Can the Twin Paradox be simplified?

Discussion in 'Physics & Math' started by timewarp, Nov 20, 2011.

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  1. RJBeery Natural Philosopher Valued Senior Member

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    Wow, I'd vote this entire post "+1, Insightful" if it were possible. My point is and has always been the search for truth. If I hold a view that's proven wrong then I change my view, period. It's that simple. There CANNOT be a reluctance to change one's views for the sake of ego; that concept is anti-science.

    Also (and almost as maddening): mainstream views are not correct de facto because they are mainstream. If you're unable to articulate the logic leading to WHY a particular viewpoint is mainstream, then you aren't making an argument whatsoever and you should stay the hell out of the conversation.

    Regarding velocity vs acceleration, I'm willing to continue the discussion but the short of it is this: the proponents of velocity-as-cause for unambiguous time dilation would need to produce a scenario in which it occurred sans acceleration, because we already agree we have scenarios in which unambiguous time dilation occurs sans relative velocity. The exposure of the Third Brother scenario as being ambiguous has placed the onus back on you guys from my perspective.
     
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  3. Tach Banned Banned

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    This scenario has been shown to you, repeatedly, it is the triple twin scenario.
    Likewise, Bailey's experiment disproves acceleration as a cause of differences in total elapsed proper time. Once more, this is not a problem of time dilation, you need to learn the proper terms (and how to calculate them) if you want to have a meaningful discussion.

    "Ambiguous" to whom? Not to mainstream scientists. The fact that you stubbornly refuse to accept it means nothing, just that you don't understand basic relativity.
     
    Last edited: Dec 15, 2011
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  5. RJBeery Natural Philosopher Valued Senior Member

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    Tach, as a reminder, I cannot read your posts (and I'm finding this forum a better place for it). Something that you may want to consider is that something in your nature appears to turn people against your cause. Somehow you appear to have maneuvered OnlyMe and Trippy against you, when you were all three ostensibly "defending" the mainstream view against my original proposal.

    If you're simply seeking attention, like a bored and misbehaving child, then so be it; I refuse to give you any more. However, if you're here to seek truth (or spread it, if you happen to possess some) then you may want to reevaluate your Tachtics.
     
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  7. OnlyMe Valued Senior Member

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    It has been my understanding that the intent, in setting up a stay at home observer vs a traveling observer, where the traveling observer is exposed to a constant and uniform acceleration throughout his/her journey, was to evaluate the effect of a "twin paradox" that involves no inertial frame of reference, for the traveling twin.

    The twin paradox, traditionally has been presented in three basic forms, all set up assuming the absence of the general relativistic effects of gravitational fields. The purpose was to evaluate or demonstrate hypothetically the time dilation effect of an inertial velocity relative to a stationary observer.

    1. The standard paradox does involve both periods of acceleration and periods of relativistic inertial velocities.
    2. The basic three observer alternate, excludes acceleration and explores the hypothetical under conditions where the traveling observer experiences only inertial velocities.
    3. A third version (which has not been discussed here), I believe originally presented by Einstein, involved one twin on the Earth and a second twin in an orbit around the Earth.

    Remember, all three of the above hypotheticals begin with an assumption that any affects involving gravitation are not involved.

    Some parties to the discussion of these hypotheticals over the years have maintained that acceleration is a required component and some have maintained that it is not. The later is largely responsible for the introduction of the alternates to the standard presentation of the hypothetical.

    Within this thread the subject has moved on to a new construction, consistent with the initial definition in this post, a hypothetical in which one observer travels for a period of time, under conditions that can be described as constant and uniform acceleration, ideally equivalent to the gravitational effect that the stay at home twin is subjected to.

    Most of the "debate" has been reduced, not to an examination of the goal of the hypothetical, but the construction of the new hypothetical.

    Tach did reference some of what he has described as "mainstream" proofs in opposition, but as far as I can tell from those references none were addressing the ideal intent of this construction and are therefore of little if any use in this discussion. Except as distractions. At least until the ideal case has been evaluated, in a manner consistent with its construction..., from the perspective of general relativity.

    This is a hypothetical and it is not required that it be constructed in a manner consistent with current technology. If that were the case the original standard twin paradox hypothetical would have never been introduced since at the time, spaceships were a thing of fiction, not even rising to the level of science fiction, as defined by the knowledge and experience of the time.

    Just as a side note. I watched the first landing on the moon in my family living room, my grandfather who was born in the late 1800s, watching the first steps on the moon along side my parents, my brother, sisters and myself. He did not believe it. He insisted we were all deceived and that this was a Hollywood fabrication. He never was convinced that man ever set foot on the moon. For him this event was a complete fiction and he had grown up during the time the twin paradoxes were initially being explored.

