time, motion and space
jjoensuu
I have some statements and conclusions here that I wanted to have
checked by the physics gurus. Just because the conclusions seem to make
sense in some way, but that there could be reasons for which they are
simply plain wrong.
Some years ago I read about an experiment in which a supposed slowing
of time was measured. The experiment involved an airplane flying at a
high altitude, and an atom clock somewhere on earth. Supposedly the
results from the experiment showed that the atom clock had slowed down
with the lower gravity in the upper atmosphere. The conclusion was that
since the clock slowed down, time slowed down. I failed to see a
connection between clocks and time because, as I understand, clocks do
not really measure time anymore than any other rotating mechanical
device (eg a car engine). OK, in the experiment they used atom clocks,
but if the cesium atom now happens to vibrate at a slower speed does
not really have anything to do with time itself. Anyway, my questions
are not really about the relationship between clocks and time.
The questions relate to the old issue that time itself is an illusion
(caused by our limited minds, the fact that we are "defined/limited" in
some way, or pick your choice). If time is an illusion, wouldn't this
mean that motion is also an illusion, since motion can only occur in
time? And taking this a step further, if motion is an illusion,
wouldn't space then also be an illusion? Does current scientific
evidence support this type of notion at all?
thanks in advance,
JJ
harry
"jjoensuu" <j_jo...@yahoo.com> wrote in message
news:1167649785.5...@k21g2000cwa.googlegroups.com...
> Hi all,
>
> I have some statements and conclusions here that I wanted to have
> checked by the physics gurus. Just because the conclusions seem to make
> sense in some way, but that there could be reasons for which they are
> simply plain wrong.
>
> Some years ago I read about an experiment in which a supposed slowing
> of time was measured.
"time" means here: readings of standard clocks, as compared to those of
reference clocks.
> The experiment involved an airplane flying at a
> high altitude, and an atom clock somewhere on earth. Supposedly the
> results from the experiment showed that the atom clock had slowed down
> with the lower gravity in the upper atmosphere.
In fact the clock should speed up: gravity slows down.
> The conclusion was that
> since the clock slowed down, time slowed down. I failed to see a
> connection between clocks and time because, as I understand, clocks do
> not really measure time anymore than any other rotating mechanical
> device (eg a car engine).
If you don't want to define time with clocks, then how do you want to
measure it? And what about temperature, how do you want to define
temperature without thermometers as basis? This is necessary in physics.
> OK, in the experiment they used atom clocks,
> but if the cesium atom now happens to vibrate at a slower speed does
> not really have anything to do with time itself. Anyway, my questions
> are not really about the relationship between clocks and time.
Fine - I hope to have answered it nevertheless!
> The questions relate to the old issue that time itself is an illusion
> (caused by our limited minds, the fact that we are "defined/limited" in
> some way, or pick your choice).
In fact the question is very much the same. Time is our concept that is
derived from periodic motion. Thus time is abstract, and exists in our
minds. But why do you call it an illusion?
> If time is an illusion, wouldn't this
> mean that motion is also an illusion, since motion can only occur in
> time?
That would be putting it on its head. See above.
> And taking this a step further, if motion is an illusion,
> wouldn't space then also be an illusion?
"space" has different meanings. The common meaning is an abstraction.
Harald
carlip...@physics.ucdavis.edu
[...]
> Some years ago I read about an experiment in which a supposed slowing
> of time was measured. The experiment involved an airplane flying at a
> high altitude, and an atom clock somewhere on earth. Supposedly the
> results from the experiment showed that the atom clock had slowed down
> with the lower gravity in the upper atmosphere. The conclusion was that
> since the clock slowed down, time slowed down. I failed to see a
> connection between clocks and time because, as I understand, clocks do
> not really measure time anymore than any other rotating mechanical
> device (eg a car engine). OK, in the experiment they used atom clocks,
> but if the cesium atom now happens to vibrate at a slower speed does
> not really have anything to do with time itself.
