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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?

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closed as unclear what you're asking by Ben Crowell, John Rennie, GiorgioP, Kyle Kanos, Carl Brannen Apr 20 at 0:22

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ The title of the question is: "Is there “artificial gravity” created by a reference frame on a spinning object?" The rest of the question seems to assume that (a) the meaning of this question is clear, and (b) there is some reason to think that the answer is yes. The meaning of the question is not clear, and if I had to answer it without any further clarification, I would just say no. Please edit the question to explain what you mean by this and why you think this might be true. $\endgroup$ – Ben Crowell Apr 19 at 2:11
  • $\begingroup$ If you were in a closed room and experiencing acceleration you could not distinguish this from being near a large mass without opening the room and seeing an external world. Therefore the space-time in the room is identical in both instances. The word artificial implies manmade or in this instance contrived by an external observer. Therefore the question is meaningful as it is a testable conjecture. Formulating the General Theory you would be drawing from two different pictures. In a closed room gravity could be perceived to turn off or on for no apparent reason. $\endgroup$ – Andrew Mills Apr 19 at 3:47
  • $\begingroup$ Under local realism there has to be enough information within a closed system to explain the state of the system without referring to anything outside the system. This seems to be violated. $\endgroup$ – Andrew Mills Apr 19 at 4:15
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    $\begingroup$ Possible duplicate of Can a ultracentrifuge be used to test general relativity? $\endgroup$ – John Rennie Apr 19 at 7:20
  • $\begingroup$ @AndrewMills: To clarify a question, please edit the question rather than providing the clarification in comments. $\endgroup$ – Ben Crowell Apr 19 at 12:09
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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!

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  • $\begingroup$ My inexpert understanding is that when you enter a rotating frame of reference in the General Theory in non-relativistic conditions the tensor equations collapse to yield the simple equations for centripetal force, so the theory holds but adds nothing. So I agree with your answer but am not totally satisfied on philosophic grounds. $\endgroup$ – Andrew Mills Apr 19 at 7:40
  • $\begingroup$ Fair enough. I actually don't know too much about the tensor equation collapse and relativistic treatment of centripetal force, so I'd like to know more on that too. Any chance you could link the site you read that on? $\endgroup$ – d_g Apr 19 at 8:02
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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.

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