Can spacetime curvature be transformed away?

[FallenApple]

This is probably a bad question, but can it be transformed away? Say Alice is on Earth and Bob is far away in outer space. Bob would think that Alice's clock is running slow. Alice would think Bob's clock is running fast.

A third observer, say Carl, anywhere in spacetime would have to observe this as well. Or can Carl somehow transform away the difference he observes between Alice and Bob?

Say Carl is somewhere between Bob and Alice. If Carl is in a rocket and tries to accelerate towards bob and away from Alice, he could claim that he isn't moving and that it's Bobs mass that is increasing, and Bob from Carl's frame of reference would be blue shifted. He could similarly claim that Alice is moving away in the opposite direction with the same acceleration. But we know that space is expanding radially in all directions. So Carl should be seeing Bob slightly more blue shifted than normal and he should see Alice slightly more red shifted than normal, which gives a slight bias in favor of Bob. Also, I'd imagine that the path between Carl and bob would be slightly length contracted and opposite for Alice. So from Carl's frame of reference, would he not see the difference in spacetime curvature between Alice and Bob to be slightly different than he would have if Carl didn't accelerate at all? Or would the Lorentz contraction/expansion cancel out the effect of the expanding universe? Would the expansion of the universe to instantaneously follow Carl so that it wouldn't even be a factor?

 

[PeterDonis]

can it be transformed away?

No. But the stuff you are talking about in the rest of your post is not spacetime curvature. Spacetime curvature is not the same thing as time dilation, or redshift/blueshift. Spacetime curvature is tidal gravity. Tidal gravity is what you can't transform away.

 

[FallenApple]

No. But the stuff you are talking about in the rest of your post is not spacetime curvature. Spacetime curvature is not the same thing as time dilation, or redshift/blueshift. Spacetime curvature is tidal gravity. Tidal gravity is what you can't transform away.

A rocket that accelerates would have more energy. Energy warps spacetime. So that rocket would have more tidal gravity?

 

[PeterDonis]

A rocket that accelerates would have more energy.

More than what? The acceleration has to be produced somehow; whatever is producing it already contains energy. So the acceleration process doesn't add any energy; it just transforms it from energy in the fuel to kinetic energy of the rocket.

 

[FallenApple]

More than what? The acceleration has to be produced somehow; whatever is producing it already contains energy. So the acceleration process doesn't add any energy; it just transforms it from energy in the fuel to kinetic energy of the rocket.

Ah ok I see. That makes sense. A rocket stationary and then accelerating would need to have the energy to move in the first place. So it experiences the same tidal gravity regardless.

 

[Dale]

This is probably a bad question, but can it be transformed away?

Curvature cannot be transformed away, it is a tensor.

he could claim that he isn't moving and that it's Bobs mass that is increasing

Mass doesn't increase with velocity. The unqualified term "mass" refers to "invariant mass" not "relativistic mass". But neither is the source of gravity.