Zwillingsparadoxon ohne Beschleunigung von Uhren.

On Mon, 24 Nov 2008 00:00:00 +0100, tenner@xxxxxxxxxxxxxxxxx (Gerhard
Tenner) wrote:

hwabnig # .- --- -. dotat@2:240/2188.911 meinte am 24.11.08
zum Thema "Re: das Ende des Zwillingsparadoxons":

Wißts ihr denn noch immer nicht daß das ZP in der SRT
überhaupt nix mit Beschleunigungen zu tun hat?
Was lernts ihr denn auf euren Schulen?

w., der sich wundert.

Du hast recht in dem Sinne, das auch Geburt und Tot nichts mit der Dauer
des Lebens zu tun haben - sie sind Momente und können daher beim Zeitraum
keine Rolle spielen.
Hast Du in der Schule nicht gelernt, das es Beschleunigung braucht um
gemeinsame Weltlinien zu verlassen und "eigene" zu begehen? Eine andere
Methode wurde nicht gefunden bisher, aber an Leuten die Beschleunigungen
da für irrelevant halten, an denen mangelt es nicht.

Das ZP kann man so konstruieren, daß "Realphysik" draußen bleibt.
Es gibt keine Raketen, keine Raumfahrer, keine verlassenen und
wiedergefundenen Weltlinien.
Nur für den Fall daß Leute mit Geometrie nichts am Hut haben,
braucht man so Modellraketen, Piloten, und den Kram.

Unlce Al in sci.physics hat das schön beschrieben, soll ichs
übersetzen. Ich kopier ihn mal in gekürzter Form.

Drei Raumfahrer vereinbaren einen ZP Test.
A der langweilt sich hinter dem Sternennebel Z.
B flieg grad auf dem Planeten X im Sonnensystem Y.
C sitzt irgendwo in der 237463. Galaxis.

Wir gesellen uns zum A.

(fixed pitch font)

Seine Weltlinie:

^
|
|
|
|
|
A

Ein grader Strich von unten nach oben.


Der B kommt von unten links und fliegt nach rechts oben

^
/
/
/
/
/
B

Sagen wir das seien 45 Grad, dann wärs schöner, geht nicht hier.
Der B kreuzt den A am unteren Ende der A Weltlinie.

Der C kommt von rechts unten und fliegt nach links oben, und trifft
den B in der Mitte seiner Weltlinie, fliegt weiter und trifft den A
am oberen Ende von dessen Weltlinie


Alles zusammen sieht dann so aus:
C
\ | B
\| /
|\ /
| \ /
| \/
| /\
| / \
| / \
|/ \
/|
/ |
A

man erkennt das berühmte Dreieck, isses so?

Nun zu den Uhren.
Üblicherweise geht man davon aus, drei Uhren
nebeneinander zu stellen, zu synchronisieren usw.
Wir tun das nicht. Jeder der drei Raumfahrer baut seine
eigene persönliche Uhr nach einer Bauvorschrift,
die sicherstellt daß alle 3 Uhren gleich schnell ticken.
Irgendwas atomares, oder was euch so einfällt.
Gemessen werden nur Zeitdifferenzen deshalb müssen
die Uhren nicht gemeinsam auf Null gestellt werden.
Laut Uncle Al bauen sie die Uhren erst unterwegs
im geradlinigen unbeschleunigten Flug.

Im Vorbeiflug tauschen B und A ihre Daten aus,
dann B und C, und zuletzt A und C.
A erfaßt seine eigene Zeitspanne hat und die Zeiten
von B und C und berechnet die Differenz.

Für einfache Gemüter hat Uncle Al außen auf seinen Raketen
Kipphebel und dergleichen montiert, um die Uhren zu
starten und zu stoppen, wir aber können abstrahieren und
erkennen das zugrundeliegende Geometrische.
Wesentlich ist das Wegfallen jeglicher Beschleunigung
von Uhren in dem Gedankenexperiment.

Wenn ich nichts vergessen hab, dann ist das alles.

Anbei Uncle Al's Original:
############################################################
A relativistic universe has four distinct
distances: luminosity (inverse square), angular diameter, parallax,
and proper motion. No two of them need agree to maintain
consistency. Clocks can only be synchronized by being local.

There is no paradox. One twin travels relativistically, one twin
stays at home. When they reunite the traveling twin is seen to have
aged much less than its genetic double. The only "paradox" is the
asymmetry (not the effect). If they *both* travel, you work out the
relative hyperbolic rotation in 4-space vs. an outside observer to
both.

Acceleration breaks the symmetry of who ages faster. To accomplish
that, the acceleration can occur before the clocks (or the twins)
exist. Only reference frames matter.

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 in SR to the running of the clocks (as opposed to
Equivalence Principle acceleration in GR). Acceleration 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. There is a difference
between the reference frame and any clocks in it.

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 past 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.

EXAMPLE: 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. The spaceship with Clock 3
is returning back over the path taken by the spaceship with Clock 2.

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" or even while existing.
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 traveling 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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