Twin Paradox: Understanding Who Ages Less

[neopolitan]

I fail to see how this example has much to do with the standard "twin paradox" scenario.

Also, don't forget to include the time it takes for Jane's signal to Joe to reach Joe.

The standard "twin paradox" is poorly stated, and that is why it appears to be a paradox (note Hurkyl's complaint in an earlier post). What I am showing here is that the same result can be achieved with no acceleration, which is often what is brought into explain the broken symmetry.

And I didn't forget the time it takes for Jane's signal to reach Joe.

Firstly, I specifically mentioned a spot which was anchored to Joe, it is a distance of L from Joe. That means that the intellectual effort required to subtract the signal's travel time is trivial. You can do it, I can do it and I assumed that Joe could do it. This is another one of these unstated assumptions.

Secondly, Joe doesn't even need a clock. We tend to always talk in terms of two clocks, because it may seem simpler, but in my scenario Joe's clock was entirely redundant. Jane moves between Joe and the spot which is at a distance of L at a velocity of v. Again, we are talking about a trivial intellectual effort. According to Joe, it should take Jane a period of L/v to travel from where he is to the spot at a distance of L. He doesn't need a clock to work that out. Once the signal's travel time is factored in, his totally redundant clock will confirm that this calculation is correct.

cheers,

neopolitan

 

[Doc Al]

The standard "twin paradox" is poorly stated, and that is why it appears to be a paradox (note Hurkyl's complaint in an earlier post).

The standard twin paradox seems clear and unambiguously stated to me. I trust you realize that "paradox" is used in the sense of "A seemingly contradictory statement that may nonetheless be true". No one really thinks that the example of the twins represents a true contradiction within relativity.

What I am showing here is that the same result can be achieved with no acceleration, which is often what is brought into explain the broken symmetry.

I fail to see why you think that your example, with its arbitrary stopping and starting of clocks, has anything to do with the "twin paradox" or is of any special interest on its own.

And I didn't forget the time it takes for Jane's signal to reach Joe.

Firstly, I specifically mentioned a spot which was anchored to Joe, it is a distance of L from Joe. That means that the intellectual effort required to subtract the signal's travel time is trivial. You can do it, I can do it and I assumed that Joe could do it. This is another one of these unstated assumptions.

Looks like you forgot it to me! (All of these calculations are trivial.)

Secondly, Joe doesn't even need a clock. We tend to always talk in terms of two clocks, because it may seem simpler, but in my scenario Joe's clock was entirely redundant. Jane moves between Joe and the spot which is at a distance of L at a velocity of v. Again, we are talking about a trivial intellectual effort. According to Joe, it should take Jane a period of L/v to travel from where he is to the spot at a distance of L. He doesn't need a clock to work that out. Once the signal's travel time is factored in, his totally redundant clock will confirm that this calculation is correct.

So? (I agree that you are talking about a trivial intellectual effort.)

 

[Mentz114]

neopolitan;

This unstated assumption of a third observer determining what is simultaneous is equivalent to the unstated assumption in the twins' paradox, namely that one twin travels between the "stationary" twin and a distant point which is at rest relative to the stationary twin.

(my emphasis).
The point where the twins meet up can be just some coordinates. It cannot be said to be at rest or moving relative to either twin.

My point is that acceleration is not the answer. It is merely an indicator.

Relative velocities arise through different acceleration histories. So in that sense acceleration is a cause.

But proper lengths and the invariance of the proper length is the best way to understand it. I urge you to read the link in my earlier post.

 

[neopolitan]

So? (I agree that you are talking about a trivial intellectual effort.)

Context, Doc Al.

I was responding to DocZaius' claim that acceleration is crucial. It isn't.

What is crucial is that in the twins' paradox it is tacitly assumed that the traveling twin travels to a location which has a fixed distance from the stay-at-home twin (for example one twin travels to Alpha Centauri - inaccurately stated, Alpha Centauri is a fixed distance from us here on Earth).

It doesn't actually have to be any special location, as Mentz rightly points out. While he may also be right in that acceleration leads to relative velocities and hence in that fashion acceleration leads to time dilation, where he is wrong is that acceleration doesn't lead to the symmetry break per se.

I explained in another thread already - https://www.physicsforums.com/showpost.php?p=1728168&postcount=14". Even if the "travelling" twin described in the linked post doesn't undergo any acceleration, it will still be that "travelling" twin who will experience less time elapsed. (And yes I am aware of the real world difficulties associated with decelerating and accelerating an extremely long rod, that's why we make use of mind experiments.)

cheers

neopolitan

 

[Mentz114]

neopolitan;

What is crucial is that in the twins' paradox it is tacitly assumed that the traveling twin travels to a location which has a fixed distance from the stay-at-home twin

This statement does not make sense to me. The distance you mention does not exist until the second coincidence. So how can it be in any way be fixed or not-fixed ?

