michel123456's relativity thread (from Time dilation dependence on direction)

[Eise]

3 hours ago, michel123456 said:

But when @Eise  quoted @Janus & explained the "However" part, that made sense to you, and it was about Relativity.

But I do not recognise my explanation clearly in what you say.

3 hours ago, michel123456 said:

Yes. B measures 75 min.

Not 45 min.

This is again as unclear as unclear can be. Switching the 2 sentences for clarity:

• According B's own clock, his trip from Earth to X takes 45 minutes.
• When B passes Earth he sees e.g. that it is 0:00 there, and when he passes X he sees 01:15 at X's clock.

Further, as Swansont already suggested pages ago, it is much easier to make the example of B already flying at 0.8c, passes Earth and sees the clock on Earth, and then passes X, and sees what its clock shows. And we take a flight very close by, so that we can neglect any delays or relativistic effects. Then you do not have to worry about such things as:

18 hours ago, michel123456 said:

I believe that in the FOR of B, X does not start to move instantaneously.

I would suggest, that you do not try to press relativity in the way you are used to think about time and distances. Try to understand relativity as it is, lookup simple derivations. If you do not understand some step in the derivation, come here and ask. The terms in which you are thinking bear no fruit in understanding relativity.

[swansont]

To Eise's comments I will add/reiterate: the problem with doing thought experiments is that they don't test anything but the self-consistency of the model. (e.g. Galilean relativity is self-consistent, but assumes an infinite speed of light.So it gives an answer, but not the correct one.) That your model gives you a number that you like or makes sense to your intuition means nothing. If you want to test whether the model is correct*, you need to compare it to an actual experiment. (This is one reason we have the rules in speculations that we do — thought experiments are not enough. They need to be tested)

If and when you wish to do so, the muon experiment is available for analysis. 

 

*technically it will only confirm that it's incorrect

[md65536]

6 hours ago, michel123456 said:

But when @Eise  quoted @Janus & explained the "However" part, that made sense to you, and it was about Relativity.

Correct! Their numbers made sense and I could repeat the calculations of SR to get them, and when they referred to "relativity of simultaneity" they were using the established meaning of the term. Your numbers are based only on a denial of time dilation (your "?=30" is based only on having B's clock match X's, nothing else), and you use your own personal redefinition of RoS that seems to mean some combination of "light is delayed, and I've modified Galilean relativity so that it is not symmetric".

Anyway, I'm not interested in discussing your alternative model, so... good day, sir.

[md65536]

9 hours ago, Eise said:

I would suggest, that you do not try to press relativity in the way you are used to think about time and distances. Try to understand relativity as it is, lookup simple derivations. If you do not understand some step in the derivation, come here and ask. The terms in which you are thinking bear no fruit in understanding relativity.

Yes, I agree. Even without the derivations, just much simpler examples, starting with the basics and without already deciding the answers before looking at the examples. One of the many problems here is that we're all looking at a relatively complicated example and trying to explain/understand step 10 of it, and Michel is effectively saying "I replaced step 3 with my own ideas, but can you keep explaining step 10 over and over? You're doing it wrong because I'm getting different results."

Though, I still think giving up and not misusing the language of SR is a good option for him.

[swansont]

4 minutes ago, md65536 said:

Yes, I agree. Even without the derivations, just much simpler examples, starting with the basics and without already deciding the answers before looking at the examples. One of the many problems here is that we're all looking at a relatively complicated example and trying to explain/understand step 10 of it, and Michel is effectively saying "I replaced step 3 with my own ideas, but can you keep explaining step 10 over and over? You're doing it wrong because I'm getting different results."

Though, I still think giving up and not misusing the language of SR is a good option for him.

I don’t know it’s the intent here, but it’s a tactic that has come up with relativity deniers in the past: after being rebuffed in objections to standard scenarios, keep making the problem more complex 

[Eise]

14 hours ago, swansont said:

If and when you wish to do so, the muon experiment is available for analysis. 

Yes, I think we should go there.

@michel123456: I think I stop too, at least for the moment, with this example. No Earth, B and planet X anymore. If you want to understand relativity, and you see that it does not bring you any further, then start with the simple examples, and as noted already several times, with a real life experiment. Just to add, I have seen a spark chamber, sparking on average every second when a muon passed through it.

