Acceleration is not important in the twin paradox

[Iggy]

Oh I see now. So the pacing twin spends the same total time accelerating in each direction as the traveling twin does, but the acceleration is split up alternating back-and-forth so the pacing twin never reaches significant speed relative to a truly inertial (stationary) twin, aging essentially the same as a truly inertial twin.

 

Precisely. That's how I understood it, yes.

 

 

This is definitely untrue. You would need to calculate for each twin [math]\tau =\int_{C}\sqrt{g_{\mu \nu }dx^{\mu }dx^{\nu }}[/math] according to their respective acceleration profiles and you would need to compare their resulting total elapsed proper times. Depending on the acceleration profiles, you would get (if you do the calculation correctly),

[math]\tau_1=\tau_2[/math]

or

[math]\tau_1 < \tau_2[/math]

or

[math]\tau_1 >\tau_2[/math]

 

I added the qualifier "qualitative" to Ydoa's description, because the numeric results of his thought experiment would be ever so slightly different from the classical twin paradox. However, the velocity is what counts, as Md says. The velocity of a person on a normal-sized carousel experiencing 2g is much, much less than the average velocity of someone accelerating in a straight line for extended periods of time at 2g.

 

BTW, the time dilation for the person on the carousel is,

 

[math]T_d = \sqrt{1 - r^2 \omega^2/c^2}[/math]

 

relative to a non-rotating observer stationary with its base. [math]\omega[/math] is the angular velocity. You can therefore make a direct comparison,

 

[math]\sqrt{1 - r^2 \omega^2/c^2} > \sqrt{1 - v^2/c^2}[/math]

 

The velocity of the person on the carousel is less than the traveling twin, and as the equations show, the traveling twin therefore has more time dilation

[xyzt]

The velocity of a person on a normal-sized carousel experiencing 2g is much, much less than the average velocity of someone accelerating in a straight line for extended periods of time at 2g.

 

For this particular case, maybe (see below). In general, no. The point was that you made a sweeping comment that isn't true. As explained, the end result for the general case depends on the acceleration profiles of the twins. The acceleration profiles determine the speed profiles. The speed profiles determine the total elapsed proper time.

 

[math]\sqrt{1 - r^2 \omega^2/c^2} > \sqrt{1 - v^2/c^2}[/math]

 

The velocity of the person on the carousel is less than the traveling twin, and as the equations show, the traveling twin therefore has more time dilation

Even this isn't true since the RHS has [math]v=2gt[/math] and the LHS has [math]r \omega=2gt[/math] , so, the two sides are equal provided that the acceleration profile is the same.

Edited June 5, 2013 by xyzt

[md65536]

the LHS has [math]r \omega=2gt[/math]

How do you figure that? Variable r is the distance from the center of the carousel, and [math]\omega[/math] is the angular velocity, right? Both are constant here. How does [math]r \omega[/math] increase with time? Edited June 5, 2013 by md65536

[xyzt]

How do you figure that? Variable r is the distance from the center of the carousel, and [math]\omega[/math] is the angular velocity, right? Both are constant here. How does [math]r \omega[/math] increase with time?

Simple: you forgot that the rotation is accelerated: [math]r \frac{d \omega}{dt}=2g[/math] .

Edited June 5, 2013 by xyzt

[Iggy]

For this particular case, maybe (see below). In general, no. The point was that you made a sweeping comment that isn't true.

 

Please understand the limiting criteria. Both twins experience equal constant proper acceleration. They both feel twice earth's gravity (2 g's) worth of acceleration for the duration.

 

A stationary observer experiences 4 years during the experiment. He notes that the traveling twin accelerates at 2g for one year away from him, decelerates (at 2g) for one year, turns around, accelerates (at 2g) for one year now toward him, and decelerates for one year at 2g before making a nice touchdown.

 

The proper time of the traveling twin for each segment is equal and found with the relativistic rocket equation,

 

[math]\tau = \frac{c}{a} \mbox{arcsinh} \left( \frac{at}{c} \right)[/math]

 

[math]\tau = \frac{c}{a} \mbox{ln} \left( \frac{at}{c} + \sqrt{1+ \left( \frac{at}{c} \right)^2} \right)[/math]

 

[math]\tau = 0.713[/math]

 

Each segment of accelerating and decelerating the traveling twin ages 0.713 years. Four segments for a grand total of 2.852 years.

