Action At A Distance
One of the problems in quantum mechanics seems to be action at a distance - that is, something happening to one particle instantaneously affecting another particle at a distance from it. Since we assume information can only travel at the speed of light, it seems something strange is going on here. What I was wondering was whether we could postulate higher dimensions as being part of the effect here? That is, the particles may be at quite some distance from each other in the dimensions we can see but not in some higher dimension. So we could say that perhaps they are transmitting information this way. To use a lower-dimensional example, if you have a squiggly line (one dimension) and need to get from one point to another along it, it may take a while. However, if you can move in the second dimension you may be able to cut across instead. Anyone with a better knowledge of physics than me want to comment on why this may/may not be the case?
Heather B.
Nice idea. But the problem here is Pythagoras’s Theorem! Assuming spacetime is Euclidean for the moment, it’s easy to show that moving through an extra dimension can only ADD distance to the trip. For example, if you start with a straight line between two points, and then try to get between them by moving through a second dimension (e.g. on a flat piece of paper), you’ll see that you always have a longer line than the straight line you started with. If you move through just one other point then you’ve drawn a triangle, which is the version of Pythagoras’s Theorem we’re all familiar with. Unfortunately (or not, whatever!) this also applies in any number of dimensions, and even if spacetime is non-Euclidean.
I suppose you could invent some VERY weird geometry to get around this, but that would be incompatible with General Relativity.
Jason
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Ah yes, I see how that would work. I suppose I was imagining a case something more like folding a piece of paper to join two points, but I can see that might cause big problems elsewhere.
Heather
Ooh! Wormholes! Actually wormholes are NOT ruled out by the geometry of General Relativity. :-)
I think the reason we haven’t discussed this in lectures is that it’s not a constant curvature model, so it’s currently considered unlikely even if it is compatible with GR. It could turn out to be right though. After all, a lot of science fiction relies on it. And (ahem, more seriously) maybe constant curvature is only an issue on a large scale, and then maybe wormholes are OK on a small scale.
Jason
And coincidentally, this appropriate lolcat turned up on icanhascheezburger just today:
http://icanhascheezburger.files.wordpress.com/2012/05/funny-cat-pictures-lolcats-aifinkso.jpg
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Action-at-a-distance through wormholes… that’s a really cool idea.
The reading I’ve done on them before suggests that creating a wormhole requires something with negative energy density, but quantum physics is probably weird enough to incorporate things like that.
Angus
There’s a terminology problem here … probably my fault, because I mentioned wormholes on a page called “Action At A Distance”. Anyway, if physical influences travel through wormholes, that’s NOT action at a distance, because the the influences are travelling through spacetime. It might just seem like action at a distance at first glance, because spacetime would be such a weird shape.
The importance of this is not just nit-picking: it’s a good illustration, I think, of why we keep saying that Relativity is all about geometry. The point is that the geometry of spacetime affects what can happen, without needing any philosophically significant things like action at a distance (although of course Relativity itself was a big philosophical change from previous theories, and actually decreased the need for action at a distance compared to Newtonian mechanics).
Jason
