Understand Special Relativity and Time paradox

[Dale]

Why don't you just learn the math?

1) After the twins reunite (after they've moved say about a million miles together--in terms of ct), would you say that they then are sharing the same inertial frame?

No, I wouldn't say that. I would say "they are at rest in the same frame".

2) Is the traveling twin at rest in the stay-at-home twin's rest frame?

Yes. (I assume you mean after they reunite).

3) When the traveling twin has momentarily decelerated to zero velocity in the stay-at-home (he stops at the turnaround then heads back toward home), is the traveling twin at that event momentarily at rest in the stay-at-home frame?

Yes, by definition. The term "at rest" means "zero velocity".

 

[SysAdmin]

if the OP want to change more perspective, let say that the galaxy is in pacman universe, if we exit from one side, we will enter from the other side.

From one side, the twin will see his brother nearly stay still, while from the other side, what will he see?

I think, the next photon will nearly never arrive also from both point of view, so from both side the other twin galaxy is look like nearly stay still.

 

[bobc2]

Based on my sketch below, would you say that my Minkowski diagram is a reasonable representation of the selected momentary lengths of the traveling twin's rocket as presented in the stay-at-home frame coordinates (the curves represent front and aft ends of the rocket during constant deceleration-acceleration, analyzed as hyperbolae)? From your previous responses I take it that you would agree that the lengths are the same before start of trip as compared to the momentary midpoint.

 

[zonde]

I don't see any difference between the two. They look the same to me.

Well, still learning the language

My continued, repeated, and, so far, unanswered question for those of you who insist on promoting a preferred frame--the so-called rest frame for each observer--why?

Classical laws of physics work in observer's rest frame.

 

[zonde]

Look at how much resistance is met by these people when it comes to explaining that Einstein's clock synchronization convention is arbitrary and a definition we put into nature rather than one we derive from nature.

Einstein's clock synchronization convention is not arbitrary given classical laws of physics.

 

[ghwellsjr]

My continued, repeated, and, so far, unanswered question for those of you who insist on promoting a preferred frame--the so-called rest frame for each observer--why?

Classical laws of physics work in observer's rest frame.

Only if the observer is inertial. The Stay-At-Home twin is always inertial. The traveling twin is not always inertial and especially not during the turn-around process.

 

[PAllen]

Based on my sketch below, would you say that my Minkowski diagram is a reasonable representation of the selected momentary lengths of the traveling twin's rocket as presented in the stay-at-home frame coordinates (the curves represent front and aft ends of the rocket during constant deceleration-acceleration, analyzed as hyperbolae)? From your previous responses I take it that you would agree that the lengths are the same before start of trip as compared to the momentary midpoint.

Yes, that's a perfectly good diagram in the indicated inertial frame.

Note that if you want to talk about measuring that instant length at turnaround you are talking about multiple measurements, taken in different places, using mutually at rest clocks synchronized in a particular way. This is all relatively straightforward because we can imagine these instruments to be mutually at rest long enough to accomplish synchronization and measurement of the passing rocket. Where you will run into complications is defining a corresponding process that the rocket could use.

 

[ghwellsjr]

Einstein's clock synchronization convention is not arbitrary given classical laws of physics.

Einstein thought it was arbitrary.

If it was not arbitrary, then there would be only one frame in which light propagated at c. Instead there are an infinite number of equally legitimate frames, each having a different clock synchronization based on light traveling at c in each one of them. That's why time is included in the Lorentz Transformation process.

Think about this. In a frame in which an inertial observer is moving, light does not propagate at c relative to him.

 

[PeterDonis]

Based on my sketch below, would you say that my Minkowski diagram is a reasonable representation of the selected momentary lengths of the traveling twin's rocket as presented in the stay-at-home frame coordinates (the curves represent front and aft ends of the rocket during constant deceleration-acceleration, analyzed as hyperbolae)?

I'm not sure "momentary lengths" is a good term, but I agree that the line segments you've drawn are the spacelike lines corresponding to the intersection of the rocket's "world tube" with slices of constant time in the stay-at-home twin's rest frame.

the lengths are the same before start of trip as compared to the momentary midpoint.

Only if the rocket is accelerated in a very special way. I don't want to start another long thread on Born rigid motion, but that's what's required here, and it's *not* what would be realized with an ordinary rocket with an engine at the rear. You would need thrust applied all along the length of the rocket, and in just the right proportions. Since this is a thought experiment, we can gloss over such details and assume that this is possible "in principle"; but it's worth noting that such a thing would be extremely unlikely to be realized in practice.