 

[math]\tau = 2.852[/math]

 

The stationary twin ages 4 years and the traveling twin undergoing constant 2gs of acceleration ages 2.852 years.

 

 

A person on a 10 meter radius carousel experiencing 2g's has the velocity,

 

[math]a = \frac{v^2}{r}[/math]

 

[math]v = \sqrt{ar}[/math]

 

[math]v = \sqrt{(2.0631 \ \mbox{light-years / year sq}) (1.057 \times 10^{-15} \ \mbox{light-years})}[/math]

 

[math]v = 4.67 \times 10^{-8} \ \mbox{light-years / year}[/math]

 

(which is to say 14 meters per second)

 

While the stationary twin experiences 4 years and the traveling twin experiences 2.852 years the carousel twin experiences,

 

[math]\tau = t \sqrt{1-v^2}[/math]

 

[math]\tau = 4 \sqrt{1-(4.67 \times 10^{-8})^2}[/math]

 

which is essentially 4 years because someone moving 14 meters per second is hardly time dilated, are they?

 

The carousel would need to be large enough to be measured in light-years for there to be any comparison.

 

 

As explained, the end result for the general case depends on the acceleration profiles of the twins. The acceleration profiles determine the speed profiles. The speed profiles determine the total elapsed proper time.

 

Then you agree. It is the speed...

The returning clock has been permanently altered by its trip (it has suffered a change in phase). The effect is uniquely associated with the fact that the acceleration has occurred, but it is quantitatively related not to the acceleration, but to the average speed...

 

One is led therefore to the conclusion that clocks having a velocity in an inertial frame are literally slowed down by the speed itself.

Some Recent Experimental Tests of the "Clock Paradox" p18

pdf

 

 

You should know intuitively, in your head, that someone experiencing a small centrifugal acceleration has nowhere near the average velocity of someone experiencing the same constant acceleration in a straight line.

 

Small constant accelerations bring a person quite close to the speed of light quite quickly. The speed of the person spinning around doesn't change.

 

 

Even this isn't true since the RHS has [math]v=2gt[/math] and the LHS has [math]r \omega=2gt[/math] , so, the two sides are equal provided that the acceleration profile is the same.

 

I don't follow. For a circle, angular velocity is velocity divided by radius. Acceleration is velocity squared divided by radius.

Edited June 5, 2013 by Iggy

[xyzt]

 

Please understand the limiting criteria. Both twins experience equal constant proper acceleration. They both feel twice earth's gravity (2 g's) worth of acceleration for the duration.

 

A stationary observer experiences 4 years during the experiment. He notes that the traveling twin accelerates at 2g for one year away from him, decelerates (at 2g) for one year, turns around, accelerates (at 2g) for one year now toward him, and decelerates for one year at 2g before making a nice touchdown.

 

The proper time of the traveling twin for each segment is equal and found with the relativistic rocket equation,

 

[math]\tau = \frac{c}{a} \mbox{arcsin} \left( \frac{at}{c} \right)[/math]

 

[math]\tau = \frac{c}{a} \mbox{ln} \left( \frac{at}{c} + \sqrt{1+ \left( \frac{at}{c} \right)^2} \right)[/math]

 

[math]\tau = 0.713[/math]

 

Each segment of accelerating and decelerating the traveling twin ages 0.713 years. Four segments for a grand total of 2.852 years.

 

[math]\tau = 2.852[/math]

 

The stationary twin ages 4 years and the traveling twin undergoing constant 2gs of acceleration ages 2.852 years.

 

 

A person on a 10 meter radius carousel experiencing 2g's has the velocity,

 

[math]a = \frac{v^2}{r}[/math]

 

[math]v = \sqrt{ar}[/math]

 

[math]v = \sqrt{(2.0631 \ \mbox{light-years / sq year}) (1.057 \times 10^{-15} \ \mbox{light-years})}[/math]

 

[math]v = 4.67 \times 10^{-8} \ \mbox{light-years / year}[/math]

 

(which is to say 14 meters per second)

 

While the stationary twin experiences 4 years and the traveling twin experiences 2.852 years the carousel twin experiences,

 

[math]\tau = t \sqrt{1-v^2}[/math]

 

[math]\tau = 4 \sqrt{1-(4.67 \times 10^{-8})^2}[/math]

 

which is essentially 4 years because someone moving 14 meters per second is hardly time dilated, are they?

