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Consider a golf ball in the center of an empty sphere (maybe a GR vacuum, I'm not so sure). Consider this empty sphere as being the only space available to the golf ball, it is surrounded by nether. Now give the ball a push.

Is there a mathematical formalism that can describe the evolution of the ball in such conditions (motion-wise, particularly at the frontier of the available space) ?

I realize that this is a highly speculative question that may pose several issues, I'm not so much interested in weither the experiment is possible as I am in knowing the theoretical frames that could represent such conditions (mainly, how do we interpret/represent nether in physics; do we ?)

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  • $\begingroup$ How can I give the ball a push when I am not there? The sphere is empty, except for the ball... that's your own rules. $\endgroup$ – CuriousOne May 20 '15 at 23:05
  • $\begingroup$ What do you mean by "nether"? If the ball is in a GR vacuum, the behaviour will obviously depend strongly on what vacuum you choose. What is keeping the ball inside this chunk of the vacuum? Is it a physical wall, or some sort of mathematical device? $\endgroup$ – Harry Wilson May 20 '15 at 23:07
  • $\begingroup$ By nether I mean that outside of this chunk of vacuum, there's no space-time. Your second question is very interesting, it is my main motivation: "what is keeping the ball inside this chunk of the vacuum". Interesting that you even ask the question, why should the ball be kept by something in the vacuum ? Where would it go otherwise ? I know realize that this may reach metaphysical levelsas many notions are unclear, and that may not the purpose of the website. But thank you for your contributions. $\endgroup$ – Golz May 21 '15 at 14:28
  • $\begingroup$ Then again, I'm highly interested in the properties of GR vacuum which are scientifically relevant, if anyone could give some details it may answer my question. $\endgroup$ – Golz May 21 '15 at 14:34
  • $\begingroup$ There is no outside of spacetime, at least it is not necessary for space-time to be embedded in something else. The whole concept of outside of space-time is the wrong kind of thinking. $\endgroup$ – Sebastian Riese May 21 '15 at 20:45
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if space has an edge, there are many ways in which you can put boundary conditions. For instance, if you make it perfectly reflective, the universe will conserve energy but not linear momentum. You can also make objects disappear at the edge so no quantities are conserved. Or you can make the objects or particles to reappear at the opposite side of the sphere, then both energy and momentum will be conserved. Annihilation into a burst of ebnergy can also be considered. The possibilities are endless.

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Usually we think of space as not having a boundary. Either because it is infinite, or because it is a compact surface (such as a three sphere). I rather think GR will not work on manifolds with boundaries.

Furthermore, the concept of "nether" is a physical concept not known to me.

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  • $\begingroup$ In case it is a "compact surface", should one expect the ball to just bounce back at the inner surface of the sphere ? Doesn't that imply that the involved space applies a significant force to the ball ? I think there's an issue there $\endgroup$ – Golz May 20 '15 at 21:54
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    $\begingroup$ Nope, the space itself is a compact surface (see my link). Otherwise, there had to be some kinde of singularity at the boundary of space, then sure the space would exert significant force, but try to find a matter distribution, that generates such a space ... $\endgroup$ – Sebastian Riese May 20 '15 at 21:57

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