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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>Regrettably, you appear to have
misread my text. If you read it again more carefully, you will see that at
NO point do I propose, or even suggest, that acceleration gives rise to time
dilation. I am well aware that, as you say, "gravity and acceleration are
different regarding [time] dilation" - so your attempts to persuade me of this
are quite unnecessary.</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>The whole point of my text was, as I
said at the outset, to resolve the 'twins going opposite directions around a
circle' paradox, with reference to classical SR (and GR, as it happens - bear
with me on this). For SR to be self-consistent (which I believe it is -
that's not the same as it being correct!) there has to be an explanation that
fits the terms of Relativity which explains how it can be that both A and B
would expect their clocks to coincide on re-meeting - as they clearly would from
the perspective of a third observer, static with respect to the circle centre,
and so they must of course coincide from everyone's perspective. If it can
be shown that they'd expect their clocks to be different then Relativity is dead
- but it is most definitely not that simple! [That's why it's survived for
over a century; it's not just that thousands of other physicists over that
century have been incapable of such analysis!]</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>Relativity states that any scenario
can validly be assessed from the perspective of any individual, who may consider
themself to be static - and that their assessment of that scenario is equally
'correct' to any OTHER assessment from any other frame of reference. SR
restricts such assessment to inertial frames, GR extends it to non-inertial
frames - but this same principle holds true.</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>We can add to this the fact that if
such an observer experiences what we might refer to as a 'G-force' acting on
them then they will know that they must be in a non-inertial frame. The
term 'G-force' is convenient for our purposes as it is used to apply both to
forces due to gravitation and to accelerating forces; it is implicit in GR
(through the Equivalence Principle) that the observer will not know which of
these two applies (Einstein's 'man in a box' thought experiment), but that if
(as he fully validly may, under Relativity) he considers himself to be at rest
then he must necessarily attribute such forces to gravitational effects (without
having to ascertain where those effects arise from - that could be tricky in our
example scenario!)</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>Please not that I am NOT saying that
these principles actually apply in our physical reality - I am simply stating
the mantra of Relativity, both SR and GR, since that's the mathematical
framework in which I'm seeking to show self-consistency. Others in the
group are proposing that Relativity is disproved by this 'twins thought
experiment', I'm observing that it is not; the truth or falsehood of Relativity
as a model of true reality is not what I'm about here - in fact I'm seeking to
show that Relativity CANNOT be disproved by such a simple setup, it needs rather
more thought than that!</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>Albrecht, I think you misunderstand
my purpose here. It's not my intention EITHER to prove OR to disprove
Relativity; my sole intention is to show that this 'twins scenario' does NOT
show an inconsistency in Relativity - it is NOT a paradox. In this respect
the question of whether Relativity does or does not match true objective reality
is totally irrelevant; the only question is whether or not Relativity agrees
with itself.</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>The importance if this exercise
shouldn't be underestimated: if we are to challenge the fundamental premises of
Relativity, it has to be on FAR stronger ground than a proposed 'paradox' that
has been refuted time and time again over the past 100 years - we do ourselves,
and science, a serious disservice if we convince fans of Relativity that our
view that it's wrong is based on a simplistic misunderstanding of its
basics!</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>So, again: external observer sees A
and B perform mirror images of each others' manoeuvres - so of course clocks
will match on re-meeting. So A and B will also see clocks coinciding
- and fully expect that to be the case. How come, given that Relativity
allows each to see their position in the universe as static?</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>Simple: since the external observer
sees A (for example) as experiencing acceleration towards the centre of the
circle, A him/herself will inevitably experience a G-force acting outward from
the centre of that observer's circle. Considering him/herself static in
