Twin Paradox: Understanding Who Ages Less

[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?

 

[Mentz114]

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?

There is no contradiction in the fact that both observers see each others rulers contracted.

Loss of what simultaneity ? There are some events that the observers would agree were simultaneous, and others they would not agree on. It means nothing.

There is no twin paradox !

 

[granpa]

There is no contradiction in the fact that both observers see each others rulers contracted.there is no contradiction if you take loss of simultaneity into account. the length of an object is the distance between the position of the front and back of the object at one simultaneous moment.

 

[Mentz114]

granpa, I can see where you're coming from. Another way of measuring the length would be to measure the time taken for the rod to pass a fixed point in your frame.

 

[neopolitan]

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

Mentz,

I admit to being pedantic here, but physics is about explaining "testable" things, measurements being the mechanism by which mosts tests are conducted. However, since physics theories must be (or at the very least ought to be) not only testable but falsifiable, then some tests won't require measurements at all. An example was Young's attempt to test the wave theory of light with the double-slit experiment. No clocks, no rulers. Either the distribution of light on the other side of the double slit would support the wave theory of light or falsify it. As it was it supported the theory (but did not prove it, since you can't "prove" a theory, just provide overwhelming support, until such time as someone clever comes along and finds a way to disprove it).

Anyway, my initial comment (which was not you but rather to DaleSpam) was about the fact that events have a temporal component irrespective of whether a clock is there or not. That temporal component can be deduced retrospectively, if you so wished, in terms of the frame in which you are at rest. Similarly, in the frame in which I am at rest, there is a spatial separation between me and a spot 3m distant from my desk about 2m above the floor, even if there is no rod between me and that spot and, to my eyes, nothing to distinguish that spot from any other spot in my room which is simularly unoccupied by people, furniture etc. However, at some point of time, that spot will be inhabited by an oxygen molecule, and I could talk about the distance between the exact centre of my skull and that oxygen molecule event despite the total and complete absence of rods.

To go further, there is no need for anything to be in that location for me to label it ... does there? Do I actually need to have a rod extending out from the centre of my skull to that spot to discuss it? Do I need to have a clock to meaningfully talk about an event 5 minutes from now? My not having a clock is not going to prevent it from happening ...

Perhaps this is all too difficult, along with the question I posed in the original offending post, to wit:

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?

To get back to "proper", this is from Wikipedia:

In relativity, proper time is time measured by a single clock between events that occur at the same place as the clock. It depends not only on the events but also on the motion of the clock between the events. An accelerated clock will measure a shorter proper time between two events than a non-accelerated (inertial) clock between the same events.

This means that "proper simultaneity" which I talked about doesn't work, since I thought about a range of locations - which means a break with a core feature of "proper time". DaleSpam was right to be leery of the term.

Note that I object to the wikipedia description to the extent that it is not the acceleration per se which causes the shorter proper time, merely that for one clock the events are in the same location (hence shorter proper time) and for another clock the events are in two different locations (hence longer "improper time").

You can prove this with mathematics and with mind experiments with clocks and rods, or at the very least you can disprove that it is acceleration which causes it. But since it is part of the popular mythology now, the idea that it is acceleration behind the phenomenon is pretty hard to shift. (Note that quite a few others, some with official status on the forums, have also stated that acceleration does not cause the shorter proper time per se.)

cheers,

neopolitan

 

[Dale]

To go further, there is no need for anything to be in that location for me to label it ... does there? Do I actually need to have a rod extending out from the centre of my skull to that spot to discuss it? Do I need to have a clock to meaningfully talk about an event 5 minutes from now? My not having a clock is not going to prevent it from happening ...

By "label it" I assume you mean "assign it a coordinate value". Whatever physical mechanism you use to assign the coordinates is equivalent to some system of clocks and rods.

The terms "clock" and "rod" in SR are thus just shorthand for "a physical method of measuring time" and "a physical method of measuring distance" respectively. In that sense if you do not use "clocks and rods" then your coordinate system is not measurable and therefore non-physical, hence Mentz's objection. I don't think that was your intention.

 

[neopolitan]

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

This is from the original post which Mentz attacked.

I don't suggest taking away methods of measuring, or even the idea of measuring. All I am saying is that I can discuss a distance in my rest frame (the frame in which I am at rest) with or without positing an actual physical rod to measure it. Similarly, I can discuss an interval of time without having an actual clock to measure it.