    There is another departure from the current hypothetical under discussion. It does not exclude the effect of time dilation resulting for the location of a clock within a gravitational field. It is in many ways a hypothetical that moves the paradox to a construction that is completely defined within the conditions of general relativity, rather than special relativity. Where the constant and ideally uniform gravitational time dilation, that the clock on earth, the stay at home observer relies on is defined by the clock's location within the Earth's gravitational field and the traveling observers clock is defined by the constant and uniform acceleration, defined within the hypothetical, which can also be evaluated as a general relativistic effect and Einstein's equivalence principle.

    The current construction of this hypothetical essentially moves the discussion to one that can be completely described by general relativity, discounting any special relativistic effect and time dilations derived from any inertially constant velocity.

    That does not mean that once the case defined within the context of general relativity, has been resolved within the context of general relativity, an examination of any special relativistic effects would not be in order. All it means is that basing an argument against this construction on special relativistic effects and conclusions is a distraction. Just as when evaluating the standard twin paradox, insisting that it is flawed because it ignores general relativistic effects and gravity, is out of order.

    To nail the coffin down! The original twin paradox and most of the alternate constructions, while excluding gravity and its effects, ignores the fact the the say at home twin's clock in all situations where that twin is on a planet is defined by the clock's location within the gravitational field of the planet. Few ever have an issue with this, though a few constructions have been suggested that do not involve planets. The point being that by just stipulating the absence of the effect of gravity is sufficient to dismiss, this point.

    When Trippy initially presented his construction of the current hypothetical he admitted there was at least one flaw and challenged others to identify it. What I would contend is that any flaws can be dealt with in the same manner that the gravitational time dilation on the stay at home twins clock in the standard paradox was dealt with, by stipulation of the intent of the ideal conditions of the hypothetical.

    The issue is.... How do the clock rates differ, when comparing a clock at rest in a gravitational field and one accelerating in a constant and uniform manner representing and equivalent g force?

    There may be and probably are, legitimate issues involving the construction of the hypothetical. These should be addressed in an attempt to clarify the construction, rather than refute the analysis and conclusions, that may be drawn from, the ideal construction of the hypothetical.

    This leads to at least three discussions:
    1. Clarification of the construction of this variation and how that construction can be defined such that it can be agreed that it involves only the equivalence principle, when evaluating the experience of the traveling observer and the effect of gravity when evaluating the experience of the other.
    2. What conclusion can be drawn from an examination of the ideal construction, based solely on the general relativistic interpretations. Time dilation due to the equivalence principle for the traveling twin and time dilation due to position in a gravitational field for the stay at home twin. Once that has been resolved.
    3. How does an application of any special relativistic interpretations, compare with the general relativistic case.

    At present, the discussion is being confused by an attempt to address all three at the same time.

    The way it seems to me this has been driven primarily by what appears to be Tach's inability to engage in an honest discussion, limited to the issues of a structured discussion.

    Tach, before you make any conclusions about any hypothetical it is necessisary to fully develope the hypotheical's construction. Including not just the hypothetical physical construction but the fundamental assumptions within which the discussion is to take place. This is something that seems to be a recurring problem when you enter any discussion or debate. You just don't seem willing to spend the time to fully define the problem and or the construction of the hypothetical before you jump into declaring absolute conclusions.

    Take one part of the hypothetical at a time. Reach some consensus and then address the next.

    Now, the order that I placed the significance of how the hypothetical should to be examined may not place the emphasis in the same order, as would anyone else. However, it cannot be argued that whether one prefers addressing the hypothetical from the perspective of general relativity or special relativity, it is not important to an intelectually honest discussion that the construction of the hypothetical be discussed and agreed upon prior to engaging in what conclusions can be drawn from it.
     
    Last edited: Dec 15, 2011
  8. OnlyMe Valued Senior Member

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    This is ripe! You demand proper terms or terminology and yet you insist on referring to a three observer alternate as "triple twin".

    That would be an improper use of the word twin and is not found, in any of the reputable "mainstream" references you have provided links for.
     
  9. Trippy ALEA IACTA EST Staff Member

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    I've been trying to figure out how to respond to this:
    And it occured to me that's the point of the experiment (not to contradict the EEP, btw).

