Re: Lesch: Zwillingsparadoxon NUR wegen Beschleunigung

On Thu, 27 Mar 2008 10:30:40 +0100, "Benno Hartwig"
<benno.hartwig@xxxxxx> wrote:


"Helmut Wabnig" <hwabnig@ .- --- -. DOT .- t> schrieb

Das SRT Zwillings Dings läßt sich komplett ohne Masse und
Beschleunigung und Kräfte und so weiter auflösen...

Wie 'löst du das _SRT_ Zwillings Dings auf', ohne ein
Geschehen zu beschreiben, in dem irgend etwas
beschleunigt wird?
Kannst du gem SRT ein Geschehen mit 'Zwillings Dings'
beschreiben, in dem tatsächlich nichts beschleunigt wird?

Benno
(das SRT habe ich mit Absicht unterstrichen)


Ich arbeite nicht gern umsonst.
Kannst es bei Uncle Al nachlesen.

(Zitat):
Acceleration is irrelevant to the Twin Paradox except to break the
symmetry of who ages faster. To accomplish that, the acceleration can
occur before the clocks exist.

Inertial frames with relative *velocities* pursue different paths
through spacetime in Special Relativity. No clock anomaly is apparent
in any of them until clocks are compared (by all being local when you
do it, initial calibration then experiment). Acceleration is
irrelevant to the running of the clocks. It is necessary at some
arbitrary time not associated with the experiment itself for breaking
the symmetry of clock observation. Acceleration defines which
reference frame takes what path through spacetime - even if it occurs
when the clocks are *off* (or not even constructed yet, or destroyed)
- so the situation is NOT symmetric.

1) Acceleration is an absolute measurement and it does not require a
clock to make the measurement (e.g, simultaneous displacement of three
independent orthogonally cantilevered masses). There is no doubt who
was accelerated even if a clock was not running/existing during
aceleration. Any accelerated reference frame has a different mixture
of space and time from an unaccelerated frame.

2) Past acceleration is irrelevant to the running of present clocks,
but not to the mixture of space and time in the reference frame that
said clocks measure. This is an important subtlety and the key to the
whole thing. You cannot synchronize clocks except by having them
local. That's what Relativity demands. If they are local at the
start, you can tell who was naughty thereafter without needing a clock
to do the acceleration measurement. Accelerometers are not clocks.

We have three identical clocks that are off (a state of not running,
or of not even having been fabricated) and zeroed. Each clock
has/will have a very short toggle jiggger switch sticking out. We
load them (or their parts, or ore and a smelter and a machine shop) in
individual spaceships and set up the experiment.

CLOCK 1: That's our clock. It sits stationary in our inertial
reference frame with a little jigger sticking out. Touch the jigger
and the "off" state becomes "on" or the "on" state becomes "off."
Clock 1 is "off." Or we can build it from parts just before we need
it, and in the "off" state, zeroed.

CLOCK 2: In a spaceship traveling at 0.999c relative to our inertial
frame of reference. Clock 2 is "off." It was built after all
acceleration ceased, and set to zero. It skims past Clock 1 (our
clock), the jiggers touch, both Clocks 1 and 2 are now "on" and
locally synchronized by touching. Elapsed time accumulates in each
one. The situation is NOT symmetric! We have an accelerometer and
they have an acelerometer. We know who accelerated to set up the
experiment even if there wasn't a clock present when it happened.

CLOCK 3: In a spaceship traveling at 0.999c relative to our inertial
frame of reference, but 180 degrees counter in direction to Clock 2.
Clock 3 is zeroed and "off." It was built after all acceleration
ceased, and set to zero.

Some arbitrary time after Clocks 1 and 2 synchronize and turn "on" by
touching, Clocks 2 and 3 brush past each other, touching jiggers.
Clock 2 is now "off," Clock 3 is now "on." Write down the elapsed
time in now "off" Clock 2, then smash the clock with a sledgehammer.
Or melt it down, or toss it over the side.

CLOCK 1: That's our clock. It sits stationary in our inertial
reference frame with a little jigger sticking out. Clock 3 rushes
past, jiggers touch. Clocks 3 and 1 are now off. All clocks are
off. No clock has accelerated while "on." Write down elapsed times,
smash each clock with a sledgehammer. Or melt them down, or toss
them.

BOTTOM LINE: Get all three slips of paper together... Accelerate as
you need. Or send all the results to all three folks by radio and
never decelerate. All clocks have been smashed, melted, tossed.
Their elapsed times were written down. The numbers on the papers
won't change when you accelerate or broadcast the data.

Acceleration is arguably General Relativity, as we did setting up the
experiment. It is irrelevant to the clocks. No clock is running or
even exists during acceleration. Numbers written on slips of paper
are unaffected by Special or General Relativity. One could as easily
build the clocks from their component parts after setting up the
experiment. No clock exists during acceleration up or down. The
*reference frame* has accelerated in the past, and that changes its
mix of space and time relative to an unaccelerated frame. The clocks
are passive observers in a presently unaccelerated setting.

Finally.... compare elapsed times. Elapsed time #2=#3 (straight line
motion for both clocks, no acceleration!), but elapsed time #2+#3 does
not equal #1, the local stationary reference frame summation. The sum
of #2+#3 elasped time is only about 4.5% that than of #1's accumulated
elapsed time. You have the Twin Paradox (or, Triplets) without any
running clock having been accelerated - or having even existed during
acceleration up or down.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!


.

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