Can the Twin Paradox be simplified?

[CptBork]

No one is arguing that there's a paradox. We're discussing specifically whether acceleration is a necessary causal component of absolute time dilation.

Sorry, but time dilation isn't absolute. Each observer sees the other one as being dilated while they are in relative motion. They also disagree on time synchronicity. But they still agree on who has aged more when the space-faring twin returns home, and that's the only part where it matters who accelerated, though the nature of the acceleration itself makes virtually no difference as long as it's relatively quick.

[RJBeery]

Sorry, but time dilation isn't absolute. Each observer sees the other one as being dilated while they are in relative motion. They also disagree on time synchronicity. But they still agree on who has aged more when the space-faring twin returns home, and that's the only part where it matters who accelerated, though the nature of the acceleration itself makes virtually no difference as long as it's relatively quick.

No problem, it's important that we all agree on terminology before we spend man-hours in discussion.

Absolute time dilation refers to that which cannot be denied by a change in measuring frame.

This knowledge can only be had in a scenario involving acceleration. That's my point. The Third Brother scenario was postulated by some as being proof of absolute time dilation without acceleration, and it was shown to be a false proof. The fact that acceleration is MANDATORY to establish absolute time dilation is not just some inconvenient triviality; it is the very definition of a necessary causal component.

[CptBork]

Yeah but if the traveling twin kept going and didn't return to Earth, and they continued communicating via radio signals, the traveling twin by all measurements would find time to be moving more slowly in the Earth twin's frame, and the Earth twin finds vice-versa. They do not agree on who is being time dilated until the traveling twin turns around and comes back.

[RJBeery]

Yeah but if the traveling twin kept going and didn't return to Earth, and they continued communicating via radio signals, the traveling twin by all measurements would find time to be moving more slowly in the Earth twin's frame, and the Earth twin finds vice-versa. They do not agree on who is being time dilated until the traveling twin turns around and comes back.

You mean to say that they don't agree on absolute time dilation until they rejoin each other. This can happen by either party accelerating (and cannot happen without it). Acceleration is necessary.

We can also change the results of the experiment by letting the relative velocities remain constant and adjust who accelerates, which is normally the procedure for establishing a causal component in an experiment. Acceleration is causal.

I find it difficult to understand how we try to claim that acceleration isn't a necessary causal component from these facts.

[OnlyMe]

Yeah but if the traveling twin kept going and didn't return to Earth, and they continued communicating via radio signals, the traveling twin by all measurements would find time to be moving more slowly in the Earth twin's frame, and the Earth twin finds vice-versa. They do not agree on who is being time dilated until the traveling twin turns around and comes back.

Or perhaps until the twin left on Earth dies and stops responding?

[CptBork]

You mean to say that they don't agree on absolute time dilation until they rejoin each other. This can happen by either party accelerating (and cannot happen without it). Acceleration is necessary.

We can also change the results of the experiment by letting the relative velocities remain constant and adjust who accelerates, which is normally the procedure for establishing a causal component in an experiment. Acceleration is causal.

I find it difficult to understand how we try to claim that acceleration isn't a necessary causal component from these facts.

I never said acceleration isn't a causal component in the scenario. Without acceleration, the two twins would never meet again. But when they try to use their radio signals to decide for whom time is being dilated, they will disagree on which twin should have aged more until the space-faring one reverses direction. But the point is that time dilation itself, between two given inertial frames, is not absolute, and does not depend on the accelerations which led to observers at rest in those respective frames having the velocities they have with respect to each other.

Or perhaps until the twin left on Earth dies and stops responding?

If they die at the same age, then there will still be messages headed for the space-faring twin which will only reach him after the space-faring twin dies, and he'll correctly measure that he has aged more than the Earth twin and is dying first.

[RJBeery]

I never said acceleration isn't a causal component in the scenario. Without acceleration, the two twins would never meet again.

OK

But the point is that time dilation itself, between two given inertial frames, is not absolute, and does not depend on the accelerations which led to observers at rest in those respective frames having the velocities they have with respect to each other.

Ahh but then we don't even disagree on anything substantial! I'm saying nothing about time dilation between two inertial frames, I'm only discussing absolute time dilation, which I defined earlier, and you already agree that acceleration is a necessary, causal component of it.

Whether or not relative time dilation "actually exists" is delving into philosophy and semantics. We may as well start with our navel lint.

[Trippy]

What matters is that one twin remains in an inertial frame, the other doesn't. This is intro-level stuff guys, it really isn't that complicated. There, done, now move along onto something of actual consequence.

This, +1

[RJBeery]

What matters is that one twin remains in an inertial frame, the other doesn't. This is intro-level stuff guys, it really isn't that complicated. There, done, now move along onto something of actual consequence.

This, +1

I concur with this as well but are non-inertial frames more closely associated with acceleration or relative velocity?

