated observer to measure clocks in the direction of his acceleration to run fast (the further away, the faster) and clocks in the opposite direction of acceleration to run slow.

During those portions of the trip I could easily calculate how long he would have to accelerate & how much because of the known difference between local G the GPS orbital G. Eventually I could extrapolate just about any figure I wanted from all those variables given an amount of time change amount of acceleration. How long he accelerated, the intesity etc etc.

What I don't understand is why the kinematic shift gets tossed into the calculation right along with the gravitational. They are completely opposite. As a matter of fact, if the acceleration phases were done at exactly 1 G at all times, though it might take a while, acceleration is no longer a consideration at all for time difference. Only Kinematic differences arise. (well I guess a little would be needed for escape velocity but that could be factored out)

I have to ask again. When do I see the clocks change, when does time rush forward on the Earth twins clock? Only during the acceleration phases? The whole time? Why?

If not only during the acceleration phases then how is the paradox resolved?

I'm still pretty confused actually...
Come to think of it I'm not getting the one detail that makes including acceleration into the mix fix the twins paradox. If you say that accelerating makes you the one moving then what if that acceleration is actually the decelleration needed to make you the one that is actually still and it's been the Earth that was accelerated at the big bang and you're finally the one that is still now on your seeming outbound trip. Being in motion at all wrt each other must cause Kinematic shift but only one can be right. Everything is being accelerated all the time so how on Earth can we say that "the one that accelerated moved" The Earth twin is being accelerated the entire trip. Why isn't he the one that moved?

again the time dilation is not due to the strength of local acceleration but to difference in potential. Since the Earth's gravity field falls off with distance, there is a maximum difference in potential you can have due to its field. The equivalent gravity field seen by the accelerating observer extends for an indefinite distance ahead and behind the ship and does not fall off with distance.

It seems like the traveling twin should be the old one because he wasn't sitting in a gravitational field the whole time getting accelerated...

What am I missing?

I think what you are missing is a conceptual grasp of what Relativity is about. You seem to keep wanting to think of it in terms of Mechanistic effects that act on clocks to physically slow them down. Instead, it deals with the nature of time and Space and how we measure them.

I'm sure you've explained this all a hundred times before, sorry if I'm asking the same old crap. I just haven't been able to get it all settled in my head from other publications etc. I usually understand better by getting answers to direct questions.

 

[yogi]

As i previously stated - there are many books with different explanations - some internally consistent, some equivalent, and they all conclude that the paradox is resolved.
The confusion arises from the interpretation that is put on Einsteins 1905 paper, In the derivation of the transforms, Einstein repeats parenthically several times that the clocks run at different speeds as measured against the other clock - that is, without more information, two spaceships passing each other can set up experiments on board that will indicate the other clock is running slow - this is all observational - because if there are two clocks, each cannot be running slower than the other. Then Einstein makes a big jump - Part IV he drops a bomb and says what the physical consequences would be if two clocks are initially synchronized in one frame, and one of them is moved - the clocks will not longer read the same. This does not follow from the derivations - it is a new hypothesis in one sense, because it is now a real time (age difference) that has taken place. You simply can't get there from the position of each clock running slow - you get there because the motion of one clock is now defined in terms of the frame in which the clocks were originally synchronized - Einstein gets the right result - but he has tacitly introduced the notion of spatial motion relative to the rest frame of the clock which stays put. In fact, he has introduced the concept of the invariance of the interval and the basis of Minkowski "spacetime" Two passing clocks each judge the other clock to be running slow - but that is an observational thing - to get the actual physically real age difference, you have to know in which frame the motion took place. In the case of the twins, the motion of the traveling twin takes place in the rest frame of the stay at home twin.