Alternative Twins Paradox

Discussion in 'Pseudoscience Archive' started by Jack_, Feb 20, 2010.

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  1. Jack_ Banned Banned

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    Alternative Twin’s Experiment

    The traditional twins experiment is generally solved such that all agree the traveling twin is younger because of non-symmetric acceleration. However, this twin’s paradox will produce symmetric acceleration and force SR to exclusively explain reciprocal time dilation up against the SR clock synchronization method which is based on the universal truth of t = d/c.

    Setup
    O and O' are observers with clocks in the same frame in the vacuum of space.

    Procedure
    1. Both set their clocks to 0 and O instantly acquires v relative to O'.
    2. O and O' are in relative motion for some agreed up time t' on the clock of O'.
    3. After time t', O' will acquire v in precisely the same way as O in precisely the same direction.
    4. At the same instant O' acquires v, O' enters the frame of O and O' sends a light pulse to O and records this as the end of the experiment at time t'.
    5. O' receives the light pulse and records the time as te.
    6. Since, O and O' are again in the same frame, O performs with O' the round trip speed of light calculation using a time trial to calculate the distance between the two. Let D be that distance. O then subtracts D/c from te and determines its proper for when O' entered the frame to determine the correct end of the experiment which will match the end for O'. Let this time be t.
    7. Finally, O and O' perform the SR clock synchronization method to determine the ordinality of the two clocks. To do this, O sends its time t1O to O'. O' immediately sends its time tO' back to the clock of O. O receives this light at t2O. In particular, Einstein concludes the two clocks are in sync if tO' = ½ (t2O - t1O). Thus, the age ordinality is established as tO' - ½ (t2O - t1O).
    http://www.fourmilab.ch/etexts/einstein/specrel/www/

    ***Note, the above can be replaced with equal agreed upon proper burn times and proper accelerations and will produce the same results according to the SR uniform acceleration equations.

    The steps above represent an effective procedure for deciding the age ordinality of O and O'. More specifically, step 7 determines the clocks of O and O' as one of the following.
    · O is younger than O'.
    · O is older than O'.
    · O and O' are the same age.

    Since each step of the procedure above is well defined and produces a unique outcome with the output at step 7 producing only one value, then this problem of determining the age ordinality of O and O' is recursive and thus logically decidable.


    Now, LT will be applied to solve the problem above.

    From O as stationary, its proper time is t. Hence, O concludes O' elapses t/λ and therefore concludes O' is younger.

    From O' as stationary, its proper time is t'. Hence, O' concludes O elapses t'/λ and therefore concludes O is younger.

    Now, Einstein’s clock synchronization method by his own admission is “free from contradictions”.
    http://www.fourmilab.ch/etexts/einstein/specrel/www/

    Therefore, we may conclude the effective procedure listed above produces one correct answer to the age ordinality of O and O' otherwise, the SR clock synchronization method does not work and hence LT fails.

    On the other hand, LT produces contradictory results and thus provides an answer that is not logically decidable.

    Hence, under SR, the problem above is logically decidable and not logically decidable depending on the method used.

    Worse, at least one of the solutions provided by LT must contradict the results of the clock synch and therefore, LT must calculate at least one incorrect result. Clearly, this proves LT is not a reliable tool for mapping proper times between frames since at least one of its solutions must be wrong above.
     
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  3. Pete It's not rocket surgery Moderator

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    Step 7 determines the relative age in one reference frame only - the rest frame of the clocks at the end of the experiment. In that reference frame, we see that O' is younger than O. But SR says that their relative ages are not absolute and unambiguous unless two "same age" events (eg the events of the clocks reaching time k) occur with one in the future light cone of the other, so in this case it's no surprise that you can find a frame of reference in which their relative ages are reversed.

    Essentially, this means that SR will not give you a frame-independent answer for who is older than who unless you bring O and O' back together again.

    Jack, you seem to think that clock synchronization is supposed to be frame-independent, that synchronized in one frame of reference means synchronized in all frames of reference. But, the whole point of clock synchronisation in SR is that it is frame dependent, that synchronization is a relative thing, that "happened at the same time" depends on your chosen reference just as much as "happened at the same place".
     
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  5. AlphaNumeric Fully ionized Moderator

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    *sigh*

    Right, I've said this before in other threads to the "OMG SR is wrong!" crowd but looks like I'll be saying it again.....