I wrote this paragraph (and the next one) for wiki some time ago, I am very familiar with the subject matter. The writeup shows the same answers but in the general form, using symbolic math rather than the particularization that you are showing. The part that you keep missing is that the above is valid for the specific case of only one twin accelerating. If both twins accelerate , the answer depends on the respective acceleration profiles. This is the third time I am pointing this out to you, I am quite sure that you can work out the math all by yourself. If you can't, I'll do it for you, just let me know.

I don't follow. For a circle, angular velocity is velocity divided by radius. Acceleration is velocity squared divided by radius.

Yes, I sensed that. You are talking about normal acceleration. If the angular speed isn't constant (and this is the case for both twins experiencing acceleration), then, you have to deal with the garden variety of tangential acceleration, [math]r \frac{d\omega}{dt}[/math], capisci?

 

 

 

 

Then you agree. It is the speed...

The returning clock has been permanently altered by its trip (it has suffered a change in phase). The effect is uniquely associated with the fact that the acceleration has occurred, but it is quantitatively related not to the acceleration, but to the average speed...

 

One is led therefore to the conclusion that clocks having a velocity in an inertial frame are literally slowed down by the speed itself.

Sure, the point is, and always was, that absent acceleration, you do NOT get the "paradox" in the twins "paradox". It is the difference in acceleration profile that determines the difference in the speed profile that determines the difference in the total elapsed proper time. See the two paragraphs I wrote for wiki, the role of acceleration is quite clear.

Edited June 5, 2013 by xyzt

[md65536]

Simple: you forgot that the rotation is accelerated: [math]r \frac{d \omega}{dt}=2g[/math] .

Why would the rotation be accelerated? Wouldn't that produce increasing proper acceleration? No one else is talking about that case.

[xyzt]

Why would the rotation be accelerated? Wouldn't that produce increasing proper acceleration? No one else is talking about that case.

Why wouldn't it? Both twins are accelerated, you don't have the monopoly of how they are accelerated. The way Iggy tried to accelerate them created a trivial disparity between them, I fixed that.

[md65536]

I wrote this paragraph (and the next one) for wiki some time ago, I am very familiar with the subject matter.

Have you read any of the rest of that wiki page?

 

Quotes:

'Eventually, Lord Halsbury and others removed any acceleration by introducing the "three-brother" approach. The traveling twin transfers his clock reading to a third one, traveling in the opposite direction.'

 

and

 

'Transfer of clock reading in a twin paradox trip

 

An "out and back" twin paradox adventure may incorporate the transfer of clock reading from an "outgoing" astronaut to an "incoming" astronaut, thus entirely eliminating the effect of acceleration. Acceleration is not involved in any kinematical effects of special relativity. The time differential between two reunited clocks is deduced through purely uniform linear motion considerations, as seen in Einstein's original paper on the subject,[9] as well as in all subsequent derivations of the Lorentz transformations.'

[Iggy]

I wrote this paragraph (and the next one) for wiki some time ago, I am very familiar with the subject matter. The writeup shows the same answers but in the general form, using symbolic math rather than the particularization that you are showing. The part that you keep missing is that the above is valid for the specific case of only one twin accelerating. If both twins accelerate

 

Excuse me. Both twins have proper acceleration in the example I just illustrated. I compared the proper time of the traveling twin undergoing constant acceleration to the rotating twin.

 

 

, the answer depends on the respective acceleration profiles. This is the third time I am pointing this out to you, I am quite sure that you can work out the math all by yourself. If you can't, I'll do it for you, just let me know.

 

Yes, please tell me how large the carousel needs to be in order for my description in post 297 to be incorrect.

 

We'll use 4 years of earth time and 2 g's. How large does the carousel need to be?

 

 

 

If the angular speed isn't constant...

 

I made very clear in post 297 that the rotating twin experiences 2 g's. The angular velocity is constant.

[md65536]

Why wouldn't it? Both twins are accelerated, you don't have the monopoly of how they are accelerated. The way Iggy tried to accelerate them created a trivial disparity between them, I fixed that.

