#### fred2028

As we all probably know, the twin paradox states that a twin goes off in a spaceship at c and returns, aging less than the twin on Earth because he traveled at c relative to Earth. However, relative to the spaceship, Earth is travelling away from it at c also, so technically, if I were on that spaceship, I'd think I'm stationary and Earth is moving, causing me to think the twin on Earth would age less since he's travelling at c relative to the spaceship. Why does the twin in the spaceship age less nevertheless?

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#### Mentz114

Gold Member
Hi Fred2028,

No spaceship will ever be able to go at c, whatever frame of reference you're in, so let's keep its velocity (relative to the earth ) at v which will always be less than c.

The difference between the twins is that the space-ship passenger has to be accelerated by rocket motors on the outward trip and then decelerated before begining the return trip. So the situation is not symmetric, and the accelerated twin ages less.

There are many threads on this subject, just scroll down the list of previous threads.

#### Fredrik

Staff Emeritus
Gold Member
Mentz explained why they don't have to age the same, but not why it's the astronaut twin that ages less. If you want to understand the twin "paradox" fully, you first have to understand space-time diagrams and how simultaneity works in SR.

http://web.comhem.se/~u87325397/Twins.PNG [Broken]

(Why doesn't the "img" tag work here?)

I'm calling the twin on Earth "A" and the twin in the rocket "B".

Blue lines: Events that are simultaneous in the rocket's frame when it's moving away from Earth.

Red lines: Events that are simultaneous in the rocket's frame when it's moving back towards Earth.

Cyan (light blue) lines: Events that are simultaneous in Earth's frame.

Dotted lines: World lines of light rays.

Vertical line in the upper half: The world line of the position (in Earth's frame) where the rocket turns around.

Green curves in the lower half: Curves of constant -t^2+x^2. Points on the two world lines that touch the same green curve have experienced the same time since the rocket left Earth.

Green curves in the upper half: Curves of constant -(t-20)^2+(x-16)^2. Points on the two world lines that touch the same green curve have experienced the same time since the rocket turned around.

From A's point of view B is aging at 60% of A's aging rate. From B's point of view A is aging at 60% of B's aging rate. The reason this isn't a paradox is that the moment before B turns around, he's in a frame where A has aged 7.2 years, and the moment after he's turned around, he's in a frame where B has aged 32.8 years.

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#### yogi

Whether Special Relativity really explains the age difference is a subject of much debate -what is not in question is the fact that two clocks in relative motion will not accumulate the same amount of time during the same spacetime interval.

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#### yogi

Read the books by Sciama, Lederman, Born, Atkins etc etc for one view --Read the books by Wheeler, Rindler, Resnick etc for another view. Then Read the papers of Selleri, Hatch and others for a third view. If there is no debate, why so many different assertions.

Einstein himself waited 13 years before attempting to explain the time difference between relativly moving inertial frames in terms of a general relativity arguement.

#### JesseM

Read the books by Sciama, Lederman, Born, Atkins etc etc for one view --Read the books by Wheeler, Rindler, Resnick etc for another view.
Can you provide quotes from two of these that you think show differing views? In the past when I've been able to read the sources you refer to, it's seemed to me that you interpret them in overly narrow ways to create the appearance of contradiction, when there are perfectly reasonable ways of interpreting the authors' quotes such that they aren't contradicting one another...

#### yogi

Jesse - we have already been over this in several threads - recall "Space, Time and Mass" and "Confusion in basic SR" Here is quote from Atkins (Physics, Universie of Pennsylvannia ) at p 509: "The problem cannot therefore be satisfactorily discussed in terms of the special theory. It is necessary to apply the general theory."

I have already in past discussions given you citations to Born's view and direct quotes from his book. The fact that some people do not see a conflict does not mean that others do not. I don't have at this location, most of my library, so I cannot oblige you with what you asked.

If I recall it was you that changed your argument as to the reality of the time difference that i cited in Part 4 of the 1905 paper - I think you began by saying that the example involving the relative motion of one of two synced clocks brought together cant mean "a real object time difference" ...that led to a lot of posts between us, and each being convinced the other was misunderstanding what Einstein was saying.