    Jack_ you claim that Lorentz transformations do not form consistent frame changes. Lorentz transforms from the Lie group SO(3,1) and so the examination of Lorentz transforms in special relativity is exactly equivalent to examining the group structure of the SO(3,1) group. Via the Weyl rotation trick this group is entirely equivalent to the SO(4) Lie group. SO(4) is the rotation symmetry group of 4 dimensional Newtonian/Euclidean space. So if Lorentz transformations are inconsistent then the entirety of group theory is wrong and by the chain I just outlined it feeds through into basic geometry. To say "Lorentz transformations are inconsistent" is equivalent to saying "Geometry is wrong".

    Now its entirely possible that Lorentz transformations do not form the kind of symmetries which Nature actually possesses, as we discovered with Galilean transformations in the early 1900s but that can only be shown via experiments. When experiments demonstrated Galilean transformations are not the symmetry of nature they didn't prove the transformations inconsistent, they simply demonstrated you couldn't use them to examine Nature if you are interested in high speeds. Proving Lorentz transforms are mathematically inconsistent would take with it ALL of geometry, including all the geometric constructions/models used before Einstein. You can't simultaneously say "Lorentz transformations are inconsistent" and "Galilean transformations are consistent" are they have the same underlying mathematical structure. Either both are consistent or neither is.

    Now if you've done a series of careful experiments designed to test the physical validity of Lorentz transformations and have found a problem, I'm all ears. Otherwise sod off and learn some basic mathematics.
     
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  7. Jack_ Banned Banned

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    Wrong.

    Step 7 has them back in the same frame.

    They started in the same frame and terminated in the same frame.

    The clock sync decides whether the clocks are synched otherwise, the clock sync is a failure.
    [Edit: I never said the results of the outcome of the clock sync when the two are back in the same frame. I said it produces only one answer. Further, it cannot be suggested just because the two are in the frame of O' that the clock of the frame is preferential since that would be choosing a prefered frame]

    Hence, the clock sync provides only one answer as to the age ordinality of the twins.

    Because of the clocks sync, the twins do no need to be bround back together for a decision on their clocks. It we do, then the clock sync is a failure.

    Hence, the clock syunc decision is to be accepted "free from contradictions" again because they are bakc in the same frame.

    Next, reciprocal*time dilation applies between the twins because of relative motion and the results of the LT calculation causes each to conclude the other is younger.

    So, we have the clock sync that provides only one answer and the LT calculation that provides contradictory answers.

    The clock sync can validates at most one LT calculation leaving at least one false.
     
    Last edited: Feb 20, 2010
  8. Jack_ Banned Banned

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    You are lecturing me on math?

    Let's get back to the math.

    Steps 1-7 are recursive. Do you know what that means?

    Because of the fact the twins are in the same frame at the termination of the experiment, then the answer of the clock sync is logically decidable since each can logically decide the start point and end point when they are in one common frame for each. No decision is made in relative motion except for O' deciding when to attain v but that is decided in its own frame regardless of the motion of O.

    Hence, all decision are made only in the stationary system.

    If you claim observers in the same frame cannot logically agree on events and timing/synchronization, then you are claiming the clock sync method of SR is wrong.
     
  9. AlphaNumeric Fully ionized Moderator

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    Yes, because it would seem you don't know certain things about it I do yet you're very vocal about them. I notice that despite your incredulity that I dare lecture you on mathematics you couldn't respond to what I actually said. If I'm wrong about the equivalence between Lorentz transformation consistency and basic geometry explain why. If the group structure of Lorentz transformations is wrong and you could demonstrate it you'd be in line for a Fields medal.

    And why are you so narked I dared lecture you. I haven't seen you display any mathematical understanding over someone with basic vector calculus understanding and I've had to point out several mistakes in how you talk about Lorentz transformations. Am I supposed to know you're some maths whiz?

    I have to go out but I suspect mix frame measurements. You use times measured in the stationary frame with quantities from the moving frame. You talk about how they are both stationary but you can't just ignore they were in relative motion for a while.

    A quick scribble involving doing it all from the stationary frame's point of view and then the moving frame's point of view doesn't make any problems jump out.
     
  10. Jack_ Banned Banned

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    There is no frame mixing as that occurs when you have frames in relative motion and attempt ro use SR conclusions frame one frame into the other.

    You may pass time to the relative frame and distance.

    We are not measuring nor calculating between relative frames.

    All operations and comparisons between the observers occur when they are stationary to each other.
     
  11. Pete It's not rocket surgery Moderator

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    That's right, Jack.
    They're at rest in the same frame, and step 7 checks their synchronization in that frame.
     
