Why Are the Two Diagrams in the Twin Paradox Not Symmetric?

[student34]

In the image below from the website http://www.mysearch.org.uk/website1/html/250.Twins.html , they try to explain why the two situations are not symmetric, but I don't understand their approach. Even if the website is not giving a sufficient explanation, I would still like to know why the two diagrams are not symmetric.

 

[Mister T]

In the first diagram the space twin turns around, but the earth twin doesn't.
In the second diagram the earth twin turns around, but the space twin doesn't.

 

[student34]

In the first diagram the space twin turns around, but the earth twin doesn't.
In the second diagram the earth twin turns around, but the space twin doesn't.

Then strictly by what you say, shouldn't that should be a symmetric situation? Why is the outcome different?

 

[robphy]

From my post at https://www.physicsforums.com/threa...y-affect-one-of-the-twins.989461/post-6346575

if you look at an asymmetric trip (different outgoing and incoming speeds),

• you'll see that the non-inertial traveler's diagram
  will generally display the inertial worldline as a discontinuous worldline,
  as well as miss some events altogether (like the event P on the inertial segment)
  and show some events twice.

You can try to clean things up by using a smooth turn-around,
but the point is, with respect to the principle of relativity,
the non-inertial traveler is not equivalent to the inertial traveler...
since no such clean-up is needed for the inertial traveler.

To see how these "franksteined spacetime-diagrams" are constructed visit my answer at https://physics.stackexchange.com/a/507592/148184

The takeaway message is
"Being able-to-be-at-rest" ≠ "Being inertial".

 

[student34]

You can try to clean things up by using a smooth turn-around,
but the point is, with respect to the principle of relativity,
the non-inertial traveler is not equivalent to the inertial traveler...
since no such clean-up is needed for the inertial traveler.

Is there anything other than acceleration that would cause something to be non-inertial?

 

[FactChecker]

Who owns that web page? On its Home page, it has this disclaimer, but I don't see anything about the credentials of the author. And that website addresses a multitude of subjects.
"Disclaimer
No claim of righteous certainty is being made on any topic discussed. As such, this website only attempts to investigate a range of topics in the spirit of honest inquiry. "

I think that you can waste a lot of time and effort on this subject if you are not careful about who you ask.

 

[student34]

Who owns that web page? On its Home page, it has this disclaimer, but I don't see anything about the credentials of the author. And that website addresses a multitude of subjects.
"Disclaimer
No claim of righteous certainty is being made on any topic discussed. As such, this website only attempts to investigate a range of topics in the spirit of honest inquiry. "

I think that you can waste a lot of time and effort on this subject if you are not careful about who you ask.

Like I said in the OP, it's not so much whether the website is wrong or right, I just want to analyze the exact difference between the 2 thought experiments. I also wanted to revisit the topic about whether or not acceleration plays a role, if not the only role, in the twin paradox.

 

[student34]

You can try to clean things up by using a smooth turn-around,
but the point is, with respect to the principle of relativity,
the non-inertial traveler is not equivalent to the inertial traveler...
since no such clean-up is needed for the inertial traveler.

Just out of curiosity, is the website's spacetime diagram wrong for the space traveler in the rest frame?

 

[robphy]

Is there anything other than acceleration that would cause something to be non-inertial?

I also wanted to revisit the topic about whether or not acceleration plays a role, if not the only role, in the twin paradox.

A non-zero acceleration anywhere along a worldline segment
will make that worldline segment non-inertial.

The clock-effect is the spacetime-path dependence of proper-time
along different worldline segments from event A to event B.
It is the analogue of the path-dependence of odometer length traveled
along different paths from point A to point B.
(The clock-effect is not necessarily about acceleration.... it's about path-lengths.)

The twin paradox is the mistaken claim of equivalence of a non-inertial traveler and an inertial traveler.
It fails to recognize that
"Being able-to-be-at-rest" ≠ "Being inertial".

(The twin paradox and the clock effect are related, but not the same thing.)