For the purpose of my post - I really don't care what camp you are in - but there is nonetheless a disagreement as to whether SR explains the cause or simply rationalizes the result

"What counts in the end is experimental predictions.

If you set up an experiment where one twin travels at a high velocity, accelerates and turns around, and then returns to a twin that has stayed in a single inertial frame, everyone agrees that the twin who has remained inertial has the longer elapsed time.

In a similar vein, one can say with definiteness that when one compares two clocks, one on a mountain top, and another in a valley, that the clock on the mountaintop will tick appear to tick faster when compared by light signals that have a constant propagation time. One can even have two clocks start out in a valley, carry one up to the mountain (via slow clock transport), let it sit for a while, then carry it back, and one will find that the clock that remained in the valley has less elapsed time.

Now there are a number of ways to explain this all philosphically, as long as one can get to the same conclusions in the end, one can take several different philosphical positions about what is "real" and what is "not real".

So my advice is not to worry too much when the phiolsophical parts of the answers differ. Focus on some experimental results (even thought experiments) - those are what must agree."

#### JesseM

Jesse - we have already been over this in several threads - recall "Space, Time and Mass" and "Confusion in basic SR"
Yes, and I recall in Confused in basic SR that you simply ignored my request to provide quotes or even page numbers for most of the various authors you listed (see my comment in post #70 and your non-response), and in the case of a few like Rindler and Einstein you interpreted them in strange ways to make it sound like they were agreeing with you, even though I pointed out perfectly reasonable ways of interpreting their quotes in ways that would be consistent with the standard textbook perspective.
yogi said:
Here is quote from Atkins (Physics, Universie of Pennsylvannia ) at p 509: "The problem cannot therefore be satisfactorily discussed in terms of the special theory. It is necessary to apply the general theory."
Context, please. What is "the problem" he refers to? I'd guess it's something more like the problem of what laws of physics to use in the non-inertial coordinate system of the accelerating twin, not the problem of why one twin ages more in itself.
yogi said:
I have already in past discussions given you citations to Born's view and direct quotes from his book.
Are you sure? I remember Rindler and Einstein quotes, but not any from Born. Doing a search for posts by you which mention Born, the only one that provides direct quotes or page numbers appears to be post #39 from this thread, but it doesn't seem relevant to your claim that SR does not resolve the twin paradox.
yogi said:
The fact that some people do not see a conflict does not mean that others do not. I don't have at this location, most of my library, so I cannot oblige you with what you asked.
I'd be happy to wait. But if you don't have the quotes handy, how can you be so sure that they cannot be interpreted in a way that's consistent with the standard textbook perspective?
yogi said:
If I recall it was you that changed your argument as to the reality of the time difference that i cited in Part 4 of the 1905 paper - I think you began by saying that the example involving the relative motion of one of two synced clocks brought together cant mean "a real object time difference" ...that led to a lot of posts between us, and each being convinced the other was misunderstanding what Einstein was saying.
And where did I "change" that argument? I have always maintained that unless two clocks start at a common location in space, you cannot say which has objectively "elapsed more time" in any frame-independent sense when they come together. You never pointed to anything in Einstein's statements that obviously conflicted with this.
yogi said:
For the purpose of my post - I really don't care what camp you are in - but there is nonetheless a disagreement as to whether SR explains the cause or simply rationalizes the result
Physics doesn't even talk about the "cause" of anything, just provides mathematical rules for how things behave, so your statement appears meaningless to me.
yogi said:
"What counts in the end is experimental predictions.

If you set up an experiment where one twin travels at a high velocity, accelerates and turns around, and then returns to a twin that has stayed in a single inertial frame, everyone agrees that the twin who has remained inertial has the longer elapsed time.

In a similar vein, one can say with definiteness that when one compares two clocks, one on a mountain top, and another in a valley, that the clock on the mountaintop will tick appear to tick faster when compared by light signals that have a constant propagation time. One can even have two clocks start out in a valley, carry one up to the mountain (via slow clock transport), let it sit for a while, then carry it back, and one will find that the clock that remained in the valley has less elapsed time.

