Tom Roberts wrote:
El Enrrabadore-mor wrote:

It is said that a speeding clock shows less elapsed time than
the stay-at-home clock, because (if already speeding) it is
running at a slower rate. Or else, because it had run at a
slower rate when it was speeding, assuming now it is
stopped near the stay-at-home clock.

While that may be "said", it is wrong in SR. In SR, the motion of a
clock does not affect its rate. But when one compares identical clocks
that have traveled different paths, their elapsed proper times can
differ, due to their different trajectories, not due to any change in
their tick rates.

Realizing the only way to resolve the twin’s paradox is to prove
either or both time dilation or the principle of relativity wrong
since the twin’s paradox is a manifestation of both time dilation and
the principle of relativity. In doing so, relative simultaneity must
be wrong, and thus absolute time must hold by each frame of reference
collectively in coherence. Since the Loretnz transform has abandoned
the absolute time, to keep the mysticism alive, you (plural) choose to
invent what you call the ‘proper time’ to function and behave like the
absolute time.

To you, MYSTICISM IS WISDOM. shrug

[... circular motion]

Bailey et al put muons into a storage ring and measured their lifetime
for their circular path. Within experimental resolutions, they have the
same lifetime as muons traveling in a straight line, so their circular
path did NOT affect the internal "clock" that controls their decay. They
were subject to an acceleration of about 10^18 g (1 g = 9.8 m/s^2),
which is FAR greater than claimed in your example. Note this experiment
is a direct implementation of the circular twin scenario, when combined
with measurements of muon decay at rest.

So, the principle of relativity must not hold in this experiment.
shrug

[...] motion does NOT
affect the proper tick rate of clocks,

According to the Lorentz transform, any motion of the observed
manifests a time slow down of the observed by the observer. shrug

but clocks that travel different
trajectories can differ in their elapsed proper times between meetings
of their trajectories.

Here you go again with your proper time nonsense. Your proper time is
nothing more than spacetime itself. Given the spacetime of the
observed, it should be observed to be the same by any observers.
shrug Unfortunately for you, time flow is always time not spacetime
or proper time. shrug

This is very basic SR, discussed in:

Taylor and Wheeler, _Spacetime_Physics_.

This is MYSTICISM. The Lorentz transform must be wrong. Since SR is
an interpretation to the Lorentz transform, SR must be wrong as well.
shrug

Nope. What this shows is that acceleration does not affect the decay
rate of muons, and by implication, the tick rate of their internal "clock"..

Thus, gravitational acceleration does not manifest gravitational time
dilation. Gravitational time dilation involves more mystery --- more
mysticism. Not that this would help to resolve the twin’s paradox,
accelerating twin thus does not benefit from the mysticism of broken
symmetry in the Lorentz transform.

Of course, this does not bother you because MYSTICISM IS WISDOM.
shrug

Bailey et al does not refute GR because when one applies GR to their
physical situation and computes what they should observe, one obtains
agreement. It does show that the acceleration does not affect the muon
decay rate.

One can analyze their experiment (including comparison to muon decay at
rest) in two different ways:
a) use the overall inertial frame of their storage ring
and apply SR.

sigh

b) use the equivalence principle of GR, and treat the LOCAL
acceleration of the stored muons as a gravitational field
and compute the gravitational time dilation in LOCAL
coordinates in which the stored muon is at rest.

This makes no sense. The local coordinate cannot tell you
gravitational time dilation. Only using your coordinate to observe a
local phenomenon can you decide if gravitational time dilation. So,
we have more mysticism at hand, and this is good because more
MYSTICISM IS more WISDOM. shrug