Now one twin experiences constant proper acceleration in each of its acceleration phases, and the other experiences increasing proper acceleration. There was nothing to fix, your modifications---all of them in this thread---are detrimental to understanding.

[xyzt]

I made very clear in post 297 that the rotating twin experiences 2 g's. The angular velocity is constant.

...which makes the problem into a trivial one. As an aside, your post 297 is sloppy, you can interpret the twin on the carousel experiencing either normal (the trivial case) or tangential (the non-trivial case) acceleration.

Do you understand the sequence:

difference in acceleration profile -> difference in speed profile -> difference in total elapsed proper time?

 

Now one twin experiences constant proper acceleration in each of its acceleration phases, and the other experiences increasing proper acceleration. There was nothing to fix, your modifications---all of them in this thread---are detrimental to understanding.

False, nothing precludes the twin on the carousel to accelerate, coast and decelerate, exactly like the twin that moves linearly. They follow similar acceleration profiles that are both perfectly realistic.

 

Have you read any of the rest of that wiki page?

 

Quotes:

'Eventually, Lord Halsbury and others removed any acceleration by introducing the "three-brother" approach. The traveling twin transfers his clock reading to a third one, traveling in the opposite direction.'

I see that you are still stuck on the misconception you espoused in the title of the thread.

 

The results don't depend on acceleration.

I see you and md65536 share the same misconception, I thought that you two were over it. Acceleration is the keystone of the "paradox" effect.

Edited June 5, 2013 by xyzt

[Iggy]

...which makes the problem into a trivial one. As an aside, your post 297 is sloppy, you can interpret the twin on the carousel experiencing either normal (the trivial case) or tangential (the non-trivila case) acceleration.

 

The carousel occupant experiences constant 2 g's of proper acceleration. I made that extraordinarily clear in my first post and all subsequent posts. Your ego doesn't interest me.

 

 

Do you understand the sequence:

difference in acceleration profile -> difference in speed profile -> difference in total elapsed proper time?

 

There is no acceleration profile for a person on a normal sized carousel undergoing constant 19.6 m/s² proper acceleration that would time dilate them as much as someone undergoing 19.6 m/s² constant linear acceleration.

 

Someone on a carousel with a 10 meter radius going faster than 14 meters per second would exceed 2 g's. The person with linear acceleration is always going faster than that, and therefore always has a greater time dilation factor.

 

I'm sorry if you understood 2 g's to mean tangential acceleration, but all my subsequent posts should have handily cleared that up.

 

Either give me a counterexample to post 297 or drop it.

 

 

False, nothing precludes the twin on the carousel to accelerate, coast and decelerate, exactly like the twin that moves linearly.

 

He is precluded from exceeding 14 m/s because he is explicitly confined to experiencing twice earth's g-force. It is that constraint which means that his traveling twin (whom is going a significant fraction of the speed of light relative to the center of the carousel) will be younger upon returning.

 

 

I see that you are still stuck on the misconception you espoused in the title of the thread.

 

 

I see you and md65536 share the same misconception, I thought that you were over it.

 

I won't be bated. If you can disprove the conjecture, offer a counter-example, or answer my question about how big the carousel would need to be... etc.

 

Vapid, arrogant disagreement doesn't interest me.

Edited June 5, 2013 by Iggy

[xyzt]

I'm sorry if you understood 2 g's to mean tangential acceleration, but all my subsequent posts should have handily cleared that up.

So, you still don't get the point :

different acceleration profile->different speed profile->different total elapsed proper time?

 

OK, let's try some very simple example, in the wiki example, make the two twins travel in opposite directions, with acceleration [math]a1[/math] and , respectively , [math]a2[/math]

 

Their total elapsed times will be :

 

[math]\Delta \tau1 = 2 T_c / \sqrt{ 1 + (a1 \ T_a/c)^2 } + 4 c / a1 \ \text{arsinh}( a1 \ T_a/c )[/math]

 

[math]\Delta \tau2 = 2 T_c / \sqrt{ 1 + (a2 \ T_a/c)^2 } + 4 c / a2 \ \text{arsinh}( a2 \ T_a/c )[/math]

 

Depending on the relation between [math]a1[/math] and [math]a2[/math] one gets:

 

[math]\Delta \tau1=\Delta \tau2[/math]

[math]\Delta \tau1>\Delta \tau2[/math]

[math]\Delta \tau1<\Delta \tau2[/math]

If you can disprove the conjecture,

 

You conjecture is nothing but a subcase of the above. Contrary to your insistent misconception that acceleration is at the root of the of the "paradox" in the twins "paradox", quite the opposite, it shows that the acceleration profile determines the relationship between the elapsed proper times.

