Twin Paradox: Understanding Who Ages Less

[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

 

[matheinste]

Hello A168.

In this never ending saga of the twins nonparadox how can the two be present at the start event and the meeting event and follow different spacetime paths without one or both accelerating. If they are not present at the two events there is no apparent paradox anyway because the whole idea is to show the "remarkable" and puzzling effect of the differential in ageing

In all the scenarios they must both be present at the two events to realistically compare their elapsed time ( ages ).

Also the one that follows the shortest spacetime path experiences the most elapsed time. An inertial, non accelerated, path is the shortest spacetime distance of all.

The resolution of his nonparadox is explained countless times in this forum and in most textbooks.

Matheinste.

 

[Doc Al]

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.

Nonsense. Not only is the turnaround point being "at rest" not the key, it's not even relevant or meaningful. The traveling twin can turn around at any point--it doesn't matter! And he must turnaround at some point, and that point has some specific distance from the other twin (different in each frame, of course).

 

[AntigenX]

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

Hi Al,

You must account for acceleration, because, without acceleration, the traveling twin and the stationary twins are equivalent. We can not decide in SR which is moving and which is traveling. So, though the twin in spaceship is traveling, he is traveling wrt the stationary twin, and thus, he will also see the stationary twin's clock slow. In such a case, without acceleration (which breaks symmetry, I don't know how!), no twin can age less!

Though I don't quite understand the effect of acceleration, without acceleration no one can age less.

 

[matheinste]

Hello AntigenX.

The acceleration breaks the symmetry by making the traveling twin's spacetime interval longer than the non-accelerated twin's spacetime interval. The object ( twin ) with the longer spacetime interval accumulates less elapsed time and hence remains younger. Do not confuse spatial distance traveled with spacetime interval. They are very different things.

As said above a spacetime diagram makes this clear.

Matheinste.

 

[robphy]

Hello AntigenX.

The acceleration breaks the symmetry by making the traveling twin's spacetime interval longer than the non-accelerated twin's spacetime interval. The object ( twin ) with the longer spacetime interval accumulates less elapsed time and hence remains younger. Do not confuse spatial distance traveled with spacetime interval. They are very different things.

As said above a spacetime diagram makes this clear.

Matheinste.

I take issue with the portion of your comment that I highlighted above.
The acceleration DOES NOT MAKE the traveling twin's spacetime interval longer... it DOES INDICATE that a noninertial worldline is being used from A to B and such a worldline is necessarily shorter than an inertial worldline from A to B.
(In addition... "travelling twin's spacetime interval" [along his worldline from A to B] is SHORTER.)

As I wrote in https://www.physicsforums.com/showthread.php?p=1738289#post1738289",
which you quoted in https://www.physicsforums.com/showthread.php?p=1739679#post1739679",
"The symmetry break (between inertial and noninertial) is the "presence of an acceleration (worldline curvature) somewhere during the trip" for the noninertial observer. Neither are causes of the shorter-elapsed-proper-time from A to B... they are correlated with the shorter-elapsed-time because they indicate that a noninertial (i.e. nongeodesic) worldline was used to experience both A and B."

(One of the best papers on the Twin Paradox/Clock Paradox:
http://www.jstor.org/pss/2309916 (requires institutional access)
"The Clock Paradox in Relativity Theory", Alfred Schild, The American Mathematical Monthly, Vol. 66, No. 1. (Jan., 1959), pp.1-18.)

 

[granpa]

longer spacetime interval


thats a strange way of putting it. in Minkowski space the interval is defined as (d^2-T^2)^0.5
so its actually shorter. that's why i was so confused earlier. but i know what you mean though.


the length of the line segment that corresponds to the interval would be (d^2+T^2)^0.5. that's what you are referring to.

 

[AntigenX]

Hello AntigenX.

The acceleration breaks the symmetry by making the traveling twin's spacetime interval longer than the non-accelerated twin's spacetime interval. The object ( twin ) with the longer spacetime interval accumulates less elapsed time and hence remains younger.

Greetings matheinste,

Yes, I understand the "translated" meaning, but can't get it how? As I have asked earlier several times and also in this (https://www.physicsforums.com/showthread.php?t=236229) thread, as acceleration is not relative to the stationary twin (but absolute), how can it's effect be relative? I mean only one clock is slowed more and not other?

