"Darwin123" escreveu na mensagem
...
On May 3, 2:25 pm, "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.

The funny thing about this is that time and length change
at the same time, but not the ratio between both (velocity).

If we keep length constant, the only possible solution is
uniform circular motion. That is a twin travelling in circles,
of constant radius r, around the first twin assumed to be
stopped at the center of rotation.

Let's say the radius r is a constant value of 100 light-seconds
(r = 100c).
The speeding twin goes on a spaceship at 0.999c.
Therefore, the angular speed 'omega' is v/r = 0.999c/100c
= 0.01 rad/s.
The speeding twin takes 628 seconds to have a complete turn
of 360 degrees.

For small values of t, the speeding twin is almost going in
a straight line, but is fact it has a centripetal force f = m c^2/r
= m c/100, being the centripetal acceleration c/100, towards
the first stopped twin in the center of rotation.

Both twins have powerful antennas that broadcast radio
spherically around the entire space. Both twins are tuned
to each other frequency/radio-station.

Since the distance r = 100c between the emitter and the
receptor is constant, obviously that both twin will hear
each other radio (music) in perfect conditions.

Nevertheless, relativity says that the clock synchronising
the emission of the speeding twin must be running at
a clock rate close to zero. Theoretically, the speeding
twin won't have any trouble receiving the stay-at-home
radio emission, but the stay-at-home twin cannot
receive the speeding twin radio emission, because
the speeding clock is running near zero.
The speeding twin radio emission will take infinite
time to broadcast one single spoken word. The
stay-at-home will be dead by the time the speeding
twin could say a single word.

The trouble seams to be the acceleration:
a = (0.999)^2 c/100 which is about c/100.
(Here the number 100 means 100 seconds).
That's a huge gravity field of 300,000g at
a radius of 100 light-seconds, just imagine
the value it will be at Earth radius based
on the inverse-square Law.)

I presume that such acceleration of 300,000g will
be responsible for a clock speed up rate that
should keep time unchanged after all.
Ys, Einstein proposed this as a thought experiment. However, his
analysis was done using the inertial frame as seen by an observer at
the center of the earth. The moving clock on the edge of the circle
will seem to be slowed down relative to the clock at the center of the
circle, the one that is not accelerating. The clock in the center will
seem speeded up compared to the clock on the circle. However, this
clock is not accelerating.
Yes, the assymmetry come from the centripetal force. The twin in
the center does not experience the centripetal force as the twin on
the circle.
The clocks relative to each other will see differences in the
rate of ticking. The clock with the largest acceleration ticks the
fastest. The other clocks lag behind. However, the clock that
accelerates least (i.e., moves at the slowest tangential speed on the
circle) lags behind the clocks with more acceleration.

Any comments welcome.
This is a description of the Hafele-Keating experiment. The
experiment was performed, and matched Einsteins predictions. Hafele
had two articles in Nature that describe both the experiment and the
analysis of the results. The experiment was performed with atomic
clocks. It is a classic validation of special relativity.


Clearly, your arguments blame acceleration to be the
cause of time dilatation. Fine.

The circular motion at constant angular velocity and
constant radius adds something more.
Not only you have acceleration, but also velocity
relative to any inertial frame of reference nearby.

You cannot add both effects: Velocity + Acceleration
If you sum both effects chances are that you come up
with the conclusion that they cancel each other out.
That's what happens for a stable orbit anyway.

a) - Acceleration causes the clock to speed up.
b) - Velocity causes the clock to speed down.
Summing both a) and b) will give what ?
1 - Absolute time?
2 - Partially absolute time?
3 - Discard one of the effects and have relativity
time dilatation solution?

I bet on conservation of energy, but I was already
told that General Relativity essentially discards nonlocal
conservation of energy. That simply shots down a
Physics pillar stone, but who cares?
Unfortunately, the local process looks to be
irreversible. If it was reversible, non-conservation
of energy locally leads to local free-energy generation.