Time Dilation in Gravitational Fields vs Acceleration on Earth

[mcgnms]

TL;DR Summary

Is the time dilation of being in a gravitational field additive to acceleration since geodesics also experience time dilation?

If I'm standing on Earth, is my time dilation actually greater than if I was in a rocket accelerating at 9.8m/s^2 in deep space due to me being in a gravitational field on top of the acceleration? Geodesics experience time dilation in gravitational fields, so it seems like there is an additive effect, right? I'm trying to eliminate special relativity and kinetic time dilation out of this equation, purely looking at three components here:

1) Time dilation just by being in a gravitational field
2) Time dilation from acceleration
3) Time dilation from resisting free fall in a gravitational field

Is #3 some combination of #1 and #2?

 

[Dale]

There is no time dilation due to acceleration, neither gravitational nor any other type.

Gravitational time dilation is due to gravitational potential, and that is the same whether it is gravitational potential from a real gravitational field or the pseudo “gravitational” potential from an accelerating reference frame.

 

[mcgnms]

There is no time dilation due to acceleration, neither gravitational nor any other type.

Gravitational time dilation is due to gravitational potential, and that is the same whether it is gravitational potential from a real gravitational field or the pseudo “gravitational” potential from an accelerating reference frame.

Right, but my question still stands. Are these effects additive? When you stand on Earth's surface, whether or not you're in free fall or standing on the surface...you have gravitational potential. Now on top of that, since you're standing (and therefore accelerating at 1G), you have even more gravitational potential, right?

Another analogy to get to the root of my question. Say Observer A is standing on the surface of Earth and Observer B, right next to them, begins free fall down a deep hole into the earth. At the very moment Observer B begins free fall, they are still just as deep in Earth's gravity well, but are also not accelerating anymore. Therefore, is their clock less dilated at that instant now?

 

[Dale]

Now on top of that, since you're standing (and therefore accelerating at 1G), you have even more gravitational potential, right?

No. Why would this be true? Gravitational potential is purely about your position in the gravitational field, not your acceleration.

 

[mcgnms]

I'm confused then, you just said that acceleration creates a pseudo gravitational field that acts like gravitational potential. Did I understand that correctly? So by resisting free fall and therefore accelerating, you presumably create gravitational potential, right?

 

[Dale]

I'm confused then, you just said that acceleration creates a pseudo gravitational field that acts like gravitational potential. Did I understand that correctly?

No. I said that an accelerating reference frame has a pseudo gravitational field and potential. If you use an accelerating reference frame then there will be “gravitational” time dilation both for accelerating and non-accelerating clocks. If you use an inertial frame there will be no gravitational time dilation for accelerating nor non-accelerating clocks.

 

[cianfa72]

If you use an accelerating reference frame then there will be “gravitational” time dilation both for accelerating and non-accelerating clocks. If you use an inertial frame there will be no gravitational time dilation for accelerating nor non-accelerating clocks.

Are you talking about proper acceleration for the clocks or just their coordinate acceleration w.r.t. the chosen reference frame ?

 

[Dale]

Are you talking about proper acceleration for the clocks or just their coordinate acceleration w.r.t. the chosen reference frame ?

I was talking about coordinate acceleration.