  12. Jack_ Banned Banned

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    The clock sync checks the ordinality of the two clocks. Let's remember, O' contends that frame is younger. So, you cannot pick a preference on the decision of the clock sync.

    Also, the O frame contends it will be older.

    The clock sync settles the argument and resolves the age ordinality.

    Guess what. LT is wrong one way or the other.
     
  13. AlphaNumeric Fully ionized Moderator

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    The time before O moves is measured in Frame 1, that which is stationary. The times seen by O' throughout and O after emitting the photon are in the second frame, which is at rest relative to O' throughout.

    Consider even the first few steps you outline from two different points of view.

    Frame 1 :

    Both at rest initially but B jumps to speed v : At t=0 x_A = 0 = x_B
    At a preset time A emits a photon towards B : At t=t_0 then x_A = 0 and x_B = v t_0
    At time t this photon reaches x_B, ie (t-t_0)c = t v so t = [c/(c-v)]t_0

    So in Frame 1 B gets the photon when t = [c/(c-v)]t_0.

    Frame 2

    t'=0 x_A = 0 and x_B = 0
    Since B is stationary it appears as if A is moving at velocity -v
    A now has to emit a photon at some point, when it has measured that t_0 seconds have passed. But this is not t' = t_0. From B's point of view A emits a photon after gamma*t_0 seconds.
    t' = g t_0 x_A = - v g t_0 and x_B = 0
    The photon is at - v g t_0 + (t'-g*t_0) c which is zero when t' = g*t_0 (1+v/c).

    Notice how from Frame 1 we have a factor of c/(c-v) = 1/(1-v/c). Also (1/g^2) = (1-v/c)(1+v/c). So taking the ratio of the Frame 1 time to the Frame 2 time gives g*(1+v/c)(1-v/c) = 1/g. Precisely the dilation factor you expect. The transformations are consistent between frames.

    I take it from the fact you utterly ignored my repeated challenge to explain why my explanation about how SR is as consistent as any other geometry that you are unable to retort it. Do you even know any group theory? You throw around terms like 'decidable' yet seem unfamiliar with basic vector calculus or groups. By using basic results from such things you can strip away the issues of "Does this match my physical intuition" and ask "Is this mathematically consistent" and, as I said, its as consistent as basic Euclidean geometry. Trying to come up with some convoluted set of transformations to apply doesn't magically make it violate basic group theory or geometry since any Lorentz transformation is, by construction, going to leave the geometry of the system invariant.
     
  14. Jack_ Banned Banned

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    AN, why are you bothering with emitting photons?

    LT decides reciprocal time dilation. If you refute this, then you refute SR.

    Hence, you must agree with the LT conclusion of reciprocal time dilation.

    Further, your analysis did not refute the logical decidability of the clock sync.

    I therefore conclude you agree with that.

    As such, your analysis adds nothing to the story and the conclusion stands.



    As to your view of some logically consistent space from LT, let's consider that.

    Assume a rigid body sphere with a light source and a moving one with the same rest radius.

    When the origins of the rigid body spheres are co-located, the light emits.
    Now, under SR, the stationary rigid body sphere will see its sphere points struck simultaneously. However, the stationary observer claims the moving rigid body sphere will not experience this simultaneity of its sphere points. Of course, the stationary observer claims the relativity of simultaneity.

    However, the moving sphere will claim its sphere points are struck simultaneously when it is considered stationary.

    Now, to address your questions of a logically consistent space generate from LT, when in the time coordinates of the stationary frame does the moving frame experience this simultaneity?

    If LT is consistent, then this answer should be known.

    So, here is the challenge. Prove in the time coordinates of the stationary observer when the the moving observer experiences simultaneity.

    If you cannot prove this, then your LT logic is not complete and possibly inconsistent.

    Also, if you cannot prove this, you cannot validate your claim the LT space correctly models reality since obviously this simultaneity of the moving frame has a unique time in the stationary frame.

    Now, if you do not know how to do this, then admit you are not intellectually up to this challenge of proving your own statements.

    Then, I will step in with a math proof and demonstrate the exact unique time in the stationary system of when the moving system sees simultaneity.

    Have at it.
     
  15. Trippy ALEA IACTA EST Staff Member

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  16. Jack_ Banned Banned

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    So what?

    With or without relativity, the frequency of light is altered by gravity.
    Thus, any device, "clock" that claims to implement time will be affected by this fact of nature.