Edited June 5, 2013 by xyzt

[Iggy]

OK, let's try some very simple example, in the wiki example, make the two twins travel in opposite directions, with acceleration [math]a1[/math] and , respectively , [math]a2[/math]

 

No. We are looking at this:

 

 

I follow what Ydoa means. The traveling twin could accelerate, decelerate, turn around, accelerate, and decelerate again all at 2g (spends the whole trip feeling twice earth's gravity -- 19.6 m/s²).

 

The stay-at-home twin could ride a carousel the whole time also feeling 2 g's (essentially, pacing back and forth).

 

The traveling twin would still be younger even though the two had matching proper accelerations throughout. They both felt the same acceleration during the experiment, but the traveling twin is younger. The results don't depend on acceleration. Like Ydoa says, "you get the same [qualitative] result [as the classical twin paradox] which shows that the result isn't strictly speaking about the acceleration."

This is incorrect...

 

If you can't give me an example where "this is incorrect", or if you can't retract your objection, then I don't know what we're talking about.

 

 

I'm reminded of these arrogant misstatements you made earlier:

 

You are still wrong, proper time does not depend on the observer, it is frame invariant. So you cannot have:

 

"According to A, A ages 4 years, while C ages 2 years.

According to C, A ages 4 years, while C ages 8 years.."

 

I cannot ever agree with the stuff you just wrote, basic SR says you are wrong and you continue along the path of being wrong.

 

...you claimed that "Everyone will agree on what time the two passing clocks read at the moment they pass each other." When I showed you that the claim is false... I cannot teach you, I am sorry.

 

With the benefit of conviction and character you could admit your mistake in all these comments, stop moving the goal post around, and have a decent discussion.

[xyzt]

No. We are looking at this:

We are looking at your oft repeated misconception that acceleration is not the root of the difference in elapsed proper time. You appeared to had finally gotten it fifty posts ago, now you are regressing. Why?

I corrected you several times, gave you the exact mathematical counter-proof to your fringe claim, yet , you persist in your error? Why?

 

 

Edited June 5, 2013 by xyzt

[Iggy]

We are looking at your oft repeated misconception that acceleration is not the root of the difference in elapsed proper time. You appeared to had finally gotten it fifty posts ago, now you are regressing. Why?

 

You linked a post that isn't mine. If you could quote something I said then I might be able to bridge any gaps in understanding about it.

 

I recognize that you can't support your claim regarding post 297 so you are now ignoring it like your other misstatements that have been refuted.

 

I'm not going to debate you on the role of acceleration in the twin paradox. I'll quote a description of the correct understanding involving the 'root of the difference in elapsed proper time',

 

Does a clock's acceleration affect its timing rate?

 

...The clock postulate generalises this to say that even when the moving clock accelerates, the ratio of the rate of our clocks compared to its rate is still the above quantity. That is, it only depends on v, and does not depend on any derivatives of v, such as acceleration.

 

So the clock postulate says that the rate of an accelerated clock doesn't depend on its acceleration. But note: the clock postulate does not say that the rate of timing of a moving clock is unaffected by its acceleration. The timing rate will certainly be affected if the acceleration changes the clock's speed of movement, because its speed determines how fast it counts out its time (i.e. by the factor γ). (The clock rate won't be affected by circular motion at constant speed.)...

 

Although the clock postulate is just that, a postulate, it has been verified experimentally up to extraordinarily high accelerations, as much as 10¹⁸ g in fact (see the faq What is the experimental basis of Special Relativity?).

 

-link

 

"doesn't depend on its acceleration" is the phrase I used, same as the article above. If you want to disagree with my statement then you are free to disagree with the source.

 

 

I corrected you several times, gave you the exact mathematical counter-proof to your fringe claim, yet , you persist in your error? Why?

 

I'm not going to debate semantics. If you truly believe you disproved the clock postulate then you should publish a paper and accept wide acclaim in the physics community.

