Time Rate at Earth's Center: Effects on Reactions?

[Gerinski]

As we get closer to the Earth's center, clocks down there tick slower that ours in the surface.

Does this have any noticeable effects? Just for example, could we notice that certain reactions such as radioactive decay happen 'too slow' down there compared to what we know as the normal rate in our surface frame of reference?

 

[jbriggs444]

The predicted effect of the Earth's gravitational field on the passage of time is tiny. The center of the Earth is 4000 miles away on the far side of high temperature rock and iron. Measuring a tiny effect at a large distance through inhospitable material... No, the effect is not noticeable there.

On the other hand, in a lab on the surface of the Earth, extremely precise measurements are possible. The effect can be detected and measured.

 

[SpiderET]

Interesting question. I would guess, nothing noticeable would happen, because the time dilation difference between surface and center is rather small. Maybe in some collapsing star it would make some major difference.

 

[phinds]

To add to the question, since one is weightless at the center of the Earth, IS there gravitational time dilation between it and, say, an object millions of miles out in space? There IS time dilation at the surface of the Earth relative to that far-away point, but at the center ... ?

 

[Nugatory]

There IS time dilation at the surface of the Earth relative to that far-away point, but at the center ... ?

There is. Gravitational time dilation doesn't come from the strength of the gravitational field at a point, but rather from the potential difference between two points. We need to compare two clocks to be able to make a statement about time dilation, and when the clocks are at different heights in the potential well the deeper clock will run slower.

(one caveat - this description in terms of gravitational potential only works for a static field so that the potential is defined, but that's the case we're considering here so it's OK).

 

[Gerinski]

Interesting question. I would guess, nothing noticeable would happen, because the time dilation difference between surface and center is rather small. Maybe in some collapsing star it would make some major difference.

Well, it is said that time dilation needs to be taken into account for GPS clocks, and I guess that the gravity potential difference between Earth's surface and the orbit of GPS satellites is much smaller than the potential difference between surface and center.

 

[A.T.]

To add to the question, since one is weightless at the center of the Earth, IS there gravitational time dilation between it and, say, an object millions of miles out in space?

Not only is there gravitational time dilation, but it has a local maximum. Gravitational acceleration always points towards greater gravitational time dilation.

 

[A.T.]

Well, it is said that time dilation needs to be taken into account for GPS clocks, and I guess that the gravity potential difference between Earth's surface and the orbit of GPS satellites is much smaller than the potential difference between surface and center.

Once humans make an expedition to the center of the Earth they will start to worry about this.

 

[phinds]

Thanks nugatory and AT for setting me straight on this.