    Think of it this way. We accelerate the travelling twin at 1G far away from an external gravity field, and after some arbitrary length of time, we take two snapshots at T[sub]1[/sub] and T[sub]2[/sub]. we find that over this period the travelling twin is travelling with an average velocity of 0.8c

    The EEP doesn't predict that the travelling twins frame is equivalent to the stay at home frame. It predicts that it is equivalent to a third frame in which the earth would be moving at a constant velocity of 0.8c

    Or, to put it another way - if we had a third observer moving in the same direction as the travelling twin, at a constant velocity such that they observe the travelling twin and the stay at home twin at that moment to be moving away from each other, with equal, but opposite velocities (if we consider the average velocity of the travelling twin). That third observer will judge that the two frames are identical at that time and that time only, because while both twins are in equivalent gravity fields, it is only at that time that the twins are in equivalent frames - frames moving with the same velocity relative to him.

    All of which seems to be supported by the behaviour of GPS clocks. GR predicts that at an altitude of 20,000 km (I think that's the right altitude) a stationary clock should tick faster than an identical clock on earth at a rate of 56 microseconds per day, but, we measure GPS clocks to be ticking faster than identical clocks on earth by only 38 microseconds per day. The difference between these two values of 18 microseconds per day is the time dilation caused by the fact that the GPS satelites aren't stationary relative to an earth based observer, they move, and that movement causes a time dialation of 18 microseconds per day.

    Which brings us back to my opening comment.

    That's the point of the experiment.

    The EEP predicts only that the gravitational fields are equivalent, and will have the same effect.
    So by considering the gravity experienced by the stay at home twin, and ensuring that the travelling twin is uniformly accelerated in his lab throughout the entirety of the trip, we make the effects 'caused' by the acceleration of the travelling twin the same as the effects 'caused' by the acceleration of the stay at home twin, and in doing so eliminate acceleration as the cause of any differences that may exist between the twins when the travelling twin returns to his point of departure.
     
  10. OnlyMe Valued Senior Member

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    I do not want to begin another debate involving the construction of a hypothetical, so if you are willing to stipulate to the ideal conditions and construction of Trippy's hypothetical, an answer can be derived without a lengthy debate on the practicality of the hypothetical.

    Assuming:
    • A stay at home observer, with a clock constantly located in a predefined position within a gravitational field, for our purposes assumed to be 1g and
    • A traveling twin, who is always experiencing a constant and uniform acceleration and
    • That Einstein's equivalence principle is valid and
    • We assume no other external conditions or forces acting on any of the observer's clocks...
    By application of the equivalence principle to the rate of acceleration of the traveling observer and his/her clock,
    1. If the traveling twin's rate of acceleration is greater than 1g, his/her clock will run slow compared to the stay at home observer's clock and
    2. If the traveling twin's rate of acceleration is less than 1g, his/her clock will run fast compared to the stay at home observer's clock.
     
    Last edited: Dec 15, 2011
  11. OnlyMe Valued Senior Member

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    I have puzzled over this on and off for some time. The paradox I see is that as per the equivalence principle both clocks should record time at the same rate and yet if we also apply the special relativistic effects of the traveling twin's instantaneous, or rms velocity, the two clocks should not agree.

    The GPS situation may provide some insight, but it does not involve acceleration and the equivalence principle, in any meaningful way which can be applied to this issue. At least not that have been able to see, yet.

    Part of the problem may be that the situation is not actually defined solely within the context of either SR or GR, and that I just don't know where the balance lies.
     
  12. Trippy ALEA IACTA EST Staff Member

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    The thing to keep in mind, is that by experimental design, both twins are effectivly at the bottom of the same gravity, but one of them is moving and the other is not.

    While they're in equivalent gravitational fields, they're not in equivalent reference frames, because one is boosted WRT the other.

    Think of it this way. In the standard treatment of the twin paradox, we must change the acceleration experienced by one of the twins, and that change in acceleration forms the foundation of RJBeery's objection to the two-brother scenario. RJ Beery's objection to the three brother scenario is that at some point the two travelling brothers must have been in the reference frame of the stay at home brother, and so at some point they must have been accelerated into their moving frames.

    All I'm doing is proposing a scenario where the two brothers are subjected to constant equivalent uniform acceleration, but one is stationary and the other is moving.
     
    Last edited: Dec 15, 2011
  13. CptBork Valued Senior Member

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    So... Has anyone come up with a flaw in the muon lifetime example I mentioned earlier? Does anyone care to dispute that the effects will be the same regardless of whether it's the muon source or the lab which initially accelerates?
     
  14. RealityCheck Banned Banned

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    Hi Trippy, everyone. Overnight I received an email from a friend telling me about your and others' attempts to 'tease out' the salient effective (velocity-versus-acceleration) factors in 'twins' etc. clock/timerate scenarios. The email was apparently prompted by my posting yesterday at physforum a gedanken aimed at mimicking the 'gravitational acceleration' scenario for the 'moving/accelerating' ORBITING 'twin' WITHOUT actually involving gravitational 'complications' for the 'stationary/non-accelerating CENTRAL 'twin' (which on earth would still usually experience the 'gravitational acceleration' factor which can easily be 'eliminated' as in my gedanken as proposed...and as can easily be 'compensated for' as in your own gedanken, Trippy!).