Now there are a number of ways to explain this all philosphically, as long as one can get to the same conclusions in the end, one can take several different philosphical positions about what is "real" and what is "not real".
I'm not sure what it even means to "explain this all philosophically". Your philosophy seems to consist of the idea that for some frame-dependent quantities (like the rate a clock is ticking at a particular moment), there is an objective truth about their "real" value, but since all frames are physically on equal footing this would have to be some sort of metaphysical position, and I don't think you'll find any physicists who say there is any good reason to believe this.

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#### Fredrik

Staff Emeritus
Gold Member
Isn't there a forum rule against repeatedly posting crackpot claims?

The claim that some of the "paradoxes" of SR can't be resolved within SR itself, but need GR, is a common misconception (even among people who are intelligent and have studied SR), but that doesn't mean it isn't absurd. Really absurd. It's right up there with "I believe there's life on all planets but perhaps not in our dimension" and "I believe that when the Maya calender ends in 2012, humans will stop living in 3 dimensions and start living in 5". (Those two claims were made in a Swedish forum about paranormal stuff).

If it had been true, just about all of mathematics would fall with it. Even the integers would have to be thrown out the window. SR is just the set $\mathbb{R}^4$ and some functions. Those functions can't introduce a contradiction into the theory, so any inconsistency would have to be present in the real numbers, but the reals are constructed from the rationals, the rationals from the integers, and the integers from the ZF axioms of set theory, so we'd have to dismiss the integers and everything else constructed from the ZF axioms.

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F

#### falc39

hehe I remember in the old physics forum, I made a post asking about the twin paradox, and I wondered why it was even a paradox, and the thread ended up being one of the top 10 most replied or something :surprised. I didn't even post after the initial post.

#### yogi

Fredrick - what gives you the right to decide who is crackpot - I suppose now I will have to hunt down Born's book and find Lederman's quote - who are you compared to these Nobel winners.

Jesse: Your last scathing criticism is not of my ideas, that was a direct quote copied from one of pervects post - gotcha

Also, jesse, to clarify, the quote from Atkins was in Chapter 25-6 entitled the Twin Paradox
I just happened to have looked up something and came across that chapter and was surprised to realize Atkins was aligned with the Lederman, Born, Sciama crowd. Here is the rest of it: "The problem cannot therefore be satisfactorily discussed in terms of the special theory. It is necessary to apply the general theory. It can then be proved that the combined effects of B's velocities and accelerations are that, when he lands back on earth, his clocks have indeed registered a shorter period of time than A's clocks"

Finally, I am not saying that it is necessary to use GR - I am not expressing a personal opinion. Einstein seemed to think something was needed by way of explanation - otherwise why would have taken the time to write the 1918 article

If Einstein considered the problem totally resolved by SR, the 1918 article is redundant.

My opinion is not in issue - all that was said is that its debated as to whether SR explains the Twin Paradox - that statement still stands - I don't care whether its resolved in the mind of any particular poster or not - it is not resolved in the minds of some real bright people

falc39 - that is almost always the case with the Clock paradox - everyone jumps in to condemn the paradox - but in different ways - so many solutions, so many authorities, very little humility

