# Lower gravity and higher time dilation?

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1. Jun 29, 2015

### SpiderET

When I started to learn about GR, I have been thinking, that there is simple relation to gravity and time dilation, that higher gravity means bigger time dilation. But later thanks to PF discussions I learned time dilation is related to gravitational potential and not directly to gravity. But I have still major problem to understand and accept that the highest time dilation is for example in center of Earth where is zero gravity.

I was looking for experiments and astronomical observations but all experiments I have checked have been showing than higher gravity means bigger time dilation. I wonder if anybody knows of any experiment or astronomical observation which would show a case where lower gravity means bigger time dilation.

2. Jun 29, 2015

### Mentz114

You are conflating gravitational potential with gravitational force ( or field strength). Force depends on the gradient of the potential but time dilation depends only on the potential itself.

3. Jun 29, 2015

### SpiderET

I know that. Im asking for experiments which would confirm that.

4. Jun 29, 2015

### Mentz114

Then why did you say

5. Jun 29, 2015

### A.T.

What exactly is the problem?

6. Jun 29, 2015

### SpiderET

Im looking for experiments which would confirm that and found none.

7. Jun 29, 2015

### Mentz114

That's fair enough. I could not find any either. The same situation is true in electrostatics, ie inside a charged spherical shell a charge feels no electrostatic force.

The calculation is straightforward in Newtonian terms and GR predicts the same result.

8. Jun 29, 2015

### harrylin

It's very difficult to conceive such a desired experiment, as most heavy masses are nearly round so that increased potential coincides with increased gravity. I can therefore not imagine an astronomical observation of an effect that is inverse of what you expect. Also, it's not doable to drill very deep inside the Earth; such an experiment could be interesting though (and probably it's already feasible, as sensitivity has increased to the point that it's not necessary anymore to drill very deep).

9. Jun 29, 2015

### Staff: Mentor

Well, considering the practical difficulties involved in putting a clock at the center of the earth (or even in a hole deep enough that gravitational acceleration at the bottom of the hole is interestingly different than than that at the top).... That's to be expected. It would be nice to have such experimental results, but realistically, it's not going to happen. So what's the next best way of attacking this problem?

Any theory that makes a prediction about the time dilation at the center of the earth is going to make predictions abut the time dilation elsewhere as well. We can and have tested these predictions, and they support general relativity and do not support the idea that the time dilation depends on the strength of the gravitational field instead of the potential difference. Furthermore, no one has been able to come up with any theory other than general relativity that matches these experimental results everywhere that we can test... So, it's not "proven" but there is no reason so far to doubt the GR prediction that the time dilation depends on potential differences and not the local strength of the gravitational field.

10. Jun 29, 2015

### A.T.

This is a qualitative description of the investigated situations, not what the experiments show quantitatively, which is dependency on potential not field strength.

Last edited: Jun 29, 2015
11. Jun 29, 2015

### Staff: Mentor

This is incorrect. All experiments that you have checked have shown that lower gravitational potential means more time dilation. For example, in the seminal Pound-Rebka experiment the difference in gravity is negligible. So if time dilation were due to gravity then we would not expect any measurable gravitational time dilation.

12. Jun 29, 2015

### SpiderET

To be exact all relevant experiments including Pound-Rebka have confirmed this equotation (simplified version for Schwarzschild metric):

In line with GR this is interpreted as confirmation of gravitational potential related to time dilation, but to be precise these experiments were all done above surface and did not disprove possibility that this equotation is valid only for r above surface. Im not saying that it is valid only for above surface, because this is not in line with current mainstream interpretation of GR and it would be just a speculation. What Im saying is what exactly is confirmed and what is not confirmed by experiments.

13. Jun 29, 2015

### Staff: Mentor

That is true.

However, the experiments already done above the surface do disprove the possibility that the time dilation is due to the gravitational acceleration. So regardless of if the GR equation is valid below the surface, the gravitational acceleration concept is not valid even above.

Furthermore, there is no sound reason to think that the laws of physics changes below the surface of the earth. There is no reason to suppose that a physical law which works above will stop working below and there is even less reason to suppose that a law which does not work above will start working below.

There is also no experiment testing the difference in time dilation for clocks painted pink vs. clocks painted white. Don't expect to see such an experiment any time soon.

Last edited: Jun 29, 2015
14. Jun 29, 2015

### Staff: Mentor

It's essentially impossible to prove a negative, but we have done experiments both below the upper surface of the earth's atmosphere and above that surface and found no evidence that being surrounded by matter changes the nature of the dependence on the potential.

So, yes... it is possible that time dilation is affected by dense matter but unaffected by not-so-dense matter, and that the unknown mechanism for this hypothetical effect doesn't affect other physical phenomena so we've never noticed it anywhere else. This is enough of a long shot that no one is going to take it seriously until and unless someone proposes a theory that both makes a new quantitative prediction different from GR and agrees with all the experimental results we have so far.

15. Jun 29, 2015

### pervect

Staff Emeritus
We can certainly test that the predictions of GR match experiment, such as the scout rocket experiments. Apparently, that does not answer your question, in order to disprove your theory that gravitational time dilation depends on "gravity" rather than potential, you'd need to actually HAVE a coherent theory with the desired relationship that is developed far enough to make physical predictions. At that point you can test this theory by comparing it to the physical predictions, and decide which theory matches them.

If you're looking for a peer reviewed theories of this sort, I'm not aware of any. Developing non-peer reviewed theories is outside the scope of PF. So in short, I think you need to convince yourself exactly what your theory predicts and how these predictions differ from the predictions made by GR before you can turn to examining the experimental evidence. What we can say is that GR does appear to match experiment, and that it does not work in the way you describe.

16. Jun 30, 2015

### Staff: Mentor

It is only valid for $r$ above the surface. Below the surface the equation for gravitational time dilation is different. The equation you wrote down is only valid in the vacuum region outside the massive body; it's not valid inside the body.

Just to be precise: the dependence of the potential on $r$ is different in the interior of the Earth, i.e., when surrounded by matter. But the fact that gravitational time dilation depends on the potential, not the "force" of gravity, does not change. (AFAIK experiments have not tested this to any great depth in the interior of the Earth, because of the obvious difficulties involved.)

Last edited: Jun 30, 2015
17. Jun 30, 2015

### PAllen

Dalespam said the following but I think you didn't get it. This formula is for potential, not force. Take the Taylor expansion and it is 1/r not 1/r2. If time dilation were proportional to change in acceleration, then Pound-Rebka could never have detected it - the effect would be orders of magnitude too small. Instead, time dilation was effectively proportional to g*h, with g constant. This was really a test of the principle of equivalence - that difference in position in an effectively static field was equivalent to difference in position in a similar height accelerating rocket as predicted by SR. Thus, the fact that Pound-Rebka had the predicted result disproves time dilation is proportional to gravitational acceleration.

18. Jun 30, 2015