Also, I assume you realize that (given Born rigid motion as above) the momentary midpoint of the traveling twin's trip is the *only* one of the line segments you've drawn that will be the same length as the one before the start of the trip; the others will all be shorter.

 

[zonde]

Einstein's clock synchronization convention is not arbitrary given classical laws of physics.

Einstein thought it was arbitrary.

If it was not arbitrary, then there would be only one frame in which light propagated at c. Instead there are an infinite number of equally legitimate frames, each having a different clock synchronization based on light traveling at c in each one of them. That's why time is included in the Lorentz Transformation process.

Think about this. In a frame in which an inertial observer is moving, light does not propagate at c relative to him.

This is a mess.

Let me try it that way:
We implement Einstein's clock synchronization convention in particular inertial frame. In every frame we implement it the same way.

If you say that Einstein's clock synchronization convention is arbitrary then I can change it and try to implement it in particular inertial frame. As a result I won't get classical physical laws in that inertial frame. And I won't get one way speed of light c.

 

[ghwellsjr]

This is a mess.

Let me try it that way:
We implement Einstein's clock synchronization convention in particular inertial frame. In every frame we implement it the same way.

Yes, and every frame has a different specification of space and a different specification of time. They all use the same definition of spacetime but it instantiates to different times and distances between frames.

If you say that Einstein's clock synchronization convention is arbitrary then I can change it and try to implement it in particular inertial frame. As a result I won't get classical physical laws in that inertial frame.

You will get the same physical laws that you would get with Einstein's convention as long as you do it in a consistent way.

And I won't get one way speed of light c.

That's true. But then that's a given if you use a clock synchronization other than Einstein's.

 

[Dale]

Based on my sketch below, would you say that my Minkowski diagram is a reasonable representation of the selected momentary lengths of the traveling twin's rocket as presented in the stay-at-home frame coordinates (the curves represent front and aft ends of the rocket during constant deceleration-acceleration, analyzed as hyperbolae)? From your previous responses I take it that you would agree that the lengths are the same before start of trip as compared to the momentary midpoint.

Assuming a rigid rocket, yes. This seems irrelevant to the discussion. Nobody has objected to any of this.

 

[Dale]

Einstein's clock synchronization convention is not arbitrary given classical laws of physics.

Only if you are talking about the classical laws of physics as written in an inertial frame. Which of course excludes the traveling twins rest frame.

So this doesn't answer ghwellsjr's question about why some people want to consider that frame instead of inertial frames. In fact, it supports his point.

 

[bobc2]

Obviously this is a thought experiment with Born rigidity. We can't have a perfectly rigid rocket without infinite Young's modulus--and that would imply stress waves traveling faster than the speed of light.

Thanks for the responses. I'll get back after work (unless I can sneak in some time from my desk). I've got to get to the machine shop with some hardware before I find myself at the end of the line (my boss would not be happy).

 

[ghwellsjr]

I would rather say "how things look to observer X" is the raw data that any theory must conform to and they are what determine what invariants must be in any viable theory.

I think we're saying the same thing. The "raw data" *are* the invariants. They are things like "the Doppler shift measured by observer X for light beam L" or "the proper time experienced by observer X between events A and B on his worldline". These are things that X can observe directly, *and* they are the things that are modeled in the theory as invariant scalar quantities. That's the whole point: once you understand that "how things look to observer X" is *entirely* specified by invariants that express X's direct observables, a lot of questions are simply dissolved and it gets a lot easier to analyze scenarios.

We are saying close to the same thing but I'm trying to emphasize an important difference. I'm trying to put ourselves in the situation before Einstein's theory of Special Relativity or even before Lorentz's Ether Theory, in fact before any theory. So it would be inappropriate to say, 'The "raw data" *are* the invariants' because until we have a theory, we don't have a definition for "invariants". So back in the early pages of this thread, I never mentioned "invariants".

These people denigrate the Doppler Analysis as a mere curiosity having no real significance to them.

I agree; but what they're missing is precisely that the Doppler Analysis is *entirely* in terms of invariants--direct observables. You can do the entire analysis without ever talking about *anything* that isn't directly observed--you don't need any coordinates, you don't need any "frames", you don't need any simultaneity conventions, you don't need *any* of that. That's the point.

Yes, and I made that point back on page #2 to LastOneStanding:

Also, the twins don't need to do any calculation, they just watch their siblings age (or their clocks) and when they return, they each agree on what actually happened. We need to do some calculation to determine what they will see, but that's a different matter and it's very easy because it doesn't involve any understanding of Special Relativity or any other theory. We don't have to learn about synchronizing clocks or defining an Inertial Reference Frame or what the Lorentz Transformation is all about.