#### JesseM

Jesse: Your last scathing criticism is not of my ideas, that was a direct quote copied from one of pervects post - gotcha
Um, except that I did not actually criticize that quote in my response, except to say I wasn't sure exactly what was meant by explaining the twin paradox philosophically:
I'm not sure what it even means to "explain this all philosophically". Your philosophy seems to consist of the idea that for some frame-dependent quantities (like the rate a clock is ticking at a particular moment), there is an objective truth about their "real" value, but since all frames are physically on equal footing this would have to be some sort of metaphysical position, and I don't think you'll find any physicists who say there is any good reason to believe this.
When I said "your philosophy seems to consist of...", I was referring to statements you have made elsewhere (like your claim that when two separate clocks are brought together, one of them must have elapsed less time), not to anything in that particular quote, which said nothing about frame-dependent quantities having a "true" value.
yogi said:
Also, jesse, to clarify, the quote from Atkins was in Chapter 25-6 entitled the Twin Paradox
I don't have that book, I was asking you to provide the context of what was meant by "the problem", perhaps by quoting the entire paragraph as well as one or two preceding.
yogi said:
I just happened to have looked up something and came across that chapter and was surprised to realize Atkins was aligned with the Lederman, Born, Sciama crowd. Here is the rest of it: "The problem cannot therefore be satisfactorily discussed in terms of the special theory. It is necessary to apply the general theory. It can then be proved that the combined effects of B's velocities and accelerations are that, when he lands back on earth, his clocks have indeed registered a shorter period of time than A's clocks"
Still doesn't explain what he meant by "the problem"--you need to provide more of the text preceding "the problem cannot therefore be satisfactorily discussed..." to show the actual context. Like I suggested, he may just have been talking about the problem of what the laws of physics look like in a non-inertial frame, which doesn't conflict with the idea that the twin paradox can be satisfactorily resolved using inertial frames in SR.
yogi said:
Finally, I am not saying that it is necessary to use GR - I am not expressing a personal opinion. Einstein seemed to think something was needed by way of explanation - otherwise why would have taken the time to write the 1918 article

If Einstein considered the problem totally resolved by SR, the 1918 article is redundant.
Because the 1918 paper was not specifically about the twin paradox--the problem he wanted to resolve was probably something more like finding laws of physics such that we could say the laws were the same in all frames, not just inertial ones. It would help if you would point out what specifically in the 1918 paper you're referring to when you talk about "the problem", though.
yogi said:
My opinion is not in issue - all that was said is that its debated as to whether SR explains the Twin Paradox - that statement still stands - I don't care whether its resolved in the mind of any particular poster or not - it is not resolved in the minds of some real bright people
You have not provided any real support for the claim that any of these "bright people" think it can't be resolved in SR, just your own distorted interpretations of a few quotes taken out of context, as well as the claim that you have lots of other quotes by people like Born and Lederman and such which you refuse to actually provide.

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#### yogi

Follow-up Jesse:

From Einstein's Theory of Relativity by Max Born

At page 356: "Thus the clock paradox is due to a false application of the special theory of relativity, namely, to a case in which the methods of the general theory should be applied."

I am not going to go through the whole development - since you don't believe anything I say - buy the book and see for yourself

#### JesseM

Follow-up Jesse:

From Einstein's Theory of Relativity by Max Born

At page 356: "Thus the clock paradox is due to a false application of the special theory of relativity, namely, to a case in which the methods of the general theory should be applied."
When he refers to "a false application of the special theory of relativity", he presumably means the paradox arises from falsely assuming the time dilation formula of SR will still work in the non-inertial frame of the accelerating observer. I would of course agree that this is a false application of SR, but it doesn't mean he's saying we can't explain why one twin ages less using SR alone, he's probably just saying that if we want to understand how things look from the frame of the accelerating twin, we need to use GR.

As it happens, much of the book is available online, and looking at p. 261 confirms my assumption that Born sees no problem in resolving the twin paradox in SR by pointing out that the time dilation formula is only supposed to work in inertial frames, although he points out that you can analyze things in a non-inertial frame if you invoke GR:
But it is superficial reasoning and the error is obvious; the principle of relativity concerns only such systems as are moving uniformly and rectilinearly with respect to each other. In the form in which it has been so far developed it is not applicable to accelerated systems. But the system B is accelerated and it is not, therefore, equivalent to A. The system A is an inertial system, B is not. Later, it is true, we shall see that the general theory of relativity of Einstein also regards systems as equivalent which are accelerated with respect to each other, but in a sense which requires more detailed discussion. When dealing with this more general standpoint we shall return to the clock paradox and show that on close examination there are no difficulties in it. For in the considerations above we made the assumption that for sufficiently long journeys the short periods of acceleration exert no influence on the beating of the clocks. But this holds only when we are judging things from the inertial system A and not for the measurement of time in the accelerated system B.
Do you see anything here which denies that the time elapsed on each clock can be adequately computed from the perspective of "the inertial system A"? Again, all he's saying is that if you want to look at things from the perspective of the non-inertial system B, it's a false application of SR to use the standard time dilation equation in this system, instead you must use GR.