space, A will have no option but to regard that as a gravitational effect from
some unknown source (note that physicists have no trouble envisaging gravitation
acting from unknown sources - we're told that such sources make up the vast
majority of the mass-energy in our universe!). Since A knows that
gravitation causes time dilation (NOTE THAT I AM <STRONG>NOT</STRONG> PROPOSING,
HERE OR ANYWHERE, THAT ACCELERATION CAUSES SUCH DILATION), he/she will
inevitably expect their clock to have been slowed, as well as knowing that B's
motion will have also slowed B's clock. So matching of clocks on
re-meeting is to be totally expected by A (and B) - no paradox.</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>This is all
about perceptions from different perspectives, and the assertion in
Relativity that all such perceptions are equally valid/true.</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>With regard to assessing time and
distance of B, as assessed by A: whilst not relevant to this analysis, the
question has arisen - so let's look at it from A's perspective. A sends
out a broadcast radio signal in the general direction of B; on receiving
that signal, B sends a time-stamped response (broadcast in A's general
direction); From the time between sending and receipt, 'knowing' such signals to
travel both ways at c relative to him/herself (according to SR), A can calculate
the distance to B at the time B responded - which will be halfway between send
and received, from A's perspective; A will also have a record of B's clock-time
at that point halfway between A's send and receive - and so an indication of how
B's time is progressing compared with A's [This is all according to SR 'rules',
I'm not proposing that A's assessments will in fact be correct in absolute terms
- though of course SR considers them to be equally correct to any other
view].</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>Having glanced briefly at Wolf's
latest response, I'd just say that mass-energy considerations can also be very
misleading in a Relativistic scenario, unless handled exceedingly carefully with
full regard for different perspectives. As a very simple illustration: A
single photon observed from one reference frame may be red- or blue-shifted
when observed from a different frame, and so carry different energy.
Extension of this to massive energetic particles, and applying mass-energy
equivalence, makes it clear that we can't simply assess the mass-energy
characteristics of an object or system from one frame then simply carry those
measures across to another frame. I don't know whether this has a bearing
on Wolf's comments, I didn't get to see much of what you sent previously, Wolf,
for some reason.</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> </DIV>
<DIV> </DIV>
<DIV> </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> Monday, August 28, 2017 4:21
PM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Re: [General] [NEW] SRT twin
Paradox</DIV>
<DIV><BR></DIV>
<P><FONT size=-1 face=Arial>Hi Grahame,</FONT></P>
<P><FONT size=-1 face=Arial>sorry, but I find a very fundamental error in your
arguments: You describe a pair of twins which observe each other in a
situation where they are permanently accelerated. And then you argue with
dilation caused by gravity. But that does not fit the physical
reality.</FONT></P>
<P><FONT size=-1 face=Arial>Gravity and acceleration are different regarding
dilation. Gravity causes dilation, no question. But acceleration does not
cause dilation. How can one know? 1) You find this in every textbook about
special relativity; 2) it was experimentally proven in the Muon storage ring
at CERN. The extension of the life time of the muons was only dependent on the
actual speed of the particles, not on the very strong acceleration in the
ring. If that would have been an effect according to an equivalent
gravitational field, their lifetime would have to be extended by an additional
factor of roughly 1000 compared to the results observed.<BR></FONT></P><FONT
size=-1 face=Arial><BR></FONT>
<DIV class=moz-cite-prefix><FONT size=-1 face=Arial>Am 27.08.2017 um 22:18
schrieb Dr Grahame Blackwell:</FONT><BR></DIV>
<BLOCKQUOTE cite=mid:0C943D193FFC4E568685FEB833FA0E59@vincent type="cite">
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<DIV><FONT color=#000080 size=2 face=Arial>Hi Albrecht,</FONT></DIV>
<DIV> </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> </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> </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></BLOCKQUOTE><FONT color=#000080><FONT size=2><FONT
face=Arial>None of the twins can view himself as being static, because they
are accelerated all the time and they will notice that. So the laws of SR are
not applicable for this process in a simple way.</FONT></FONT></FONT><BR>
<BLOCKQUOTE cite=mid:0C943D193FFC4E568685FEB833FA0E59@vincent type="cite">
<DIV> </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).