Here two references:

• Hyperphysics
• minutephysics (youtube, only 4.5 minutes)

Take the advice from a seasoned physicist (Swansont) and a 'physics tourist' (who also happened to be a teacher for some time): concentrate on the muon example first. To understand complex problems, it is better to start with the simpler problems, and then slowly work to the more complex ones.

If you want to play the piano, do you start practicing with Liszt or with Satie? If you want to understand mathematics, do you start with differential calculus, or with simple linear equations with one variable?

[Markus Hanke]

I don't really wish to involve myself in this discussion, but there is one point I'd like to make - from my personal experience, I found that a top-down approach works much better when learning relativity. That means you start with the general overarching principle, and then drill your way down and see how those apply to individual scenarios. Getting yourself lost in complicated scenarios seems not the right way to go.

But maybe that's just me

[Eise]

20 minutes ago, Markus Hanke said:

I don't really wish to involve myself in this discussion, but there is one point I'd like to make - from my personal experience, I found that a top-down approach works much better when learning relativity. That means you start with the general overarching principle, and then drill your way down and see how those apply to individual scenarios.

Hmmm. You would start with the Minkowski metric? Do you think that approach would help michel12345?

21 minutes ago, Markus Hanke said:

Getting yourself lost in complicated scenarios seems not the right way to go.

There I fully agree, but my reaction is to take simple scenarios to begin with.

22 minutes ago, Markus Hanke said:

But maybe that's just me

Maybe. Maybe a shared characteristic of a scientific genius? Easy grasping of very abstract concepts?

What I do notice however, is that starting to understand the most abstract principles of special relativity, everything falls much better into place.

[Markus Hanke]

2 hours ago, Eise said:

Hmmm. You would start with the Minkowski metric? Do you think that approach would help michel12345?

I don’t know what would help Michel. I seem to remember he’s an architect by trade (right?), so he would have been explicitly trained and experienced in thinking in Euclidean terms, since this is the kind of geometry we use to construct everyday objects. But relativistic spacetime is not Euclidean, so maybe this is where the problem lies.

2 hours ago, Eise said:

Easy grasping of very abstract concepts?

The geometry of Minkowski spacetime isn’t particularly abstract, it’s just different from the kind of geometry we learn at school. But when one does not make that paradigm shift away from Euclidean thinking, nothing about relativity will ever make much sense, irrespective of whether the particulars are understood or not. 

2 hours ago, Eise said:

Maybe a shared characteristic of a scientific genius?

I don’t think so lol  Relativity really isn’t that difficult to grasp, and Michel is clearly very intelligent, so I don’t think the problem is one of understanding.

[joigus]

5 hours ago, Markus Hanke said:

I don't really wish to involve myself in this discussion, but there is one point I'd like to make - from my personal experience, I found that a top-down approach works much better when learning relativity. That means you start with the general overarching principle, and then drill your way down and see how those apply to individual scenarios. Getting yourself lost in complicated scenarios seems not the right way to go.

But maybe that's just me

 

4 hours ago, Eise said:

Hmmm. You would start with the Minkowski metric? Do you think that approach would help michel12345?

Probably not.

I'm of the same mind as Markus here --and I don't mean in genius, and probably he didn't mean that either. In my case it's more of an "on the shoulders of giants" kind of idea. Though to me, that doesn't mean I don't value contributions from people analyzing complicated scenarios. Quite the contrary. Some explanations I've found here are nothing short of a masterpiece. But I for one need the shortcuts that the big picture gives you (these words "big picture" have appeared on another thread recently.) If only some people saw what many of us can see thanks to these great minds. It's as if someone had given you night-vision goggles to see in the dark. Why won't Michel put on the goggles and see the vistas? That's what I ask myself.

The big picture gives you power, even if you're not a powerful thinker. Mathematical tools take you farther and farther afield, and uphill. It's as if someone took you with a helicopter to the top of the mountain and you said, "oh, I see." Then you can follow the terrain downstream. It's such a pleasure!

I think that this self-indulgence is both the greatest advantage and the first deadly sin of the theorist. You need to see the landscape, and you must cover a lot of ground.

[michel123456]

I have read this thread again and again

On 10/15/2020 at 5:44 PM, Markus Hanke said:

so I don’t think the problem is one of understanding.

However, all the answers from valuable members here are based on the assumption that I don't understand relativity.

On 10/15/2020 at 5:44 PM, Markus Hanke said:

Relativity really isn’t that difficult to grasp

Exactly, it is not so difficult to grasp.

Here below some new diagrams that I hope will make you think again.