[xyzt]

I'm not going to debate semantics. If you truly believe you disproved the clock postulate then you should publish a paper and accept wide acclaim in the physics community.

But we aren't debating the clock postulate. What we are debating is your fringe claim that acceleration is not what causes the "paradox" in the twins "paradox". To wit, you have created a scenario (post 297) that you think that it supports your fringe claim, see below:

 

Please understand the limiting criteria. Both twins experience equal constant proper acceleration. They both feel twice earth's gravity (2 g's) worth of acceleration for the duration.

 

A stationary observer experiences 4 years during the experiment. He notes that the traveling twin accelerates at 2g for one year away from him, decelerates (at 2g) for one year, turns around, accelerates (at 2g) for one year now toward him, and decelerates for one year at 2g before making a nice touchdown.

 

The proper time of the traveling twin for each segment is equal and found with the relativistic rocket equation,

 

[math]\tau = \frac{c}{a} \mbox{arcsinh} \left( \frac{at}{c} \right)[/math]

 

[math]\tau = \frac{c}{a} \mbox{ln} \left( \frac{at}{c} + \sqrt{1+ \left( \frac{at}{c} \right)^2} \right)[/math]

 

[math]\tau = 0.713[/math]

 

Each segment of accelerating and decelerating the traveling twin ages 0.713 years. Four segments for a grand total of 2.852 years.

 

[math]\tau = 2.852[/math]

 

The stationary twin ages 4 years and the traveling twin undergoing constant 2gs of acceleration ages 2.852 years.

 

 

A person on a 10 meter radius carousel experiencing 2g's has the velocity,

 

[math]a = \frac{v^2}{r}[/math]

 

[math]v = \sqrt{ar}[/math]

 

[math]v = \sqrt{(2.0631 \ \mbox{light-years / year sq}) (1.057 \times 10^{-15} \ \mbox{light-years})}[/math]

 

[math]v = 4.67 \times 10^{-8} \ \mbox{light-years / year}[/math]

 

(which is to say 14 meters per second)

 

While the stationary twin experiences 4 years and the traveling twin experiences 2.852 years the carousel twin experiences,

 

[math]\tau = t \sqrt{1-v^2}[/math]

 

[math]\tau = 4 \sqrt{1-(4.67 \times 10^{-8})^2}[/math]

 

which is essentially 4 years because someone moving 14 meters per second is hardly time dilated, are they?

 

The carousel would need to be large enough to be measured in light-years for there to be any comparison.

OK, let's have a look at your scenario. What you've done is that you have applied the same acceleration value (2g) in a different manner to the two twins: the "carousel twin" has the acceleration normal to the direction of motion , thus having no influence on the speed involved in the evaluation of his elapsed proper time whereas for the other twin, you applied the acceleration in the direction of motion , such that it has direct influence on the speed involved in the evaluation of his elapsed proper time.

In other words, you think that you have created a counter-example justifying your oft repeated fringe claim that the disparity in the elapsed proper time "doesn't depend on acceleration", when, in reality, you have created a disparity in the speeds of the twins based on applying the same value for the acceleration (2g) in different manner to the two twins, orthogonal to the motion for the "carousel twin" and tangential to the motion to the other twin. So, you have proven exactly the opposite to your fringe claim, that the disparity in elapsed proper time between the twins, does depend on acceleration.

I follow what Ydoa means. The traveling twin could accelerate, decelerate, turn around, accelerate, and decelerate again all at 2g (spends the whole trip feeling twice earth's gravity -- 19.6 m/s²).

 

The stay-at-home twin could ride a carousel the whole time also feeling 2 g's (essentially, pacing back and forth).

 

The traveling twin would still be younger even though the two had matching proper accelerations throughout. They both felt the same acceleration during the experiment, but the traveling twin is younger. The results don't depend on acceleration. Like Ydoa says, "you get the same [qualitative] result [as the classical twin paradox] which shows that the result isn't strictly speaking about the acceleration."

But the results do depend on acceleration.

The fact that you are applying the "same acceleration" (correction: the same scalar value of the acceleration) in differing ways to the two twins means that you have proven exactly the opposite, that the outcome of the twins "paradox" does depend on acceleration. Like I said:

 

differing acceleration profiles -> differing speed profiles -> differing total elapsed proper times.

