[General] [NEW] SRT twin Paradox

Sun Aug 27 13:18:53 PDT 2017

Hi Albrecht,

I'm afraid I have to disagree with you on a couple of points.

First, I agree completely that gravitation doesn't come under SR.  However the concept of gravitation is essential to explanation of the 'twins going in opposite directions around a circle and meeting on the far side' (non-)paradox.  [It may be that in your view this scenario cannot then be simply a playing-out of SR, it must be a GR issue?]

Consider: Twin A and twin B each view themselves as being static, with the other twin tracing out a path that takes them away and then brings them back into proximity from a different direction, having formed a loop of some kind; however, from the point of view of an observer static with respect to the centre of a large circle, A and B have started together at some point on the perimeter of that circle and have each followed opposite halves of that circle to meet again on its other side.  I.e. from the perspective of that observer the motions of A and B are symmetric, so their clocks (synchronised at the start) will still be synchronised when they meet again.  [We're assuming here that this all takes place in deep space, far from any gravitational influences.]

>From A's point of view, A has remained static and B has performed a large loop in space, finally coming back alongside A.  According to SR, therefore, A will observe a slowing-down of B's clock and so will expect B's clock to have lost time, in real terms as measured in A's frame (if it were an inertial frame).  [We can deal with the issue of A reading B's clock whilst B is on the move by B digitally emitting their clock-time at intervals, to be received by A who will assess those transmissions on the basis of their crossing space at speed c across the distance that A measures B to be from him at times of transmission - this could be done fairly easily by A keeping a record of B's distance at all times as measured on A's clock.]

B will have a corresponding mirror-image experience of A's motion, and so will expect A to have lost time in real (B-frame) terms.  This appears to suggest that both A and B would each expect the other's clock to have fallen behind their own - a paradox.

However, our external observer will have seen A performing a circular course - so A will inevitably have experienced a 'G-force' of some kind (centripetal, from our observer's persective).  Since A considers him/herself to be static, he/she MUST attribute this to some gravitational influence - indeed, from the SR/GR perspective there must indeed be a gravitational influence in A's frame, from the perspective of that frame; one just does not get G-force without either acceleration or gravitation.  (Here, of course, Relativity begins to become unravelled, as A is far from any massive body that could give rise to a gravitational field - maybe they'll need to start inventing their own local 'dark matter').  Note that the scenario being considered - A and B traversing opposite sides of a circle - involves NO gravitational fields - BUT A and B would HAVE TO PRESUME the existence of such a field in their reference frame if they are to reconcile a force they're experiencing with their assumption that they are static (a totally valid assumption, in Relativity terms).

Resolution of this (apparent) paradox, as I said before, rests on A (and likewise B) considering themselves to have been subject to a gravitational field - and experiment shows us that gravitational fields slow time - so their own clock will have slowed as well as the others.  So they will both expect their clocks to be synchronised on re-meeting.

As I say, this is where Relativity begins to become unravelled: A and B will either each have to acknowledge that they are NOT in fact static, or they will have to invent a convincing explanation for a gravitational effect in the absence of any 'ponderous mass' (to use Einstein's term).  But given that, synchronisation of clocks is not an issue - as long as we allow A and B to each presume existence of a gravitational field in their frame (which, as you say, takes it into the sphere of GR).

Second point: in your case of the travelling-twin versus the stay-at-home twin, the traveller would again experience G-force, which they could if they wish regard as a gravitational effect (since under Relativity they are free to consider themselves as static).  They would therefore expect their clock (including biological clock) to have slowed (Pound-Rebka again), and so know that they have actually been travelling more than one year in 'objective' terms - whatever that might mean in this context.

But of course the reality is that slowing of time is NOT symmetric, it's a consequence of motion with respect to the unique objectively-static universal reference frame.  Only when serious scientists start asking WHY Relativity does (or appears to do) what it does will we make any progress on this issue.