And what was his response? None, he totally ignored what I said. I didn't follow through with him because he dropped out but bobc2 picked up the ball on page 3 saying:

The attempt to replace the direct Lorentz based relativity of simultaneity with the doppler approach is just an argument based on philosophical ideas.

To which you responded by saying exactly what you more recently said:

I'm sure PAllen will respond to this too, but I have to disagree with this comment. The doppler effect is a direct observable; it's relativity of simultaneity, time dilation, length contraction, etc. that are derived concepts that can bring in "philosophical" issues. As PAllen commented in a prior post (I think it was in this thread, but there have been so many lately on this general theme that I've lost track), you can analyze a scenario like the "twin paradox" *entirely* in terms of the doppler-shifted light signals that each observer directly *observes* coming from the other; you don't *need* relativity of simultaneity, time dilation, length contraction *at all* to predict that the "traveling" twin will have aged less when the two reunite. So the doppler effect is the *last* thing that I would say is likely to bring "philosophical" baggage into a discussion about physics.

And bobc2 responded:

I totally disagree with your assessment. Relativity of simultaneity is a well defined concept in special relativity. Everyone doing special relativity understands the motivation and significance of it. The concept is a direct outcome of the Lorentz transformations. Now, the doppler approach is based on the Lorentz transformations as well, but this approach just adds on another layer of complexity--transmitting and receiving light signals.

As I said before, it is very instructive to examine what observers actually measure--this should be, and typically is (doppler approach), included in any special relativity course. By the way, in the final analysis you will discover that doppler results are derived, resulting from measurements of more fundamental quanties than normally presented as "measurements."

But, the tendency to dismiss the concept of the hyperplanes of simultaneity based directly on the Lorentz transforms (removing the results of light travel delays, etc.) is probably motivated out of a philosophical preference for dismissing concepts that do not result directly from measurement. Theoretical physicists typically do not carry that philosophy to such an extreme as to lose concepts as important as time dilation, length contraction and relativity of simultaneity.

So, I think further discussion on this just spirals into philosophical arguments having to do basically with "...what are the real 3-D worlds that various observers live in, and can evidence of them be measured?" "...and to what extent can we rely on derivations based on measurements?"

To them, something else is real.

It appears so, but I think it's because they (or at least bobc2, who has expressed this explicitly) are so worried about not being "positivists" that they end up actually giving direct observables *less* weight than abstractions. That's not what a "realist" is supposed to do. Direct observables are not infallible, certainly, and in order to make sense of them we do end up with no real choice but to believe in things we can't directly observe. But direct observables are where you start from: without those there is nothing to explain and nothing to anchor anything else to.

Whatever the reason, bobc2 does not realize that it is possible to answer the OP's question about the twin's relative aging without resorting to any analysis from any theory such as SR. That's what I'm trying to get him and others to see. That's what I did in post #7. [NOTE: As I mentioned earlier, I made a mistake at the end of that post, my simplification of the formula is incorrect.]

And I'm also trying to get him to see that the "raw data" will be presented correctly in any viable theory that you want to use to analyze the twin situation. Both LET and SR will do this. I've asked him to include the "raw data" in any analysis that he does but, again, he dismisses it as an uninteresting observation. He always wants to focus on what he considers to be other interesting observations which are frame dependent.

And now he's going off in yet another attempt to fortify his defense of those interesting observations but do you think he will include the "raw data"? Do you think he will show how each twin will continue to see exactly what they see in any IRF? Do you think he will show how the light signals sent once a year by each twin will propagate and arrive at the other twin just as they do in the Stay-At-Home twin's rest IRF or any other IRF? This was a further request from the OP in post #13 and which I provided the answer to the OP's satisfaction in post #23 but bobc2 took this thread in an entirely different direction in post #32 and here we are hundreds of posts later all dealing with his sidetrack that has nothing whatsoever to do with the OP's issues and to which the OP has not shown any interest.

Can we please hit the nail on the head and state clearly that "how things look to observer X" is the reality to which Special Relativity must conform?

Again, I think we're saying the same thing. See above.

I know we agree. But it's not getting through to some others.

Maybe it would be helpful if you would actually do your own version of presenting how the "raw data" answers the OP's questions without invoking SR and without alluding to "invariants".

 

[PeterDonis]

I'm trying to put ourselves in the situation before Einstein's theory of Special Relativity or even before Lorentz's Ether Theory, in fact before any theory. So it would be inappropriate to say, 'The "raw data" *are* the invariants' because until we have a theory, we don't have a definition for "invariants".