If only one kind of clock -- say, a particular type of atomic clock
-- slowed down, you would have a point. But as far as we can tell,
*every* type clock, and everything else that changes with time,
slows down, and all by exactly the same amount. We observe this for
"clocks" based on weak interactions (e.g., particle decays), those
based on electromagnetic interactions (e.g., atomic clocks), those
based on strong interactions (e.g., other types of decays -- though
this is not really well tested for gravitational effects), those
based on gravitational interactions (e.g., orbits in binary systems),
as well as for "mechanical" clocks (e.g., rotating neutron stars).
We believe that chemical reactions -- and with them, human perceptions
of time -- will slow down by the same amount.
Now, you are free to invent some abstract concept of "time" that does
not slow down. But if all physical processes slow down by the same
amount in a gravitational field, that makes your "time" inherently
unobservable. It's no longer what physicists mean by the word.
Worse, it seems to be a useless concept: it can't be observed, it
can't be affected, it has no effect on anything that can be observed.
To a physicist, if everything that changes with time slows down by
the same amount under some condition, that *means* that time slows
down.
Steve Carlip
Uncle Al
<http://en.wikipedia.org/wiki/Hafele-Keating_experiment>
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html>
<http://metrologyforum.tm.agilent.com/pdf/flying_clock_math.pdf>
http://metrologyforum.tm.agilent.com/cesium.shtml
http://arxiv.org/abs/physics/0008012
Hafele-Keating Experiment
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2
Dirk Bruere at NeoPax
Time is measured by clocks.
What are the implications from the QM POV when simply looking at a clock
alters its 'tick rate' through the QM Zeno Effect?
--
Dirk
http://www.onetribe.me.uk - The UK's only occult talk show
Presented by Dirk Bruere and Marc Power on ResonanceFM 104.4
http://www.resonancefm.com
--Boundary_(ID_tL0VbM5+zyrW97QuK2G+aA)--
Oh No
>Time is measured by clocks.
>What are the implications from the QM POV when simply looking at a
>clock alters its 'tick rate' through the QM Zeno Effect?
>
It's not clear to that it should also apply to the observation of
classical processes like those of clocks, even on a time scale much
smaller than that which can be measured by a clock.
In fact it is not even clear to me that a quantum process is slowed down
by continuous or near continuous observation. As I understand, we are
talking here about something like observing a particle to see whether a
decay takes place within any given time interval. As we refine our
apparatus such that the time interval tends to zero we find that the
rate of observed decay also tends to zero. This is a prediction of
quantum theory and I believe has also been observed in practice. But I
am not sure that I can conclude from this that the likelihood of decay
per second tends to zero. I don't see how the formalism of quantum
theory allows us to eliminate the possibility that actually the decay is
just as likely, but that in refining the apparatus we are necessarily
more likely to fail to observe it taking place.
Anyway, I think this is a very confusing effect, and if anyone has a
better take on it than I do, I hope they will correct me.
Regards
--
Charles Francis
substitute charles for NotI to email
John B. Fairson
> Hi all,
>
> I have some statements and conclusions here that I wanted to have
> checked by the physics gurus. Just because the conclusions seem to make
> sense in some way, but that there could be reasons for which they are
> simply plain wrong.
>
> Some years ago I read about an experiment in which a supposed slowing
> of time was measured. The experiment involved an airplane flying at a
> high altitude, and an atom clock somewhere on earth. Supposedly the
> results from the experiment showed that the atom clock had slowed down
> with the lower gravity in the upper atmosphere. The conclusion was that
> since the clock slowed down, time slowed down.
It was on a Concorde, Great Britain-France's noisiest jewel. It was to test
special relativity, not general relativity and gravitation. The plane made
a turn around the earth, and a discrepancy was observed between two
identical atomic clocks, one in the plane and one remained on the ground.
According to the theory, the reason is the speed difference. The Concorde
could be as fast as mach 2.