Do not confuse spatial distance traveled with spacetime interval. They are very different things.

Have I?

As said above a spacetime diagram makes this clear.

Matheinste.

Well, space time diagrams are good If you understand the things. I'm not clear about the things, so spacetime diagrams are just boring math for me. I don't want to get into the habit of learning physics via math. Though others may not agree, this is just absurd for stupids like me.

Thanks for the suggestion anyways...

 

[DocZaius]

Well, space time diagrams are good If you understand the things. I'm not clear about the things, so spacetime diagrams are just boring math for me. I don't want to get into the habit of learning physics via math. Though others may not agree, this is just absurd for stupids like me.

I think this quote is applicable:

“To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature … If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.”

–R. Feynman

 

[Doc Al]

Of the several ways to understand relativistic effects, the use of spacetime diagrams is probably the least mathematical (and most profound). Sure, it takes a bit of effort to figure out how to interpret them, but well worth it if you're serious. Verbal handwaving won't help.

 

[AntigenX]

I think this quote is applicable:

“To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature … If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.”

–R. Feynman

Oh yes, But I think you are getting me wrong. By calling myself stupid I don't propose to say I don't know math (neither you would have inferred it, I suppose), instead, It's just what einstein used to say "... equations and math are for book-keeping, not for learning or understanding...". But of course, It was einstein, and his thinking may be different like mine, yours and R. Feynman's.

 

[DocZaius]

Oh yes, But I think you are getting me wrong. By calling myself stupid I don't propose to say I don't know math (neither you would have inferred it, I suppose), instead, It's just what einstein used to say "... equations and math are for book-keeping, not for learning or understanding...". But of course, It was einstein, and his thinking may be different like mine, yours and R. Feynman's.

As you have said, I wasn't inferring you don't know math. My only point was that the application of mathematics to your study of nature is very useful and brings out much more meaning (in my opinion) than the lack of it.

I'm surprised Einstein said that equations and math are not for learning or understanding. They seem to be invaluable tools.

 

[AntigenX]

As you have said, I wasn't inferring you don't know math. My only point was that the application of mathematics to your study of nature is very useful and brings out much more meaning (in my opinion) than the lack of it.

I'm surprised Einstein said that equations and math are not for learning or understanding. They seem to be invaluable tools.

Don't worry about that, and it doesn't matter even if you consider me stupid, as long as you are teaching me something or trying to help me learn something.

Einstein said them in some of his lectures, where he was explaining the importance of clocks and rods and thought experiments and their philosophical and physical interpretations. Even he himself has never relied on spacetime diagrams but thought experiments and their interpretations were his tools of the trade (as far as I have read him)...

EDIT: He also said later that the theories of relativity (especially GR) have become so mathematical that he himself doesn't understand it (jokingly of course)...

 

[matheinste]

Hello robphy.

I apologise for my error.

granpa.

You are correct instead of spacetime interval i should have said length of spacetime worldline.

Mateinste

 

[AntigenX]

Of the several ways to understand relativistic effects, the use of spacetime diagrams is probably the least mathematical (and most profound). Sure, it takes a bit of effort to figure out how to interpret them, but well worth it if you're serious. Verbal handwaving won't help.

I have never disregarded it, and several people told me about this as well. It's just I wish to try the other way. "Verbal handwaving" is doing a good job currently, and is my time tested method. I don't see any way to convince you that I am serious, but I wish only if you could believe me...

 

[Al68]

Hello A168.

In this never ending saga of the twins nonparadox how can the two be present at the start event and the meeting event and follow different spacetime paths without one or both accelerating. If they are not present at the two events there is no apparent paradox anyway because the whole idea is to show the "remarkable" and puzzling effect of the differential in ageing

In all the scenarios they must both be present at the two events to realistically compare their elapsed time ( ages ).

No they don't. The Earth twin could have an agent at the distant star system with a clock.

Also the one that follows the shortest spacetime path experiences the most elapsed time. An inertial, non accelerated, path is the shortest spacetime distance of all.

The resolution of his nonparadox is explained countless times in this forum and in most textbooks.

