Acceleration is not important in the twin paradox

[xyzt]

 

 

Is it possible that you're inventing a hidden effect to explain something that you don't understand?

No. Perhaps one day you'll figure it out.

[md65536]

I must admit that I am starting to wonder what the actual purpose of this thread really is. Of course it is possible to make up the elapsed proper time of an accelerating observer by combining the times of two purely inertial observers.

In about 9000 threads on these forums, there are people struggling to understand (or debunk???) the twin paradox effect using the same arguments over and over, including trying to explain the effect in terms of acceleration, while neglecting time dilation. I was trying to help steer people away from that futile line of reasoning, because the effect is present without the acceleration. However, I COMPLETELY underestimated the role of "belief" in people's understanding of the paradox, so this thread, like every reply in every thread that uses math and reasoning and goes completely ignored because it doesn't fit the reader's beliefs, has no point for those readers. Edited May 12, 2013 by md65536

[xyzt]

In about 9000 threads on these forums, there are people struggling to understand (or debunk???) the twin paradox effect using the same arguments over and over, including trying to explain the effect in terms of acceleration, while neglecting time dilation.

The twins paradox has nothing to do with time dilation, it has everything to do with differences in elapsed proper time caused by asymmetries in the setup. Perhaps one day you will come to grips with this fact. Negging my explanations will not help you in learning rellativity.

Edited May 12, 2013 by xyzt

[md65536]

If you eliminate the asymmetry, you eliminate the discrepancy between the two twins after they are brought back together in the same frame at relative rest, defeating the purpose.

As soon as you introduce specific events on the world-lines of the two reciprocal observers, you can have asymmetry. You may have 2 events that are simultaneous for one observer and not the other---that is asymmetry.

 

In the experiment in post #1, observer A ages 4 years between AB and AC, and B ages 1 year between AB and BC, and everyone agrees. There's no way to change that with arguments about symmetry. Yes, according to A, A ages 4 years while B ages 2, and according to B, B ages 4 years while A ages 2, and that's reciprocal and doesn't demonstrate any twin paradox effect, but that has little bearing on the proper times between the events that are defined, it only affects the relative simultaneity of any events in question.

 

So, the premise of the thread that "acceleration is not important in the twin paradox" is clearly false. You can consider alternatives to the typical twin paradox scenario to achieve the same outcome, but these are then different scenarios, which are not physically equivalent.

Alright, I can agree with that. The wording of the title is misleading and poorly chosen, and I've taken back the claim in the title. I meant that acceleration is not important in certain respects, but stated it's not important in any respect, which is wrong.

Agreed they're not physically equivalent. However they use the same theory and the same equations, meaning that in theory (assuming the clock postulate), the difference in the scenarios, ie. any effect attributed to the acceleration, has no effect on the predicted calculated timing discrepancies.

 

The different scenarios I've presented are equivalent with respect to calculation of proper times between any pair of events, not with respect to all measurable phenomena (most notably any measurable effects of acceleration). I've been referring only to the difference in proper times ie. aging, when speaking of the "twin paradox effect". I agree the classical experiment's twins experience a difference in aging and also a difference in experience of the experiment, and I've only considered the former here.

 

The measurable effects of acceleration besides determination of velocity, do not affect the relative timing of the twins within the domain of SR.

 

The twins paradox has nothing to do with time dilation, it has everything to do with differences in elapsed proper time caused by asymmetries in the setup. Perhaps one day you will come to grips with this fact.

I doubt I will.

 

"In the theory of relativity, time dilation is an actual difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses."

http://en.wikipedia.org/wiki/Time_dilation

 

So your statement is nonsense. Sorry I take that back, you can still make a distinction between proper time and coordinate time in yours and my respective statements. However the difference in proper times is still an effect of time dilation. (and other things)

 

Anyway, I have learned some things over the course of this debate, and I realize there's still so much I don't know and I'm far from being able to express everything perfectly.

Edited May 12, 2013 by md65536

[xyzt]

 

So your statement is nonsense. Sorry I take that back,

This is what you have been doing throughout the thread. You admit to being wrong only to take it back in the next sentence.