> I failed to see a
> connection between clocks and time because, as I understand, clocks do
> not really measure time anymore than any other rotating mechanical
> device (eg a car engine). OK, in the experiment they used atom clocks,
> but if the cesium atom now happens to vibrate at a slower speed does
> not really have anything to do with time itself. Anyway, my questions
> are not really about the relationship between clocks and time.
Time is what is measured by a clock, in the historical construction of
relativity. It's just a definition, but one that allows application to the
real world. A physical theory describes the relations between measurements
made with a well defined procedure, it doesn't "explain" anything.
The atomic clock is based on the period of the electromagnetic wave emitted
by the transition between two states of a given isotope of cesium. As those
atoms are identical, and even indiscernible, the clock is absolutely stable,
as can be checked by measuring one with another. The precision is something
as crazy as 10^-10.
JBF
Uncle Al
<http://en.wikipedia.org/wiki/Hafele-Keating_experiment>
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html>
<http://metrologyforum.tm.agilent.com/pdf/flying_clock_math.pdf>
http://metrologyforum.tm.agilent.com/cesium.shtml
http://arxiv.org/abs/physics/0008012
Hafele-Keating Experiment
If you do not like oscillators, go for radioactive decay. Muons
generated in the upper atmosphere show extended half-lives by reaching
the ground. No clock is necessary. We know how fast they travel, we
know their half-life at rest. Do the arithmetic and make the
inarguable observation.
Grouchy
Hmmm. Here's a link to NIST:
http://tf.nist.gov/timefreq/general/museum/847history.htm
The operational tolerance (error deviating from an expected range) of a
cesium fountain(atomic clock) operating up into the Ku band of the
atmosphere on an airplane compared to the performance of a very similar
apparatus kept stationary on the ground is the Ockhams razor
explanation for the off-set... basically, the clock works by directing
a constant beta emission across a measurement field. The problem
occurs because the emitted beam of beta decay is effected in a number
of ways as it's imperfectly shielded casing is flown up into a layer of
the atmosphere where the propagation of the apparatus compared to that
sitting stationary on earth changes the performance metrics, from how
the lasers exciting and directing the beta emission operated, to the
quality of the beam of particles, to the sensitivity of the measurement
field to motion within a new basket of variables. And we're talking A
LOT of changes between the ground and upper atmosphere.
In fact, the latest atomic clocks will reveal a degree of skewing
between one building and another next door (forget about the upper
atmophere!). Although there is typically an observed altitude effect
on performance, there's also other observed variances between slaved
clocks at the same altitude but different spacial orientation. Plus,
there's certainly nothing like an inverse squares falloff one would
expect if classic gravitational forces were the main culprit for the
performance decline.
So no, "time" is not changing. The apparatus that we've used as a
"clock" to define the second in a highly controlled labratory doesn't
work as well when it's packed into an airplane and flown up where the
propagation media and magnetic field conditions degrade it's ability to
consistantly conform to the numerical definitions performance
tolerance.
The mistake occurs in assuming that a "clock" is a "clock" no matter
where it is or how a particular set of "clocks" work. If we took two
swiss watches, synced them, and then kept one stationary while we moved
the other to a place where a strong enough magnetic field existed, the
gears of the second would have to overcome this or that change due to
the magnetic field mussing with various clock elements performance.
Compared to the watch we kept as our control "clock", the twin "clock"
would run differently. In the case of the cesium fountain, the 166
isotope wouldn't be effected by the laser array just right, or there
might be a drag in the cavity fields response time, or any of a very
large number of exotic new variables. This has nothing to do with the
nature of "time", although it does suggest that spacecraft are going to
need a different kind of clock in the future (the new SV's use rb.
(The short answer to your question is: you're basically correct).