 

So, "Acceleration IS important in the twins paradox". It is what creates the "paradox" in the first place. Markus explained that to you, I explained that to you.

Edited June 5, 2013 by xyzt

[Iggy]

In other words, you think that you have created a counter-example justifying your oft repeated fringe claim that the disparity in the elapsed proper time "doesn't depend on acceleration",

 

You are free to disagree with the clock postulate. I'll quote wikipedia:

 

 

The clock hypothesis is an assumption in special relativity. It states that the rate of a clock doesn't depend on its acceleration but only on its instantaneous velocity...

 

The clock hypothesis was implicitly (but not explicitly) included in Einstein's original 1905 formulation of special relativity. Since then, it has become a standard assumption and is usually included in the axioms of special relativity, especially in the light of experimental verification up to very high accelerations in particle accelerators.

 

-Clock hypothesis

 

If you feel that you are the first to disprove the principle that clock rate doesn't depend on acceleration in 100 years then you should publish a paper and accept wide acclaim in the physics community.

 

There really is no point in trying to bait me. I'd be happy to continue quoting sources that support what I said, but I'm truly not going to debate this with you.

[xyzt]

 

You are free to disagree with the clock postulate. I'll quote wikipedia:

But the clock postulate is not in discussion, I am pointing out your misconceptions in terms of how acceleration affects the total elapsed proper time. These are two different subjects you keep co-mingling liberally. You are confusing clock rate (unaffected by acceleration) with total elapsed proper time (affected by acceleration, albeit through the speed profile).

On a different note, I addressed your post 297 directly and I pointed out the conceptual errors that you are making in that post. I thought that you wanted to discuss your famed post 297, no?

Edited June 5, 2013 by xyzt

[Iggy]

I am pointing out your misconceptions in terms of how acceleration affects the total elapsed proper time... You are confusing clock rate (unaffected by acceleration) with total elapsed proper time (affected by acceleration, albeit through the speed profile).

 

Proper time:

 

Notice that in general relativity, the equations describing the proper time of a moving clock are expressed solely in terms of the instantaneous value of its velocity and the potentials of the gravitational field. It does not depend on acceleration and/or derivatives of the gravitational field as a consequence of the first clock postulate... The fact that atomic processes are not affected by acceleration has been verified experimentally by Pound and Rebka (1960) who measured the thermal dependence of the fractional frequency shift for samples of Fe. They confirmed an excellent agreement with the proper time delay equation up to extraordinarily high precision, excluding any dependence on acceleration being as much as 10¹⁷ m/s²

 

Relativistic Mechanics -- google book, p 290

 

Proper time does not depend on acceleration.

Edited June 5, 2013 by Iggy

[xyzt]

Proper time does not depend on acceleration.

Not directly, the correct statement is "proper time does not depend directly on acceleration". I already explained to you the dependency on acceleration:

 

differing acceleration profiles->differing speed profiles->differing total elapsed time

 

Are you still claiming that "Acceleration is not important in the twins paradox"?

Do you want to discuss the mistakes in your post 297?

Edited June 5, 2013 by xyzt

[Iggy]

Are you still claiming that "Acceleration is not important in the twins paradox"?

 

Please quote where I said those words.

 

Do you want to discuss the mistakes in your post 297?

 

No.

 

Proper acceleration is the reading of an accelerometer. Post 297 explicitly discusses proper acceleration. The proper acceleration of the person in the centrifuge is equal to the traveling twin for the duration of the thought experiment. That was my claim.

 

If you want to discuss something different then by all means. It won't be a mistake in post 297. Feel free to keep moving the goalpost. I'll be here.

[md65536]

differing acceleration profiles -> differing speed profiles -> differing total elapsed proper times.

Well yes, everyone agrees that acceleration causes different speed which in turn results in time dilation. But why mislead people into thinking that acceleration is the cause of the time dilation, instead of the "differing speed profiles"? It just confuses people who don't understand, because they look at the effects of the acceleration and try to figure out how that has a direct effect on aging or clocks, when the only important effect of acceleration in the typical twin setup is its effect on velocity.

 

It's like saying "Jerk is the root of the twin paradox, because differing jerk profiles -> differing acceleration profiles -> differing speed profiles -> differing total elapsed proper times".

