Re: definition of a clock in relativity theory

From: Eric Baird (eric_baird_at_compuserve.com)
Date: 08/26/04 

Date: Thu, 26 Aug 2004 01:19:41 +0100

On Mon, 16 Aug 2004 22:57:17 GMT, h@..(Henri Wilson) wrote:

>On Sun, 15 Aug 2004 19:21:46 +0000 (UTC), Eric Baird
><eric_baird@compuserve.com> wrote:
>
>>On Thu, 12 Aug 2004 09:59:00 GMT, h@..(Henri Wilson) wrote:
>>
>>>What matters is that neither the clock nor the rod actually changes in any way.
>>>Therefore presynched clocks always read the same times when reunited no matter
>>>how they are moved.
>>
>>
>>Not neccessarily.
>>If you take two presynched clocks, and dangle one in a high-gravity
>>region, then pull it out and reunite the two clocks, then the
>>gravitational time dilaiton effect ought to result in the dangled
>>clock having aged less by the end of the experiment (even if we don't
>>like and don't accept special relativity).
>
>A perfect clock is not affected by a gravitational field.
>The best manmade clocks DO vary slightly when placed in a free fall situation.

It depends on how we choose to define our "perfect" clock.

In modern relativity theory, I think it's natural to take a "clock" as
being an idealised physical process that can be used to measure the
passage of time, whether that's the rate at which a known mass
accelerates when a known force is applied, or the rate of an isotope's
atomic decay, a natural resonant frequency, or the rate at which a
lightbeam is supposed to bounce between two mirrors, or some other
fairly "pure" idea of something that produces a measurable indication
of apparent timerate.

In studies of supposed changes in timerate in inertial physcs, it's
also important to specify that the "clock" should be capable of
functioning in freefall.
That's why there's a footnote in the "Dover Press" republication of
the 1905 "electrodynamics" paper (p50) reminding us:
: "Not a pendulum clock ... "
That footnote wasn't in the original paper, so it's presumably either
been added in the German-language republication, or in the authorised
Lawson translation, but it /is/ in there.

>>
>>Increasing the background gravitational field strength around a test
>>object seems to be equivalent to increasing "inertial field strength"
>>in the region,and increasing the object's inertia woudl seem to reduce
>>the rate of the nuclear and chemical and inertial processes that we'd
>>normally use to measure time. Increase the inertia of a pocket-watch's
>>flywheel and it ticks more slowly. Increase the inertia of an atomic
>>nucleus and its resonant frequencies drop, and it takes longer to
>>decay.
>>
>>
>>So gravity really /does/ seem to screw up preset clockrates, as a a
>>matter of principle, even if we are still using Newtonian mechanics
>>(and appending Einstein's 1911 gravity-shift argument).
>
>These are purely unavoidable mechanical effects. They are not related to any
>silly known theory.

Well, these calculated gravitational effects would /seem/ to be valid
irrespective of what sort of clock is being used.

If your "clock" floating out in space is constructed using
marshmallows and elastic bands and mice running around on wheels
chasing cheese, and it produces visible "ticks", then looking at the
the optical signal stream leaving the clock and arriving at an
observer who happens to have jumped into a stronger-gravity region,
then if that observer sees the light to have increased it's energy as
it moved into the gravity-well, and if that energy-change shows up as
an increase in frequency and a reduction in wavelength in the received
light, (as opposed to a change in amplitude), then if the EM signal
leaving the clock contains a certain number of EM wavepeaks between
the parts of the signal that contain the "tick" signal, then if this
number does not change en route, if the deep-gravity observer sees the
stream of wavepeaks to be compacted into a smaller amount of time
(because of the frequency-shift), then they ought to also see the
stream of clock-ticks carried on the back of that signal to be
compacted into a smaller amount of time, too.

So (by this loooong chain of arguments) the stronger-gravity observer
ought to see the mouse-marshmallow-cheese clock to appear to be
running at an increased rate, with an amount of apparent speed-up
depending on the strength of the gravitational gradient along the
viewing path, regardless of how the clock in question happens to be
constructed.

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.

I suppose that we could try to compensate for this effect in order to
produce a "compensated" clock (which would be more like one of
Newton's hypothetical "absolute" clocks), but Machian arguments
suggest that if we try to calculate the rate of a clock if the
gravitational field is taken away completely, we get a meaningless
result (infinity, perhaps?).
The more general principles of relativity seem to suggest that the
gravitational field acts as a sort of physical aether and physically
defines the local concepts of time and distance, and if you take the
field away completely, there's nothing left: the field "is" space, so
in the most extreme interpretation of gravitational time dilation, the
gravitational field density is not messing up a "natural" underlying
clockrate, it's _defining_ the natural underlying clockrate.

>Until we can establish a direct connection between gravity, mass, magnetism,
>time and god knows what else, there is nothing much we can say about the
>subject except that all known clocks appear to be affected by gravity due to a
>number of factors, one of which relates to their own self-compression when
>restricted from free falling.

The above argument was for free-falling clocks.

The "stronger-gravity" observer could still be inertial and at a
constant distance, for instance they could be floating at the centre
of gravity of a compact double-star system, so that there is a
definite gravitaitonal gradient between them and the cheese-clock, but
both parties are still in freefall

>>
>>The next complicating issue is acceleration ... if we apply the
>>principle of relativity in its most general form, acceleration effects
>>ought to be equivalent to the effects generated by (a particular odd
>>sort of) gravitaitonal field (= a Coriolis field), so if we have two
>>spaceships coasting away from each other at a high proportion of the
>>speed of light, and one fires its retro rockets and turns around, and
>>catches up with its twin, then we'd expect the ship that turns around
>>to have aged less when they meet up again, as an acceelration effect,
>>and, again, we should probably expect this to be true even if we think
>>that special relativity is rubbish.
>
>A perfect clock should not be affected by acceleration.
>All manmade clocks appear to suffer in some way.

