Re: Transverse paradox parallel question

On Apr 20, 9:31 pm, Peri of Pera <rie...@xxxxxxxxxxx> wrote:
Gravity on the spaceship has been engineered to be the
same as on earth.
Now here is the tricky part. How does that "gravity" on the space
ship work work? Look at it this way. Does this "gravity" work during
the deceleration of the space ship? To decelerate, that space ship has
to have a force exerted on it and the gravity mechanism.


Can he notice any difference in time watching the
two time pieces?
If the "gravity" on earth follows a Lorentz invariant rule, for
instance a Hamiltonian which is Lorentz invariant, then yes. Because
during the turn around, during the deceleration, the gravity in the
space ship can't be Lorentz invariant. The force on the space ship is
shifting the space ship and the clock it contains into different
inertial frames. The earth is staying in the same inertial frame. So
the gravity on the space ship is Lorentz invariant.
So there is no way the gravity on the space ship can be exactly
like the gravity on earth, at least during the deceleration of the
space ship. If SR is true, every force in the universe as seen in an
inertial frame is Lorentz invariant. Force laws that aren't Lorentz
invariant, that don't transform according to the Lorentz equations,
are not allowed. Therefore, the gravity on earth and the spaceship may
be the same while the space ship is moving at a constant velocity, but
the forces are going to be different during the turn around.
Therefore, by merely saying "the gravity is the same" you have
introduced an internal contradiction. One can not have the same force
law in an inertial frame as one that is accelerating relative to an
inertial frame. It is impossible.

Will the hour glass empty in 45 minutes and why?
The hour glass and the atomic clock on board the space ship will
agree. Both clocks on the space ship will disagree with their
counterparts on earth.
What synchronizes the atomic clock and the hourglass on earth is
the fact that both the electromagnetic forces on the atoms and the
gravity on earth are Lorentz invariant. Even though they look like
different types of forces, all forces in an inertial frame have the
same transformation properties.
What synchronizes both the hour glass and the atomic clock are the
forces that deviate from Lorentz invariance. The forces that deviate
from Lorentz invariant also have to obey certain rules to first order
in vx/c^2. Otherwise, the clocks won't work right when the
acceleration stops.
instruments including hour glass and atomic clock on board are
monitored by observers back on earth. Can they measure any time
dilation effects on the spaceship and how? Five easy (maybe >difficult) questions to answer.
The observer on earth will see a time dilation, but the changes
in the ship clocks during the deacceleration will seem negligible. The
clocks on earth and on ship will seem almost unffacted by the
acceleration. The ship clocks will seem to click slower than the
earth clocks, but this will follow the Lorentz time dilation formula
with no modifications necessary for acceleration.
The observer on the ship will see a big difference during the
acceleration. The clocks (atomic and hourglass) on earth will seem to
click slower during the part of the journey where there was no
acceleration. However, the clock on earth will seem to tick faster
during the deceleration. In fact, the clock on earth will seem to jump
ahead during the rapid deceleration. The Lorentz time dilation formula
will NOT work during deceleration. A modification using the
acceleration is necessary. The ships clocks will seem totally
unaffected by anything. So the the observer on the ship, the force of
the rockets speeded up the clock on earth.
One can argue that the observer on the ship experienced an
hallucination. When he gets back to earth, his clocks will not seem to
have advanced as much as the earth clocks.
The difference is the force or its equivalent QM concept. Force
does exist in special relativity, it is the key to everything. The
force on the ship clocks, which turned the ship around, made the twin
clocks behave like there was a speed up on earth.
.

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