I bow out of this thread with a final injunction to read a good essay on SR ( and forget about simultaneity !).

 

[Doc Al]

Context, Doc Al.

I was responding to DocZaius' claim that acceleration is crucial. It isn't.

What is crucial is that in the twins' paradox it is tacitly assumed that the traveling twin travels to a location which has a fixed distance from the stay-at-home twin (for example one twin travels to Alpha Centauri - inaccurately stated, Alpha Centauri is a fixed distance from us here on Earth).

No, that's not relevant.

It doesn't actually have to be any special location, as Mentz rightly points out. While he may also be right in that acceleration leads to relative velocities and hence in that fashion acceleration leads to time dilation, where he is wrong is that acceleration doesn't lead to the symmetry break per se.

Wrong again.

I explained in another thread already - https://www.physicsforums.com/showpost.php?p=1728168&postcount=14". Even if the "travelling" twin described in the linked post doesn't undergo any acceleration, it will still be that "travelling" twin who will experience less time elapsed. (And yes I am aware of the real world difficulties associated with decelerating and accelerating an extremely long rod, that's why we make use of mind experiments.)

Your "explanation" in the other thread is incorrect. For the twins to reunite, one must have accelerated. And it's the one who accelerates, regardless of whether he drags a rod along or not, that experiences less proper time.

 

[Hurkyl]

Sort of. I wondered if anyone would pick up on this or whether I would have to explain it.

I implied something that gives you the information to make the conclusion. You probably overlooked it.

I'm pretty sure that, if you choose any two positive numbers for the readings on the clocks, I can devise a scenario where Alice's clock and Bob's clock have those readings (in that order), and is consistent with the provided information.

For example, I think one main conceptual omission you've having is that Alice and Bob need not have the same velocity relative to your third observer.

(I will confess to having misread the scenario the first time -- otherwise my initial objection would simply have been that your scenario is ill-defined, because their 'separation' is not an absolute notion)

 

[Mettra]

Mentz114, I'm relatively (no pun intended) new to the theory of relativity, how come acceleration is not relative? If the traveling twin is the frame of reference, Earth is accelerating away from the rocket. Time, as well is space, is relative, therefor ms^{-2} should be relative. None of the above posts have cleared this up for me.

Instead of thinking of it like that, think of it for the moment from this angle:

When astronauts go up into space using a rocket, they feel a very large acceleration during the trip. Do we on Earth feel that acceleration (forget Newton's third law forces for now, some people on the ground near the takeoff site will feel some affects of the rocket - but that's not what I'm talking about)? See, in this case, we have considered the Earth to be the reference frame of choice (so we consider it at rest).

Now let's take that example again, taking the Earth to be our at rest reference frame (except this time, forget the rotational motion). The astronauts are in space, but are still going, still accelerating until they get to Mars. Do we on the Earth feel the acceleration that these astronauts feel? The answer is: no we don't. Acceleration is special because you can feel it. Where there is acceleration, there is a force.

When you ride in a car along the highway at constant velocity (if there is not much air resistance) you can travel at a constant velocity. Here you feel no forces, since velocity is 'free' (Newton's first law). If the driver suddenly nailed the gas, you would be pushed by a very real force into your seat. If the driver suddenly nailed the breaks, you would pushed again by a very real force into the windshield. The rest of the world does not feel the acceleration that you feel.

So in summary, if acceleration were relative, then different observers might disagree on the results of an experiment (they can disagree on measurements, not results). You could juggle forces around by picking different frames of reference.

There are deeper, more mathematical explanations of this, but an intuitive grasp is probably more useful. Anything beyond either of these is getting to be a philosophical question.

 

[MeJennifer]

So in summary, if acceleration were relative, then different observers might disagree on the results of an experiment (they can disagree on measurements, not results). You could juggle forces around by picking different frames of reference.

There are deeper, more mathematical explanations of this, but an intuitive grasp is probably more useful. Anything beyond either of these is getting to be a philosophical question.

As I wrote before acceleration is relative under general relativity but not under special relativity.

 

[Dale]

As I wrote before acceleration is relative under general relativity but not under special relativity.

Although coordinate acceleration is relative under GR, physical acceleration* is not relative. Physical acceleration can be unambiguously detected with an accelerometer in both theories.