I think we're agreed on the key issues.  Perhaps it's time to stop discussing how a self-consistent mathematical system (which doesn't happen to match true reality) copes with paradoxes of its own making!

Best regards,
Grahame

----- Original Message ----- 
  From: Albrecht Giese 
  To: general at lists.natureoflightandparticles.org 
  Sent: Sunday, August 27, 2017 7:48 PM
  Subject: Re: [General] [NEW] SRT twin Paradox

  Hi Grahame,

  without going into details of this discussion I only want to point to the following fact:

  Whereas you are of course right that the twin situation is not a paradox but logically clean, what we all as I think have sufficiently discussed here, the following is not correct in my view:

  The twin situation has absolutely NOTHING TO DO with gravity.

  Two arguments for this:

  o  The so called twin paradox  is purely Special Relativity. Gravity on the other hand, is General Relativity. This is the formal point.

  o  From practical numbers it is visible that gravity cannot be an explanation. Take the usual example saying that one twin stays at home and the other one travels - as seen from the twin at home - for twenty years away and then twenty years back. From the view of the twin at home, at the other ones return 40 years have gone. For the travelling twin only one year has gone (This case is theoretically possible if the proper speed is taken, about 0.9997c)). Then the travelling twin would have saved 39 years of life time. Now look at the possible influence of gravity: Assume it takes the travelling twin  a year to change his speed from almost c to almost - c , then, even if the speed of proper time would decrease to zero, he would have saved only one year. But, in this example, he has saved 39 years. How could this work? No one in physics assumes that proper time can run inversely. So this is no possible explanation.

  How is it explained? I do not want to repeat again and again the correct (but a bit lengthy) explanation, but I attempt to give a short version: In Einstein's relativity the run of time in different frames can  logically not be continuously compared, it can only be compared at interaction points where two clocks (or whatever) are at the same position. And the determination of the situation at such common position has to be done by the Lorentz transformation. And this determination works, as many times said here, without logical conflicts.

  If you solve this problem using the Lorentzian SRT, then the result is the same but the argument is different, more physics-related, and also better for the imagination. If wanted, I can of course explain it.

  Albrecht

  Am 27.08.2017 um 01:13 schrieb Dr Grahame Blackwell:

    I'm sorry Wolf, but it seems that you're still not getting it.

    This situation can be explained fully logically WITHOUT either twin making any assumptions about SR or GR - simply from their own observations and from well-proven experimental findings.

    If we label the twins A and B, then their situations are effectively symmetric* - so we'll consider the scenario from the viewpoint of twin A.
    A considers him/herself static, and all motion to be attributable to twin B.  So - and this agrees with experimental observation of clocks at high speed (in planes and in GPS satellites) - twin A will observe twin B's clock running slow, if A's own clock is not upset by any effect.  HOWEVER, since A is actually travelling in circular motion, (s)he will experience a centripetal force; assuming him/herself to be static, this will necessarily be attributed to gravitational effects - and it's well known from experiment (Pound-Rebka and successors) that gravitational fields cause time dilation - so A will expect their own clock to be running more slowly also due to that 'gravitational' effect (note that this is not any assumption of SR or GR, simply inference from proven experimental results) [and so also A's observation of B's clock, measured against A's own clock, will not fit the standard SR time-dilation model, for reasons that A will fully comprehend].  For A, the cumulative time-dilation for B's perceived relative speed and for A's own perceived 'gravitational' effect exactly balance - so A will fully expect both clocks to coincide when the twins meet again (as B will also).

    No paradox.

    * It needs to be said that further study of causation of 'relativistic time dilation' leads to the understanding that this is an objective effect due to travelling at speed relative to the unique objectively-static universal reference frame.  So if the centre of the circle traced out by A and B is itself in motion relative to that reference frame then it cannot be assumed that A's and B's motions will be symmetric; in that case their clocks may well not be precisely synchronised on their meeting again.  This is an observation relating to physical reality, which in no way contradicts the self-consistency of SR (or GR) as a mathematical system.

    Best regards,
    Grahame
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