In the same way as the "observers" don't have to be real observers, rods and clocks don't have to be real.

The difference is between my pointing to two events on my hypersurface of simultaneity and your discussing "two clocks, A and B, at rest wrt each other are synchronized by some arbitrary synchronization convention in their rest frame" (and then there is Mentz with his "forget about simultaneity, read a good essay on SR").

For me, the clocks being synchonised has little to do with simultaneity - since two clocks reading completely different times can in fact be simultaneous (like my watch and your watch, which are probably in different time zones, simultaneous, but reading a few hours apart - give or take). The same applies with rods, I can put two scratchs close to each end of a rod and write 1m between them. Then I can get a shorter rod, and do the same thing. It's not the rod. It is the distance that the rod represents that matters.

In reality, I should talk about changing the intervals between the ticks of a clock, not the time shown, to make it equivalent to using different length rods. Usually when we synchronise clocks or watches, we make sure they read the same, not check that they keep time with each other. Making sure clocks keep time is possibly more important, but the synchronisation conventions usually discussed on this forum are about making clocks at rest with respect to each other read the same - with an assumption that they will keep time once synchronised. But, this is getting bogged down in actual clocks again, rather than thinking about what the clocks represent.

I have no problem with what you have to say, DaleSpam and I don't think we have any substantial disagreement.

cheers,

neopolitan

 

[Mentz114]

neopolotan,

I'm sorry if my post seemed like an 'attack'. You obviously think about these things a lot, but in my opinion you have missed a vital thing. You say above,

But, this is getting bogged down in actual clocks again, rather than thinking about what the clocks represent.

Clocks don't 'represent' anything, and time in physics can only be defined as 'what is measured by a clock'. Just as distance can only be defined as 'what is measured by a ruler'.

Any other definitions are mostly philosophical. 'The End of Time' by Julian Barbour is a good read.

I don't have time to write anymore now.

M

 

[neopolitan]

I'm sorry if my post seemed like an 'attack'.

"You have absolutely no understanding of physics." If it was meant as helpful advice, I missed the subtlety. Sorry.

Clocks don't 'represent' anything, and time in physics can only be defined as 'what is measured by a clock'. Just as distance can only be defined as 'what is measured by a ruler'.

Any other definitions are mostly philosophical.

Perhaps I am getting philosophical here, but I would agree that "time in physics is 'that which could be measured by a clock'" - note I object to your use of "is". You are implying, perhaps unintentionally, that there was no time until someone invented a clock to measure it. And think we all agree that that is a bit silly.

Similarly with distance.

Time and space existed before clocks and rods. They existed before clocks and rods and will almost certainly exist long after all the clocks and rods have been burnt up or crushed in a passing black hole. Unless of course you believe in a god who has a supply of clocks and rods and will be handing them out in heaven to good physicists who know their assumptions from their elbow.

 

[Mentz114]

neopolitan,

You are implying, perhaps unintentionally, that there was no time until someone invented a clock to measure it. And think we all agree that that is a bit silly.

You're being silly. I did not imply any such thing.

There can be no physics without clocks and rulers. This is a physics forum.

You still don't understand what physics is about, in spite of all the time people have wasted trying to set you straight.

 

[Al68]

Hi all,

neopolitan, I brought up your point on this forum a couple of years ago, and got similar replies, but, like now, the obvious point was ignored. The "twins paradox" can be setup many ways, with or without acceleration. With or without anyone changing reference frames. Just have the traveling twin pass Earth at speed, start clocks, and stop the clocks when he passes the distant star system (the Earth twin will have to subtract light transit time from his clock reading, or have a clock at the destination) the traveling twin's clock will read less time. No acceleration, no change of reference frames. Same result. Common sense tells me that if we get the same result without acceleration, then acceleration isn't the reason for the result. This even seems too obvious to bother pointing out. Maybe I'm missing something.

And, like neopolitan says, there is an obvious asymmetry in the twins paradox that has nothing to do with acceleration. The turnaround point is defined to be a fixed distance (at rest with) one of the observers, but not the other. This is the key to the whole thing.

The traveling twin has less elapsed time because the distance traveled is smaller. Whichever twin measures the smaller distance between the events will also measure less elapsed time between the events. Can someone come up with a scenario where this is not true?

This is the only asymmetry I can see in the twins paradox that will not go away simply by slightly changing the scenario.

Al