Re: Twin Paradox paper available
From: Uncle Al (UncleAl0_at_hate.spam.net)
Date: 08/25/04
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Date: Wed, 25 Aug 2004 07:44:39 +0000 (UTC)
John T Lowry wrote:
>
> I've written a pedagogical paper, "The Twin Paradox in Special
> Relativity." It's a 17-page pdf file with only 9 displayed equations and
> 5 graphs. If you'd like a copy via email attachment, just let me know.
>
> Features include: (1) treatment of a single sample twin paradox "trip"
> using three alternative frames of reference (S, the earth and
> stay-at-home twin; S', the outgoing spaceship; and S'', the incoming
> spaceship); (2) a discussion and graph about the traveling twin's need
> to accelerate/decelerate at start, stop, and turnaround points; and (3)
> use of an inhomogeneous Lorentz transform (for frame S'').
>
> Comments and criticism encouraged.
http://sheol.org/throopw/sr-twin-01.html
One twin travels relativistically, one twin stays at home. When
they reunite the traveling twin is seen to have aged much less
than his genetic double. Triplets are more elegant.
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) http://www.mazepath.com/uncleal/qz.pdf
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