The basis has been stolen from the animations of @Janus on page 9.

Find the error:

 

diag 1

E and X are at rest, B is moving. I have inserted a solid rod 1LH long in order to evade the comments like "space does not move & thus do not contract"

Since B is moving together with its rod, both are time dilated & space contracted. The rod of B is 1LH long in the frame of B (see below diag 4).

The notation 1LH(B) means 1 Light Hour from the FOR of B.

diag 2

Exactly the same diagram, with the position of 0,6LH which is the contraction of B's rod from the FOR of Earth and planet X

diag 3

Exactly the same diagram with the position of 0,6LH in the rod of B (from the FOR of E & X).  I have labeled the point as Xb, that is 0,6LH from B.

diag 4

Now the things as from the FOR of B: E and X are moving together with their rod, thus they are time dilated & length contracted.

diag 5.

Exactly the same diagram with annotated the 0,6 LH traveled by E & X.

diag 6

Exactly the same diagram with annotated the point Xb that is on the rod of B at 0.6 LH from him. X will reach this point in 45 min from the FOR of B. It is the same point Xb that is shown in diag 3.

Xa is the label for the point at the end of the rod of B

AND NOW THE QUESTION:

diag 7

Return to Earth and planet X FOR. Where is the correct contraction?

Is it along diagonal 1 or along diagonal 2?

We can check out:

Here with diagonal 1, the upper part has been stretched along the direction of movement in order to make correspond point Xb and planet X (because that is the result of calculations that say the travel of B will last 45 min in the FOR of B)

diag 8

And here below with diagonal 2.

diag 9

Which one is the correct one, where is the error?

 

Edited October 17, 2020 by michel123456

[Eise]

44 minutes ago, michel123456 said:

I have read this thread again and again

Then you should have read the multiply given advice to start with simple examples, examples where we know exactly what the outcome of experiments is. 

44 minutes ago, michel123456 said:

Here below some new diagrams that I hope will make you think again.

No, I am tired of trying to understand your depictions and arguments. 

I think you have a choice:

1. Trying to understand relativity
2. Behaving like a crackpot who is not different than any other saying 'Einstien was wrong' (intentional typo)

To 1 you should know:

• the experiments have been done, and they show relativity is correct (muons e.g...)
• relativity is the basis of understanding different phenomena, as magnetism; the colour of gold; mass-energy equivalence; Quantum Electro Dynamics; and also general relativity, because it is based on the requirement that also in gravity fields, Lorentz invariance must be locally valid; and how it is possible that we measure too many muons on the earth's surface (yes, muons again...)
• several technologies that would not work if relativity were wrong: e.g. GPS; or particles in accelerators (muons, e.g...), bringing them on speeds extremely close to the speed of light (the calculations must take relativity into account). Classical calculations would lead to errors, and we would only be able to accelerate particle to an energy of about a few Mega-electron Volt (a cyclotron that works perfectly according to classical electro magnetism fails when relativity becomes relevant); CERN's hadron collider gets at 6.5 Tera eV

When you really understand the simple examples, then it could become clear how to apply relativity to more complex examples. I am not principally declining to talk about E, X and B ever again. But I must first get convinced that you understand the simple examples.

So it is your choice. Understanding relativity, or arguing against it (which definitely is a lost case).

 

Ah, the battle of the rep-points...

sigh...

Edited October 17, 2020 by Eise

[md65536]

I don't care whether you ever learn relativity. It's still interesting to find errors in what seems like paradoxes, but you're just adding complication on top of previous errors. Why not go simpler instead of more complicated? You don't have a solid foundation to build on, but you're building anyway.

9 hours ago, michel123456 said:

diag 6

Exactly the same diagram with annotated the point Xb that is on the rod of B at 0.6 LH from him. X will reach this point in 45 min from the FOR of B. It is the same point Xb that is shown in diag 3.

I think that's wrong. How do you get that X takes 45 minutes?

If B starts at E, and the length to X is length-contracted to 0.6 LH (in B's frame), then X is already at that location (in B's frame) at B's time 0.

 

A problem when introducing rods like this is that you can't just compare both ends of a rod at a single time that applies in multiple frames. You have to consider relativity of simultaneity (the real one, not "what I'm calling RoS" etc). You could always label the events that you're describing, in the frames you're describing (so it's not just an x-coordinate like Xb, but an x and a time coordinate, and they're different in different frames).