    We need to be very careful to distinguish our theoretical a priori concept of time and our a posteriori implementations of time.

    We need to have the intelligence to understand they are different.

    So, your article proves a well known fact proved by GPS that light frequency is altered by gravity.



    5 Relativistic Effects on Satellite Clocks

    For atomic clocks in satellites, it is most convenient to consider the motions as they would be observed in the local ECI frame. Then the Sagnac effect becomes irrelevant. (The Sagnac effect on moving ground-based receivers must still be considered.) Gravitational frequency shifts and second-order Doppler shifts must be taken into account together.
    http://relativity.livingreviews.org/Articles/lrr-2003-1/
     
  17. Trippy ALEA IACTA EST Staff Member

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    The break throughs are twofold.

    1. the degree of accuracy to which GR successfully models the situation.
    2. The methodology used to do so.

    I'm sure that some of the mor eintelligent members will not only be able to appreciate the work for what it is, but will be able to see how it applies directly to the current discussion.
     
  18. Jack_ Banned Banned

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    LOL, you don't know what it proves. I tried to teach you.
    Oh well, I tried.
     
  19. Trippy ALEA IACTA EST Staff Member

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    Please Register or Log in to view the hidden image!

     
  20. Jack_ Banned Banned

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    Looks like tripe, you eat it?
     
  21. Trippy ALEA IACTA EST Staff Member

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    No, I posted it because it bears quite a striking resemblance to your post.
     
  22. Jack_ Banned Banned

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    Do you have a scientific or a logical basis for this or is this just an opinion?
     
  23. AlphaNumeric Fully ionized Moderator

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    It isn't 'my view', it's a logical implication of geometry. Given any vector space V with a metric h such that h(X,Y) is in a field F for X,Y in V, there exists a group G and representation r such that for all g in G you have h(r(g).X,r(g).Y) = h(X,Y). This provides a map between (V,g) to (G,r). Though I doubt you've come across it (since I doubt you actually know much mathematics or you wouldn't be saying what you say) this is basically the relationship between a vector bundle and a G-bundle.

    I've already told you about this when I described how I could pick a 4x4 representation of Spin(3,1) or a 2x2 representation of SL(2,C), which is isomorphic to Spin(3,1). If there's an inconsistency in one side of the isomorphism it'll be mapped into the other side. Therefore you can examine the mathematics of any given geometry by examining its symmetry group.

    I've just demonstrated to you that the two frames follow the expected timings. I didn't have to just 'agree with SR', I could go through it myself.

    Flawed logic. The inability to provide an answer is not proof there is no answer. In fact the onus is on you. There's 100 years of testing and examination behind SR. You have claimed there's a fundamental mistake in it. So you should demonstrate it. I can't help but notice you aren't going through any calculations, you just default to "Its decidable and not so its wrong". If there's some fundamental conflict surely you can get SR to work out the time someone measures in two different ways and come up with different answers. At the moment you're complaining different people measure different things. And we seem to be going around the houses because you refuse to actually nail your maths down, ignore direct questions and ask vague questions.

    Ah, so because someone on an internet forum doesn't immediately spoon feed you an answer to a hypothetical question you're allowed to disregard a century of experiments by many thousands of research groups in dozens of different areas of science? Good one.

    Wow, nice hypocrisy. Funny how when you're asked direct questions you ignore them but then you complain other people aren't 'up to this intellectually' because they don't spoon feed you. Use special relativity to predict 1=2 and you'll prove your claim. You're asking me to basically prove the entirety of geometry is consistent to you, because you and I both know that no matter how many specific examples you're walked through you'll just come up with another one. You've already got two threads on different setups! In order to prove geometry consistent someone would have to do a hell of a lot of work and teach you basically a mathematics degree. You only have to provide one, just one, example of SR saying 1=2 and you prove your claim. But you haven't and instead you're just coming up with different scenarios again and again and trying to give the impression that because people either can't or won't respond you're somehow validated.

    An internet forum is hardly going to be the best form of review. If you're so sure you're right submit it to a journal. I'll happily wage $1000 or £1000 or whatever your currency is that you will not get a paper which claims Lorentz transformations are an inconsistent mathematical structure published.

    I asked you before if you know any group theory (and you just ignored me, along with all my other questions). Do you? Because its trivial to demonstrate the Lorentz transformations are a group and thus consistent mathematically. But something tells me you haven't come across such things before...

    So you say "If you can't provide an answer SR might be inconsistent" and then say you have the answer?
     
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