Ah, ok. Yes, if you're taking this perspective, then instead of saying "the raw data are the invariants", you would say "the invariants are the raw data". The raw data are logically prior; we know them first, before we have a physical theory that models them. I agree with that.

it is possible to answer the OP's question about the twin's relative aging without resorting to any analysis from any theory such as SR.

I'm not sure that's true. You can certainly state all of the observed data during the experiment (the observed Doppler shifts and the respective clock readings after the twins meet up again), after the experiment has been run, without resorting to theory; but how would you predict the result, *before* the experiment has been run, without resorting to theory? That's really the question the OP was asking. See further comments below.

Maybe it would be helpful if you would actually do your own version of presenting how the "raw data" answers the OP's questions without invoking SR and without alluding to "invariants".

As I said above, I don't think this can be done, because answering the OP's question requires predicting what will be observed during the experiment, before the experiment has been run. I don't think that can be done without a theory.

However, I would agree that the theory that's required is not the full "machinery" of SR. All you need is a theory of how the observed Doppler shift during the experiment relates to the observed difference in clock times at the end. That's a pretty simple theory, yes, but it's still a theory: you still need, at a minimum, to deny Newtonian "absolute time" so that you can even admit the possibility of a difference in observed clock times between the twins at the end.

 

[ghwellsjr]

Ah, ok. Yes, if you're taking this perspective, then instead of saying "the raw data are the invariants", you would say "the invariants are the raw data". The raw data are logically prior; we know them first, before we have a physical theory that models them. I agree with that.

Good, I'm glad I was finally able to express myself in a way that made sense to you.

it is possible to answer the OP's question about the twin's relative aging without resorting to any analysis from any theory such as SR.

I'm not sure that's true. You can certainly state all of the observed data during the experiment (the observed Doppler shifts and the respective clock readings after the twins meet up again), after the experiment has been run, without resorting to theory; but how would you predict the result, *before* the experiment has been run, without resorting to theory? That's really the question the OP was asking. See further comments below.

As I said above, I don't think this can be done, because answering the OP's question requires predicting what will be observed during the experiment, before the experiment has been run. I don't think that can be done without a theory.

Let's look carefully at what the OP's question was:

I'm studying special relativity and I can't understand the following.

Let's imagine me and my twin brother making the following experiment: I stay in Earth and my brother travels in a spaceship with velocity 0.5c. For moving referentials the time passes more slowly, but for the first principle of special relativity, the Physics laws are the same for any inertial referential. So for me, my brother are in slow motion (I became older). But for my brother, he became older. When he arrives here, who will be older?

Note that he was not asking a question about the Theory of Special Relativity. He was asking a question about the Principle of Relativity, Einstein's first postulate. They're not the same thing. The PoR is based on observable raw data that among other things concludes that things will be reciprocal between two inertial observers and so the OP was wondering how from the PoR you could determine which of the two observers would be older when they both conclude that the other one is aging more slowly. Note that he specified his brother would travel at a constant speed.

So I introduced him to Bondi's brilliant analysis which only requires one additional piece of "raw data", that the propagation of light is independent of the speed of the source--a fact that has been observed experimentally. This fact is also specifically stated as part of Einstein's second postulate, but it is not enough to establish Einstein's Theory of Special Relativity. It is also a fact that is in agreement with Lorentz's Ether Theory, by the way.

And so from these experimentally based observations, Bondi concludes that the rates at which the traveling brother sees the Stay-At-Home brother's clock ticking between coming and going at the same speed are reciprocals of each other and from this it is easy to conclude that the traveling brother can predict ahead of time that he will see his brother's clock accumulate more time than his own during the trip. See post #7.

However, I would agree that the theory that's required is not the full "machinery" of SR. All you need is a theory of how the observed Doppler shift during the experiment relates to the observed difference in clock times at the end. That's a pretty simple theory, yes, but it's still a theory:

I agree that if you want to establish the formula for calculating the Doppler Factor based on the speed, then you need a simple theory but that's not what I did to answer the OP's first question. I specifically avoided making the connection between speed (or distance or time) and Doppler Factor--I didn't even mention Doppler--that came up by LastOneStanding.

you still need, at a minimum, to deny Newtonian "absolute time" so that you can even admit the possibility of a difference in observed clock times between the twins at the end.

I'm not sure you have to deny absolute time, you just have to deny that clocks keep track of absolute time which is what Lorentz did.