Yes. And not only are they unsatisfactory, they contradict each other.

Al

 

[Al68]

Nonsense. Not only is the turnaround point being "at rest" not the key, it's not even relevant or meaningful. The traveling twin can turn around at any point--it doesn't matter! And he must turnaround at some point, and that point has some specific distance from the other twin (different in each frame, of course).

Why does the traveling twin have to turn around? Just so we can have the novelty of the twins meeting again?

Al

 

[Al68]

Hi Al,

You must account for acceleration, because, without acceleration, the traveling twin and the stationary twins are equivalent. We can not decide in SR which is moving and which is traveling. So, though the twin in spaceship is traveling, he is traveling wrt the stationary twin, and thus, he will also see the stationary twin's clock slow. In such a case, without acceleration (which breaks symmetry, I don't know how!), no twin can age less!

Though I don't quite understand the effect of acceleration, without acceleration no one can age less.

Again, since we get the same result even if there is no acceleration involved, it seems to me that I don't have to account for acceleration. Even in the standard twins paradox, I ignore acceleration and get the same result.

The simple fact is that at a given speed, it will take less time to traverse a smaller distance. It will always take less time to traverse a smaller distance. Whichever twin measures the most distance between events will have the most elapsed time between those events.

This is true no matter how we set up the scenario, with or without acceleration, is it not?

Al

 

[matheinste]

Hello A168.

Quote:-

-----No they don't. The Earth twin could have an agent at the distant star system with a clock.-----

That is not how the paradox is presented. The whole idea is to make it look like a contradicton. ( but of course the resolutions should not be contradictory )

Quote:-

---Why does the traveling twin have to turn around? Just so we can have the novelty of the twins meeting again?-----

For the same reason.

If you find the reasons for the age difference unsatisfactory i can't help you. If you find them contradictory have you considered that some of the answers may be wrong.

Matheinste.

 

[AntigenX]

Again, since we get the same result even if there is no acceleration involved, it seems to me that I don't have to account for acceleration. Even in the standard twins paradox, I ignore acceleration and get the same result.

What same result? that the traveling twin will age less? We don't get the same result. Because, as I pointed out earlier, we don't really have any means to say that traveling twin is really traveling!

The simple fact is that at a given speed, it will take less time to traverse a smaller distance. It will always take less time to traverse a smaller distance. Whichever twin measures the most distance between events will have the most elapsed time between those events.

How will you measure the speed of the traveling twin?

This is true no matter how we set up the scenario, with or without acceleration, is it not?

Al

No. Though I don't understand the effects of acceleration, without the acceleration the situation is perfectly symmetric. In such a case, both twins will observe the other twin to age less, and we have no reasons to prefer anyone over the other.

 

[matheinste]

Hello AntigenX.

I believe some of your reasoning is inceorrect and contradict's the generally accepted answer as derived from the axioms of SR. Textbooks which give the resolution to the seeming paradox agree on the answer. There should be no problem

Matheinste.

 

[Mentz114]

AntigenX,

What same result? that the traveling twin will age less? We don't get the same result. Because, as I pointed out earlier, we don't really have any means to say that traveling twin is really traveling!

It doesn't matter what the situation is, the twin with the longest proper interval will age less. There's no paradox or difficulty. Just learn how to calculate the proper interval and all these cases can be worked out with the same recipe.

 

[AntigenX]

Hello AntigenX.

I believe some of your reasoning is inceorrect and contradict's the generally accepted answer as derived from the axioms of SR. Textbooks which give the resolution to the seeming paradox agree on the answer. There should be no problem

Matheinste.

Sorry for that. I thought twice before posting though!

Can you please tell me which are those points? I am asking this because, may be my english is not proper, and hence I am misinterpreted many times.

 

[matheinste]

Hello AntigenX

Your english is fine.

Quote:-

----Whichever twin measures the most distance between events will have the most elapsed time between those events.----

It is the other way around. The traveling twin ( the accelerated one in the case of the proposed paradox ) follows the longer spacetime path and so accumulates the lesser elapsed time.

Matheinste.

 

[AntigenX]

Hello AntigenX

Your english is fine.

