0

Believing the answer is yes, how then is spacetime curved? Will the spacetime uncurve when rotation stops? According to special relativity you can only see things from one's own reference frame. I do not know how to reconcile the apparently rectilinear view from an object's surface with the perceptual differences one sees as the universe rotates about the observer -- and also use the invariances of general relativity.

While this may be obvious, what I am really wondering concerns our distinguishing "normal" gravity from what one might call "imitation" gravity, as on a spinning wheel. Should that be thought of as curved spacetime?

Qmechanic
  • 220,844
Andrew Mills
  • 11

2 Answers2

2

According to general relativity, the curvature of spacetime in the frame of the spinning object is exactly zero. Curvature is a tensorial quantity and doesn't depend on the observer.

Now you might be wondering how you can get apparent centrifugal forces if there isn't any curvature, if everything in relativity is supposed to follow from local curvature. This is a very common question that troubles a lot of philosophers, and it's not really done justice in the standard textbooks or by pop-science.

The solution is that the fundamental object in relativity really isn't the spacetime curvature, it's the metric, which determines the distances between nearby points. From the metric, you can construct the curvature, but you can also construct a notion of straight lines. These are the curves between two points that are locally as short as possible. An inertial observer is defined to be one which travels along such a straight line. If you don't follow such a line, you will observe fictitious forces, because objects that do freely fall along these lines will appear to be accelerating relative to you, and you'd attribute that to a fictitious force like the centrifugal force.

In other words, there's no real philosophical puzzle here. Everything is determined by local information just as it should be.

knzhou
  • 107,105
0

I think the answer to this comes down to the nature of gravity. You are referring to gravity as a force, whereas according to general relativity, gravity is not a force but an effect of travelling across curved spacetime. This effect is created by the presence of mass-energy on the spacetime fabric.

However the kind of artificial gravity you are referring to is not really artificial 'gravity', but it is simply a centripetal force. When there is a rotating frame of reference, the equations indicate the presence of a centre-seeking force (sometimes this takes the form of the Coriolis force), but this is a real force (or rather behaves like a real force, but that is something for another time). This force is not the result of mass-energy being present and warping spacetime but rather a result of your changing frame of reference. It would not warp spacetime like gravity and so no, technically artificial 'gravity' is not created. A similar effect is created, but not gravity.

PS: I think it would anyways be problematic because if rotating your coordinates did warp spacetime, that would mean you have some extra mass-energy spontaneously created out of nothing, which would violate conservation of energy. I think, I'm not too sure about this tho.

Hope this helps!

d_g
  • 722