Anyway, I got the impression from your statement that you knew a way to go further with Bondi's analysis without establishing a theory so I'm glad for the clarification. And thanks for your continued feedback.

 

[PeterDonis]

Note that he specified his brother would travel at a constant speed.

But he also implicitly specified that his brother turns around--otherwise he wouldn't come back to Earth. What piece of observable data corresponds to the turnaround? The shift from Doppler redshift to Doppler blueshift.

So I introduced him to Bondi's brilliant analysis which only requires one additional piece of "raw data", that the propagation of light is independent of the speed of the source--a fact that has been observed experimentally.

Bondi's analysis, as you present it, also includes the observation I stated above. Perhaps he didn't use the word "Doppler", but if we want to talk about each twin "seeing" the other's clock "run slower", the only piece of raw data that that can correspond to is the observed Doppler shift--or equivalently the observed "tick rate" of light signals emitted by each twin, as received by the other twin. Each twin does not see, as raw data, the other twin's "adjusted" clock rate; he only sees the Doppler-shifted raw data itself. See further comments below.

And so from these experimentally based observations, Bondi concludes that the rates at which the traveling brother sees the Stay-At-Home brother's clock ticking between coming and going at the same speed are reciprocals of each other and from this it is easy to conclude that the traveling brother can predict ahead of time that he will see his brother's clock accumulate more time than his own during the trip. See post #7.

The problem with this as it stands is that the stay-at-home twin also sees two reciprocal "clock rates": he sees the traveling twin's clock ticking slower than his outbound and faster than his inbound, and the two rates are reciprocals of each other. In fact they are exactly the *same* rates as the traveling twin sees. So just this observation alone isn't sufficient to account for the different elapsed times.

The difference, as the Usenet Physics FAQ page on the Doppler Shift Analysis makes clear, is *when* each twin sees the change from slower to faster ticking of the other's clock. The traveling twin sees it when he turns around, halfway through the trip; the stay-at-home twin sees it only when the light signals emitted by the traveling twin at the turnaround reach him--i.e., much *later* than halfway through the trip.

*That* is the key asymmetry, the *observable* asymmetry, between the two twins. Your analysis in post #7 was fine as far as it went; it explains how the traveling twin can predict that the stay-at-home twin's clock reading will be greater than his. But it does *not* explain why the stay-at-home twin can't apply exactly the same reasoning. That requires including the observed asymmetry I just described in the analysis: this shows that the stay-at-home twin *does* apply the same reasoning, but he applies it to different observed data (observed change from redshift to blueshift is towards the end of the trip vs. halfway through). If you do the same calculation you described in post #7 for the stay-at-home twin, averaging the two reciprocal clock rates but with the correct weighting for the relative times (your formula assumed 50-50 weighting, but that's only valid for the traveling twin--for the stay-at-home twin the slower tick rate is weighted much more than the faster tick rate), you will get the stay-at-home twin's (correct) prediction that the traveling twin will have aged less when they meet.

I'm not sure you have to deny absolute time, you just have to deny that clocks keep track of absolute time which is what Lorentz did.

True, this is really what I meant by denying absolute time. Newton's version of absolute time required that all clocks track it.

Anyway, I got the impression from your statement that you knew a way to go further with Bondi's analysis without establishing a theory

I don't know if Bondi included the additional observable I described above (when during the trip each twin observes the turnaround). If he didn't, then what I said above does go further than his analysis.

And thanks for your continued feedback.

You're welcome!

 

[BruceW]

explaining the twin problem by the light signals that are sent between the twins is an interesting way to do it. Once we define electromagnetism as a 'law' of physics, then say that the laws of physics are the same in all reference frames, then we have effectively only used the principle of relativity. (after all, this is how Einstein first came up with his relativity). I don't really understand what ghwellsjr meant by saying that the principle of relativity and the theory of special relativity are different things... I had always thought of them as synonymous.

Edit: well, maybe special relativity is a subset of the principle of relativity, because I would think that the theory general relativity is also a part of the principle of relativity.

Another edit: "principle of relativity" could be used in a different context, too. For example, there is also Galileo's relativity, so you could also use Galileo's relativity to explain the twin problem. You could get the correct answers, but the laws of electromagnetism would be horribly complicated, compared to the laws of electromagnetism in Einstein's relativity.

 

[Austin0]

First to clarify:
I am not interested in determining simultaneity only in coordinate synchronization. Nor am I advocating the MCIF implmentation as a preferrable convention.
As stated, my sole ain is to gain a picrure of a chart generated with that convention to compare with the anomalous behavior in the area under discussion.