[Trippy]

CptBork, I'm willing to discuss this with you if you are intellectually sincere about it. I've quickly read over your post. What you're saying is that acceleration plays no role in determining the absolute time dilation of the duo, Albert and Bob. Therefore, it shouldn't matter if, after Bob reaches the beacon, Bob returns to Albert from the beacon or if Albert catches up to Bob from Earth, because the relative velocity would be the same, correct? I mean, the ONLY difference would be "who" did the acceleration, and acceleration is irrelevant, right? Well, guess what happens if Albert does the catching up...no age difference between them.

Acceleration is not the only assymetry in the scenario.

[Tach]

I didn't ask about any observer and I didn't ask about the rate of measured time dilation. I had assumed there would be no dispute about the fact that A and B will mutually agree that A's clock is "ticking more slowly"; the extent of that effect is irrelevant to the point. The point is exactly what I asked:

How can we conclude it is relative velocity that causes time dilation in this scenario?

I answered that earlier, this is an exercise for introductory class in GR. I could post the answer but you will only argue , so not.
I can tell you that the answer is independent of acceleration, i.e. depends on velocity only.

[OnlyMe]

If they die at the same age, then there will still be messages headed for the space-faring twin which will only reach him after the space-faring twin dies, and he'll correctly measure that he has aged more than the Earth twin and is dying first.

Touché!

[Pincho Paxton]

I know the answer...


Not allowed to post...

[RJBeery]

Acceleration is not the only assymetry in the scenario.

I'm listening, let's discuss.

[Tach]

When you initially claimed that acceleration had no affect on time dilation, I invoked GR and the equivalence principle.

...and I told you that your argument is wrong, that I can easily prove you wrong but because the argument involves some math, you will reject it out of hand. It is an exercise routinely given in introductory GR classes. While the solution involves EP, the results show that acceleration has nothing to do with gravitational time dilation.

One question and I will let this drop. Do you still not understand that using twins as clocks in the paradox requires initial co-location and that at least one twin undergoes some acceleration to change inertial frames of reference?

Yes, I understand and you are wrong on both accounts, I would point you again to prof. Simonetti's website, to the excellent introductory books of D.Mermin and Max von Laue but I know that it is useless, you will stick your fingers in your years, cover your eyes and repeat the same incorrect stuff, so not. Look, this problem was decided in 1913, ok?

PS: I forgot an excellent explanation in David Morin book, section 11.19. It is free, why don't you read it?

[OnlyMe]

PS: I forgot an excellent explanation in David Morin book, section 11.19. It is free, why don't you read it?

Again Tach you have made reference to a hypothetical that includes a twin in the title only. The modification consists of arranging the thought experiment using observers and clocks, not twins....

The following IS section 11.19 from your above link. Make note of the two times that the word twin is used and the context.

11.19 Modified twin paradox ***

Consider the following variation of the twin paradox. A, B, and C each have a clock. In A’s reference frame, B flies past A with speed v to the right. When B passes A, they both set their clocks to zero. Also, in A’s reference frame, C starts far to the right and moves to the left with speed v. When B and C pass each other, C sets his clock to read the same as B’s. Finally, when C passes A, they compare the readings on their clocks. At this moment, let A’s clock read TA, and let C’s clock read TC.

(a) Working in A’s frame, show that TC = TA/γ, where γ = 1/��1 − v2/c2.
(b) Working in B’s frame, show again that TC = TA/γ.
(c) Working in C’s frame, show again that TC = TA/γ.

This proves my point Tach, not yours! Can't you understand something as simple as this?

A, B & C are not twins or triplets. They are observers with clocks...

This really is the same situation as CptBork mentioned earlier and a bit less elaborate version than the one you linked to in another thread.

[CptBork]

Acceleration is not the only assymetry in the scenario.

Yeah, for instance the distance at which the Earth observer sees his twin reverse direction is greater than the distance at which that same twin measures Earth when he chooses to reverse course.

[Tach]

Again Tach you have made reference to a hypothetical that includes a twin in the title only. The modification consists of arranging the thought experiment using observers and clocks, not twins....

And, for the n-th time you fail to understand that there is no difference. The "twins" are observers equipped with clocks.

[OnlyMe]

And, for the n-th time you fail to understand that there is no difference. The "twins" are observers equipped with clocks.

You are beginning to sound desperate now, Tach. You are not stupid.

Yes, twins can be thought of as observers and/or with clocks, but if they are twins then for them to wind up in separate intertial frames of reference at least one of then has to have experienced some acceleration.

And every, "mainstream" reference you have offered as support, of your position has included twin or twins only within the title and in the last reference, the word twin was specifically denoting the hypothetical as, an alternate to the more traditional "Twin Paradox".

If your observers are Twins one of the has to have experienced acceleration, before or during the hypothetical.

[Tach]

Yes, twins can be thought of as observers and/or with clocks,

Then why do you keep repeating the same nonsensical claim that they are different entities?

but if they are twins then for them to wind up in separate intertial frames of reference at least one of then has to have experienced some acceleration.

Prove it. All the references say "no" . Max von Laue explained this 100 years ago, will it take you 100 years to understand?

If your observers are Twins one of the has to have experienced acceleration, before or during the hypothetical.

Nope, try reading (and comprehending) the references. This is freshman physics, not difficult to understand.