Is the Twin Paradox Really a Paradox?

[Ibix]

What? I didn't say there was absolute rest. I just said that SR imposes that presumption on any inertial observer.

So you said that there was an assumption of absolute rest, as I said.

As an inertial observer in SR, I can NEVER deem myself to be moving.

This is completely false. Are you seriously saying that the traveling twin cannot say "I'm moving at 0.8c for this whole journey, so I'll only age 0.6 as much as my twin"? The point is that (very important edit: if you are inertial) there is no experiment that you can do that will detect whether or not you are moving. Not that you cannot treat yourself as moving.

 

[PeroK]

Here's a quick "reference" from wiki as far as the point I am making goes. There are millions of others, no doubt:

"Special relativity indicates that, for an observer in an inertial frame of reference, a clock that is moving relative to him will be measured to tick slower than a clock that is at rest in his frame of reference."

https://en.wikipedia.org/wiki/Time_dilation

Like I said, it's always everything else in the universe that's moving, never you.

This is just a basic misunderstanding. Notice the word "relative".

Note that you don't have to study things in your reference frame. I was helping someone with a homework problem recently about a moving elevator. You could solve that problem from the rest frame of the Earth. Or, you could solvevtgat problem from the initial rest frame of the elevator. Or, you could solve that problem from the elevators accelerating reference frame (rest frame).

The first two reference frames are inertial so you can use Newton's laws. In effect, the initial velocity of the elevator had no relevance to the problem.

The third reference frame is non inertial. To study the problem in that reference you would have to modify Newton's laws and include a fictitious force.

What you're objecting to here is not SR but the concept of different rest frames, which goes back beyond Newton even to Galileo.

Think about it. I've got to go now.

 

[sweet springs]

Observer in both inertial and noninertial frames will see the accelerating observer as being moving, not "at rest."

A counterexample. Let you be a pilot of accelerating rocket. You are an accelerating observer. Your frame of reference is noninertial one and you are at rest there toghether with co-pilot sitting next to you and passengers at their backseats. They all are accelerating observers and "at rest" in their own nonineratial frames.

 

[Moronium]

So you said that there was an assumption of absolute rest, as I said.
This is completely false. Are you seriously saying that the traveling twin cannot say "I'm moving at 0.8c for this whole journey, so I'll only age 0.6 as much as my twin"? The point is that there is no experiment that you can do that will detect whether or not you are moving. Not that you cannot treat yourself as moving.

Yes, I'm seriously saying that he CANNOT say that if he conforms to the dictates of SR. Otherwise, sure.

As far as detecting your own motion, the twin paradox itself provides one method for doing that. If either twin has any doubts about who'smoving, all they need to do is see whose clock has accumulated less time when they reunite. Per SR, the slower clock will be the one that was moving, if they didn't already know.

That's the problem. SR says that "you can never tell who's moving." Not only is that objectively false, but it is refuted by SR's own examples.

 

[Moronium]

,

A counterexample. Let you be a pilot of accelerating rocket. You are an accelerating observer. Your frame of reference is noninertial one and you are at rest there toghether with co-pilot sitting next to you and passengers at their backseats. They all are accelerating observers and "at rest" in their own nonineratial frames.

I agree, Sweet. As Zeno noted centuries ago, a flying arrow never moves relative to itself. But that's not the point in the context I was making it. In SR, acceleration is treated as absolute motion, not relative motion. It is not "frame dependent."

 

[Ibix]

Yes, I'm seriously saying that he CANNOT say that if he conforms to the dictates of SR.

Seriously? It's somehow wrong? Even though it uses correct information and a correct process to get to the correct answer it's not correct?

As far as detecting your own motion, the twin paradox itself provides one method for doing that.

I should have said "as long as you are moving inertially there is no experiment that you can do that will show if you are moving or not" - apologies - typing too quickly on a small screen. The twin paradox does not violate this corrected statement. It is simply a demonstration of the fact that if you treat yourself as inertial when you are not, results that only apply for inertial observers do not work.

SR says that "you can never tell who's moving."

SR says that if you are inertial then there is no absolute sense in which you are either moving or not moving. You are free to choose whichever is convenient for your analysis.

 

[Moronium]

This is just a basic misunderstanding. Notice the word "relative".

Note that you don't have to study things in your reference frame.

How did I misunderstand the word "relative?" However you say it, you get the same result in SR. It is always the other guy, and ONLY the other who is deemed to be moving.

Of course you don't have to "study things" in your own reference frame. Not normally, anyway. But in SR you must.

This is were all the contradictions come in, no matter how much you try to deny them. Here's the basic contraction (which is why the twin paradox is a paradox).