 

[robphy]

Just out of curiosity, is the website's spacetime diagram wrong for the space traveler in the rest frame?

In Minkowski spacetime. a non-inertial traveler's diagram is not a complete map of spacetime.
As I said, its frankensteined spacetime-diagram omits some events and duplicates some other events.

That is... the worldlines might look correct, and may be correct in some cases,
but the rest of the diagram may have troubles described above....
so any attempt at equivalence fails.

In my opinion, the event-labels of each event (e.g. what the clock along the worldline reads at each worldline event) should be preserved between the diagrams... as I have done in my diagrams.
(I am not going to try to reproduce the analysis and intent of the original diagrams.)

From the stackexchange link I posted, here is the symmetric case (for v=0.8c):

 

[student34]

A non-zero acceleration anywhere along a worldline segment
will make that worldline segment non-inertial.

The clock-effect is the spacetime-path dependence of proper-time
along different worldline segments from event A to event B.
It is the analogue of the path-dependence of odometer length traveled
along different paths from point A to point B.
(The clock-effect is not necessarily about acceleration.... it's about path-lengths.)

Yes, but we are putting in the path-lengths to show what happened. I am trying to figure out the exact reason for the difference between the two diagrams.

*** (I edited because I did not write what I should have written) ***

The twin paradox is the mistaken claim of equivalence of a non-inertial traveler and an inertial traveler.

I guess then it comes down to whether or not non-inertial is defined only by acceleration?

If this is the case, I would have to think that the only reason the twin paradox is not a paradox is because of acceleration.

 

[Ibix]

Even if the website is not giving a sufficient explanation, I would still like to know why the two diagrams are not symmetric.

They are symmetric. The right hand one doesn't correspond to any meaningful analysis, obviously so because the clock ticks on the black worldline are wrong in the upper half.

 

[phinds]

I am trying to figure out the exact reason for the difference between the two diagrams.

Becasuse, as @Ibix said directly above, the second scenario posits an assumption (the Earthbound character turns around, i.e. accelerates) that has no basis in reality and thus is a bogus analysis of anything meaningful.

Said, another way, the diagrams are symmetrical on paper, but that fact is meaningless because the second diagram is meaningless.

 

[student34]

They are symmetric. The right hand one doesn't correspond to any meaningful analysis, obviously so because the clock ticks on the black worldline are wrong in the upper half.

I don't think I explained what I really wanted to in the OP. Whether or not the diagrams make any sense, I would like to really analyze what breaks the symmetry between the two scenarios.

 

[phinds]

I don't think I explained what I really wanted to in the OP. Whether or not the diagrams make any sense, I would like to really analyze what breaks the symmetry between the two scenarios.

Nothing breaks the symmetry. Were we not clear? They ARE symmetrical, it's just that one represents reality and one does not.

 

[Ibix]

Whether or not the diagrams make any sense, I would like to really analyze what breaks the symmetry between the two scenarios.

Specify exactly what you think the two scenarios are. Who feels proper acceleration in each case? How long does each twin coast between meetings and/or accelerations?

If the list of specifications is different then you have your asymmetry. If the list of specifications is the same then you don't have two scenarios, you have one, and the right hand diagram is just a wrong depiction of it.

 

[student34]

Nothing breaks the symmetry. Were we not clear? They ARE symmetrical, it's just that one represents reality and one does not.

I would like to know why one does not represent reality. Why does the scenario on the right turn into the image that robphy posted (since the image in the OP is not really correct) on the right side of the screen in post #4. Why aren't they symmetrical diagrams? Is it only because of non-inertial frame/acceleration, or are there other reasons?

 

[phinds]

Is it only because of non-inertial frame/acceleration

As you have been told repeatedly, YES.

I suggest you do the exercise presented by @Ibix in post #16

 

[student34]

In Minkowski spacetime. a non-inertial traveler's diagram is not a complete map of spacetime.
As I said, its frankensteined spacetime-diagram omits some events and duplicates some other events.