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#### yogi

That is the very issue - see the last two lines of the page (261) and p 355 .."when the system of reference is altered, definite gravitational fields must be introduced during the times of acceleration"

I think he is saying "we can't explain why one twin ages less using SR alone" contrary to your interpretation. I call that a debateable point - My assertion still stands.

We seem to always be interpreting words differently - for me the meaning is clear - the development of Born is based upon the need to explain the aging in terms of a pseudo gravitational field - of course, as you pointed out earlier, we don't really explain things in physics

I will get you a citation of the 1918 paper

#### JesseM

That is the very issue - see the last two lines of the page (261) and p 355 .."when the system of reference is altered, definite gravitational fields must be introduced during the times of acceleration"

I think he is saying "we can't explain why one twin ages less using SR alone" contrary to your interpretation. I call that a debateable point - My assertion still stands.
But that's the thing, he never actually says that, you're "reading between the lines" here (all he actually says is that we can't understand how things look in the non-inertial frame of the accelerating twin using SR alone, which is entirely different). I think the problem is basically this--if someone states the twin paradox by referring to twins A and B, with A moving inertially and B accelerating to turn around, and then says "each twin sees the other in motion, so each should predict that the other ages less", then there are two basic ways a physicist can respond to this:

1. "The apparent paradox comes from falsely trying to apply SR's time dilation formula to the non-inertial frame of twin B; that formula is only supposed to work in inertial frames. As long as we stick to inertial frames, we will correctly predict that B ages less than A."

2. "The apparent paradox comes from falsely trying to apply SR's time dilation formula to the non-inertial frame of twin B; that formula is only supposed to work in inertial frames. If we want to analyze things from the perspective of B's non-inertial frame, we must use GR, not SR."

You see physicists making statements of type #2, and you "read between the lines" to infer that they're saying that the twin paradox itself can not be adequately resolved by SR. But in fact there is absolutely no inconsistency between #2 and #1; someone who agrees with #2 (like me) can also agree with #1, and both would certainly be correct under the standard understanding of relativity. I'm sure everyone on this forum who agrees that SR can resolve the twin paradox would basically agree with #2 (with the caveat that some would say that a 'uniform gravitational field' on flat spacetime is not really an application of GR since there's no spacetime curvature...I'm sure everyone would at least agree that in order to analyze things from the perspective of a non-inertial frame, one must go beyond the standard algebraic equations of introductory SR like the time dilation equation $$\Delta t' = \Delta t / \sqrt{1 - v^2/c^2}$$). So it seems fairly perverse for you to interpret physicists who say things along the lines of #2 as somehow denying #1; unless you can find a mainstream physicist specifically denying that SR alone is sufficient to tell us how much each twin ages, I think this is just a case of you misinterpreting their words.

#### Fredrik

Staff Emeritus
Gold Member
he's probably just saying that if we want to understand how things look from the frame of the accelerating twin, we need to use GR.
And even that is false, at least if we define SR as the claim that space and time can be represented by Minkowski space.

But I suppose we could define a "weirdo-Minkowski" space as the set $\mathbb{R}^4$ with the standard topology and the same metric tensor as Minkowski space, but with an atlas of coordinate systems that only includes the Poincaré group transformations, instead of a maximal atlas (including all $C^\infty$-related coordinate systems). Then we can define an alternative theory, "weirdo-SR", as the claim that space and time can be represented mathematically by "weirdo-Minkowski" space.

If these authors define "SR" the way I defined "weirdo-SR", then it's technically correct to say that "SR" (really meaning "weirdo-SR") doesn't include the accelerating twin's point of view. It would however still be incorrect to say that we need GR. What we need is a version of SR that isn't crippled by its definition.

And as you (unlike Yogi) already understand, there's no actual paradox in "weirdo-SR" either. The twin "paradox" would arise from an incorrect application of that theory, exactly the same way as it arises as an incorrect application of "real" SR.