Quote by Austin0 View Post

Given an extended coordinate frame (v -->+x) of conventionally synched clocks with a range from x= -100 to x=100 with the Traveler at x=0 and the center of resynchronization.
...
In this case if vx' is less than dT =20 the -x clocks continue to increment forward. At x=-200 they would remain at the same value and beyond that would actually be decrementing back from previous time.
...
Hopefully you will agree that such a chart would be without gap or overlap throughout the defined domain?

I do agree if by "defined domain" you specifically mean x=-100 to x=100. It appears that you are applying the usual MCIRF synchronization convention that bobc2 is using, but over a limited spatial domain. That is the correct way to do it. Once you try to extend it into a region with an overlap then you have problems. You are avoiding those problems by limiting the domain, which is a perfectly legitimate thing to do, assuming I understood you correctly.

Well at least we seem to have some agreement ;-)
But I suspect you are viewing what I am describing through an a priori assumption that the limited domain i am describing must fall inside the problematic area where intersection and divergence occurs in the standard diagram. not really analyzing the implications of what I am outlining. in the case under discussion per bobc2's diagrams the bad patch occurs in the positive x sector.

In the chart i am outlining the limit to valid coordinate assignment , the point where coordinates overlap and have redundant assignments occurs in the negative x sector.

In the positive x direction they can be extended indefinitely until reaching the actual limit of the Rindler Horizon , which I think we agree lies outside the range of the intersection and divergence we are talking about.

So ,yes i am proposing that such a chart would cover the problem sector without internal problem whatsoever.
With no anomalous events or temporal ambiguities. It appears to me that a complete chart constructed in the manner I outlined before

T₀
x=-100,t₀ and x=100, t₀

T₁=T₀+20..
x=-100,t₁=t₀+10,,,x=100,t₁=t₀+30

T₂=T₀+40
x=-100,t₂=t₀+20 ,,,x=100,t₂=t₀+60

could not possibly contain any such artifacts. From this I infer that such artifacts could only come from the Minkowski graphing of such a frame and is not inherent in the use of the convention as the basis of an accelerated chart..

So if you see flaws in my thinking please let me know.

 

[ghwellsjr]

But he also implicitly specified that his brother turns around--otherwise he wouldn't come back to Earth. What piece of observable data corresponds to the turnaround? The shift from Doppler redshift to Doppler blueshift.

Bondi's analysis, as you present it, also includes the observation I stated above. Perhaps he didn't use the word "Doppler", but if we want to talk about each twin "seeing" the other's clock "run slower", the only piece of raw data that that can correspond to is the observed Doppler shift--or equivalently the observed "tick rate" of light signals emitted by each twin, as received by the other twin. Each twin does not see, as raw data, the other twin's "adjusted" clock rate; he only sees the Doppler-shifted raw data itself. See further comments below.

Whether the OP was referring to Doppler or Time Dilation, his question was targeting the issue of how can the Principle of Relativity which implies symmetry result in an asymmetry between the observers. Of course, since the OP is inertial and his brother is not, the scenario is not symmetrical and that was what DaleSpam pointed out in post #2 where he also gave the answer to the OP's question (who will be older?) but he didn't explain why or how that could be determined. So that's what I did in post #7.

The problem with this as it stands is that the stay-at-home twin also sees two reciprocal "clock rates": he sees the traveling twin's clock ticking slower than his outbound and faster than his inbound, and the two rates are reciprocals of each other. In fact they are exactly the *same* rates as the traveling twin sees. So just this observation alone isn't sufficient to account for the different elapsed times.

You are providing a good explanation for much more than the OP asked. He just wanted to know which one would be older and for that, you only have to examine one of the observers and that's what I did (for his brother).

The difference, as the Usenet Physics FAQ page on the Doppler Shift Analysis makes clear, is *when* each twin sees the change from slower to faster ticking of the other's clock. The traveling twin sees it when he turns around, halfway through the trip; the stay-at-home twin sees it only when the light signals emitted by the traveling twin at the turnaround reach him--i.e., much *later* than halfway through the trip.

*That* is the key asymmetry, the *observable* asymmetry, between the two twins. Your analysis in post #7 was fine as far as it went; it explains how the traveling twin can predict that the stay-at-home twin's clock reading will be greater than his. But it does *not* explain why the stay-at-home twin can't apply exactly the same reasoning. That requires including the observed asymmetry I just described in the analysis: this shows that the stay-at-home twin *does* apply the same reasoning, but he applies it to different observed data (observed change from redshift to blueshift is towards the end of the trip vs. halfway through). If you do the same calculation you described in post #7 for the stay-at-home twin, averaging the two reciprocal clock rates but with the correct weighting for the relative times (your formula assumed 50-50 weighting, but that's only valid for the traveling twin--for the stay-at-home twin the slower tick rate is weighted much more than the faster tick rate), you will get the stay-at-home twin's (correct) prediction that the traveling twin will have aged less when they meet.

