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

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Discussion Overview

The discussion revolves around the effects of gravitational time dilation at the Earth's center compared to the surface, particularly regarding its impact on physical reactions such as radioactive decay. Participants explore the theoretical implications of time dilation in extreme gravitational environments and the practical challenges of measurement.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants suggest that clocks at the Earth's center tick slower than those on the surface, raising questions about noticeable effects on reactions like radioactive decay.
  • Others argue that the predicted effect of gravitational time dilation is minimal and not noticeable at the center due to the significant distance and inhospitable conditions for measurement.
  • One participant speculates that in extreme environments, such as collapsing stars, time dilation might have more pronounced effects.
  • There is a discussion about whether gravitational time dilation exists between the center of the Earth and distant objects in space, with some asserting that it does due to potential differences.
  • Participants mention the relevance of time dilation in practical applications, such as GPS technology, and compare the potential differences involved.
  • Some express uncertainty about the implications of being weightless at the Earth's center on gravitational time dilation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the noticeable effects of time dilation at the Earth's center, with multiple competing views on its significance and implications for physical processes.

Contextual Notes

Limitations include the challenges of measuring tiny effects of time dilation through dense materials and the dependence on specific definitions of gravitational potential in static fields.

Gerinski
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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?
 
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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.
 
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.
 
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 ... ?
 
phinds said:
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).
 
SpiderET said:
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.
 
phinds said:
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.
 
Gerinski said:
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.
 
Thanks nugatory and AT for setting me straight on this.
 

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