Twin Paradox: Understanding Who Ages Less

[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

 

[matheinste]

Hello Hurkyl

I don't think i used the word distance, except in quotes, for a spacetime path. I was just using the term spacetime path, perhaps inacurately, as a sort of measure of some sort of separation between events. If i gave the impression that i meant spatial distance this was unintended as of course what you say is correct.

Matheinste.

 

[Al68]

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.


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

No, but I meant that we could redefine the end of the experiment, too.

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.

1) u pick em
2) I mean cumulative distance traveled.
3) no constraints, as long as each twin measures everything properly.

Really, I would just like to see why people believe that acceleration is crucial, when the experiment could be presented without acceleration with the same result. By same result I mean that the twin who measured the shorter distance has less elapsed time, not that the twins reunite. For example, it has been presented as two separate trips with a third observer traveling from the distant star system to earth, nobody accelerates, and we just add up the two trips and get the same result. Or the experiment could end when the ship passes the turnaround point. With a third observer there with a clock. The twins don't have the novelty of reuniting, but we have the same result of two defined events, and one twin has less elapsed time between them than the other.

And I think it's worth mentioning that, in the normal twins paradox, that the twins' reunion doesn't really change anything. It's not like the laws of physics change because they reunite.

I don't dispute that the traveling twin will age less, but he will age less (have less elapsed time between events) during a one-way journey as well. And we don't need to reunite the twins to show this. Unless we consider the most important thing here is to have two twins look at each other and have one say "Gee, you're older than me, how did that happen?"

Sure, in the common example, the twin who accelerates does indeed age less, but is there any evidence (or logical deduction) that shows that this is the reason? SR certainly doesn't make such a claim. Using SR, we can ignore acceleration altogether and get the same result. We can even say that the ship never accelerated, and the Earth (and distant star system) were moved by magic/God/Unknown reasons, and when the twins reunite, the one in the ship is younger according to SR. Yes, that's silly, I know. Just making a point.

And I have seen many posts saying I'm wrong, but none that say how, or provide any substantiation of the claim that acceleration is important as a general rule, not just in a specific scenario where the accelerated twin happens to age less.

That's what I'm asking for.

Al

 

[Al68]

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.

I agree. I never said otherwise. I said: "Whichever twin measures the most distance between events will have the most elapsed time between those events."

Al

 

[Hurkyl]

Really, I would just like to see why people believe that acceleration is crucial

When people seek to resolve the twin paradox, they seek to point out a flaw in the logical argument in the twin paradox. If you are talking about something that isn't the twin paradox (e.g. any experiment involving twins that don't reunite), then that is something irrelevant.

I don't dispute that the traveling twin will age less, but he will age less (have less elapsed time between events) during a one-way journey as well.

In a one-way journey, it is impossible for both twins to be present at both events. And there is no intrinsic way to compare their ages.

 

[Hurkyl]

2) I mean cumulative distance traveled.

Events don't travel; they're events. This doesn't make sense.
Similarly, you mentioned 'elapsed time'; elapsed time of what?

3) no constraints, as long as each twin measures everything properly.

You do realize that, in any experimental setup, by choosing the appropriate coordinate chart, I can make either twin (properly!) compute any value I want for any coordinate-dependent quantity I want, right?