In SR, two observers, A and B, completely agree that they are moving relative to each. However, there are other details which they don't (because SR won't allow them to) agree on, to wit:

1. A claims that he is at absolute rest and that B is the one moving. Simultaneously...

2.B claims that he is at absolute rest and that A is the one moving.

Obviously, at least one of them MUST be wrong. If they were both "at rest," then there could be no relative motion between them

As it turns out, in the twin paradox, one IS wrong, notwithstanding his denial. The spacetwin thinks he is at rest and that, therefore, his Earth twin is the one who is aging slower. But he is just flat WRONG. The Earth twin's frame is the preferred frame, because it gives the right answer.

 

[Moronium]

SR says that if you are inertial then there is no absolute sense in which you are either moving or not moving. You are free to choose whichever is convenient for your analysis.

No. The problem is that SR contradicts itself a lot. Oh, sure, it starts out by saying that all frames are equivalent and equally valid. That would seem to imply that you are free to choose any frame of reference you want to.

But SR retracts that claim as soon as you start doing calculations. You can't treat yourself as moving, however appropriate that might otherwise be. It's not allowed.

In SR, a passenger on a train is not allowed to ask the conduct "Does this train stop in Podunk?" The only proper question would be "Does Podunk stop here?"

 

[Ibix]

How did I misunderstand the word "relative?" However you say it, you get the same result in SR. It is always the other guy, and ONLY the other who is deemed to be moving.

If you define yourself to be at rest, this is trivially true. You need not define yourself as at rest, as my example of the traveling twin assessing his expected aging using the stay-at-home's frame shows.

Of course you don't have to "study things" in your own reference frame. Not normally, anyway. But in SR you must.

No you need not. The correct claim is that, in SR, an inertial observer may consider themself at rest. Or in motion if that's easier. And if you let go of that wrong claim, the rest of your objections fall away.

The spacetwin thinks he is at rest and that, therefore, his Earth twin is the one who is aging slower.

The bit after "therefore" only follows if the space twin forgets that he was not inertial for the whole flight. The point of this thought experiment is to show that forgetting that leads to incorrect conclusions. Students often forget that the reciprocal time dilation result only applies to analysis carried out in a single inertial frame, and that the traveling twin is not doing so.

 

[Ibix]

No. The problem is that SR contradicts itself a lot. Oh, sure, it starts out by saying that all frames are equivalent and equally valid.

No! It says that all inertial frames are equivalent and equally valid. The twins thought experiment shows that this does not generalise to non-inertial frames.

You can use non-inertial frames, but care is necessary.

 

[Moronium]

No! It says that all inertial frames are equivalent and equally valid. The twins thought experiment shows that this does not generalise to non-inertial frames.

You can use non-inertial frames, but care is necessary.

No! It says that all inertial frames are equivalent and equally valid. The twins thought experiment shows that this does not generalise to non-inertial frames.

You can use non-inertial frames, but care is necessary.

Yes, I agree, excuse me for not endlessly repeating the word "inertial."

But you are NOT responding to the point. The spacetwin is, ex hypothesis, traveling inertially for virtually the whole trip (the accelerations are ignored as insigificant). It is during that time that he age difference is accumulating. But during that time, he maintains (as he must) that he is NOT moving.

Is he moving? Hell yes. That exactly why he ends up younger. But SR says he can't know this. And it does NOT allow him to assume that he is moving. He must assume that he is at rest.

Think about it.

 

[sweet springs]

As far as detecting your own motion, the twin paradox itself provides one method for doing that. If either twin has any doubts about who'smoving, all they need to do is see whose clock has accumulated less time when they reunite. Per SR, the slower clock will be the one that was moving, if they didn't already know.

Who's moving is not an appropriate way to ask the question. Everybody is at rest during the journey in his own frame of reference, mostly non-inertial, as I said in the previous post. Nobody is moving in this sense. It is better to change the question, whose frame of reference where he is at rest during the journey is an inertial one.

 

[Moronium]

Who's moving is not an appropriate way to ask the question. Everybody is at rest during the journey in his own frame of reference. In this sense nobody is moving.

Of course it's "appropriate." How else would you ever apply the LT? But you're right. Supposedly everybody's moving in SR while, at the same time, nobody is moving.

There only one problem with all that. The clock retardation is absolute. Only one twin ends up younger, and only one ends up older. That's means than only one of their frames is the correct one. It's not "either" and it's not "both." The Earth twin's frame is correct. And only it is correct.

Why? Because, as between the two, one "really is" at rest, and one "really is" moving.

When they reunite, each is not younger than the other, for some damn reason.

 

[Ibix]

Yes, I agree, excuse me for not endlessly repeating the word "inertial."

All of your issues stem from your failure to put the word "inertial" in the correct places.

But you are NOT responding to the point. The spacetwin is, ex hypothesis, traveling inertially for virtually the whole trip (the accelerations are ignored as insigificant).