[Markus Hanke]

Alright, I can agree with that. The wording of the title is misleading and poorly chosen, and I've taken back the claim in the title. I meant that acceleration is not important in certain respects, but stated it's not important in any respect, which is wrong.

Agreed they're not physically equivalent. However they use the same theory and the same equations, meaning that in theory (assuming the clock postulate), the difference in the scenarios, ie. any effect attributed to the acceleration, has no effect on the predicted calculated timing discrepancies.

 

Fair enough

You see, what is called the "twin paradox" in relativity textbooks & literature is a fairly specific setup with quite specific specs - one of them is the presence of acceleration for one of the twins. Yes, we can find other setups which lead to the same result even without acceleration ( which is what you were referring to ), but I truly believe that calling these alternatives "twin paradox" as well leads to a lot of confusion, as unfortunately happened on this thread.

 

Anyway, I think it is all cleared up now. I am more of a "GR guy", but sometimes going back to the basics is interesting too.

Edited May 13, 2013 by Markus Hanke

[phyti]

In the simplest abstract case of the 'twin paradox', with instantaneous velocity changes, the change of paths for the traveling twin is the most obvious difference, and so becomes the solution to an asymmetrical case.

The reality is this paper.

 

twin clocks130518.doc

 

[StringJunky]

In the simplest abstract case of the 'twin paradox', with instantaneous velocity changes, the change of paths for the traveling twin is the most obvious difference, and so becomes the solution to an asymmetrical case.

The reality is this paper.

 

twin clocks130518.doc

 

I copied it to here for you:

 

Twin Clocks

1. inertial vs. non-inertial

fig. 1 fig.2

In fig.1, two identical clocks A and B are initially moving in the direction B1. At event-1 A decelerates (red) and moves onto path A. At event-2 B decelerates (red) and moves onto path B2. At event-3 A decelerates to move onto path B2. The red segments of the A path are formed by cutting a copy of the red B segment by the line from event-2 perpendicular to the A-path. The two segments are shifted to the endpoints of the A-path in the same order.

 

fig.3

 

Fig.3 shows the velocity vectors (black) at the start and finish of each red segment. The speed profile for the two separate segments when joined together is equivalent to the single B-segment in form and duration (t). The accumulated time for the profile is determined by integration of the instantaneous speed along the path, and therefore independent of the clocks.

 

Considering the method just described, there is no fundamental difference in inertial motion and non-inertial motion. The clock serves as a mechanical integrator, that adjusts to variable speed, and records the results. The accumulated time during deceleration is thus the same for any clock following that profile, and any difference for two clocks must occur during the straight line (inertial) portions of the paths, as shown in fig.2, where the straight portions are rejoined to form a scaled down version of the original triangle.

Edited May 20, 2013 by StringJunky

[md65536]

The accumulated time during deceleration is thus the same for any clock following that profile, and any difference for two clocks must occur during the straight line (inertial) portions of the paths, as shown in fig.2, where the straight portions are rejoined to form a scaled down version of the original triangle.

Interesting. So here, A and B have identical periods of acceleration, with the same experience of proper acceleration, but with different periods of inertial motion before and after the accelerations. And still the twin paradox effect occurs here.

 

This is probably a much better example than mine. Acceleration is still important here, in order to get the twins to follow different paths and return to a common path. However this is done here with twins while I relied on swapping one of the twins with a surrogate. The point is slightly different but I think this more clearly shows that it is time or distance traveled at particular velocities that produces the entirety of the difference in aging in SR, and not the acceleration.

Edited May 19, 2013 by md65536

[Delta1212]

Realizing that clocks with different inertial paths but identical acceleration would have different elapsed times is actually what got me over that common conceptual hurdle of "maybe time dilation occurs during acceleration!"

[DimaMazin]

Realizing that clocks with different inertial paths but identical acceleration would have different elapsed times is actually what got me over that common conceptual hurdle of "maybe time dilation occurs during acceleration!"

No. Acceleration remits time into slower or faster status.

[ydoaPs]

I think you are missing the point here.