<BR></FONT></DIV></BLOCKQUOTE><FONT color=#000080><FONT size=2><FONT
face=Arial>No, it is not an inertial frame.</FONT></FONT></FONT><BR>
<BLOCKQUOTE cite=mid:0C943D193FFC4E568685FEB833FA0E59@vincent type="cite">
<DIV><FONT color=#000080 size=2 face=Arial>[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></BLOCKQUOTE><FONT
color=#000080><FONT size=2><FONT face=Arial>Also this is not possible. A can
receive signals from B, but he does not know the distance. According to SR
this distance is not clearly defined because the assessment of any distance
depends on the motion state of the observer. Which speed will A assume for
himself? He cannot assume to be static as he notices to be
accelerated.</FONT></FONT></FONT><BR>
<BLOCKQUOTE cite=mid:0C943D193FFC4E568685FEB833FA0E59@vincent type="cite">
<DIV> </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></BLOCKQUOTE><FONT color=#000080><FONT size=2><FONT
face=Arial>Also regarding time a similar problem like for distance is
applicable. When are signals in different frames synchronised or when is time
is running faster or slower? For any observer in different frames the result
of this question may be different. </FONT></FONT></FONT><BR>
<BLOCKQUOTE cite=mid:0C943D193FFC4E568685FEB833FA0E59@vincent type="cite">
<DIV> </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></BLOCKQUOTE><FONT
color=#000080><FONT size=2><FONT face=Arial>As said above, even if both, A and
B, attribute the force of acceleration to gravity, they are in error; and it
does anyway not help the situation. For your consideration they need a
gravitational field for dilation, but this does not exist, and acceleration
does not replace it.</FONT></FONT></FONT><BR>
<BLOCKQUOTE cite=mid:0C943D193FFC4E568685FEB833FA0E59@vincent type="cite">
<DIV> </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></BLOCKQUOTE><FONT
color=#000080><FONT size=2><FONT face=Arial>That is anyway true also in the
absence of dilation.</FONT></FONT></FONT><BR>
<BLOCKQUOTE cite=mid:0C943D193FFC4E568685FEB833FA0E59@vincent type="cite">
<DIV> </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></BLOCKQUOTE><FONT
color=#000080><FONT size=2><FONT face=Arial>Not applicable as mentioned
above.</FONT></FONT></FONT>
<BLOCKQUOTE cite=mid:0C943D193FFC4E568685FEB833FA0E59@vincent type="cite">
<DIV> </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></BLOCKQUOTE><FONT
color=#000080><FONT size=2><FONT face=Arial>The twin travelling, B, cannot
assume that he is static because he has to notice his acceleration. And that
is different from gravity. And even if it could be identified with gravity
this would not solve the example which I have given.</FONT></FONT></FONT><BR>
<BLOCKQUOTE cite=mid:0C943D193FFC4E568685FEB833FA0E59@vincent type="cite">
<DIV> </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></BLOCKQUOTE><FONT color=#000080><FONT size=2><FONT
face=Arial>Which progress to you expect? There is no symmetry in the case
where twin B returns and so you cannot conclude anything from
symmetry.</FONT></FONT></FONT><BR>
<BLOCKQUOTE cite=mid:0C943D193FFC4E568685FEB833FA0E59@vincent type="cite">
<DIV> </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> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>Best regards,</FONT></DIV>
<DIV><FONT color=#000080 size=2
face=Arial>Grahame</FONT></DIV></BLOCKQUOTE><FONT color=#000080><FONT
size=2><FONT face=Arial>As I have mentioned in the other mail: It is in
conflict with Einstein's relativity to compare clocks residing in different
frames. The result of any comparison depends on the motion state of the
observer. That is what Einstein says.<BR><BR>But the other solution is to
follow the Lorentzian relativity. In that case the imagination becomes easy
(in contrast to Einstein).<BR><BR>Greetings
back<BR>Albrecht.<BR></FONT></FONT></FONT>
<BLOCKQUOTE cite=mid:0C943D193FFC4E568685FEB833FA0E59@vincent type="cite">
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV>----- Original Message ----- </DIV>
<BLOCKQUOTE
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"
moz-do-not-send="true">Albrecht Giese</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A
title=general@lists.natureoflightandparticles.org
href="mailto:general@lists.natureoflightandparticles.org"
moz-do-not-send="true">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>
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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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