Is the Twin Paradox Really a Paradox?

[Papo1111]

Thanks. This made a lot of things clear to me.

But there's one last thing that I want to check: Twins paradox is not a paradox, right?

It says that one twin goes to space at near light speed and the other stays back on Earth. Then the one in space returns like f.eg. after 30 years. The twin on Earth has aged but the one sent to space didn't age that much. This just represents time dilation. So it's not really a paradox, right?

 

[sweet springs]

Twins paradox is not a paradox, right?

Right.
One stays still in a IFR. The other does not. This imbalance explains aging difference when they meet again.

 

[Nugatory]

Thanks. This made a lot of things clear to me.

But there's one last thing that I want to check: Twins paradox is not a paradox, right?

It says that one twin goes to space at near light speed and the other stays back on Earth. Then the one in space returns like f.eg. after 30 years. The twin on Earth has aged but the one sent to space didn't age that much. This just represents time dilation. So it's not really a paradox, right?

You're right that it's not a paradox, but there is more to it than "just time dilation".

The problem with trying to explain it using time dilation is that time time dilation is symmetrical: if A and B are moving relative to one another, than A will find that B's clock is slow, but B will also find that A's clock is running slow. In the twin paradox, we have Earth twin and space twin. They're moving relative to one another, so throughout the journey the space twin finds that the Earth clock is running slow - yet when they reunite the Earth twin is older. That sure looks like a paradox.

Fortunately we have about 83 megabazillion threads explaining what's really going on and why it's not really a paradox. Try reading some of these, and also http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

Also, be sure that you understand relativity of simultaneity - google for "Einstein train simultaneity" and if it's not clear we have just as many threads about it here to help. Relativity of simultaneity is often skipped over in the popularizations you've been reading, but it's really important. If you don't understand Einstein's thought experiment about trains and simultaneity, you don't understand relativity.

 

[Papo1111]

Thank you very much. I'll be sure to look into this.

 

[Ibix]

Twins paradox is not a paradox, right?

Right.

This just represents time dilation. So it's not really a paradox, right?

The apparent paradox is in the principle of relativity. You are always entitled to regard yourself as "at rest". So the traveling twin says that the stay-at-home twin is moving and the stay-at-home twin's clock is running slow, and the stay-at-home should be younger.

The resolution is to realize that time dilation isn't the only thing going on here. There's another effect called the relativity of simultaneity that affects the traveling twin's calculations that resolves the paradox.

Strictly speaking, this isn't an example of time dilation. Time dilation only works between non-accelerating clocks and very great care is needed to work out when and for who it applies for clocks that accelerate. It's an example of a phenomenon called differential aging, which applies between clocks that start next to each other, move apart, and return, possibly with different elapsed times.

 

[vanhees71]

It's very simple algebraically, and there's indeed no paradox, even not when by the argument that "time dilation is symmetrical". That's the case for uniform motion of the two observers, which however is not the case for one twin turning around, i.e., being accelerated relative to the inertial other twin. That's most easily understood by remembering that each of the twins' "aging" is given by each of the twins proper time, which are Lorentz scalars and thus independent of any reference frame. In this way it's easy to see that the traveling, i.e., the non-inertial twin, ages less than the inertial twin.

Another good thing is to draw the Minkowski diagram for this case. You'll see that indeed due to the acceleration part of the noninertial twin's world line the inertial twin ages objectively more. A very nice didactical explanation can be found here (unfortunately there seems to be no (legal) free preprint version of this article):

https://aapt.scitation.org/doi/abs/10.1119/1.4947152

 

[Dale]

Twins paradox is not a paradox, right?

It is not a paradox in the sense of a genuine logical contradiction. It is a paradox in the sense of a result that is surprising and often causes confusion.

The confusion results from students grasping at the idea of relativistic symmetry and over-applying it.

 

[Moronium]

It is not a paradox in the sense of a genuine logical contradiction. It is a paradox in the sense of a result that is surprising and often causes confusion.

The confusion results from students grasping at the idea of relativistic symmetry and over-applying it.

What do you mean by "over-applying it," Dale?

As I understand it, the alleged paradox does not arise because the two twins age differently. There is certainly nothing paradoxical about that.

The paradox is that SR ends up providing an absolute age difference, while maintaining that time dilation is reciprocal (relative). How can a "relative" theory give an absolute answer? A preferred frame of reference is implied by the absolute age difference calculated.

 

[PeroK]

What do you mean by "over-applying it," Dale?

SR postulates that the laws of physics are the same in all inertial reference frames.

Many people overstate this as: the laws of physics are the same in all reference frames (whether inertial or not).

The traveling twin changes his or her reference frame at the turnaround point, which is where the asymmetry arises.