*there may be better terms than coordinate and physical acceleration

 

[MeJennifer]

Although coordinate acceleration is relative under GR, physical acceleration* is not relative. Physical acceleration can be unambiguously detected with an accelerometer in both theories.

*there may be better terms than coordinate and physical acceleration

I disagree, physical acceleration is relative under GR. In fact under GR all forms of motion are relative.

 

[robphy]

Although coordinate acceleration is relative under GR, physical acceleration* is not relative. Physical acceleration can be unambiguously detected with an accelerometer in both theories.

*there may be better terms than coordinate and physical acceleration

I disagree, physical acceleration is relative under GR. In fact under GR all forms of motion are relative.

It seems DaleSpam is referring to "4-acceleration", aka "worldline curvature", u^a\nabla_a u^b which measures the deviation of the worldline from being a geodesic.

MeJennifer, what is your definition of "[physical] acceleration"?

 

[A.T.]

I disagree, physical acceleration is relative under GR. In fact under GR all forms of motion are relative.

Proper acceleration (what an accelerometer measures) is absolute. Just like proper time (what a clock measures).

 

[MeJennifer]

Proper acceleration (what an accelerometer measures) is absolute.

What an accelerometer measures could be the result of acceleration or gravity it cannot be determined by the measurement which one it is. Similarly as in special relativity where it cannot be determined which object is at rest and which object is moving we can only say that they are in relative motion.

 

[A.T.]

What an accelerometer measures could be the result of acceleration or gravity it cannot be determined by the measurement which one it is.

No, it is always the result of acceleration. In GR an object held up by a force against a gravitational field is accelerated, just like a rocket in open space firing its engines.

But the question was: "Is it absolute?" And since every observer will agree what the accelerometer measures, it is absolute.

 

[Dale]

Proper acceleration (what an accelerometer measures) is absolute. Just like proper time (what a clock measures).

Thanks, I knew there was a better term than "physical acceleration" but I just couldn't think of it.

If proper acceleration is not absolute then GR is an easily falsified theory.

 

[MeJennifer]

If proper acceleration is not absolute then GR is an easily falsified theory.

Really? How is it falsified?

No, it is always the result of acceleration. In GR an object held up by a force against a gravitational field is accelerated, just like a rocket in open space firing its engines.

Think how an accelerometer can indicate acceleration in a strong gravitational field due to tidal forces.

In other words the state of acceleration in a rod can in principle be caused by gravitation, hence acceleration is relative.

 

[Dale]

Really? How is it falsified?

If a theory claimed that proper acceleration were relative then accelerometer readings would be frame variant, which would lead to logical inconsistencies like an accelerometer reading 0 and g at the same time.

In general, all experimentally measureable outcomes must be invariant, not relative. Hence, although coordinate time is frame variant, proper time is absolute. Similarly with coordinate acceleration which is relative and proper acceleration which is absolute.

 

[neopolitan]

... although coordinate time is frame variant, proper time is absolute.

Proper time. Hm, if we have proper time, can we have "proper simultaneity"? Since we can take a single event as our reference, it can be the big bang event or it could be the flash of a light which conceptually radiates photons throughout the universe, can we then not work out proper time for each location in space and therefore have "proper space"?

Probably there are limitations to the application of "proper time" :)

cheers,

neopolitan

 

[Dale]

if we have proper time, can we have "proper simultaneity"?

I am 90% sure that you are going to misinterpret this, but the short answer is yes.

If two clocks, A and B, at rest wrt each other are synchronized by some arbitrary synchronization convention in their rest frame and pass through events, Ea and Eb, then all observers will be able to determine wether or not the clocks read the same or different. Iff they read the same then the events were simultaneous in their frame and by their synchronization convention.

Note, there is still no physical significance to the simultaneity because if the events are spacelike separated in one frame they will be spacelike separated in all frames and thus not causally connected.

Since we can take a single event as our reference

A single event does not define a reference frame in any sense. There is nothing "proper" about it. What direction does a single point define?

 

[neopolitan]

A single event does not define a reference frame in any sense. There is nothing "proper" about it. What direction does a single point define?

I didn't say the event was a reference frame, did I?

You seem to be talking about "proper synchronisation" not about "proper simultaneity".

People seem to hung up about clocks and rods, which are supposed to be representative. Can you not point to a location on a spacetime diagram drawn from the perspective of the frame in which you are at rest and say "according to me, this is now"? Or are you limited to point to clocks? Same with a distance, can you not point to a location and say "this is a distance of L from me"? Or do you have to have a rod?