 

The twin paradox has three elements :

1. Both twins start off at rest in the same frame of reference

2. One twin remains at rest throughout the experiment, the other twin undergoes phases of acceleration and uniform relative motion along a closed path which eventually returns him to the first ( stationary ) twin

3. The twins reunite once again at rest in the same frame of reference, and find that their clocks do not agree

 

Let us take a look at their proper times; in general terms proper time is defined as the arc length of an observer's worldline, which is

 

[math]\displaystyle{\tau =\int_{C}d\tau =\int_{C}\sqrt{g_{\mu \nu }dx^{\mu }dx^{\nu }}}[/math]

 

where C is the path taken.

 

Without even needing any specific figures we can immediately evaluate what happens for our twins; the stationary twin travels only through time and does not experience acceleration, so his proper time is simply

 

[math]\displaystyle{\tau =\int_{C}d\tau =\int_{C}\sqrt{\eta _{\mu \nu }dx^{\mu }dx^{\nu }}=\int_{C}dt}[/math]

 

On the other hand, the travelling twin moves through time and space, and does experience acceleration; his proper time is therefore

 

[math]\displaystyle{\tau =\int_{C}d\tau =\int_{C}\sqrt{g_{\mu \nu }dx^{\mu }dx^{\nu }}=\int_{C}\sqrt{g_{00}dt^2-\sum_{i=1}^{3}g_{ii}(dx^{i})^2}}[/math]

 

which is always less than the stationary twin. Due to the equivalence principle the metric tensor in the above expression encapsulates the acceleration information. This shows us that stationary observers not subject to acceleration always experience the longest proper time.

 

It remains to be noted that trying to consider this scenario without acceleration is not physically meaningful, because the travelling observer would not be able to return to his stationary twin, so their clocks could not be compared in any meaningful way. Bear in mind that any deviation from uniform relative motion always involves acceleration.

Try it with the "stationary" twin pacing back and forth so that the acceleration matches the "moving" twin.

[Markus Hanke]

Try it with the "stationary" twin pacing back and forth so that the acceleration matches the "moving" twin.

 

You can do that of course ( "back and forth" equates to acceleration ), but then you have officially left the confines of the "twin paradox" scenario.

[ydoaPs]

You can do that of course ( "back and forth" equates to acceleration ), but then you have officially left the confines of the "twin paradox" scenario.

But you get the same result which shows that the result isn't strictly speaking about the acceleration.

[Markus Hanke]

But you get the same result which shows that the result isn't strictly speaking about the acceleration.

 

In order to get the same result, you would need to match the net effects of the accelerations in both frames. Their proper times will then agree.

But again, the "twin paradox" is a well defined scenario, where you compare an accelerated with an unaccelerated frame. If you alter that setup you can no longer call it "twin paradox", but some other experimental setup of your own making.

[ydoaPs]

That's worthless semantics and not strictly speaking true as thought experiments are notoriously malleable and have a history of having several substantial variations under the same name. Having the grounded twin pacing hardly deserves another name. But, as I said, it's pointless to argue about the name of the scenario. The question is more general than that. It's about why one twin ages less than the other when you send one away and back. It is not the acceleration. We know this, because we can ever so slightly alter the experiment to make the accelerations match and get the same result.

[Markus Hanke]

That's worthless semantics and not strictly speaking true as thought experiments are notoriously malleable and have a history of having several substantial variations under the same name. Having the grounded twin pacing hardly deserves another name. But, as I said, it's pointless to argue about the name of the scenario. The question is more general than that. It's about why one twin ages less than the other when you send one away and back. It is not the acceleration. We know this, because we can ever so slightly alter the experiment to make the accelerations match and get the same result.

 

You are contradicting yourself here - first you say that it is not the acceleration, then you say that you need to match the accelerations to get the same result. So which one is it ?

 

Regardless of the exact circumstances though, the difference - if there is one - in proper times arises because one of the frames is inertial, whereas the other one is not. If both frames where inertial, you could never get differences in proper times between the same two events; if one or both are non-inertial, then the result depends on the space-time geometry within those frames, in other words, the metric tensor. This is what I tried to demonstrate with the maths you quoted me on earlier.