 

And jerk can cause acceleration that changes velocity that can lead to a twin paradox effect, but it's not important because the basic paradox analysis does not have to consider jerk. Nor acceleration... only velocity will suffice. And as I showed in post #1, the different aging still happens in cases where there is no acceleration.

 

You called it "hidden acceleration", which I think is BS, it is hidden because it doesn't physically exist, is hidden from the equations, has a hidden value... I think it's fair to say that no imaginary hidden variables are important in understanding the resolution of the twin paradox.

[xyzt]

I follow what Ydoa means. The traveling twin could accelerate, decelerate, turn around, accelerate, and decelerate again all at 2g (spends the whole trip feeling twice earth's gravity -- 19.6 m/s²).

 

The stay-at-home twin could ride a carousel the whole time also feeling 2 g's (essentially, pacing back and forth).

 

The traveling twin would still be younger even though the two had matching proper accelerations throughout. They both felt the same acceleration during the experiment, but the traveling twin is younger. The results don't depend on acceleration. Like Ydoa says, "you get the same [qualitative] result [as the classical twin paradox] which shows that the result isn't strictly speaking about the acceleration."

This is the third time I am pointing to your erroneous claim.

Let's cut to the chase:

 

Acceleration is:

 

A. Important in the twins paradox

B. Not important in the twins paradox.

 

Is it A or B? Please give a straight answer.

 

 

Here is post 318 addressing the errors in your scenario.

But we aren't debating the clock postulate. What we are debating is your fringe claim that acceleration is not what causes the "paradox" in the twins "paradox". To wit, you have created a scenario (post 297) that you think that it supports your fringe claim, see below:

OK, let's have a look at your scenario. What you've done is that you have applied the same acceleration value (2g) in a different manner to the two twins: the "carousel twin" has the acceleration normal to the direction of motion , thus having no influence on the speed involved in the evaluation of his elapsed proper time whereas for the other twin, you applied the acceleration in the direction of motion , such that it has direct influence on the speed involved in the evaluation of his elapsed proper time.

In other words, you think that you have created a counter-example justifying your oft repeated fringe claim that the disparity in the elapsed proper time "doesn't depend on acceleration", when, in reality, you have created a disparity in the speeds of the twins based on applying the same value for the acceleration (2g) in different manner to the two twins, orthogonal to the motion for the "carousel twin" and tangential to the motion to the other twin. So, you have proven exactly the opposite to your fringe claim, that the disparity in elapsed proper time between the twins, does depend on acceleration.

But the results do depend on acceleration.

The fact that you are applying the "same acceleration" (correction: the same scalar value of the acceleration) in differing ways to the two twins means that you have proven exactly the opposite, that the outcome of the twins "paradox" does depend on acceleration. Like I said:

 

differing acceleration profiles -> differing speed profiles -> differing total elapsed proper times.

 

So, "Acceleration IS important in the twins paradox". It is what creates the "paradox" in the first place. Markus explained that to you, I explained that to you.

Ok,

Here is again the explanation of your misconceptions, replete with your original posts. So, to cut to the chase, please answer this simple question:

 

Acceleration is:

 

A. Important in the twins paradox

B. Not important in the twins paradox.

 

Which one it is? A or B?

Well yes, everyone agrees that acceleration causes different speed which in turn results in time dilation.

This is not what I am saying, you mangle badly what I've been trying to teach you. First off, it is not "time dilation", it is "elapsed proper time". Two different concepts. Secondly, what I've been trying to teach you is that your claim: "Acceleration is not important in the twins paradox" is FALSE. In reality, acceleration is at the very root of the twins paradox by virtue of the asymmetry it produces in the speed profiles of the twins. So, the claim in your title is false, no matter how many times you have recanted: "Acceleration IS important in the twins paradox".

 

 

You called it "hidden acceleration", which I think is BS, it is hidden because it doesn't physically exist, is hidden from the equations, has a hidden value... I think it's fair to say that no imaginary hidden variables are important in understanding the resolution of the twin paradox.

I called it hidden wrt to your scenario, where you were jumping frames. I thought that you finally understood your error. The proper time is definitely dependent on the acceleration profile (see the presence of the variables [math]a,T_a[/math]) , contrary to your unsubstantiated claims.

Edited June 5, 2013 by xyzt