General relativity question: Gravity clock

[logicalmorality]

TL;DR Summary

Would a gravity powered clock increase or decrease speed? For example an hourglass.

Would a gravity powered clock increase or decrease speed? Take an hourglass. It should increase speed as gravity increases because it's powered by gravity... But it should also decrease speed because of general relativity...

 

[Orodruin]

What you call a ”gravity powered clock” is not a clock in the sense of relativity. It presumes a particular gravitational field to convert a measurement into a corresponding time.

 

[Ibix]

There can be competing effects. In fact, you can easily stop an hour glass from working at all by letting it be in free fall.

Assuming you mean "an hour glass at fixed altitude", it's rate decreases compared to an atomic clock colocated with it as you increase in altitude. This is because an hourglass (or pendulum clock) must be recalibrated for the local gravitational field strength.

Independent of that, all clocks in a gravitational field run slightly slow compared to clocks at infinity. So once you've recalibrated your hourglass to match a co-located atomic clock, it'll still be running slightly slow compared to a clock at infinity.

Essentially, the problem is, as Orodruin just said, that such "gravity powered" clocks are not reliable clocks if they are moved to different gravitational field strengths.

 

[PeterDonis]

Take an hourglass. It should increase speed as gravity increases because it's powered by gravity... But it should also decrease speed because of general relativity...

Your reasoning here is faulty. You can't do physics by waving your hands and stringing words together. You need to use the math of the theory to make predictions and then compare those predictions with what is actually observed. As long as there is a consistent mathematical model of the scenario that makes predictions that match what we observe, it doesn't matter that that model does not match whatever vague intuitive sense you have of what "looks right".

Also, you are making a simple and common but fundamental error: "gravity" in GR is not just one thing. An hourglass with greater "gravity" in the sense of "acceleration due to gravity" will run out faster, as seen by an observer right next to it, if we just take that one effect into account. But "gravity" in the sense of gravitational time dilation is different from "acceleration due to gravity", and deals with what the hourglass's behavior looks like to an observer who is not right next to it. There is nothing that requires what those two different observers observe to be the same.

Further, you cannot make a blanket statement that greater "acceleration due to gravity" always corresponds to greater gravitational time dilation. That is false as a general statement.