In terms of the question of "time". "Time" is an abstract idea
relating the notion of continuous linear change that can be used
without qualification to standardize "duration". In the sense of
"Time" existing as an idea about changing systems.... it exists as an
idea. In the sense of "Time" as a universal linear absoulte, it CAN
exist if defined correctly and is well below our current technological
ability so as to seem linear. Obviously there are systems that
continuously change at a more or less linear ratio between each other
when observed within a super-system and BY a third system, but a neat
Victorian numerical representation is (as you write) an illusion. More
typically metrology uses an algorithmic or analytic representation of
the process and apparatus currently the most technologically stable,
and then computer programmers and engineers translate the resulting
data into a neat numerical representation using secondary statistical
and normalization schemes.
(the short answer is: "Time" is just another word for "observed
change".)
jacque...@neuf.fr
> "jjoensuu" <j_jo...@yahoo.com> wrote:
>
> > Hi all,
> >
> > I have some statements and conclusions here that I wanted to have
> > checked by the physics gurus. Just because the conclusions seem to make
> > sense in some way, but that there could be reasons for which they are
> > simply plain wrong.
> >
> > Some years ago I read about an experiment in which a supposed slowing
> > of time was measured. The experiment involved an airplane flying at a
> > high altitude, and an atom clock somewhere on earth. Supposedly the
> > results from the experiment showed that the atom clock had slowed down
> > with the lower gravity in the upper atmosphere. The conclusion was that
> > since the clock slowed down, time slowed down.
>
> special relativity, not general relativity and gravitation. The plane made
> a turn around the earth, and a discrepancy was observed between two
> identical atomic clocks, one in the plane and one remained on the ground.
> According to the theory, the reason is the speed difference. The Concorde
> could be as fast as mach 2.
>
> > connection between clocks and time because, as I understand, clocks do
> > not really measure time anymore than any other rotating mechanical
> > device (eg a car engine). OK, in the experiment they used atom clocks,
> > but if the cesium atom now happens to vibrate at a slower speed does
> > not really have anything to do with time itself. Anyway, my questions
> > are not really about the relationship between clocks and time.
>
> relativity. It's just a definition, but one that allows application to the
> real world. A physical theory describes the relations between measurements
> made with a well defined procedure, it doesn't "explain" anything.
>
> The atomic clock is based on the period of the electromagnetic wave emitted
> by the transition between two states of a given isotope of cesium. As those
> atoms are identical, and even indiscernible, the clock is absolutely stable,
> as can be checked by measuring one with another. The precision is something
> as crazy as 10^-10.
International Universal Time is currently defined according average
time given by a network of atomic clocks located in several places on
Earth.
To day (short term) accuracy is close to 10^ -15. This should be
improved by using atomic clocks working in microgravity on orbit in
satellites (Pharao project) or in using other atoms providing higher
reference frequencies (improving ratio df/f) .
The issue is about long term accuracy, this why some suggest to use
some very old pulsars, having a very stable rotation speed (up to 10 ^
-19 ?) as reference for calibrating long term time.
+++
jambaugh
Before you get caught up in whether "time is an illusion" keep in mind
an illusion is a perception which is distinct from reality. So you
might argue "time dilation is an illusion" (thought it is not) or
"absolute time is an illusion" but saying "time is an illusion" is not
meaningful. Illusion is not the antithesis to reality.
That said clocks move, wheels move and particles move. We compare
their motions and we generate a parameter to order the sequence of
observations of their dynamic evolution. We call that parameter time.
We specifically see certain physical systems have very regular time
evolutions namely pendulums, mass spring systems and harmonic
electromagnetic circuits, and so on. We use these as "clocks" and it
is the empirical observations of harmonic systems which gives us a well
founded precise definition of what the time parameter means.
So when we say "time slows down" or "time speeds up" we are saying that
in the circumstances given that all dynamical system slow down/speed up
in a uniform way relative to dynamical system not in the stated
circumstances. The example you cited is the atomic clock in the plane
relative to the atomic clock on the ground. But there is a more recent
example and that is the GPS system. The satellites must use very
precise clocks and the effects of both their altitude (General
Relativistic effect of being higher in Earth's gravity well) and their
orbital motion (Special Relativistic effect of their relative motion to
the receivers on the ground) must be programmed into the GPS system.
