Evaluating the Elapsed Time Difference Between Clocks in a Gravitational Field

[MeJennifer]

Clocks show less elapsed time in gravitational field right?
So clocks on Earth seem to apply.

Consider one clock stationed on the north pole and one somewhere on the equator, both at sea level.

It seems there are a couple of factors in order to calculate the difference in time between each clock and a fictional observer in flat space.

Looks like we have to take into consideration the following things

They are in a gravitational field
The EM-force accelerates in the opposite direction
The Earth is rotating,
Both clocks are accelerating due to the rotation (each one slightly different).
The Earth is not a perfect sphere.

My main question concerning this problem is the "cancellation" of the EM-force. How does the EM force interact with the curvature? Are there well established theories for this?

 

[pervect]

It's somewhat well known that all clocks on the geoid (intuitively, at sea leve) tick at the same rate.

I'm not sure what your concerns with the "EM field" are. You don't need to know the acceleration of a clock to know how it keeps time - you only need to know the metric, and the velocity of the clock.

 

[Entropia]

Yes, you are correct in your understanding that clocks in a gravitational field will show less elapsed time compared to a clock in flat space. This phenomenon is known as gravitational time dilation and is a consequence of Einstein's theory of general relativity.

To calculate the difference in time between the two clocks in your scenario, we do indeed have to take into consideration all the factors you listed. The gravitational field of Earth will cause time to pass slower for the clock on the equator compared to the one on the north pole. This is due to the fact that the gravitational force is stronger at the equator, causing time to pass slower.

In terms of the EM-force and its interaction with the curvature of space, there are indeed well-established theories for this. According to general relativity, gravity is not a force itself, but rather a result of the curvature of space and time caused by the presence of mass or energy. The electromagnetic force is also affected by this curvature and can be described by the same equations used to describe gravity.

So in essence, the EM-force will also be "canceled out" by the curvature of space and time in a gravitational field. This means that the effect of the EM-force on the difference in time between the two clocks can be ignored.

Overall, the calculations for the difference in time between clocks in a gravitational field can become quite complex, especially when taking into account all the factors you mentioned. But thanks to the well-established theories of general relativity, we are able to accurately predict and understand these effects.