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Most modern clocks use electromagnetic phenomena to measure time. There are perhaps some older clocks that involve gravity to some degree (hour glass, pendulum), but I believe they still have a healthy dose of an EM component to them.

One could imagine a nearly pure gravity clock: a repository of water (or perhaps ball bearings) lofted some distance above a sensor. The path between the repository and the sensor below would be in vacuum. An initial drop would be released and when it triggered the sensor an EM signal would be sent back up to the repository indicating that the next drop should be released.

Such an apparatus could be tuned such that each cycle took exactly one second to occur. In that case, the EM component of the time delay would be very small.

I have an idea that predicts that such a gravity clock would not experience time dilation (aside from the minor EM component). But, in trying to imagine an experiment to test such an idea there seems to be numerous challenges.

Certainly, engineering a gravity clock with atomic clock-esque accuracy in-and-of-itself would be highly challenging. But, in this case we need to make the clock move and move in away that doesn’t effect its accuracy (e.g., with vibrations) or perhaps more dauntingly, that doesn’t vary its gravitational field.

As such placing clocks in airplanes or anything that affects the clock's altitude will not work. Also, where as a satellite may have a relatively stable gravitational field, the experiment requires a change in velocity to measure any potential difference which isn’t possible with a satellite (at least not while maintaining a constant gravitational field).

The best I can come up with placing a gravity clock and an EM clock on stationary maglev train; calibrating the two clocks; quickly accelerating the train to max speed (which is about 300 mph these days?) and then syncing the clocks once you hit cruising speed. At that point, let the train run for as long as possible (in a perfectly straight line on a perfectly flat track with as little geographic variation around as possible). Just before the train is to start decelerating compare the two clocks to determine if there is any shift in their timing.

So, two questions:

1: Is it conceivable in such a setup to obtain the accuracy necessary to detect such a signal? (I hypothesize that the gravity clock will not experience time dilation at all.)

2: Is there perhaps a different setup that would be able to achieve the necessary accuracy to detect such a signal?

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    $\begingroup$ One can treat the precision of the perihelion of Mercury as a measure of the time it takes the planet to fall and rise in a gravitational field by comparison to the time it takes to go around (slightly complicated by the non-constant distance, alas). In that view the experiment has already been done and is consistent with General Relativity. That experiment can only achieve the necessary precision by running for decades at a time. $\endgroup$ – dmckee Jun 28 '15 at 17:32
  • $\begingroup$ @dmckee Do you have a reference by any chance? There are so many variables, curvature of space, effect of other planets, accuracy of our measurements of Mercury over a few centuries. I'm having difficulty relating that to my simplistic experiment. $\endgroup$ – aepryus Jun 28 '15 at 17:53
  • $\begingroup$ Actually, perhaps this is a reasonable reference? en.wikipedia.org/wiki/Two-body_problem_in_general_relativity $\endgroup$ – aepryus Jun 28 '15 at 17:58
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    $\begingroup$ What you are suggesting is called a "freefall gravimeter" and you can buy it commercially e.g. here microglacoste.com/fg5x.php. It does not act as a clock, of course, since the time of the fall depends directly on the gravitational acceleration. If you think that time stands still in zero gravity, then the folks on the ISS are proving you 100% wrong right now... their clocks (mechanical, electronic, atomic, biological) are moving at a pretty good pace. $\endgroup$ – CuriousOne Jun 28 '15 at 19:12
  • $\begingroup$ @CuriousOne Thanks, I'll check it out. I definitely don't think it stands still. I have an idea that argues that such a clock won't experience special relativity's dilation (i.e., that special relativity is an EM (i.e., standard model) phenomena). $\endgroup$ – aepryus Jun 28 '15 at 19:18
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I'm afraid you're overcomplicating things, aepryus. Yes, most modern clocks use electromagnetic phenomena, but your pendulum clock employs gravity in much the same fashion as your water-drop clock. The clock rate doesn't depend on gravitational potential, it depends on the first derivative of potential, the "slope" as it were. The force of gravity. And this decreases as altitude increases. So the pendulum clock goes slower when it's higher up. Not faster like your quartz wristwatch.

As for putting your clocks in a satellite, this is effectively what is done for GPS. See Phil Fraundorf's picture showing the GR gravitational time dilation and the SR time dilation caused by relative speed:

enter image description here

Re your questions:

Is it conceivable in such a setup to obtain the accuracy necessary to detect such a signal? (I hypothesize that the gravity clock will not experience time dilation at all).

Yes, your hypothesis isn't quite right, but's it's good to see somebody thinking for themself. One brownie point.

Is there perhaps a different setup that would be able to achieve the necessary accuracy to detect such a signal?

Just take your clocks down a mine and up a mountain. And remember this: in physics, some things are easier than you think.

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  • $\begingroup$ I'm trying to tease out the time dilation effect between an atomic clock and a gravitational clock. If the gravitational field strength changes, such as by shifting altitude, the gravitational clock will be instantly messed up. $\endgroup$ – aepryus Jun 29 '15 at 21:44
  • $\begingroup$ Yes it will. See the picture on the right on the Wikipedia gravitational potential article. (It's Newtonian but it's good enough.) Imagine you place clocks throughout an equatorial slice of space through and around the Earth. The height of the plot at some location denotes the atomic clock rate, whilst the slope denotes the gravitational clock rate. They are both "messed up". $\endgroup$ – John Duffield Jun 29 '15 at 21:55
  • $\begingroup$ A gravity clock is going to be highly sensitive to changes in gravitational field strength which will dwarf any effect caused by dilation. I'm trying to devise a situation where both clocks should only be affected by dilation effects (i.e., a constant gravitational field), so that if there were a difference in how they are affected by dilation it would show up. $\endgroup$ – aepryus Jun 29 '15 at 22:01
  • $\begingroup$ @aepryus : it will show up, and it's easier than you think. You synchronise your grandfather clock and your quartz wristwatch at sea level, and you wait for a week to make sure they stay synchronised. Then you take them up a mountain and wait for another week. Now they don't stay synchronised. The grandfather clock goes slower, the quartz wristwatch goes faster. $\endgroup$ – John Duffield Jun 30 '15 at 7:15

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