But I still think you're wasting your time. I think you would do better trying to learn Galilean relativity.

Edited October 17, 2020 by md65536

[Markus Hanke]

19 hours ago, michel123456 said:

However, all the answers from valuable members here are based on the assumption that I don't understand relativity.

As an uninvolved and largely silent reader, I got a very different impression - that you think you understand relativity, but actually you are just shoehorning specific relativistic phenomena into a Euclidean worldview (not very successfully, I might add). You have not yet understood on a deep enough level that the world simply is not Euclidean, except as an approximation in the low-energy, low-velocity domain. I am also getting the impression that you are not prepared to even entertain the possibility that the world might not in fact be Euclidean.

19 hours ago, michel123456 said:

Find the error:

No, thank you. As stated previously, I have no wish to involve myself in this discussion. I am also able to rigorously see on the highest level, using simple linear algebra, that it is mathematically impossible to construct any kind of physical paradoxes within the axioms of SR, so I do not have any need to find errors in specific scenarios, because the very existence of such errors means that the proponent of the scenario has failed to apply the model correctly. It’s like a third grader getting his long division wrong - their getting the wrong answer doesn’t mean that long division isn’t a valid operation; it means they haven’t used it right. Relativity is just the same. And in both cases, it is best to get them to understand the bigger picture before letting them loose on specific problems.

This is what I mean by top-down approach. I’m sorry to be so blunt, but you are just wasting your time with all these specific use cases. You need to get out of your Euclidean mindset, or else none of this will ever make any sense to you.

Edited October 18, 2020 by Markus Hanke

[michel123456]

12 hours ago, md65536 said:

I don't care whether you ever learn relativity. It's still interesting to find errors in what seems like paradoxes, but you're just adding complication on top of previous errors. Why not go simpler instead of more complicated? You don't have a solid foundation to build on, but you're building anyway.

I think that's wrong. How do you get that X takes 45 minutes?

If B starts at E, and the length to X is length-contracted to 0.6 LH (in B's frame), then X is already at that location (in B's frame) at B's time 0.

 

A problem when introducing rods like this is that you can't just compare both ends of a rod at a single time that applies in multiple frames. You have to consider relativity of simultaneity (the real one, not "what I'm calling RoS" etc). You could always label the events that you're describing, in the frames you're describing (so it's not just an x-coordinate like Xb, but an x and a time coordinate, and they're different in different frames).

But I still think you're wasting your time. I think you would do better trying to learn Galilean relativity.

Think you for being constructive. I understand that some are getting tired, but for me also it is exhausting. It is so evident to me that the paradox is wrong that it blows my mind that it has been accepted and become a mainstream element of Relativity. The paradox must be wrong, not generally Relativity. One may accept that the traveler ages differently than the one ate rest, that is not an issue. But since velocity is relative, you cannot know who is at rest and who is moving (and all attempts to evade this point are BS- Bad Science). Since you don't know who is the one in motion, and who is not, the phenomena must be symmetric: what one observes is the same as the other observes , independently of Euclidian or other geometry. If you rely on the fact that geometry is not Euclidian to resolve the paradox, then you may be very intelligent but not very at the same time (like the twin younger than his sibling), another paradox.

12 hours ago, md65536 said:

22 hours ago, michel123456 said:

diag 6

Exactly the same diagram with annotated the point Xb that is on the rod of B at 0.6 LH from him. X will reach this point in 45 min from the FOR of B. It is the same point Xb that is shown in diag 3.

I think that's wrong. How do you get that X takes 45 minutes?

If B starts at E, and the length to X is length-contracted to 0.6 LH (in B's frame), then X is already at that location (in B's frame) at B's time 0.

Yes X is at that location, when moving toward B, it will take 45 min* to reach B.

*the 45 min. have been calculated by others. I disagree with this.

[joigus]

Just curious, @michel123456. Can you explain to me, so that I can see clearly that you understand, what synchronizing clocks mean? Please add some explanation of how observers (both in the same inertial frame and in different ones) synchronize their clocks.

There is a reason why Einstein took pains to define very clearly this concept both in his papers and his popular books from the start. All observers, no matter what their state of inertial motion, must agree on one event as the origin of coordinates for space and time. That way, all transformations become linear and homogeneous. As Markus says:

3 hours ago, Markus Hanke said:

I am also able to rigorously see on the highest level, using simple linear algebra, that it is mathematically impossible to construct any kind of physical paradoxes within the axioms of SR,

(My emphasis.)

