Can a Box be Bigger on the Inside? | Dr. Who Fans

[mrspeedybob]

Is it theoretically possible to bend space in such a way that the inside Dr. Who's box is or appears to be larger then the outside?

I have already thought of the posibility that the door to the box may be one end of a wormhole that connects to a remote location, but the BBC seems to have killed this theory by implying that the inside of box necessarily assumes the same orientation as the outside.

Yes, I am aware that it is all fiction and that fiction writers seldom pay much attention to science, but the idea intrigued me and I hope a discussion of the imposibility, possibility, and/or methods of making a box bigger on the inside may prove educational.

 

[bcrowell]

If you try to make a quantitative version of your question, it needs to be modified. Having the inside bigger than the outside doesn't quite make sense if you think of it in terms of volume. The outside universe is at least ~10^30 cubic light years in volume, and I assume you don't mean that the inside of the box is bigger than that.

One modification that makes sense is this. For simplicity, let the box be spherical. Ordinarily we expect that for a sphere of radius 1, the volume to surface ratio is 1/3. Can it be greater than this?

The answer then is yes. Omitting a lot of technical details, the deviation of this ratio from 1/3 is basically the definition of a thing called the Ricci scalar: http://en.wikipedia.org/wiki/Ricci_scalar General relativity allows the Ricci scalar to be positive, negative, or zero.

One thing that's different, though, is that space doesn't have "handles," so the whole idea of reorienting the box doesn't really apply AFAICT. Or maybe someone here who's more clever than I am can figure out a way to make this correspond to some concept in general relativity. For comparison, if you want to slide a wormhole's mouth around, you can't just grab it; you have to bring some huge mass close to it and use gravitational attraction to accelerate it to one side or the other. (There is a description of this kind of throught experiment in the final chapter of Kip Thorne's book Black Holes and Spacewarps.)