Spacetime curvature due to acceleration causing gravity?

[Dale]

The point I was trying to make was that without spacetime curvature at the Earth, you would not feel a proper acceleration while standing on the Earth because you would not be forced to deviate from an inertial path through spacetime.

Again, no. It is the unbalanced real contact force with the ground that causes the proper acceleration.

Any scenario in which there is an unbalanced real force will lead to the sensation of proper acceleration (with or without curvature). Any scenario in which there is no unbalanced real force will lead to the absence of proper acceleration (with or without curvature). The presence or absence of curvature is irrelevant.

Remember that spacetime curvature is tidal gravity, the sensation of proper acceleration is not. So what does spacetime curvature do in this scenario? It allows you to have proper acceleration in the opposite direction of a person on the other side of the world without the distance between you increasing.

That being said, doesn't it follow that if there is no curved spacetime at the surface of the Earth, one would not feel proper acceleration while standing on the surface of the Earth?

This is getting annoying. No matter how many times you repeat it the answer will still be no.

 

[1977ub]

"Early versions of Einstein's theory did not include the curvature of the geometry of ordinary space around the sun."
https://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/general_relativity_massive/

Is this the same as "tidal gravity" ?

 

[Buckethead]

You're making an implicit comparison here which isn't really meaningful. When you say "without spacetime curvature at the Earth", what are you comparing the actual situation with? And how are you going to pick out "the same place" in whatever you are comparing the actual situation with?

Am I not comparing it to empty space where there is no curvature? I visualize spacetime curvature as something that shapes the geodesics through spacetime and as a result, when you stand on the Earth, you and the Earth are being forced to deviate from an inertial path through spacetime. This causes the "push" between you and the Earth and the result is the sensation of proper acceleration. Is this not a good way to look at this?

 

[PeterDonis]

Am I not comparing it to empty space where there is no curvature?

How are you going to do the comparison? Empty space has no distinguishable places; how are you going to pick out the place where the "Earth" is and compare the proper accelerations at the two places?

Is this not a good way to look at this?

No. As has already been said a number of times in this thread. And it has been repeatedly explained why.

 

[PeterDonis]

The OP question has been answered. Thread closed.

 

[Dale]

Sorry @PeterDonis, I wanted to post one last explanation of what curvature actually does

I visualize spacetime curvature as something that shapes the geodesics through spacetime

This is true, but spacetime curvature is not just any shape. The specific shape that spacetime curvature gives to geodesics is that spatially separated geodesics diverge. Around Earth the shape of the curvature means that geodesics at your head and foot are pulling apart while geodesics on your left and right are squeezing together. Hopefully you recognize this as tidal gravity.

In a given region with a fixed spacetime curvature you can get rid of the proper acceleration simply by removing the floor. The proper acceleration disappears but the curvature doesn’t. However, the tidal force is present whether you are in free fall or not, it does not disappear under any condition as long as there is curvature.

 

[PeterDonis]

The specific shape that spacetime curvature gives to geodesics is that spatially separated geodesics diverge.

Or converge.