Hence the precision and accuracy of the GPS system is an ongoing
experimental test of Einstein's theory. And so far no corrections to
the theory have been needed while the corrections predicted by the
theory have been absolutely necessary.
See the wikipedia article:
http://en.wikipedia.org/wiki/Global_Positioning_System
and the sources it references.
Regards,
James Baugh
Igor Khavkine
> So no, "time" is not changing. The apparatus that we've used as a
> "clock" to define the second in a highly controlled labratory doesn't
> work as well when it's packed into an airplane and flown up where the
> propagation media and magnetic field conditions degrade it's ability to
> consistantly conform to the numerical definitions performance
> tolerance.
If you have evidence that the drift, which was due to the enviromental
disturbances, of the atomic clocks used in the airplane experiment was
larger or even comparable to the difference expected from special
relativity, please provide a reference.
Igor
Grouchy
http://www.usno.navy.mil/library/index.html
Pick your poison from the papers provided. The main USNO Library has
the information from the original series of experiments (from before I
was born if I recall correctly) you want specifically. I provided the
1998-present link because that's the limit of my personal experiences
working with the data. The USNO 2001-2004 yearly reports are where
you'll find the comparison between the relativistic corrections and the
newer series (and a mid-range), as thats when it became clear that the
FAME II wasn't going to provide as good a substitute as the corrections
owning to a different explanation.
http://www.aas.org/publications/baas/v35n1/052351bas.pdf
http://www.bipm.fr/static/gpst/mail/index.html
[ Mod. note: Links edited for conciseness. -ik ]
For what it's worth, the Magnetic model the Russians produced at the U
of Mich as well as a lot of the MIT work on solar wind was also
adjusted with beneficial results (and funny anecdotes).
I have the time dilation IEEE papers on a different computer, but can
explain that in a paragraph now that the solar weather database has
delivered so well.
Wait until everyone gets to learn all the gory details (I'm still not
off the hook with the Feds so can't publish everything I'd like...
sorry). It's always something of a game on these forums regarding
what'll get pulled and what'll pass.
Igor Khavkine
> On Jan 13, 10:10 pm, Igor Khavkine <igor...@gmail.com> wrote:
> > Grouchy wrote:
> > > So no, "time" is not changing. The apparatus that we've used as a
> > > "clock" to define the second in a highly controlled labratory doesn't
> > > work as well when it's packed into an airplane and flown up where the
> > > propagation media and magnetic field conditions degrade it's ability to
> > > consistantly conform to the numerical definitions performance
> > > tolerance.
> >
> > If you have evidence that the drift, which was due to the enviromental
> > disturbances, of the atomic clocks used in the airplane experiment was
> > larger or even comparable to the difference expected from special
> > relativity, please provide a reference.
> http://www.usno.navy.mil/library/index.html
> http://www.aas.org/publications/baas/v35n1/052351bas.pdf
> http://www.bipm.fr/static/gpst/mail/index.html
Only one of the links you provided is a USNO annual report. It is not
even clear how the other ones are relevant. In any case, none of them
seem to have information relevant to comparing the size of different
sources of drift the atomic clock experiment previously discussed. I'm
afraid you'll have to be more specific.
> Wait until everyone gets to learn all the gory details (I'm still not
> off the hook with the Feds so can't publish everything I'd like...
> sorry). It's always something of a game on these forums regarding
> what'll get pulled and what'll pass.
Don't know which "Feds" you are referring to, but FYI postings to this
newsgroup are not under the control of any government organization.