All very true, but, like you said, in post #7, I only went as far as I had to in order to answer the OP's question. But I did provide these other details in post #23 where I presented the spacetime diagrams to illustrate the different Inertial Reference Frames and to explain in great detail how the identical Doppler shifts apply differently to the two observers.

...
I don't know if Bondi included the additional observable I described above (when during the trip each twin observes the turnaround). If he didn't, then what I said above does go further than his analysis.

Bondi does go further but he doesn't do it immediately for a twin scenario. He does it for three inertial observers and he states the formula that I mentioned at the end of post #7. I find his book very difficult to read because he is goes into a lot of detail and he repeats himself. In any case, my only interest in his book was his brilliant scheme to identify the Doppler ratios as being reciprocal and the idea of averaging them to determine that the inertial observer would be older than the traveler.

 

[ghwellsjr]

explaining the twin problem by the light signals that are sent between the twins is an interesting way to do it. Once we define electromagnetism as a 'law' of physics, then say that the laws of physics are the same in all reference frames, then we have effectively only used the principle of relativity. (after all, this is how Einstein first came up with his relativity). I don't really understand what ghwellsjr meant by saying that the principle of relativity and the theory of special relativity are different things... I had always thought of them as synonymous.

Einstein based his Theory of Special Relativity on two principles, the first being the Principle of Relativity and the second being that all light propagates at c. Look at section 2 of his 1905 paper introducing SR.

Edit: well, maybe special relativity is a subset of the principle of relativity, because I would think that the theory general relativity is also a part of the principle of relativity.

No, it's the other way around, the PoR is a subset of SR. SR encompasses more than the PoR, namely that second principle. And SR is a subset of GR.

Another edit: "principle of relativity" could be used in a different context, too. For example, there is also Galileo's relativity, so you could also use Galileo's relativity to explain the twin problem. You could get the correct answers, but the laws of electromagnetism would be horribly complicated, compared to the laws of electromagnetism in Einstein's relativity.

As Einstein mentions in the second paragraph of his introduction, he is extending Galileo's PoR for mechanics to include electromagnetism. But I don't know how you could explain the twin problem with just the PoR applied to mechanics.

 

[Mentz114]

Something I absolutely cannot understand is this fascination with the twins paradox. It's been analysed in such detail so often, one would think there was some magic new physics in there just waiting to be discovered. There is no gold mine. The twins paradox happens because clocks show a time that is dependent on their worldlines, not universal Newtonian time. And SR gives us the means to calculate this for a given worldline.

Can anyone tell me what this detailed burrowing is hoping to achieve.

I don't mean to be critical, but I don't remember going through this phase when I first encountered relativity ( not for long, in any case) so what am I missing ?

 

[PeterDonis]

I did provide these other details in post #23

Yes, I see you did. Another thread that has gone too long...

 

[PAllen]

As Einstein mentions in the second paragraph of his introduction, he is extending Galileo's PoR for mechanics to include electromagnetism. But I don't know how you could explain the twin problem with just the PoR applied to mechanics.

I'm almost done with a blog entry on a topic related to this. What I come up with is that the one minimal approach is that you need to assume there is some form of signal (e.g sound) whose speed is independent of emitter's speed; and also that Doppler for this type of signal is symmetric: if A and B moving inertially relative to each other, each sees the same Doppler factor (this is not true for sound). Given the existence of a signal type with these properties, differential aging can be deduced. Nothing else is needed. (To get an explicit formula for differential aging, you do need more; but what I stated is all you need to show there must be differential aging).

 

[BruceW]

The twins paradox happens because clocks show a time that is dependent on their worldlines, not universal Newtonian time.
...
I don't mean to be critical, but I don't remember going through this phase when I first encountered relativity ( not for long, in any case) so what am I missing ?

I think it is because integrating the proper time along a worldline is left until later on in a course on SR. Therefore, we will get students that are partway through their course asking about the twin paradox.

 

[BruceW]

No, it's the other way around, the PoR is a subset of SR. SR encompasses more than the PoR, namely that second principle. And SR is a subset of GR.

I would say the principle of relativity is a more general concept that could potentially be used in other theories than just in SR and GR. But I guess it doesn't matter, because I can't think of any other examples right now.