Otherwise you're working with affine transformations in space-time and the discussion becomes an unwholesome indigestible mess, if not mathematically, conceptually at least. And if not for others, at least for me. Sorry for the extra work that I'm giving you. I'm following the conversation from a distance, and I need some precautions in order not to turn mad. I won't participate much, I promise.

If other users don't need this, it's OK with me. I'll try to keep up as best I can.

[Markus Hanke]

21 minutes ago, michel123456 said:

If you rely on the fact that geometry is not Euclidian to resolve the paradox, then you may be very intelligent but not very at the same time (like the twin younger than his sibling), another paradox.

Right...all the best with this, then.

[michel123456]

And here the solution.

Diagram 1 is correct:

diag 1.

From E and X, because of its relative state of motion, B is contracted and its rod is contracted too. The effect is a scale factor along the line of motion: the units of length of B look to have be scaled by a factor of 0.6, because of the 0.8c velocity.

diag 1 annotated

The diagram says that B's rod that E observes as 1 LH corresponds to 0.6 LH in the frame of E.

IOW the distance 1LH toward X (as observed in E) corresponds to 0.6 LH again in the frame of E. (and not in the frame of B)

IT DOES NOT SAY THAT THE DISTANCE IS 0.6 LH IN THE FOR OF B.

The 45 min calculated in several posts before does not correspond to anything.

In the FOR of B, the distance is still 1 LH. And to travel 1 LH, the clock on B will tick for 75 minutes.

Here below the situation from the FOR of B

diag 10

It corresponds exactly to diag 1. The labeling has been reversed (E for B). In both, the distance to travel is 1LH. And in both, the time to travel is 60min / 0.8 = 75 min.

 

 

Edited October 18, 2020 by michel123456

[Eise]

On 10/18/2020 at 10:44 AM, michel123456 said:

If you rely on the fact that geometry is not Euclidian to resolve the paradox, then you may be very intelligent but not very at the same time (like the twin younger than his sibling), another paradox.

You realise this is very insulting, don't you? Where all people here, Swanson, Janus, Joigus, MD>number here>, and me fully agree with him. Obviously you even think Markus is a liar, when he says:

On 10/18/2020 at 7:01 AM, Markus Hanke said:

I am also able to rigorously see on the highest level, using simple linear algebra, that it is mathematically impossible to construct any kind of physical paradoxes within the axioms of SR

Now I can react quickly, because your error is plainly obvious:

15 hours ago, michel123456 said:

The diagram says that B's rod that E observes as 1 LH corresponds to 0.6 LH in the frame of E.

IOW the distance 1LH toward X (as observed in E) corresponds to 0.6 LH again in the frame of E. (and not in the frame of B)

There is your error. In the frame of E-X the distance is 1 Lh.

15 hours ago, michel123456 said:

IT DOES NOT SAY THAT THE DISTANCE IS 0.6 LH IN THE FOR OF B.

So you are saying the distance E-X is not length contracted? In your third diagram, just make the projection of X on B's rod, and you see that the distance E-X is not 1Lh according to B.

So once again, this is the way to see it, all the rest is irrelevant complication from your side:

• According the FOR E-X, B's clock ticks slower. So E-X observes that B's clock only shows 45 minutes travel time when it arrives at X.
• According to B, he travels only a distance of 0.6 Lh, which costs him 45 minutes according his own clock.

So E-X and B agree: B's clock shows 45 minutes when it arrives at X (or X arrives at B...).

If we would have looked at muons, this would have been obvious. I think you want to stick to your example, because only there you think you can find a contradiction. But you are lost in the complexity of your example, wringing it with irrelevant details (e.g. a 1 Lh rod attached to B, which plays no role at all, and the rod attached to E-X, because it exactly matches a distance we already have: the distance between E and X).  

On 10/17/2020 at 11:33 AM, michel123456 said:

On 10/15/2020 at 4:44 PM, Markus Hanke said:

so I don’t think the problem is one of understanding

However, all the answers from valuable members here are based on the assumption that I don't understand relativity.

I think you understood Markus wrong. It is a not a problem of that you were not capable to understand special relativity; it is a problem of not wanting to understand.  This, and seeing your first use of full capital sentences, shows me you prefer the 'crackpot' way. I am just very disappointed about this.

