Can the Twin Paradox be simplified?

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

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  1. OnlyMe Valued Senior Member

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    Boy Tach, I take a little time to watch a movie what do I find when I get back? For two whole pages you have posted nothing on topic or even worth quoting for a response.

    And you still have avoided not only RealityCheck's questions/challenge, you still haven't answered my question.., or is it questions either.

    If someone can walk in cold like this and get the kind of impression of you that RealityCheck has, you have to stop and think. Or maybe not.

    At some point you just have to step up and actually offer an explanation of what ever your position might be.

    Well it is time for me to call it also, so later....
     
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  3. prometheus viva voce! Moderator

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    Tach: 7 day ban (due to active warnings and infractions)
     
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  5. CptBork Robbing the Shalebridge Cradle Valued Senior Member

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    That's one way to do it. However, you don't have to smash protons to make muons; you can produce them in a vast number of different types of particle collisions as long as there's plenty of energy involved, and you can set experiments up to produce a nice, clean beam of muons moving within a narrow velocity range. After a muon is produced it can also be accelerated by EM fields just like any other charged particle in an accelerator. In fact, dedicated muon colliders are in development right now for certain experiments.

    I should make note of one important QM implication I didn't mention before. We don't have to track a muon from the moment of its creation until decay. Once you start tracking a muon, regardless of where it originally came from or how it got up to speed, the probability of it decaying over a given time period is the same regardless of its past history, so rather than tracking a muon from creation until decay you can track its lifetime after it triggers a clock by some fixed, consistent criteria. The only independent control variable is the velocity of the muons when they trigger the lab's tracking systems.

    Yet the results don't depend on how the lab frame accelerates as the Earth spins, how it shifts velocity as it orbits around the sun, and the sun orbits around the centre of the galaxy, etc. etc. All that matters is the relative velocity of these muons with respect to the lab frame, regardless of the history by which they were produced and accelerated up to whatever velocity, and regardless of the lab frame's own acceleration history. It's easy to show that Relativity requires such a hypothesis to be true, and from a century of extensive testing we know that nothing has yet contradicted Relativity, nor is there any evidence that the Earth and the labs on its rotating surface always happen to live in magically preferred rest frames.

    It only has logical merit if you casually disregard all the known facts which contradict your logic.



    This does nothing to address the muon lifetime example I gave you. They could come from cosmic rays, they could come in copious numbers from an accelerator, all that matters is that if you set a consistent criterion for tracking muons and observe their decay rates, those decay rates drop off with increased relative velocity, in the exact same manner as predicted by Relativity, regardless of the past history of the muons, their accelerations and the lab frame's own accelerations. You don't seem to be aware of the extreme precision or the techniques by which these measurements can be made, tracking a charged particle's pathway as a known function of time. It doesn't have to be done by measuring flight distances, I can assure you of that.

    Besides, it's actually pretty silly to think that a brief gravitational acceleration at \(\sim 9.81\,m/s^2\) will have any meaningful effect on the behaviour of a particle moving at near lightspeed.

    Actually yes we do, you're just willfully blinding yourself to them.

    Well of course you believe it's forgivable to discard examples which contradict whatever it is you personally want to believe on this matter. That's not how it works in science, though. You could have asked me for more details and specifics, asked me about muon sources or muon tracking technology, or asked me to put up some equations and numbers, but instead it looks like you simply replaced my muon example with a strawman of your own construction.​
     
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  7. CptBork Robbing the Shalebridge Cradle Valued Senior Member

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    We don't even have to restrict my example contradicting RJBeery's claims to mere muons, it's known to hold for any particle moving at Relativistic velocities. We could also consider kaons, D-mesons, B-mesons, pions, positronium, etc. Probably hundreds of known examples we can use just from existing data.
     
  8. OnlyMe Valued Senior Member

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    This is consistent with my understanding. I over simplified my question to "protons", as the progenitor particle (if that is even an acceptable phrasing).

    The acceleration issue was primarily, focused toward addressing where the muon's final velocity comes from rather than whether they can be accelerated and focused by EM fields.

    This I also understood, not the mechanisms involved so much as the functional concept of measurement timing. I think that the OPERA neutrino paper described this, at least in part...

    It also addresses the issue that might have involved, when or how the muon is accelerated, as this should at least define the measurement, of its relativistic velocity, to after the initial acceleration. Correct?

    What follows is most likely not phrased well. Try to take it within the whole context, rather than as individual statements.

    This is where I begin to have some question, as to the applicability of the results. Not that I do not understand that the data is there, when locally defined in the lab and must be then applicable to the lab's relationship within the Earth's frame of reference.

    What I am unsure of is that, when we measure this kind of relativistic situation in the lab, whether we can really assume that all of those levels of inertial and sometimes non-inertial velocities, involve detectable influences on what we observe in the lab. It might be that for practical purposes the Earth and the lab in this case, represent an essentially, at least a partially isolated inertial system, within the greater context, of the galaxy and the universe, as a whole. At least to an approximation beyond our ability to measure the impact of external influences.

