"El Enrrabadore-mor" wrote in
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"bz" escreveu na mensagem
98.139...
"El Enrrabadore-mor" wrote in
:


"Tom Roberts" escreveu na mensagem
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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.
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.
These obtain the same answer.

Moreover:
Your a) appeals on velocity as the cause of
time dilatation.
Your b) appeals on acceleration (or gravity
by equivalence principle) to be the cause on
time dilatation.

It is not the velocity or the acceleration (in SR) that explains the
time difference.
It is the different trajectory.
Trajectory through space-time.

And that space-time is a Gaussian coordinate
system made of curved lines like two orthogonal
mirror spirals?

Please explain Bob.

Look at the particle that has just made one trip around the ring.
It is now back at its starting point in space but has moved in time.
The particle that stayed stationary at the center of the ring has NOT
moved in space but it, too has move in time. The integral along both
trajectories must have the same length. Therefore the moving particle has
traveled less distance along 'its time axis' (but the same distance along
the 'Lab' time axis.






Physics say:
c) Acceleration is the time derivative of velocity.

My c) proves your a) and b) to be incompatible,
since time used on the derivative is ABSOLUTE
TIME.

a = dv/dt says nothing about ABSOLUTE time.

Where did you get the impression that it did?

dt is CHANGE in time.


I wonder how derivatives will be if the said changing
time had been already affected by time dilatation.

Just imagine that velocity changes.
Time dilatation will change too.
You get a derivative where time himself changes.
What a mess I presume.

Use partial derivatives when the function is a function of more than one
thing.




--
bz

please pardon my infinite ignorance, the set-of-things-I-do-not-know is an
infinite set.

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