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

In summary, as we approach the Earth's center, the gravitational time dilation becomes smaller and less noticeable. However, in a lab on the Earth's surface, precise measurements can still be made to detect this effect. The time dilation is based on the potential difference between two points, rather than the strength of the gravitational field at a point. This is why it is still present at the center of the Earth, where gravity is zero. Furthermore, the time dilation has a local maximum at the center and always points towards greater gravitational acceleration. While this effect may not be noticeable for humans on Earth's surface, it may become more significant in a collapsing star or for GPS clocks in orbit.
  • #1
Gerinski
323
15
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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  • #2
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.
 
  • #3
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.
 
  • #4
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 ... ?
 
  • #5
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).
 
  • #6
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.
 
  • #7
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.
 
  • #8
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.
 
  • #9
Thanks nugatory and AT for setting me straight on this.
 

1. What is the time rate at Earth's center?

The time rate at Earth's center refers to the rate at which time passes at the Earth's center compared to the surface. It is affected by factors such as gravity and the Earth's rotation.

2. How does the time rate at Earth's center affect reactions?

The time rate at Earth's center affects reactions by altering the speed at which chemical reactions occur. This is due to the differences in gravitational forces and the Earth's rotation, which can impact the movement and interaction of molecules.

3. Is the time rate at Earth's center constant?

No, the time rate at Earth's center is not constant. It can vary depending on factors such as altitude, latitude, and the composition of the Earth's core. However, these variations are very small and only measurable with precise instruments.

4. How can we measure the time rate at Earth's center?

The time rate at Earth's center can be measured using atomic clocks, which are extremely accurate timekeeping devices that measure the vibrations of atoms. By comparing the time rates at different locations on Earth, scientists can calculate the time rate at the Earth's center.

5. Why is it important to study the time rate at Earth's center in relation to reactions?

Studying the time rate at Earth's center in relation to reactions can provide insights into the fundamental laws of physics and how they affect chemical reactions. It can also help us better understand the Earth's structure and how it impacts the world around us.

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