Re: definition of a clock in relativity theory

From: Eric Baird (eric_baird_at_compuserve.com)
Date: 08/29/04 

Date: Sun, 29 Aug 2004 23:10:10 +0000 (UTC)

On 26 Aug 2004 06:32:33 -0700, suzysewnshow@yahoo.com.au
(suzysewnshow) wrote:

>> And if the strong-gravity observer can see the image of the clock to
>> be apparently running "fast", and running at that accelerated rate for
>> an arbitrarily long time-period, we seem to run out of explanations
>> for how this situation could be sustainable in real life, unless the
>> "natural" rates of clocks in the strong-gravity and weak-gravity
>> regions is different by the same amount as the observational mismatch
>> in apparent clockrates that we just worked out.
>
>Indeed!
>If the pitcher throws 1 ball per second for 1 hour and the catcher
>catches more than one ball per second, higher frequency due to the
>"over the plate blue shift", then at the end of the hour the catcher
>should have more balls at his feet than the pitcher ever threw. I
>suppose it has something to do with trusting a scholar with a slide
>rule before he masters the abbacus or the bribery of umpires. I am not
>really sure.

Well, I think that in this case, The Great Umpire sneakily tampers
with the relative rates of the players' wristwatches, and then
sneakily alters their overall rates of timeflow by the same amount so
that they don't know who to blam efor the discrepancy!
<heh heh

Seriously, though, the basic form of the problem probably goes back
over a century, we have:

1: the idea that light changes energy as it crosses a gravitational
gradient,

2: the idea that this energy-change shows up as a change in the
character of the light, rather than as a change in quantity (change in
wavelength rather than amplitude, Michell, 1783),

3: and then at some time during the 1800s we probably have the
corrected relationship between energy and frequency, telling us that
energy-gain is associated with a blueshift and energy-loss with a
redshift (Newton seemingly got that bit back-to-front).

And by this point, some time during the C19th, we have all the pieces
in place for the clock problem. Loads of mathematicians and physics
people must have looked at it, chewed the ends off their pencils, and
then binned their calculations because they couldn't find any possible
way to resolve the issue without allowing the clocks to run at
dfifferent rates.
Einstein comes along, looks at the problem, and publishes it as-is,
saying that since there doesn't seem to be any conceivable
agreed-clockrate solution ... the clocks would seem to be running at
/different/ rates. <ker-ching!
It's such a simple argument, that I'm sure a lot of researchers were
spitting blood for not having taken the math seriously and published
it themselves. Doh!

-------------------

We can also run the idea backwards.
If we start off with the idea that two regions have different rates of
timeflow (with a transitional region in between), then if we try to
aim a pulse of light between the two regions, at right angles to a
line joining them, then since the fast side of the wavefront should
advance faster than the slow side, the pulse should end up being
steered more towards the region of slowest lightspeed (eg refractive
index arguments), and an attempt to aim a lightbeam along the line
should result in the lightbeam being bent.

If we then try to throw a ball along this line, if the EM and other
forcesinside the ball are deflected in the same way, including the
forces in equilibrium inside the atoms comprising the ball, then the
change in internal equilibria should result in the ball's trajectory
also being smoothly deflected towards the region of slowest
lightspeed.

Finally, if we simply place a ball between the two regions, the same
sort of imbalance in inertial forces inside the ball ought to make it
start to magically start moving towards the slow-lightspeed region,
picking up speed as it goes, even if the ball is initially not moving
when it is deposited in the region.

So if we start out by assuming a gravitational differential we seem to
end up with a description of a "timeflow" differential, and if we
start out by assuming a timeflow differential, we seem to end up with
a description of something that seems to be indistinguishable from a
"real" gravitational field.

So the arguments for gravitational differentials and timeflow
differentials seem to be very tightly intertwined, and that kinda
suggests that the two ideas may actually be synonymous, or at least
strongly interdependent in some way.

Newton already said that a gravitational field seemed to be associated
with a change in density of the light-aether (= an apparent change in
spatial density), so going one step further and saying that yes,
gravity warps a light-metric, but it can also be said to warp apparent
temporal coordinates as well as spatial ones ... I really don't think
that it's a big step.

=============

PS: "Believing" in gravity-shifts doesn't seem to necessarily require
one to "believe" in special relativity (if that's what's worrying
people), because the gravity-shift idea can be implemented using the
SR shift equations, =or= by using the older Newtonian set.
There's two different available routes, here.

Using the SR set as a starting point for gravitaitonal theory
generates simpler, "tidier" gravitational physics (it's arguably
responsible for GR's simple clean inescapable black holes, for
instance), but since we don't seem to live in a simple and tidy world,
I think that the SR-based gravitational theories are more like "toy"
models, easy to play with but not to be taken too seriously.
I think that the "Newtonian" set is far more powerful and gives us
more "sophisticated" gravitational physics, and a more powerful set of
tools to work with.

It's possible to "approve of" a lot of the GR arguments without
neccessaily "approving of" special relativity.

=Erk= (Eric Baird)
: "Nobody cares anything about history any more"
: -- Captain Atom, "Justice League Europe"

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