The time spent accelerating is very short, yes. But so what? The point isn't about the duration of the acceleration. It's about the error you make by ignoring the effects of doing half the analysis in one inertial frame and half in another.

Use the Lorentz transforms. In the outbound inertial frame, work out what time clocks on Earth show at the moment of turnaround. Then work in the inbound frame and work out what time clocks on Earth show at the moment of turnaround. You'll find that the answers are different and that the difference exactly accounts for the "missing" aging of the stay-at-home compared to the naive calculation.

During that time, he maintains (as he must) that he is NOT moving.

No! He may maintain this, but he need not. Drop this incorrect claim about SR and you'll have a lot easier time understanding what SR actually says!

Is he moving? Hell yes. That exactly why he ends up younger.

No - he ends up younger because there is less interval along his worldline. He took a shortcut, basically.

But SR says he can't know this.

No it does not. It simply says that inertial frames are equivalent. The traveling twin is not inertial, so if he makes claims about reciprocal time dilation based on the idea that he is moving inertially, he is wrong.

And it does NOT allow him to assume that he is moving. He must assume that he is at rest.

You keep claiming this - but it is wrong. He may assume that he is at rest. But in that case he must either remain inertial (and not turn around) or must use results adapted for non-inertial frames - not including the reciprocal time-dilation result that only applies to inertial frames.

 

[Orodruin]

@Moronium : Essentially every post you have made in this thread suggests that you simply do not understand the theory of special relativity to the extent that you believe that you do. Your posts seem to be predicated on fundamental misunderstandings about what SR actually states. The reciprocity of time dilation is not paradoxal in SR, but you, as most people who do not understand this, seem to miss the underlying reason for why this can be (relativity of simultaneity).

There only one problem with all that. The clock retardation is absolute. Only one twin ends up younger, and only one ends up older.

Which is perfectly well described in SR once you actually understand the relativity of simultaneity.

The Earth twin's frame is correct. And only it is correct.

This is simply wrong. You can do the computations in any frame as long as you do it correctly. The result will be the same. What you are talking about here is differential ageing, not time dilation.

Why? Because, as between the two, one "really is" at rest, and one "really is" moving.

Again, wrong. You cannot make that assertion. If this were true, you could set up an experiment to test for absolute motion. All attempts at doing just that have come back negative.

 

[Ibix]

Because, as between the two, one "really is" at rest, and one "really is" moving.

No. One is inertial for the whole journey and one is not. The one who is not makes an error if he naively applies results that assume he's inertial.

The problem is not with SR. It's with you applying a result (reciprocal time dilation) that assumes that both parties are inertial to a case where one party is not (the one who turns around).

 

[Moronium]

I can remain in inertial motion for 20 years, accelerate for one second, and then revert to inertial motion. It's not one or the other, all the time. And the one second doesn't change the prior 20 years. The spacetwin is treated as if his motion is inertial the whole time. It is a serious mistake to say that is is not inertial because he had to accelerate to achieve his crusing speed.

 

[sweet springs]

Say distance of origins of frame of reference A and B increase with time,
A is moving against B and B is moving against A reciprocally. It is a matter of mathematics not physics. A is inertial/non inertial, B is inertial/non inertial does not harm it.
Absolute motion has no meanings if you do not give a standard of absolute at rest entity for everybody to measure speed against it.

 

[Orodruin]

It is a serious mistake to say that is is not inertial because he had to accelerate to achieve his crusing speed

This is about as wrong as you can get. Stop a moment and think about what you are saying, which is in essence: "It is a serious mistake to say that he is accelerating, because he is accelerating".

Furthermore, you can treat the space twin as being at rest all of the journey if you correctly take into account the differences between the two inertial frames where he is at rest, which includes relative simultaneity. This will result in the same prediction as that of the Earth twin.

 

[Moronium]

Say distance of origins of frame of reference A and B increase with time,
A is moving against B and B is moving against A reciprocally. It is a matter of mathematics not physics. A is inertial/non inertial, B is inertial/non inertial does not harm it.
Absolute motion has no meanings if you do not give a standard of absolute at rest entity for everybody to measure speed against it.

I agree that you're talking about math, not physics.
You DO give a standard of rest, every time you calculate a lorentz transformation. YOU are at absolute rest, then.

 

[Ibix]

I can remain in motion for 20 years, accelerate for one second, and then revert to inertial motion. It's not one or the other, all the time.

Of course. What you cannot do is stitch together the two implied inertial frames without doing so carefully. Did you carry out the computation I suggested in post #44 yet?

And the one second doesn't change the prior 20 years.

