"Tom Roberts" escreveu na mensagem
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El Enrrabadore-mor wrote:
"Tom Roberts" escreveu na mensagem
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For circular motion, |v(t)| is constant:
\tau = sqrt(1-|v|^2/c2) (T2 - T1)

I just didn't realise that you've simplified that much the problem.

Look at the subject of this thread. "simplifying" to circular motion is
what is being discussed.


Such simplification makes your solution ridiculous, that's all.

It's not "ridiculous", it is what this thread is about. I gave a general
equation (in response to an inquiry), and then applied it to the subject
of this thread. shrug


If you find the thread subject (the original inquiry) ridiculous,
I must say it is not, since it is just a limit case of a very
real and possible situation.
We have about 7 planets that have almost perfect circular orbits
around the Sun. All of which have different speeds and different
gravitational fields. One can build 7 atomic clocks and place
one per each planet during, say, 10 Years.
After 10 Years running at different rates, clocks can be
brought back to Earth and its elapsed time compared.
If time has to differ, relativity must be able to predict those
differences. That's what the inquiry is all about.

If you find the above example not feasible and real enough,
and have a better one.
Draw a straight line from the center of the Sun passing
by the center of the Earth. such line will cross the Earth
surface in two points, one closer to the Sun and another
the Earth diameter long. Such two points will have a
differential speed of around 3,000 km/h due to daily
Earth rotation, plus a square term additional velocity
due to the radius increase relative to the Sun.
Also you can consider the GPS satellites that revolve,
if I remember correctly, around a 24,000 km radius.
For GPS satellites the speed difference is much larger.

According to Your "relativity circular motion" theory
one should measure daily, or in a matter of hours,
changes in the clock rates. Actually, the accuracy of
GPS system must show deviations along the day and
in a matter of hours too. But they don't, because as
I remember nobody accounted for the radius distance
change relative to the Sun during Earth circular orbit.


[...]
To compare, or to say, that circular motion is the same
thing as linear motion, sounds ridiculous to me.

What is ridiculous is your "sound bite" approach to physics.

Nowhere does anybody claim "circular motion is the same thing as linear
motion". But when the formula in question depends only on |v|, and when
one considers a constant |v| (which can apply to either linear or circular
motion), then THE FORMULA gives THE SAME ANSWER for the two types of
motion. This does not in any way imply the motions themselves are "the
same".

This is not limited to just linear and circular motion
-- ANY motion with constant |v| obtains the same answer
from this formula.

Sounds fair enough, but things are not that simple.
For starters, there are no massless particles.
The equivalence principles simply removes the mass from
the theory. Therefore, forces like centrifugal force, centripetal
acceleration and gyroscopic momentum (Iw) have been
conveniently removed.

And what about the length?
There's one thing I'm sure about circular motion. You cannot
have time dilatation and length contraction at the same time
for circular motion.
You cannot say that a circle doesn't measure 6,28... radians
anymore. You cannot say that for a speed equal to the speed
of light the perimeter of the circle is zero.
And so on...


I'm about to say that, relative to the XXI Century, relativity
theory is in its Stone Age. ...and people stoned with it.

Obviously you do not understand it, so your opinion is irrelevant.

This is not a matter if I understand or not (and I don't understand).
This is a matter of describing the real world and a manner that
must be in agreement with experiment/observation.
Clearly that your description doesn't fit reality.
Nevertheless, everybody is free to dream and it is said that
dreams are very important for life. Dream on.


Tom Roberts