Twin paradox

  1. 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?
  2. jcsd
  3. Mentz114

    Mentz114 4,112
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    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.
  4. Fredrik

    Fredrik 10,170
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    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.

    This diagram explains everything that's relevant about the twin paradox:


    (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.
    Last edited: Jan 18, 2008
  5. 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.
  6. Fredrik

    Fredrik 10,170
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    That's not true at all. There's no debate about this.
  7. 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.
  8. JesseM

    JesseM 8,491
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    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...
  9. 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."
  10. JesseM

    JesseM 8,491
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    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.
    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.
    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.
    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?
    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.
    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.
    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.
    Last edited: Jan 20, 2008
  11. Fredrik

    Fredrik 10,170
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    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 [itex]\mathbb{R}^4[/itex] 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.
    Last edited: Jan 20, 2008
  12. 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.
  13. 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
  14. JesseM

    JesseM 8,491
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    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:
    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.
    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.
    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.
    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.
    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.
    Last edited: Jan 21, 2008
  15. 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
  16. JesseM

    JesseM 8,491
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    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:
    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.
    Last edited: Jan 21, 2008
  17. 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
  18. JesseM

    JesseM 8,491
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    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 [tex]\Delta t' = \Delta t / \sqrt{1 - v^2/c^2}[/tex]). 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.
  19. Fredrik

    Fredrik 10,170
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    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 [itex]\mathbb{R}^4[/itex] 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 [itex]C^\infty[/itex]-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.
  20. 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
  21. Fredrik

    Fredrik 10,170
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    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.
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