Re: Twin Paradox paper available

From: RP (no_mail_no_spam_at_yahoo.com)
Date: 08/26/04 

Date: Thu, 26 Aug 2004 09:30:48 +0000 (UTC)

Uncle Al wrote:
> 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.

 From the FoR of #2, his elapsed time will be more than that of #3 on
these slips of paper, because from his frame #3's clock is ticking slower.
Assume #3 had a laser clock on board, oriented parallel to y. This clock
will tick slow wrt #3 by the factor 1/gamma, that is, since light
propagates at c wrt #2.

Thus, since #2 perceives the spacelike separation of the first two
events to be equal to the spacelike separation of the 2nd and 3rd
events, then he must find that his slip of paper will record more
elapsed time than #3's slip of paper.

And yes, the triplets argument is indeed much more elegant, it proves
the fallacy of special relativity without ambiguity, and with a minimum
of effort.

Al, these observers, if all born in other frames, and located distant
from the Earth, do not know but that they've accelerated back into
Earth's rest frame. I think that's the part the slips past you. Without
absolute acceleration histories dating back to the beginning of time,
your argument is worthless, since you must rely on a de facto never
accelerated frame, i.e. a "master" frame. The correct transformation
must be noncommutative, i.e. there is a local at rest reference frame.

Thank you,

Richard Perry

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