5 ms·
In the limit of weak gravity, gravitational time dilation depends only on the gravitational potential, and not at all on the local gravitational field. So going
by knzhou 7y ago
In the limit of weak gravity, gravitational time dilation depends only on the gravitational potential, and not at all on the local gravitational field. So going down to the center of the Earth just has the opposite effect of going up to space, i.e. the clock will run slower. Nothing special happens just because the field happens to cancel out. The equivalence principle essentially tells us that local gravitational field values don't have meaning, anyway.
- ars 7y agoYou are claiming you can distinguish between freefall inside the center of the earth, from freefall traveling between the stars, solely by the effect on time dilation?
- fsh 7y agoYes, one can measure the difference in gravitational potential between two locations by comparing clocks. This is precisely what was done in the Skytree experiment.
- ars 7y agoBy definition in free-fall there is no gravitational potential!
- fsh 7y agoOf course there is. The gravitational potential does not depend at all on the (non-relativistic) velocity.
- ars 7y agoHow would you measure this gravitational potential?
- fsh 7y agoFor example by comparing two extremely good clocks. Or the same way the earth's gravitational potential is mapped - by measuring the relative height and the gravitational acceleration in many points and numerically integrating along the way.
- ars 7y agoI feel like we are speaking different languages - you are in free fall. There is no gravitational acceleration to measure. It's zero.
- fsh 7y agoYes, you seem to have a fundamental misunderstanding about what free fall means. In the absence of other forces, a body in a gravitational field experiences a constant acceleration that only depends on the strength of the field. In the accelerating reference frame of the object, there are no net forces. You could for example measure the gravitational acceleration of earth by jumping from a plane and measuring how fast the ground is coming towards you.
- ars 7y agoYou are inside a box, you do not see the ground, so how can you use it to measure anything (to measure "how fast the ground is coming towards you")? Time dilation of a clock does not depend on the clock being able to reference some external object, like the earth. (I do recognize you can not measure time dilation until you compare to some other clock.) So, let's reframe with a thought experiment and maybe you can answer: A clock in the center of the earth, and a clock dropped from a tall tower on earth (ignore the rotation of the earth). Each clock sends two laser pules, exactly 1/100 of a second apart toward the other clock. (The falling clock sends its pulses moments after being dropped, so it has essentially zero speed relative to the clock in the center of the earth.) The partner clock then measures how far apart in time it received the two pules. After that we collect the reports from the clocks and evaluate. Will the two clocks each report the same time interval? For an even better experiment lets add a third clock, this one resting on the surface of the earth.