#### yogi

Born is one of the physicists that is frequetly referred to by the SR group advocates as representative of those who think the clock paradox requires GR - they read his analysis the same as I do. No tortured interpretation of the words to bring it into alignment with what you want the world to be. The issue is not whether he is right - the issue is whether he believes the clock paradox requires something more than SR. Read page 356 and see the formulations he uses to arrive at the age difference are the ones that define the time lapse between two clocks in an accelerating frame separated by L. In this case, L represents the turn around distance

#### Fredrik

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Fredrick - what gives you the right to decide who is crackpot - I suppose now I will have to hunt down Born's book and find Lederman's quote - who are you compared to these Nobel winners.
I don't care much about quotes that are out of context, but if you really have proof that these guys don't understand SR, then you should post it.

#### Fredrik

Staff Emeritus
Gold Member
The issue is not whether he is right - the issue is whether he believes the clock paradox requires something more than SR.
I doubt that Born believed this, but I suppose he could have. If he did, he either didn't understand SR fully, or was using some strange definitions. I think it's quite possible that he understood how to use the theory very well, but never really thought hard about it philosophically. Maybe he never even thought about such questions as, "what exactly does this theory say"? Hm, now that I think about it, that seems unlikely, but you never know.

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#### JesseM

Born is one of the physicists that is frequetly referred to by the SR group advocates as representative of those who think the clock paradox requires GR - they read his analysis the same as I do.
Who are these "SR group advocates"? Are they mainstream scientists themselves?
yogi said:
The issue is not whether he is right - the issue is whether he believes the clock paradox requires something more than SR. Read page 356 and see the formulations he uses to arrive at the age difference are the ones that define the time lapse between two clocks in an accelerating frame separated by L. In this case, L represents the turn around distance
But on p. 356 all he's doing is using GR to figure out what things look like from the perspective of the accelerating twin, in accordance with my statement #2:

2. "The apparent paradox comes from falsely trying to apply SR's time dilation formula to the non-inertial frame of twin B; that formula is only supposed to work in inertial frames. If we want to analyze things from the perspective of B's non-inertial frame, we must use GR, not SR."

Do you agree that this statement is entirely compatible with my statement #1? Namely:

1. "The apparent paradox comes from falsely trying to apply SR's time dilation formula to the non-inertial frame of twin B; that formula is only supposed to work in inertial frames. As long as we stick to inertial frames, we will correctly predict that B ages less than A."

If you agree these statements are compatible, then you need to show where Born says that SR is insufficient to calculate the elapsed time on both clocks, showing that he said you need GR to calculate things in the frame of the accelerating twin is insufficient.

#### Fredrik

Staff Emeritus
Gold Member
But on p. 356 all he's doing is using GR to figure out what things look like from the perspective of the accelerating twin...
I wouldn't say that he's using GR just because he's using a non-inertial coordinate system on Minkowski space. If it's Minkowski space, it's SR.

#### JesseM

I wouldn't say that he's using GR just because he's using a non-inertial coordinate system on Minkowski space. If it's Minkowski space, it's SR.
Like I said earlier, some might not call this is GR, but it is at least going beyond the usual equations of SR stated in non-tensor form (the time dilation equation can't be used in the accelerated twin's non-inertial frame, for example). The "General Relativity" explanation of the twin paradox page on John Baez's site discusses the issue of whether it should be called GR or not, I don't think there's any universally agreed-upon definition of what precisely qualifies as GR vs. SR (as evidenced by Born, who did call it GR when he analyzed things from the accelerating twin's perspective).

#### yogi

As near as I can figure, Born and the others adopted Einstein's 1918 scenerio that attempted to explain the paradox from a dynamic point of view rather than a pure kinematic solution as per SR..for example in the common explanation that is based upon the shift in the lines of simultaneity, the so called missing time is graphically apparent - but there is no physics per se. By viewing the turn around as a g force, Born, Einstein and the others that adopted the dynamic solution were able to arrive at the same time dilation from the perspective of the traveling twin -

IMO, both solutions are unsatisfying. They artifically attribute the final age difference to the abrupt change at turnaround - in actuality, the traveling twin has been losing time (relative to the fixed clocks in the earth frame) all along the outbound journey -

I will not discuss this further, as my only interest was to show that reasonable people having sound scientific backgrounds can differ about whether SR adequately explains the clock paradox

Yogi

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