Quote:-

----Whichever twin measures the most distance between events will have the most elapsed time between those events.----

It is the other way around. The traveling twin ( the accelerated one in the case of the proposed paradox ) follows the longer spacetime path and so accumulates the lesser elapsed time.

Matheinste.

Thanks Matheinste for the compliment! But I never said that... In fact I contradicted that, and as you are saying, I was correct.

 

[matheinste]

Hello AntigenX.

Many apologies. I of course retract my statement about the incorrectness of your post

Matheinste.

 

[Al68]

Hello AntigenX

Your english is fine.

Quote:-

----Whichever twin measures the most distance between events will have the most elapsed time between those events.----

It is the other way around. The traveling twin ( the accelerated one in the case of the proposed paradox ) follows the longer spacetime path and so accumulates the lesser elapsed time.

Matheinste.

I think I had it right. In this case the traveling twin (with the longer spacetime path) measures a shorter distance between events, and a shorter elapsed time.

 

[Al68]

Hello A168.

Quote:-

-----No they don't. The Earth twin could have an agent at the distant star system with a clock.-----

That is not how the paradox is presented. The whole idea is to make it look like a contradicton. ( but of course the resolutions should not be contradictory )

Quote:-

---Why does the traveling twin have to turn around? Just so we can have the novelty of the twins meeting again?-----

For the same reason.

If you find the reasons for the age difference unsatisfactory i can't help you. If you find them contradictory have you considered that some of the answers may be wrong.

Matheinste.

Hi Matheinste,

I think you said it. The whole point of the way the scenario is normally presented is for the novelty of making it look like a contradiction.

And I don't have a problem with the age difference. I get the same answer if I pretend the Earth twin accelerated with everything else the same. Just pretend (for no reason) that the Earth twin "felt" the turnaround and do the math. Ship's twin still ages less. Amazing. SR math will work exactly the same and show the twin who measures the shorter distance traveled to have the shorter elapsed time. Amazing again.

It is simple to have a scenario where neither twin accelerates during the test. just have the ship's twin stop his clock just before he turns around, and have a clock at the turnaround point (synched with earth) record the time of the same event. Then the twins can turnaround, fly in circles, or whatever, it won't change the clocks since they are stopped. And again, the twin who measures the shorter distance will have the least elapsed time.

How about a challenge for all: Come up with a scenario in which my claim is wrong. The claim is that whichever twin measures the shorter distance between two events will have less elapsed time between those events.

Al

 

[Hurkyl]

I think you said it. The whole point of the way the scenario is normally presented is for the novelty of making it look like a contradiction.

It's not simply a novelty -- it's for educational purposes. People really do make that mistake and other similar ones (even people that should know better), so its important to spend some time teaching students to identify the flaw, and demonstrating that it really is flawed.

It is simple to have a scenario where neither twin accelerates during the test. just have the ship's twin stop his clock just before he turns around

Stopping the clock during an experiment doesn't stop the experiment.

How about a challenge for all: Come up with a scenario in which my claim is wrong. The claim is that whichever twin measures the shorter distance between two events will have less elapsed time between those events.

State your claim precisely, please. Current problems include:
(1) Which events?
(2) If you mean the events where the twins separate and reunite, then they are timelike separated, and there is no intrinsic meaning to the 'distance' between them. (It would make sense to ask about the proper duration, but of course, everyone would measure the same value)
(3) If you mean to refer to coordinate-dependent quantities, then I think you are going to need to put some constraints on what coordinate charts each twin uses.

 

[matheinste]

Hello Al68

Quote:-

----I think I had it right. In this case the traveling twin (with the longer spacetime path) measures a shorter distance between events------

He experiences a shorter elapsed time but travels a longer spacetime path. Having less accumulated time does not mean he travels a shorter spactime path.

Matheinste.

 

[Hurkyl]

The traveling twin ( the accelerated one in the case of the proposed paradox ) follows the longer spacetime path

In this case the traveling twin (with the longer spacetime path)

The "spacetime path" traveled by an object¹ is time-like; the notion of 'distance' doesn't make sense. The 'duration' of the path, however, is exactly what the observer's wristwatch measures.


1: A tardyonic object, at least. This doesn't apply to tachyons