In fact, Newtons laws of motion only apply in inertial reference frames. You can find as many paradoxes as you like by applying Newton's laws directly in an accelerating reference frame, say.

 

[Moronium]

It's very simple algebraically, and there's indeed no paradox, even not when by the argument that "time dilation is symmetrical". That's the case for uniform motion of the two observers, which however is not the case for one twin turning around, i.e., being accelerated relative to the inertial other twin.
https://aapt.scitation.org/doi/abs/10.1119/1.4947152

The twin paradox scenario ignores the non-inertial motion involved. Its question can be posed without involving a "turnaround," and acceleration has no effect on time dilation to begin with per the so-called "clock hypothesis." In SR the "moving clock" runs slow pursuant to the equations of the LT. Since the traveling twin has the slow clock, the implication is that he is the one moving.

No problem understanding that. Since he was the one who "blasted off," he would be the one moving with respect to the Earth twin, and not vice versa. The problem in that SR maintains that all inertial frames are equivalent and "equally valid." No one can be preferred over another. Put another way, there is supposedly no way to tell which of two relatively moving clocks is the one which is "actually moving." But the "resolution" to the paradox repudiates this supposition.

 

[Moronium]

The traveling twin changes his or her reference frame at the turnaround point, which is where the asymmetry arises.

OK, but that's not the issue. No one claims the situation is symmetrical. One who didn't restrict his thinking to SR would simply say, "Of course they're not symmetrical. One is moving (relative to the other) and the other isn't. That's why they age differently." The moving clock always runs slow.

But SR, with its "reciprocal time dilation," wants to say that neither is moving, or that both are. Essentially that there is no way to ascertain which one is moving.

Under the mandate of SR, the spacetwin, while moving inertially on his journey, MUST assume that he is at absolute rest, but he isn't. That's the problelm.

 

[PeroK]

OK, but that's not the issue. No one claims the situation is symmetrical. One who didn't restrict his thinking to SR would simply say, "Of course they're not symmetrical. One is moving (relative to the other) and the other isn't. That's why they age differently." The moving clock always runs slow.

But SR, with its "reciprocal time dilation," wants to say that neither is moving, or that both are. That there is no way to ascertain which one is moving.

Under the mandate of SR, the spacetwin, while moving inertially on his journey, MUST assume that he is at absolute rest, but he isn't. That's the problelm.

He doesn't assume he is at absolute rest. He can test that he is moving inertially.

Ultimately this question goes back to the Michelson Morely experiment. The Earth orbits the Sun, so it can't be at rest all the time, and you could detect differences in the speed of light in different directions. And at different times of year.

Anyway, in effect, you are 114 years too late with your objections. A century of particle physics has been conducted on the basis of SR. Science moves on. SR is a done deal.

 

[Ibix]

What do you mean by "over-applying it," Dale?

Under the mandate of SR, the spacetwin, while moving inertially on his journey, MUST assume that he is at absolute rest, but he isn't. That's the problelm.

That's what Dale means by "over-applying it".

There is no "absolute rest". The space twin may assume he is at rest, or may assume he is moving. The analysis, carried out correctly, will come out the same either way. And the key point to realize is that the symmetric time dilation result only applies to clocks at rest in different inertial frames, and the space twin (who has to accelerate at least once) cannot treat himself as at rest in an inertial frame for the whole journey.

 

[Moronium]

He doesn't assume he is at absolute rest. SR is a done deal.

Of course he does, and he must, according to SR. That' the very definition of an inertial reference frame. When you're in one, then you must treat yourself as if you're in the Lorentizian aether frame of reference. Everything in the entire universe which is moving with respect to YOU is moving. You are not.

 

[Ibix]

That' the very definition of an inertial reference frame.

Reference, please.

 

[Moronium]

There is no "absolute rest". The space twin may assume he is at rest, or may assume he is moving.

No he may NOT "assume that he is moving." Not if he accepts SR. He MUST assume he is stationary. Without every observer contradicting every other, SR self-destructs as a theory. The Earth and space twin cannot be allowed to agree about who's moving. Once that happens, the speed of light is no longer the same in every inertial frame of reference, the LT are not reciprocal, etc. If they agree, you have effectively established a preferred frame (that of the non-moving Earth twin). But SR strictly prohibits the acknowledgment of a preferred frame.

That's why the twin paradox is paradox.

 

[Moronium]

Reference, please.

Reference? Do you dispute that, in SR, every observer in an inertial frame must presume that he is motionless? It's always the "other guy" who is moving, never him.

 

[PeroK]

Of course he does, and he must, according to SR. That' the very definition of an inertial reference frame. When you're in one, then you must treat yourself as if you're in the Lorentizian aether frame of reference. Everything in the entire universe which is moving with respect to YOU is moving. You are not.