Take one event and allow photons to radiate out from it in all directions. If you have "proper time", is the distance from the reference event traveled by a photon in that "proper time" not "proper separation"? Are not all the 4-space locations associated with the photons which are causally linked to the reference event (since the event spawned all the photons we are discussing) properly simultaneous? (Note that I am not saying they are simultaneous with anything other than themselves. They may be, but we don't have the information necessary to make that determination.) Does that hypersurface of simultaneity spring into existence because the photons are released, or does it exist even if we don't release photons, since we can say these events constitute the 4-space locations which the photons would have reached iff and we released them?

Perhaps I am misinterpreting you :) Either way, I don't feel an overwhelming need to talk about clocks and synchronisation conventions.

cheers,

neopolitan

 

[Dale]

Either way, I don't feel an overwhelming need to talk about clocks and synchronisation conventions.

Me neither.

FYI, I have never seen the term "proper simultaneity" before your post; it doesn't have an established meaning. I was simply providing a possible meaning, but I won't try to argue for it since I see no value in it.

 

[Mentz114]

'Proper' means - 'as measured by an observer in his own frame'. There cannot be such a thing as proper simultaneity.

People seem to be hung up about clocks and rods, which are supposed to be representative.

You have absolutely no understanding of physics. It is about measurements, which are always done with clocks and rulers.

It is you who is 'hung up' on simultaneity.

 

[Bosemann]

For anyone having trouble understanding why the acceleration is crucial, take a look at this link. If you don't understand it (I didn't the first time through), then slow down and read it very carefully. I've found skimming through these sorts of things is just a waste of time.

Acceleration is not really the answer.
Think of it this way: one twin travel to a distance L and turn around, another twin travel to a distance L/2 and turn around. The twin travel longer will age less when they meet again.
Since they both experience acceleration, so acceleration is not the cause of age difference

 

[DocZaius]

Acceleration is not really the answer.
Think of it this way: one twin travel to a distance L and turn around, another twin travel to a distance L/2 and turn around. The twin travel longer will age less when they meet again.
Since they both experience acceleration, so acceleration is not the cause of age difference

I didn't say acceleration is the only cause of age difference. I said that acceleration was the crucial factor explaining why there was a break in symmetry in that particular scenario.

 

[Bosemann]

I didn't say acceleration is the only cause of age difference. I said that acceleration was the crucial factor explaining why there was a break in symmetry in that particular scenario.

Was there a break in symmetry in this particular scenario (both twins experience acceleration)?
If yes, was acceleration the crucial factor explaining why there was a break in symmetry?

 

[DocZaius]

Was there a break in symmetry in this particular scenario (both twins experience acceleration)?
If yes, was acceleration the crucial factor explaining why there was a break in symmetry?

In the scenario in which they both experience acceleration? Of course acceleration is not the crucial factor there.

 

[neopolitan]

'Proper' means - 'as measured by an observer in his own frame'. There cannot be such a thing as proper simultaneity.


You have absolutely no understanding of physics. It is about measurements, which are always done with clocks and rulers.

It is you who is 'hung up' on simultaneity.

I had to have a bit of a laugh at this. Is this a faith based thing for you Mentz? If so, I apologise for questioning your faith.

But as far as I am concerned physics is not just measuring things. It is more about understanding how things work, even simultaneity. And part of the process of improving understanding is to ask questions and challenge assumptions. When it comes to religious thought you just ask the experts and accept the doctrine. When it comes to science (including Physics) you are actively encouraged to challenge the theories - a theory after all must be falsifiable.

The use of ad hominem arguments in a physics discussion indicates that perhaps it is not (only) me who has no understanding of it. (Note I said "People seem ..." Your statement is far more categorical.)

Relax and be open to challenges to your assumptions. Defend your assumptions if are not able to challenge your assumptions yourself. But if you attack people who challenge your assumptions, then any wrong assumptions you have will never be addressed.

And that is not physics, is it?

cheers,

neopolitan

 

[Mentz114]

neopolitan,

are you saying that the statement 'physics is all about clocks and rulers' is an assumption, or an article of faith ?
If that's the case, you don't know your assumptions from your elbow.

Physical theories try to explain measurable things. Theories about non-measurable things are just hot-air.

Everything you've said above merely strengthens my point.

M

 

[granpa]

consider this similar question:
if observer a sees b as being length contracted then why does b see a as being length contracted instead of seeing a as being stretched out. clearly the answer is because of loss of simultaneity. couldn't the same be true for the twin paradox?