Igor
Grouchy
On Jan 21, 8:22 am, "Igor Khavkine" <igor...@gmail.com> wrote:
> Grouchy wrote:
> > On Jan 13, 10:10 pm, Igor Khavkine <igor...@gmail.com> wrote:
> > > Grouchy wrote:
> > > > So no, "time" is not changing. The apparatus that we've used as a
> > > > "clock" to define the second in a highly controlled labratory doesn't
> > > > work as well when it's packed into an airplane and flown up where the
> > > > propagation media and magnetic field conditions degrade it's ability to
> > > > consistantly conform to the numerical definitions performance
> > > > tolerance.
>
> > > If you have evidence that the drift, which was due to the enviromental
> > > disturbances, of the atomic clocks used in the airplane experiment was
> > > larger or even comparable to the difference expected from special
> > > relativity, please provide a reference.
> >http://www.usno.navy.mil/library/index.html
> >http://www.aas.org/publications/baas/v35n1/052351bas.pdf
> >http://www.bipm.fr/static/gpst/mail/index.htmlOnly one of the links you provided is a USNO annual report. It is not
> even clear how the other ones are relevant. In any case, none of them
> seem to have information relevant to comparing the size of different
> sources of drift the atomic clock experiment previously discussed. I'm
> afraid you'll have to be more specific.
>
> > Wait until everyone gets to learn all the gory details (I'm still not
> > off the hook with the Feds so can't publish everything I'd like...
> > sorry). It's always something of a game on these forums regarding
> > what'll get pulled and what'll pass.Don't know which "Feds" you are referring to, but FYI postings to this
> newsgroup are not under the control of any government organization.
>
> Igor
Well Igor...
Look through the bipm.fr index for the references to specific
corrections on the L2 carrier freq. due to performance problems in the
upper ionosphere, amongst other interesting subjects. The firmware
wasn't in need of updating for nothing. Also, as that's a French site,
it should be fairly easy to see if you can find a similar index in the
US. If you can, please post the link as I'd be interested in looking
over it.
The USNO annual report refers to a number of related subjects, and
although it doesn't explicitly mention anything about very old
experimental observations, it does note performance variance observed
in relation to correction methods, which might or might not conform to
existing models sans additional adjustments. Between those three
links, and perhaps with the addition of the ESA on their navcom
satellite networks carrier frequencies (and encoding process) there's
enough technological esoterica relating to signal and clocking
performance to get the picture. If you're really that determined,
going back and comparing the series 5, series 7, and more recent data
sets and adjustments applied over the years to each should be enough to
set the theoretical wheels spinning. The reference below, which is
from the bipm.fr index is an interesting example:
http://www.bipm.fr/static/gpst/mail/22Feb02.1
This provided, hopefully you won't just race to the series 5 data and
pretend it's sufficient verification. One would assume that theorists
would be interested in such suggestive gifts. Obviously the authors
would be the appropriate people to contact regarding the theoretical
contradictions stemming from their technical papers dating back almost
a decade, as it's quite possible they weren't as concerned with broad
theory as with performance improvements to their specific projects.
Murat Ozer
On Jan 4, 5:54 pm, carlip-nos...@physics.ucdavis.edu wrote:
> jjoensuu <j_joen...@yahoo.com> wrote:[...]
>
> > Some years ago I read about an experiment in which a supposed slowing
> > of time was measured. The experiment involved an airplane flying at a
> > high altitude, and an atom clock somewhere on earth. Supposedly the
> > results from the experiment showed that the atom clock had slowed down
> > with the lower gravity in the upper atmosphere. The conclusion was that
> > since the clock slowed down, time slowed down. I failed to see a
> > connection between clocks and time because, as I understand, clocks do
> > not really measure time anymore than any other rotating mechanical
> > device (eg a car engine). OK, in the experiment they used atom clocks,
> > but if the cesium atom now happens to vibrate at a slower speed does
> > not really have anything to do with time itself. If only one kind of clock -- say, a particular type of atomic clock
> -- slowed down, you would have a point. But as far as we can tell,
> *every* type clock, and everything else that changes with time,
> slows down, and all by exactly the same amount. We observe this for
> "clocks" based on weak interactions (e.g., particle decays), those
> based on electromagnetic interactions (e.g., atomic clocks), those
> based on strong interactions (e.g., other types of decays -- though
> this is not really well tested for gravitational effects), those
> based on gravitational interactions (e.g., orbits in binary systems),
> as well as for "mechanical" clocks (e.g., rotating neutron stars).