    In a way we might be able to, define the lab's frame of reference in practice, as representing a flat spacetime consistent with SR. While if we then assume that we can or could accelerate the lab relativistically, we would be doing that within the context of a much larger inertial frame of reference, which can no longer be described, in a similarly limited way, as a flat spacetime. What might then have been trivially undetectable inertial contributions, from the lab's frame of reference in practice, once the lab is moving relativistically, could no longer be associated with the same essentially flat spacetime conditions.

    While we know that there are layers of inertial components to our relationship to the universe, these remain trivial to the muon experiment, as we experience it, when compared with the notion of the lab itself having a relativistic velocity within the "universe".


    In some respects this, hypotheical vs practical, highlights some of the problems that have been standing in the path of understanding GR from a QM perspective. Relativistic velocities are achievable within particle physics and not so much, within the context of higher orders of scale.
     
  9. Neddy Bate Valued Senior Member

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    Yes, but there was some acceleration somewhere, therefore, uhm, something!
     
  10. CptBork Robbing the Shalebridge Cradle Valued Senior Member

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    Et tu, Brute? Then fall, physics!
     
  11. OnlyMe Valued Senior Member

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    I don't think any of this represents any breakdown in physics. What is happening is we, very often attempt to apply the conclusions we draw from idealized hypotheticals directly to practical experience.

    In the muon case the issue becomes confused, because from the lab's frame of reference where the muons have a relativistic velocity, the muons undergo time dilation relative to the lab. The result is that we measure the muon life to be longer than comparable muons "at rest", in the lab's frame of reference. In this situation the muons can be comparred to the traveling twin in the twin paradox whose age is being comparred to a clock in a rest frame relative to its velocity. The lab's clock.

    The question is or was whether if the lab were accelerated to a relativistic velocity, would not the same observations be consistent from the lab's frame of reference. The answer based on SR and the ideal conditions would be yes. The difficulty in assigning to these two POVs any equivalence is that, in this second case the lab becomes the traveling twin. Yes, consistent with the simutaneity of relativity, the lab will measure things to be consistent from its new frame of reference to be consistent with the first case. This however, relies once more on the lab's clock which is itself time dilated, due to its relativistic velocity.

    In the first case the lab's clock represents the "at rest" clock relative to the experiment. In the second case the muon itself represents the "at rest" clock. They are equivalent as a function of the simutaneity of relativity, not because the results would be equivalent, were we able to return both the lab and the muons, to the same rest frame, as we can the twin, in the twin paradox hypothetical.
     
  12. CptBork Robbing the Shalebridge Cradle Valued Senior Member

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    It was just a sarcastic quip, I don't think Neddy was being serious either.

    I think one of the key points is that time dilation is a relative concept. Regardless of their past acceleration histories, an inertial muon sees a dilated lab clock, and the lab sees a dilated muon clock. When Relativistic simultaneity is taken into account under this scenario, it's unambiguous that the lab clock ticks more time than the muon clock, but that's not the same thing as pure time dilation itself.

    Just to note, we could also have the lab accelerate a bit and the muon source accelerate a bit too, doesn't have to be all one or the other. The result is identical in all cases. In the case of the twins paradox we have an accelerating twin, and that's key to resolving this particular problem. What I take issue with is RJBeery's assertion, as I understand it, that there's some mechanism which causes perceptions of time dilation, length contraction and relative simultaneity and that this perception is tied to one's past acceleration with respect to some mysteriously chosen reference frame.

    If you accept that there's at least one reference frame in which the Lorentz transformations apply with respect to all other inertial reference frames, then it automatically follows that the Lorentz transformations (with the correct usage of velocity addition) will hold between any two inertial frames, period. Nonetheless, this doesn't give you any means whatsoever of selecting a preferred frame as the standard against which all other velocities are to be measured before determining their respective spacetime relations. If one wants to argue that the act of acceleration relative to some special preferred frame is what causes time dilation, then they must also accept that the relative time dilations will be the same regardless of who did the accelerating and how.
     
  13. lukmaa Registered Member

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    I love this thread, a long discussion about time dilution without a clear definition of time. Aristotle told us that time is a series of before and after. Einstein made us aware of the difficulties with that definition regarding distant events.

    The twin paradox involves two completely different aspects, the biological age and chronological age. In all my readings regarding the twin paradox those to entities are intermixed. Perhaps that´s because physics had become a mathematical introverted science.

    Back to the twin paradox:

    Firstly we want the answer the question regarding the chronological age of the two twins when they reunite. This is a simple question to answer, we don´t need relative movement or acceleration. The two twins are not separated in space and time when they separate or reunite. When they reunite both have the same chronological age of one twin-roundabout. Let the twins be immortals separating and reunite again and again without stopping. Their roundabout-clocks will in perfect sync and their chronological age will remain the same for eternity.