That is... the worldlines might look correct, and may be correct in some cases,
but the rest of the diagram may have troubles described above....
so any attempt at equivalence fails.

In my opinion, the event-labels of each event (e.g. what the clock along the worldline reads at each worldline event) should be preserved between the diagrams... as I have done in my diagrams.
(I am not going to try to reproduce the analysis and intent of the original diagrams.)

From the stackexchange link I posted, here is the symmetric case (for v=0.8c):
View attachment 320710 View attachment 320709

This looks very interesting. I am going to learn exactly what it means.

 

[student34]

As you have been told repeatedly, YES.

I suggest you do the exercise presented by @Ibix in post #16

But on the other thread called "Sabine on GR", there were advisors here that did not believe acceleration was the only reason.

 

[Ibix]

But on the other thread called "Sabine on GR", there were advisors here that did not believe acceleration was the only reason.

You are conflating different things.

I do not think there are two scenarios here. There are two diagrams of one scenario, one of which is wrong. That's why I want you to list what the two scenarios are in terms of instructions to the two twins on what to do, so we both understand whether there are two different situations or not.

If there are two scenarios then the asymmetry is because they are not the same scenario. If there is one scenario, the diagram on the right is wrong because it's an attempt to stitch together parts of two inertial frames into one non-inertial frame, and it fails.

All of this has absolutely nothing to do with whether "acceleration causes time dilation", which is just wrong.

 

[student34]

You are conflating different things.

I do not think there are two scenarios here. There are two diagrams of one scenario, one of which is wrong. That's why I want you to list what the two scenarios are in terms of instructions to the two twins on what to do.

If there are two scenarios then the asymmetry is because they are not the same scenario. If there is one scenario, the diagram on the right is wrong because it's an attempt to stitch together parts of two inertial frames into one non-inertial frame, and it fails.

You don't seem to be addressing what you quoted from what I wrote. Instead, I feel like you are going into a semantic argument.

All of this has absolutely nothing to do with whether "acceleration causes time dilation", which is just wrong.

I do not understand how it is wrong to attribute acceleration to time dilation. Does a non-inertial imply acceleration? If so, then what you say in your 3rd paragraph seems to contradict that acceleration does not cause time dilation.

 

[Ibix]

I do not understand how it is wrong to attribute acceleration to time dilation.

Because time dilation is an effect between inertial clocks. Acceleration does not come into it. And differential aging (what Sabine was calling "real time dilation") depends on path length, not acceleration. As I told you in the Sabine and GR thread, in fact.

Acceleration and non-inertial frames are not the same thing.

 

[PeterDonis]

I would still like to know why the two diagrams are not symmetric.

Because the diagram on the right is not a diagram of an inertial frame. In fact it's not even a diagram of a non-inertial frame. It's just something the website author waved their hands and drew to look like a mirror image of the diagram on the left, without even asking the question whether that mirror image diagram represents any actual valid coordinate chart. It doesn't.

You would be much better served by reading this:

https://www.physicsforums.com/threads/when-discussing-the-twin-paradox-read-this-first.1048697/

 

[student34]

Acceleration and non-inertial frames are not the same thing.

Okay, this is interesting. I looked for exact definitions of non-inertial, and all I could find is that acceleration implied non-inertial. What else can be considered non-inertial that the twin would experience? Whatever this is, if it exists, will help narrow down the difference that I am looking for.

 

[PeterDonis]

I would like to know why one does not represent reality.

Because the website author just made it up. They didn't use physics to produce it.

This website is not a good source. Ignore it. Read the link I gave in post #24 instead.

 

[PeterDonis]

I looked for exact definitions of non-inertial

Non-inertial frame. The fact that an object, in this case the traveling twin, has nonzero proper acceleration does not mean you have to use a non-inertial frame to describe their motion. Conversely, the fact that an object, in this case the stay at home twin, is inertial all the time does not mean you have to use an inertial frame to describe their motion.

 

[PeterDonis]

The reference given in the OP is not a valid basis for PF discussion.

Thread closed.