Well, if acceleration affects the apparent background gravitational
field-strength that the clock is effectively immersed in, then that
can be used to calculate a clockrate change from those gravitational
principles, with the gee-forces being used as an indicaiton of the
expected equivalent change in background gravitaiton ... but if you
also want to work out the more difficult issue of how physical
accelerations themselves might screw up the particular operating
mechanism of the particular type of "real-life" clock that you've
built, due to the local physics now being verifiably different, in a
way that the clock itself "sees", than yes, that sounds a lot more
difficult.

>>... and again, if we have a centrifuged clock, even if we think all
>>the SR definitions and arguments are junk, the general
>>gravitation/equivalence principle arguments would lead us to expect
>>that the accelerated clock at the centrifuge rim should age more
>>slowly than a non-accelerated clock hovering at the centrifuge axle,
>>even if we know nothing about SR.
>
>Bull!
>You are preaching SR.

Nope it's the general gravity-shift idea, coupled with the equivalence
principle.
If it makes you any happier, most of the SR folks don't seem to like
the idea of a "gravitational" explanation for the centrifuge test, it
makes claims that the result can't be explained without SR look a bit
hollow.

For the record, I count myself a as relativist, but I don't like SR's
partial implementation of the idea. I personally think that the
special theory cuts too many corners, and that some of these
idealisations probably have bad consequences.
 

>Try centrifuging a pendulum clock.
>It will go either slower or faster depending which way you lean it.
>
>>
>>
>>So I think that these arguments about SR's validity should not be so
>>much about whether these effects exist or not ... they do /seem/ to
>>exist, and we'd arguably expect them to exist regardless of whether SR
>>was right or wrong ...
>>... but rather whether the effects as predicted by SR can be
>>distinguished from the similar effects that we get from more general
>>principles, and that, when we find a situation where the two sets of
>>predictions diverge and can in principle be told apart, which set of
>>predictions is /really/ the most accurate.
>
>SR claims that TIME itself is somehow linked to a gravity field.

I think that that this sort of claim pops up in General Relativity
(and in general Machian theory), but I dont think I'd say that it's
really an SR thing.
Parts of SR do seem to overlap into gravitational territory, but SR
itself isn't supposed to be up to the job of doing full-blown
gravitational physics ... it can give indications of how parts of
gravitational phyuscs /might/ operate, but those SR-based indicaitons
won't /necessaily/ be completely right.

 
>There could be some truth in that but no relationship has been found.
>
>One thing we CAN say however is that TIME is definitely not affected by the
>characteristics of any clock.
>You seem to be claiming that a clock DEFINES time flow.

I think I'm saying that when you have a "real" difference in effective
local timeflow between two regions, you can use clocks placed in those
regions as a useful way of illustrating and revealing the existence of
the difference, and you can also use the predicted change in frequency
of light passing between those clocks (altered by gravitational
shifts) as a way of calculating what the difference in "effective"
timeflow between those regions ought to be.

If there's no difference in timeflow between those regions, or if we
are using a "gravity-compensated" idea of timeflow, and
gravity-compensated clocks, then of course the whole exercise becomes
a bit redundant. But even if you prefer to use gravity-compensated
clocks showing a sort of agreed standardised time, then I think its
still useful to be able to calculated the strength of the expected
"gravitational time dilation" effects, so that you know what to
compensate for.

The situation with relatively-moving clocks, where there are also
distance-change-related effects to be considered, and the issue of
whether or not the existence of a moving mass affects light
propagation (experiment says yes, SR says no), is more fraught, and I
don't think that I'd be happy defending the way this is dealt with
under SR.

>
>>Unfortunately, the pro-SR crowd seem to be doing the opposite ...
>>concentrating on the experiments and thought-experiments where SR's
>>predictions are the most difficult to tell apart from more general
>>theory, and then claiming those as being the important tests of SR,
>>with the comparisons that /really/ might be capapble of either
>>significantly supporting or breaking SR arguments being sidelined and
>>forgotten about.
>
>Precisely!
>They don't want to know. Too many heads would roll.

Well, it seems that we do the circular storage-ring test, get the
exact acceleration-shift result that the gravity-shift calculations
give us, and then claim the entire effect for SR by saying that of
course we "know" that the acceelration effects are negligible.
I'd suggest that we "know" no such thing, and that the SR community
seem to be misrepresenting the competing gravitaitonal math (knowingly
or unknowingly) in order to make their favourite theory look good.

If they are really certain that the verifiable centrifufge time
dilation effect (known ring circumference, known number of clircling
particle-pulses passing the observer per second, known number of
circuits of the ring traversed by the particles before decay), is 100%
due to the particles' speed wrt the lab, and not at all due to the
geeforces, then it would be nice to see tham actually testing that
assertion by seeing how long their "centrifuged muons" live when the
storage ring incorporates some straight-line sections where we still
have relative velocity, but where the geeforces are absent.
 
I've never seen a physics person willing to even acknowedge the idea
of this sort fo experiment, perhaps becuase they aren't 100% sure that
it would give the sort of SR result that they'd want.

>Henri Wilson.
>www.users.bigpond.com/hewn/index.htm
>See proof that light speed is source dependent.
>www.users.bigpond.com/hewn/variablestars.exe

=Erk= (Eric Baird)
: " Hey, that was just a theory! There are LOTS of theories that didn't pan out ...
: Lone gunmen, Communism, geometry ... "
: --- Joey Tribbiani, "Friends"

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