The definition of an inertial reference frame is "one in which Newton's first law holds".

This idea in fact predates Einstein and SR. It's clear, for example, that the Earth cannot be absolutely at rest all the time. Yet, all classical physics and engineering takes the rest frame of the Earth as it's reference frame.

To be honest, you have confused "rest frame" with "absolute rest".

Every object has its own rest frame, some are inertial some are not.

 

[Moronium]

This idea in fact predates Einstein and SR. It's clear, for example, that the Earth cannot be absolutely at rest all the time. Yet, all classical physics and engineering takes the rest frame of the Earth as it's reference frame.

Yes, of course. When I said "definition of," I just meant that in SR (not classical physics) the assumption of absolute rest is built into, part and parcel of, an inertial frame of reference as far as an observer in that frame is concerned.

 

[Ibix]

No he may NOT "assume that he is moving."

If you believe that, I suggest that you go and look up the principle of relativity, and keep staring at it until the meaning sinks in.

You can analyse any experiment in any inertial frame and the laws of physics are the same. You are under no obligation to use the frame in which you are at rest. Indeed, the traveling twin cannot do so because he is not at rest in a single inertial frame for the whole experiment. Encouraging students towards this realisation is the point of this thought experiment.

With every observer contradicting every other, SR self-destructs as a theory.

You really only have two options after a claim like this:
(A) Learn SR properly
(B) Continue to be wrong

Reference? Do you dispute that, in SR, every observer in an inertial frame must presume that he is motionless? It's always the "other guy" who is moving, never him.

I want you to show me a source that says an inertial reference frame has anything to do with absolute rest. Because that claim is flat wrong. As is your last sentence - that's true of rest frames, which may or may not be inertial and which you may or may not choose to use.

 

[PeroK]

Reference? Do you dispute that, in SR, every observer in an inertial frame must presume that he is motionless? It's always the "other guy" who is moving, never him.

You can always construct a reference frame (system of coordinates) in which one object is at rest. But that says nothing about an absolute state of motion.

For example, you can model the Solar system with the Sun at rest at the centre. And, you can study astronomical navigation charts that take the surface of the at rest And use the "motion" of the stars.

But neither of these examples requires that anything is absolutely at rest.

A reference frame, really, is just a system of coordinates. And, if you keep yourself at the origin, then voila you have your rest frame!

 

[Ibix]

Yes, of course. When I said "definition of," I just meant that in SR (not classical physics) the assumption of absolute rest is built into, part and parcel of, an inertial frame of reference as far as an observer in that frame is concerned.

Again - please cite your source for this claim. It is incorrect.

 

[Moronium]

Every object has its own rest frame, some are inertial some are not.

I'm not sure what you mean by this. In SR, a non-inertial (accelerating) frame is absolute, not relative. It is not "frame dependent." Observer in both inertial and noninertial frames will see the accelerating observer as being moving, not "at rest."

 

[Moronium]

Again - please cite your source for this claim. It is incorrect.

I believe it is quite correct, and can be found in any SR textbook. But you need look no further than the lorentz transformations, as applied by SR. Tell me, when performing such a transformation, which frame is treated as having a velocity of zero, and which one is treated as moving? It is, after all the "moving" frame which has it's clocks and lengths distorted by motion, right?

 

[Ibix]

In SR, a non-inertial (accelerating) frame is absolute, not relative

This is not correct. A body's proper acceleration is invariant. This has absolutely nothing to do with a choice of reference frame, unless you insist on working in your rest frame.

 

[Ibix]

I believe it is quite correct, and can be found in any SR textbook.

Which textbook did you use?

But you need look no further than the lorentz transformations, as applied by SR. Tell, when performing such a transformation, which frame is treated as having a velocity of zero?

The one whose measurements you are transforming. That is, of course, any frame at all. So there's no "assumption of absolute rest" here.

An inertial frame can be defined by using a set of objects at rest with respect to one another. Any textbook that leaves out the "with respect to one another", as yours apparently does, is doing you an enormous disservice.

 

[Moronium]

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.

 

[Moronium]

The one whose measurements you are transforming. That is, of course, any frame at all. So there's no "assumption of absolute rest" here.

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

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

 

[Ibix]

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.

And that is why you shouldn't trust Wikipedia. It should say "Special relativity indicates that for an inertial observer, a clock that is moving relative to him will be measured to tick slower than a clock that is at rest with respect to him."

 

[Moronium]

And that is why you shouldn't trust Wikipedia. It should say "Special relativity indicates that for an inertial observer, a clock that is moving relative to him will be measured to tick slower than a clock that is at rest with respect to him."

What's the difference? I'll agree with your revison.. That's what I'm saying.

Don't forget that it is always the MOVING clock which runs slow.

 

[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."