Quote

Twin paradox and moving clocks

Bailey et al. (1977) measured the lifetime of positive and negative muons sent around a loop in the CERN Muon storage ring. This experiment confirmed both time dilation and the twin paradox, i.e. the hypothesis that clocks sent away and coming back to their initial position are slowed with respect to a resting clock. Other measurements of the twin paradox involve gravitational time dilation as well.

In the Hafele–Keating experiment, actual cesium-beam atomic clocks were flown around the world and the expected differences were found compared to a stationary clock.

From here.

You are arguing against empirical evidence.

 

Edited October 19, 2020 by Eise

[michel123456]

This is the world upside down.

A paradox is usually an argument that is very (very) bad for a Theory. If a new pet theory was presented here that drives into a paradox, the pet theory would be rejected immediately.

In this case, the twin paradox has become a feature of Relativity.

As if the paradox helped the Theory, instead of hurting it.

Now, some may argue that there is no paradox, because “we know who is moving and who is at rest”.

Is that correct? If B moves relative to E, or if E moves relative to B, does it matter for the equations of physics who is “really” moving? I don’t think so.

[Eise]

7 minutes ago, michel123456 said:

A paradox is usually an argument that is very (very) bad for a Theory. If a new pet theory was presented here that drives into a paradox, the pet theory would be rejected immediately.

Yes, but the twin 'paradox' isn't a paradox. It is just called that, because intuitively it feels paradoxical. But the most important insight to overcome the paradox is to see that the twin 'paradox' is not symmetrical: one of the twins changes its inertial frame, the other doesn't. And the other thing is of course that nature does not allow paradoxes: the experiments have been done, agree with the theoretical predictions, so there really is no paradox. I don't understand why you are arguing against experiments that have been done. 

It would be a paradox if the staying twin and the traveling twin would disagree about empirical facts, but they simply don't: they agree that the staying twin has become older than the traveling twin.

14 minutes ago, michel123456 said:

Now, some may argue that there is no paradox, because “we know who is moving and who is at rest”.

Nobody said something like that here. It makes no sense to ask who is moving and who isn't. But it does make sense to ask who changes its inertial frame, and who doesn't.

16 minutes ago, michel123456 said:

Is that correct? If B moves relative to E, or if E moves relative to B, does it matter for the equations of physics who is “really” moving? I don’t think so.

Indeed, that does not matter. But we can see that the interpretation of why B's clock shows only 45 minutes travel time differs between E-X and B. It is like a rotation in 3-D space: for one observer it is 'the thing at the left', for another it is 'the thing at the right'. But as long as the observers agree on what actually happens, and if they know how to transform their coordinates, there is no problem. And Lorentz transformations are like rotations, but in non-Euclidean spacetime. Where in normal Euclidean space one must exchange coordinate values between the x, y, and z axis, in Minkowski space you must also take the time axis in account. 

[Ghideon]

26 minutes ago, michel123456 said:

Now, some may argue that there is no paradox, because “we know who is moving and who is at rest”.

My version:
Now, those with knowledge about relativity will argue that there is no paradox, because we know who was accelerating and who was not.

 

[michel123456]

3 hours ago, Eise said:

3 hours ago, michel123456 said:

Now, some may argue that there is no paradox, because “we know who is moving and who is at rest”.

Nobody said something like that here. It makes no sense to ask who is moving and who isn't. But it does make sense to ask who changes its inertial frame, and who doesn't.

 

3 hours ago, Ghideon said:

My version:
Now, those with knowledge about relativity will argue that there is no paradox, because we know who was accelerating and who was not.

 

I disagree. You can set up the "paradox" without acceleration & without any change in inertial frame. IIRC it has been stated in this same thread previously.

[swansont]

8 minutes ago, michel123456 said:

I disagree. You can set up the "paradox" without acceleration & without any change in inertial frame. IIRC it has been stated in this same thread previously.

How does the traveling twin return without accelerating (which changes their frame)?

[michel123456]

6 minutes ago, swansont said:

How does the traveling twin return without accelerating (which changes their frame)?

 

 You could imagine a 3rd "twin", bypassing X in the opposite direction.

But that is not necessary, you can consider the outbound trip only, it is sufficient. If there is a temporal difference between the traveling clock & the synchronized clock on planet X, then the paradox will arise.

 

In previous examples on this thread, the concept of "bypassing" instead of "starting" is clearly used to avoid the effects of acceleration.

In such a way that all the components, Earth, planet X and traveling clock B are inertial.