Re: Honest Question Re Traveling Triplets
- From: Uncle Al <UncleAl0@xxxxxxxxxxxxx>
- Date: Tue, 7 Jun 2005 22:47:33 +0000 (UTC)
kk wrote:
>
> Third-party reference:
> http://mentock.home.mindspring.com/twins.htm
> "To avoid accelerations in the thought experiments above,
> we can simply make the second Bob frame into a 'messenger'
> Carl that never accelerates, but passes by Bob as they set
> their watches together. Messenger Carl then travels to Ann
> and compares watches as they pass each other. That makes it
> clear that there are three ... inertial frames involved."
>
> * Yes, there are _no_ accelerations (using triplets).
> * Yes, SR's math yields the correct numerical values.
>
> However, physics calls for a physical explanation, and
> yet math cannot provide such (as everyone knows).
>
> The only explanation given at the above web site is the
> fact that the triplets are in different frames, but this
> does not tell us why being in different frames causes
> triplets to age differently.
>
> So here is the question:
> What is the "official" physical explanation for the
> observed difference in ages for traveling triplets?
>
> Disclaimers:
> This is not a trick question, nor is it a leading one;
> it is presented purely in the spirit of sincere enquiry,
> sans any speculation of any sort.
The clock(s) that move(s) further through space is(are) seen to have
had less time pass when all clocks are again made local and compared.
That is the whole of it. If you don't like oscillators or living
tissue as clocks, divide a homogeneous isotropic sample of
radioisotope into equal activity portions and send them on the trips.
Compare activities and decay product concentrations relative to
undecayed material upon return.
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html>
Hafele-Keating Experiment
http://www.hawaii.edu/suremath/SRtwinParadox.html
<http://physics.syr.edu/courses/modules/LIGHTCONE/twins.html>
Twin Paradox
The ratio by which all clocks have aged at the end when they are back
together again is the same in all reference frames:
ratio = sqrt(t^2 - x^2 - y^2 - z^2)/t (with units of c=1)
Acceleration breaks the symmetry of who ages faster. To accomplish
that, the acceleration can occur before the clocks (or the twins or
triplets) 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). 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 or laser ring gyros).
There is no doubt who was accelerated even if a clock was not
running/existing during aceleration - vs. the fixed stars. 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 (compare) 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 know who is moving how fast
vs. the fixed stars.
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 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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