As Einstein mentions in the second paragraph of his introduction, he is extending Galileo's PoR for mechanics to include electromagnetism. But I don't know how you could explain the twin problem with just the PoR applied to mechanics.

I wouldn't use the PoR applied to mechanics. I would not use mechanics at all. I meant that you could use Galilean relativity (i.e. simultaneity being absolute, and additive velocities), with a slightly weird kind of electromagnetism, which incorporates the movement of a 'luminiferous ether'. (And in fact, this is what they did before Einstein's theory). Of course, this gives the same predictions as Einstein's relativity, and since physics is simpler in Einstein's relativity, we use Einstein's relativity instead of Galilean relativity.

By 'same predictions', I mean for electromagnetic phenomena. Using Galilean relativity will give incorrect results for mechanics when velocities are near the speed of light. They never noticed this before Einstein came up with his relativity, because such velocities are rare on human scale.

 

[ghwellsjr]

I would say the principle of relativity is a more general concept that could potentially be used in other theories than just in SR and GR. But I guess it doesn't matter, because I can't think of any other examples right now.

Just because PoR is a subset of SR doesn't mean it can't be used in other theories. I can think of one, Lorentz Ether Theory, which denies Einstein's second principle and instead assumes that light propagates at c only in the ether rest frame.

But I can see how saying that PoR is a subset of SR might be confusing, but I was just bouncing off your terminology. The important thing is that they are different and it's Einstein's arbitrary second principle that is added to PoR to make SR. That sounds to me like PoR is a subset of SR, but if it's still confusing, don't use the term "subset".

I wouldn't use the PoR applied to mechanics. I would not use mechanics at all. I meant that you could use Galilean relativity (i.e. simultaneity being absolute, and additive velocities), with a slightly weird kind of electromagnetism, which incorporates the movement of a 'luminiferous ether'. (And in fact, this is what they did before Einstein's theory). Of course, this gives the same predictions as Einstein's relativity, and since physics is simpler in Einstein's relativity, we use Einstein's relativity instead of Galilean relativity.

I wouldn't use mechanics at all either, in fact, I don't even know how you would. But I think the real distinction is between Galilean Transforms and Lorentzian Transforms, the former being an incorrect basis for relativity while the later is correct as a basis for relativity but not exclusive to Einsteinian relativity. Otherwise, I agree with your statements.

By 'same predictions', I mean for electromagnetic phenomena. Using Galilean relativity will give incorrect results for mechanics when velocities are near the speed of light. They never noticed this before Einstein came up with his relativity, because such velocities are rare on human scale.

That is also a good point.

 

[Dale]

From this I infer that such artifacts could only come from the Minkowski graphing of such a frame and is not inherent in the use of the convention as the basis of an accelerated chart..

So if you see flaws in my thinking please let me know.

I will have to look in detail at your mapping. It would have been helpful if you could actually write down the equation for transforming coordinates.

However, if you do not get overlap in the region where the graphing shows the overlap then I guarantee that you are not using the momentarily co-moving reference frame notion of simultaneity. There is nothing wrong with that, but it is a different simultaneity convention and doesn't have any bearing on the Minkowski diagrams that bobc2 has presented.

In other words, bobc2's drawings are correct and accurately reflect the inherent problem in the "MCIRF convention". His problem is that he refuses to recognize that as a problem and exclude that region from coverage (as you seem correctly willing to do).

 

[BruceW]

But I can see how saying that PoR is a subset of SR might be confusing, but I was just bouncing off your terminology. The important thing is that they are different and it's Einstein's arbitrary second principle that is added to PoR to make SR. That sounds to me like PoR is a subset of SR, but if it's still confusing, don't use the term "subset".

Yeah, that was my bad, really.

I wouldn't use mechanics at all either, in fact, I don't even know how you would. But I think the real distinction is between Galilean Transforms and Lorentzian Transforms, the former being an incorrect basis for relativity while the later is correct as a basis for relativity but not exclusive to Einsteinian relativity. Otherwise, I agree with your statements.

hmm. I think the idea was that EM phenomena was dependent on velocity relative to the ether. These dependencies were Lorentzian transforms, but it was assumed that these transforms had nothing to do with transforms of true time and space, they were only thought of as part of the theory of EM. So in this way, time and space were assumed Galilean, while EM phenomena had this Lorentzian transform property. So the explanation of light signals being sent between the twins could be explained by Galilean relativity, using this weird form of EM equations. But what does this mean for the ageing of the twins? It depends on what you assume is the mechanism for the ageing process, and if it also is affected by travel through the ether.