Dear Dr. Carlip:
Will you please elucidate on "gravitational interaction clocks" and
"mechanical clocks" ? I know how atomic clocks work and used for
time keeping (in electromagnetic processes). What are gravitational
interaction and mechanical clocks? Is a (simple) nonaccalerating
pendulum in a gravitational field a "gravitational interaction clock"?
Any references?
Best regards,
Murat Ozer
carlip...@physics.ucdavis.edu
> On Jan 4, 5:54 pm, carlip-nos...@physics.ucdavis.edu wrote:
[...]
>> If only one kind of clock -- say, a particular type of atomic clock
>> -- slowed down, you would have a point. But as far as we can tell,
>> *every* type clock, and everything else that changes with time,
>> slows down, and all by exactly the same amount. We observe this for
>> "clocks" based on weak interactions (e.g., particle decays), those
>> based on electromagnetic interactions (e.g., atomic clocks), those
>> based on strong interactions (e.g., other types of decays -- though
>> this is not really well tested for gravitational effects), those
>> based on gravitational interactions (e.g., orbits in binary systems),
>> as well as for "mechanical" clocks (e.g., rotating neutron stars).
> Will you please elucidate on "gravitational interaction clocks" and
> "mechanical clocks"? I know how atomic clocks work and used for
> time keeping (in electromagnetic processes). What are gravitational
> interaction and mechanical clocks? Is a (simple) nonaccalerating
> pendulum in a gravitational field a "gravitational interaction clock"?
A pendulum in isolation is not a clock, much less a gravitational
clock. A pendulum in a fixed location on Earth *plus the Earth* is
a gravitational clock, that is, a clock whose operation is controlled
by gravitational interactions among its parts (which include the Earth).
It's not a very useful one for measuring time dilation, though.
As I said, a gravitationally bound binary system -- the Earth and Moon,
for instance, or a binary pulsar -- is a more useful gravitational clock.
For a binary pulsar, for instance, the period observed from Earth changes
with the motion of the Earth. In a frame in which the Earth is at rest,
this corresponds to a frequency that depends on the motion of the pulsar.
For the Hulse-Taylor pulsar, even the change in velocity over time due
to acceleration in the galaxy's gravitational field is observable --
see Damour and Taylor, Ap. J. 366 (1991) 501.
We also see time dilation in supernova light curves -- see, for example,
Goldhaber et al., astro-ph/0104382, Ap. J. 558 (2001) 359. These are
not quite purely gravitational systems, but certainly gravitational
interactions are a crucial element.
A simple mechanical clock, as I said, is a rotating neutron star. A
pulsar is just such a star, with a "special point" marked by the beam.
We can use it directly as a clock, counting each pulse as a "tick"; in
fact, pulsars provide clocks that are comparable in accuracy to the best
atomic clocks. (Note that the period here is the period of rotation
of the neutron star; the period I referred to above was a different
one, the orbital period of one neutron star around another.)
For a binary pulsar -- a pulsar in orbit around another neutron star --
unless the orbit is exactly circular, the velocity will change with
time (Kepler's laws). The resulting time dilation is clearly observable.
For details, see section 12.1 of Will's _Theory and experiment in
gravitational physics_, or for a brief summary, the beginning of a
conference talk by Esposito-Farese, gr-qc/9612039. (This paper contains
a nice clear discussion of the parameter gamma_{timing}, which measures
the time dilation in question.)
Steve Carlip