Edited June 2, 2013 by Markus Hanke

[ydoaPs]

You are contradicting yourself here - first you say that it is not the acceleration, then you say that you need to match the accelerations to get the same result. So which one is it ?

I neither contradicted myself nor did I say that. I said it's not the acceleration because you STILL get the interesting result when you match the accelerations.

[Markus Hanke]

I neither contradicted myself nor did I say that. I said it's not the acceleration because you STILL get the interesting result when you match the accelerations.

 

I don't really follow you, to be honest...what exactly is the scenario you are considering, and what are the conclusions you draw ?

[DimaMazin]

If time is relative then acceleration relatively of gravitational fields is important. If time is scalar then only speed in gravitational fields is important.Signal can show only past age.

[md65536]

I neither contradicted myself nor did I say that. I said it's not the acceleration because you STILL get the interesting result when you match the accelerations.

I'm not quite following this. Are you saying that a "pacing back and forth" observer is the same as a stationary one? If so that's false.

 

If for example you have a vibrating observer who can maintain a relative velocity of +/-0.866c with negligible time spent accelerating, it still ages at half the rate of a truly stationary observer.

 

Scale that up and you get pacing back and forth. Scale that up and you can get orbiting the planet, and time dilation still applies relative to a stationary observer.

 

Perhaps you have some other specific plan that could work, eg. you could implement the effect of post #283 with pacing, but it depends on the details. At the very least you would have to match the accelerations but at different times.

 

For example, a rocket that follows the traveling twin but stops after negligible time, then spends a few years hanging around near Earth before accelerating back and arriving with the traveling twin, has the same acceleration as the traveling twin (out, stop, return, stop) but ages the same as the Earth twin, with which it has been relatively at rest for all but a negligible time. That could be expressed in terms of "pacing for a negligible time" and experiencing the same acceleration as a rocket.

You can do that of course ( "back and forth" equates to acceleration ), but then you have officially left the confines of the "twin paradox" scenario.

The whole point of the thread, which maybe wasn't clear at the start, is that you can measure the same difference in aging, as of the twins in the typical setup, using different setups, including ones where acceleration is taken out of the picture.

 

As long as the different setups have the same essential components, ie. relative velocity maintained for a specific time, different inertial frames etc, the same aging can be calculated using the same equations of the same theory in different setups.

 

 

And I agree with your other statements, ie. to make it a true "twin" experiment and measure it using only two clocks, acceleration seems to be needed to get one clock to use multiple inertial frames (perhaps by definition, because the clock is not inertial). However the theory doesn't distinguish one clock from another in identical conditions, and the equations don't change if a clock is substituted for a similar one.

 

That is, if 3 clocks are used instead of 2, the experiment is different but the effects are the same, and the effects on an ideal clock's aging due to proper acceleration are postulated to be none.

Edited June 2, 2013 by md65536

[Iggy]

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."

[xyzt]

I neither contradicted myself nor did I say that. I said it's not the acceleration because you STILL get the interesting result when you match the accelerations.

This is incorrect, if the twins exhibit identical acceleration profiles, they will have the same exact total elapsed proper time.

The situation gets more complicated if the twins exhibit different acceleration profiles. In this case, their total elapsed can be equal, less than or larger than, all depending on the integrand [math]\sqrt{g_{\mu \nu }dx^{\mu }dx^{\nu }}[/math].

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 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]

Edited June 4, 2013 by xyzt

[md65536]

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."

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.

 

Edit: Ehh, I may have ruined your example by comparing a constantly accelerating twin with an inertial twin and not using GR.

 

Yes xyzt, a slow pacing twin would still age less than an inertial twin, but the relative speed could be kept low even with high acceleration, so that the difference in aging could be made negligible. If you calculate it in terms of acceleration only, you should find that the acceleration in one direction counteracts the acceleration in the other direction?

 

Edit: I'll just take all that back because I don't actually know how this case is properly handled.

Edited June 5, 2013 by md65536

[xyzt]

 

If you calculate it in terms of acceleration only, you should find that the acceleration in one direction counteracts the acceleration in the other direction?

No, it doesn't "counteract". The effects are cumulative.