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<DIV><FONT color=#000080 size=2 face=Arial>Hi Albrecht,</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>I'm afraid I have to disagree with
you on a couple of points.</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>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?]</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>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.]</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>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.]</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>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.</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>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).</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>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.</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>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).</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>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.</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>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.</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>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!</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>Best regards,</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial>Grahame</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV>----- Original Message ----- </DIV>
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style="BORDER-LEFT: #000080 2px solid; PADDING-LEFT: 5px; PADDING-RIGHT: 0px; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px">
<DIV
style="FONT: 10pt arial; BACKGROUND: #e4e4e4; font-color: black"><B>From:</B>
<A title=phys@a-giese.de href="mailto:phys@a-giese.de">Albrecht Giese</A>
</DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A
title=general@lists.natureoflightandparticles.org
href="mailto:general@lists.natureoflightandparticles.org">general@lists..natureoflightandparticles.org</A>
</DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Sunday, August 27, 2017 7:48
PM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Re: [General] [NEW] SRT twin
Paradox</DIV>
<DIV><BR></DIV>
<P>Hi Grahame,</P>
<P>without going into details of this discussion I only want to point to the
following fact:</P>
<P>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:</P>
<P>The twin situation has absolutely NOTHING TO DO with gravity.</P>
<P>Two arguments for this:</P>
<P>o The so called twin paradox is purely Special Relativity.
Gravity on the other hand, is General Relativity. This is the formal
point.</P>
<P>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.</P>
<P>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.</P>
<P>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.</P>
<P>Albrecht<BR></P>
<P><BR></P><BR>
<DIV class=moz-cite-prefix>Am 27.08.2017 um 01:13 schrieb Dr Grahame
Blackwell:<BR></DIV>
<BLOCKQUOTE cite=mid:CCE2F4D7ECF5430E943629241B634443@vincent type="cite">
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<DIV><FONT color=#000080 size=2 face=Arial>I'm sorry Wolf, but it seems that
you're still not getting it.</FONT></DIV>
<DIV> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>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.</FONT></DIV>
<DIV> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>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.</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial>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).</FONT></DIV>
<DIV> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>No paradox.</FONT></DIV>
<DIV> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>* 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.</FONT></DIV>
<DIV> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>Best regards,</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial>Grahame</FONT></DIV>
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