    Secondly we want to answer the question regarding the biological age of the to twins when they reunite. This is the tricky question that had created the whole twin paradox controversy. Perhaps it is more correct to say that the hard nut to crack is if we can answer that question within the framework of special relativity. That’s boils down to if we are Lorentzians or Einsteinians. Experimental physics has not been able to tell us which of those to religions that is the true one.

    For Lorentzians the answer is straight forward, there is no paradox. Their absolute velocity in regard to the Lorentzian Ether will affect the biological age of the twins.

    Einsteinians follows three different paths regarding the twin paradox:

    1. Roundabouts are not a part of special relativity and the twin paradox is irrelevant.
    2. Roundabouts are not a part of special relativity. It will been solved by general relativity (that reintroduces the Ether).
    3. Asymmetry makes the two twins non-reciprocal.

    1 and 2 does not address the twin paradox and should not be considered. There seems to be a major fault in 3. How does asymmetry transforms a relativistic time dilution to an absolute time dilution? My interpretation of 3 is that it is a strong argument against the Einsteinian religion. If velocity dependent time dilution indeed is absolute, then we need something absolute.

    PS. A quote from Einstein

     
    Last edited: Jul 11, 2012
  14. Tach Banned Banned

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    The above dichotomy is false, "Lorentzian" and "Einsteinian" "relativities" are experimentally indistinguishable, they make the same exact predictions for the outcome of any experiment.


    False, SR deals with accelerated motion just fine. Google Hyperbolic Motion and/or Rindler Coordinates.

    False, SR deals with accelerated motion just fine. Google Hyperbolic Motion and/or Rindler Coordinates.


    False, GR does not reintroduce any "Ether".


    This is precisely the mainstream answer.


    Don't beat your strawman so hard.

    Time "dilution"?

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    Your "interpretation" is one of an ignorant crank, nowhere does SR claim that "velocity dependent time dilution indeed is absolute". What is KNOWN is the fact that acceleration, as opposed to speed is indeed absolute, the twin that accelerates can tell (with the help of accelerometers) that he is different from the inertial twin.
     
    Last edited: Jul 11, 2012
  15. lukmaa Registered Member

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    Dear Tach,

    Did you read the Einstein quote? Do it, and you will see ether. I notice that you argues that acceleration is what causes the different biological ages of the two twins. You did not comment on the fact that both twins will have the same chronological age, any comments on that?

    A simple excercis:

    Take a sheet of paper, make it a cylinder, and you can play with a completely symmetrical twin paradox. Enjoy.

    Best regards

    PS. Please stop using your "mainstream" argument.
     
  16. Tach Banned Banned

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    Yours is the typical crank misquote of the well known Einstein Leiden speech.


    I do not argue with cranks, it is a waste of time.
     
  17. RJBeery Natural Philosopher Valued Senior Member

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    What do you mean by this? Each twin's biological age will be exactly reflected by any timepiece that he keeps with him. There is nothing special about the "roundabout twin" that makes the numbers on his timepiece authoritative.
     
  18. OnlyMe Valued Senior Member

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    Tach and I are often butting heads.., not in this case. Your Einstein quote and how your seem to read and understand it are flawed.

    Something to keep in mind when reading historical statements, books, papers, lectures etc. is the context of the day, in which they were first made.

    The quote you reference came from an address delivered, by Einstein, on May 5th, 1920, at the University of Leyden. The special theory of relativity had been published only 15 years earlier and the general theory of relativity only 5 years earlier. Einstein was addressing university professors and students, who had been educated from an understanding of physics that was firmly grounded in the concept of the Luminefierous aether of the 1800s. People who had some small, and at times not so small investment in the concept of the ether, to begin with. That is to say, his audience was accustomed to an understanding of physics that was not consistent with, the new ideas he was presenting. His address, to be effective had to demonstrate some logical transition from the idea of a fixed Newtonian ether, to the dynamic relationship that space or spacetime has with matter, within the context of general relativity. To that end Einstein was essentially saying that space or spacetime as described in general relativity, was the equivalent (with respect to the propagation of light) of the ridgely defined space of Newton and the concept of the ether, that came out of the early attempts to explain the propagation of light and EM radiation, through vacuum.

    To be clear he was debunking the, at the time achedemically accepted concept of the luminiferous aether, by telling his audience that from the perspective of general relativity, space or spacetime itself were, both dynamically interacting with the matter in the universe and could be THOUGHT of as the ether of general relativity. — The concept of space and spacetime, as presented within the context of general relativity, replaced the fixed space of Newton and the rigidly defined Luminiferous Aether of the 1800s.

    It has seemed from what I have read that Einstein did not set out to overturn the aether. His objective was more to demonstrate that the (or an) ether was not required to explain experience. Personnally I am not entirely sure if Einstein actually thought of spacetime as like a dynamically interacting ether. At this point it really does not matter. What Einstein believed does not represent the totality of our current understanding of physics or even general relativity. It was only a beginning...
     
    Last edited: Jul 11, 2012
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