# The Naked Scientists Forum

### Author Topic: Has Time Rate Underground Compared to at the Surface Been Measured?  (Read 3256 times)

#### AndroidNeox

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##### Has Time Rate Underground Compared to at the Surface Been Measured?
« on: 17/07/2015 01:50:38 »
As one moves deep into the Earth, the force of gravity will drop. At the Earth's center of mass, the force of gravity will be zero, since gravity will pull equally in all directions. General Relativity requires that time will flow faster in regions of lower acceleration (gravity or motion). Time should run faster below-ground than above.

Has an experiment been done to verify that time runs faster below ground than at the surface, by the expected amount?

#### evan_au

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##### Re: Has Time Rate Underground Compared to at the Surface Been Measured?
« Reply #1 on: 18/07/2015 04:49:26 »
Quote from: AndroidNeox
Has an experiment been done to verify that time runs faster below ground than at the surface?
There have been many tests of gravitational redshift that have been done above ground, and in satellites. Some of the equipment is small enough to be used down a mineshaft, but I can't see a description of these experiments being done.

I think the result will be the opposite of what you expect.

Time runs slower the further you go down a gravitational well (as measured by a distant observer). So the centre of the Earth is the farthest down the Earth's gravitational well as you can go, and I expect that time will run slowest there.

#### AndroidNeox

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##### Re: Has Time Rate Underground Compared to at the Surface Been Measured?
« Reply #2 on: 18/07/2015 21:23:52 »
I agree that time will run slower, deeper down the shaft. My point is, that's not what the current interpretation of Relativity predicts.

#### jeffreyH

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• The graviton sucks
##### Re: Has Time Rate Underground Compared to at the Surface Been Measured?
« Reply #3 on: 20/07/2015 19:50:36 »
If we don't have the data then we are speculating.

#### evan_au

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##### Re: Has Time Rate Underground Compared to at the Surface Been Measured?
« Reply #4 on: 21/07/2015 00:05:07 »
Quote from: AndroidNeox
At the Earth's center of mass, the force of gravity will be zero, since gravity will pull equally in all directions. General Relativity requires that time will flow faster in regions of lower acceleration (gravity or motion). Time should run faster below-ground than above.

I think this might be confusing two concepts?
• A hypothetical "distant observer", far from any gravitational well, in an inertial frame of reference, is in free fall. This is the reference for measuring gravitational time dilation*. This observer will see time flowing more slowly for all other observers further down a gravitational well.
• An observer who managed to tunnel to the center of the Earth, and hollow out an air-conditioned room, would also be in free-fall. However, this observer is at the bottom of a gravitational well, and time will flow more slowly for her.
• Perhaps the use of the term "free fall" in both cases (often misleadingly called "zero gravity") might be causing confusion? This might suggest that the observer at the center of the Earth would see time moving more rapidly than an observer at the surface of the Earth.

*This would also need to assume an (unstable) static universe, otherwise velocity considerations would dominate time dilation.

#### PmbPhy

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##### Re: Has Time Rate Underground Compared to at the Surface Been Measured?
« Reply #5 on: 21/07/2015 07:39:46 »
Quote from: AndroidNeox
General Relativity requires that time will flow faster in regions of lower acceleration (gravity or motion).
That's incorrect. The rate that time flows is unrelated to acceleration. It's solely related to the difference in gravitational potential.

#### AndroidNeox

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##### Re: Has Time Rate Underground Compared to at the Surface Been Measured?
« Reply #6 on: 28/07/2015 03:31:20 »
Thanks for straightening me out. I had looked at Einstein's elevator thought experiment and the "equivalence principle" and misunderstood. So, if the acceleration vector isn't what's referred to in the equivalence principle, how should one interpret the equivalence principle?

#### CPT ArkAngel

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##### Re: Has Time Rate Underground Compared to at the Surface Been Measured?
« Reply #7 on: 28/07/2015 04:26:25 »
Inertia is equivalent to gravity. I prefer to give a further explanation by saying inertial mass is equivalent to the gravitational mass.

The equivalence principle alone doesn't solve time dilation. You have to include the concept of GR stress energy.

#### David Cooper

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##### Re: Has Time Rate Underground Compared to at the Surface Been Measured?
« Reply #8 on: 28/07/2015 18:20:33 »
It looks as if the experiment hasn't been done to settle whether time would be slowed at the centre of the Earth or not. However, if you could hold a clock between the Earth and moon at the point where their gravity cancels out, you might then be able to make the necessary measurements to compare it with another clock the same distance as the moon out from the opposite side of the Earth. If depth in a gravity well is what slows time, then the first clock will run more slowly than the second, but if gravitational pull slows time (and can cancel out rather than adding), the first clock will run faster than the second. (Corrections would need to be made for the difference in speed of movement of the clocks through space, but we know exactly how to do this.)
« Last Edit: 29/07/2015 18:41:36 by David Cooper »

#### AndroidNeox

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##### Re: Has Time Rate Underground Compared to at the Surface Been Measured?
« Reply #9 on: 30/07/2015 07:49:59 »
Good thinking.

One might cancel Special Relativistic effects by synchronizing the clocks in one location, moving clock (1) to the opposite Lagrange point, waiting, then having clock (2) follow the identical trajectory to clock (1), where their times can be compared.

#### AndroidNeox

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##### Re: Has Time Rate Underground Compared to at the Surface Been Measured?
« Reply #10 on: 30/07/2015 07:59:08 »
Thanks for the excellent replies. Makes sense to me, now.

#### The Naked Scientists Forum

##### Re: Has Time Rate Underground Compared to at the Surface Been Measured?
« Reply #10 on: 30/07/2015 07:59:08 »