If you use the inertial frame in which you were at rest, and then naively switch to the inertial frame in which you are at rest after the acceleration, you've just changed your definition of "at the same time". It doesn't affect your history, but it does affect your assessment of what time it is elsewhere - and you fail to account for this change in assessment at your peril.

The spacetwin is treated as if his motion in inertial the whole time.

You are treating him as such, yes. And you are finding paradoxes. Perhaps you should consider not treating him as such and see if the paradoxes go away? As we've been telling you for the last hour or two?

It is a serious mistake to say that is is not inertial because he had to accelerate to achieve his crusing speed.

It's a mistake to describe someone as not inertial because he's not inertial?

 

[Orodruin]

You DO give a standard of rest, every time you calculate a lorentz transformation. YOU are at absolute rest, then.

This is also not correct. The Lorentz transformation relates two inertial frames, it says absolutely nothing about absolute rest.

I don't know what your background is or who you think you are debating this with, but you should understand that you are talking with actual physicists. Some of which teach relativity at university level.

 

[Moronium]

. This will result in the same prediction as that of the Earth twin.

Having the same "prediction" is not really even the problem. This is the paradox, not the resolution to it. The fact that they do agree (which they will be forced to once they reunite and compare clocks) is the problem.

They both agree that one clock was slower, the other faster. This is tantamount to them agreeing about which one was moving, whether they predicted it, or not. As it turns out, the Earth twin did predict it accurately. But, either way, the clock difference, and hence the motion associated with it, is ABSOLUTE, not relative. It is unilateral, not reciprocal.

I can't make much sense out of the rest of your post.

 

[Ibix]

This is tantamount to them agreeing about which one was moving, whether they predicted it, or not.

No. It's tantamount to agreeing that at least one of them was not inertial for the whole time. Because that is a correct conclusion.

 

[Moronium]

This is also not correct. The Lorentz transformation relates two inertial frames, it says absolutely nothing about absolute rest.

What are you trying to say here? The obvious?

Yes, two frames are involved, one of which is deemed to be stationary, and the other moving. You're just making my point for me.

 

[Ibix]

I can't make much sense out of the rest of your post.

In that case, I suggest you look up the relativity of simultaneity. And/or carry out the calculation I suggested in post #44.

 

[Orodruin]

Having the same "prediction" is not really even the problem. This is the paradox, not the resolution to it. The fact that they do agree (which they will be forced to once they reunite and compare clocks) is the problem.

This is a lie. The classic paradox is that, failing to account for the relativity of simultaneity, you would get different predictions. That the theory actually predicts the same time difference just means that it is a consistent theory and not paradoxical at all.

You also seem to insist that there is something special about the Earth frame. There is not. You could start with the space twin going away and the Earth twin then blasting after him to catch up. If you did so the space twin would be older when they meet.

Yes, two frames are involved, one of which is deemed to be stationary, and the other moving. You're just making my point for me.

No. You are just interpreting it that way, but you are wrong. The Lorentz transformation says exactly nothing about one of the frames being "stationary". Claiming anything else is a lie.

 

[Moronium]

In that case, I suggest you look up the relativity of simultaneity. And/or carry out the calculation I suggested in post #44.

I don't have to "look it up." Nor do I have to accept that bogus notion as being determinative. It is relative simultaneity which creates all the "paradoxes" because it's ultimately inconstent. Only a presumption of absolute simultaneity, as is used in the GPS, can generate consistenly accurate predictions of time dilation

 

[Orodruin]

I can't make much sense out of the rest of your post.

Then you should probably sit down and take a deep breath, because it means that you are seriously confusing yourself in regards to SR, what it says, and what is paradoxical or not.

I don't have to "look it up." Nor do I have to accept that bogus notion as being accurate. It is relative simultaneity which creates all the "paradoxes" because it's ultimately inconstent.

No it is not ultimately inconsistent. Your insistence on this is. Do you really think something like that would have eluded physicists for over 100 years?

Only a presumption of absolute simultaneity, as is used in the GPS, can generate consistenly accurate predictions of time dilation

This is simply wrong. There is no assumption of absolute simultaneity in GPS. There is a choice of coordinates, which is definitely not the same thing. Every post you have made here has just suggested to me that you do not have the faintest idea about what you are talking about.

 

[Ibix]

Only a presumption of absolute simultaneity, as is used in the GPS

The GPS does not assume absolute simultaneity. If it did, it wouldn't have to go through the whole rigmarole of defining a master clock and specifying which frame's simultaneity convention it uses.

Nor do I have to accept that bogus notion as being accurate.

OK - you aren't required to accept anything.

I'm out of this conversation at this point. You clearly don't understand SR, and I've pointed out repeatedly what you are doing wrong (applying results from inertial frames to non-inertial frames). At this point, if you won't consider revising your ideas to see if the paradoxes go away (they do) then I can't help you.