    Perhaps my own initially-simplified scenario (quoted below) will at least help remove altogether some of the variables which seem to confuse Tach? And THEN you can proceed to take into account and calculate etc each further 'complication' that arises in your and others more complicated scenarios actually involving gravitational effects on the 'central' twin 'on earth' that need to be allowed for and negated as in your own gedanken.

    Please bear in mind that my initial outline of my gedanken at physforumt was intended to initially set the scene for FURTHER posts by me there when the initial setup was 'digested' by all intended participants before going the further with discussion/evolution/analysis of my quoted gedanken there....

    Again I stress that this first post was only setting the scene for further discussion aimed at eventually finding INHERENT/EXPERIMENTAL ways of actually teasing out and distinguishing between and measuring/calculating the actual contributions of acceleration per se versus velocity/speed per se either exclusively or in proportions of either, as the case may turn out to be.

    I post this here only in the spirit of trying to add to Trippy and others' desire to discuss scientific conundrums in good faith. That is the sole reason I just now registered for the purpose of posting at sciforums.

    Cheers, good luck and good thinking (and good discussing in good faith!) everyone. If I get other emails bringing to my attention other discussions here at SciForums which may interest me, I may again visit and read (and maybe even post!) here again. I hope I haven't intruded too much with this post.

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    Last edited: Dec 15, 2011
  15. OnlyMe Valued Senior Member

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    To be honest CptBork, I can't remember the example....

    I even get confused about two posts on the same page sometimes.

    Do you remember which post (#) your introduced it in? Even a page or some thing to narrow it down from the other 550 posts?
     
  16. Tach Banned Banned

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    Yes, you are reading my posts. And I will continue to expose your anti-mainstream views for what they are.
     
  17. Trippy ALEA IACTA EST Staff Member

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    But if he dilly-dallies at the half-way mark, he is no longer subjected to a uniform acceleration.
     
  18. Trippy ALEA IACTA EST Staff Member

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    I think he means this post:

     
  19. Tach Banned Banned

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    First off, the twin problem has nothing to do with clock rate per se, it has to do with elapsed proper time, I think this might be the tenth time I explained it to you. Secondly, you got the above backwards. A simple application of gravitational time dilation shows you that. A clock accelerated at proper acceleration \(a<g\) is equivalent to a clock sitting in a gravitational well of \(a\). Compared by a common observer situated at arbitrary altitude \(h\) above the ground the frequency of such a clock is redshifted as in \(f_{oa}=f_e(1-\frac{ah}{c^2})\) while the frequency of the other clock is redshifted as \(f_{og}=f_e(1-\frac{gh}{c^2})\) where \(f_e\) is the native frequency of the ground clocks.
    1. Since \(a<g\) simple algebra says \(f_{oa}>f_{og}\), exactly backwards from your claims above.
    2. If \(a>g\) then \(f_{oa}<f_{og}\), exactly backwards from your claims above.
    Congratulations, you managed to get things completely backwards, this is what happens when you don't understand the underlying physics.
     
    Last edited: Dec 15, 2011
  20. OnlyMe Valued Senior Member

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    Tach, once more you have managed to respond to a post in a manner that is completely irrelevant to the conditions as described in the post.

    Nothing you just posted has anything to do with the conditions as defined in that post! You are taking one part out of context and addressing that from outside the hypothetical.

    Re-read, if you can the whole contex and try to keep your comments to the issues that the hypotheical was designed to highlight. I did begin with a statement setting out an ideal construction and only two issues to be compared.

    Can you read? And if so do you even atempt to understand what it is you have read?
     
  21. Tach Banned Banned

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    It is a simple exercise in basic GR. Beginner stuff. You simply got it backwards, admit your goof and move on with life.


    Actually, you are wrong but because you don't understand the physics and you cannot follow the math you simply claim that I am wrong. You have done this countless times.

    Yep, I can read, you goofed. Again. Where did you say you studied physics?
     
  22. Trippy ALEA IACTA EST Staff Member

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    Personally I infered from our previous discussions that you understood it but made a simple transposition error (you transposed the two reference frames as you were typing) and simply didn't catch the error.

    I had meant to ask if that was what you meant, but I see a Tachtical Nuke has already been used on it, and implications of ignorance have already been made.
     
  23. Tach Banned Banned

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    IF he understood, he would have admitted instead of arguing that I didn't understand even AFTER I provided him with the solution. Besides, this is not the first time he's doing this, he's done it many times before.
     
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