It's orthogonal, dammit!

Alternate Title:  It's a point, dammit!

Also from the realm of physics ruminations that won't leave me alone...

Why do physicists consider higher-order (beyond our standard three) dimensions to be "rolled up" into a small space within the existing three dimensions?  They even spend a lot of time working out just how small this space must be given various theoretical and experimental results.  Yet if these additional dimensions are anything like the dimensions we know and love, I don't think there's any reason to think of them this way.  If they are orthogonal to the existing three dimensions, just extending in a direction we happen to be unable to perceive, then they needn't have any size at all in our existing set of dimensions.

I mean, if you look at a two-dimensional painting and then examine a line extending out of the plane of the painting into the third dimension, does it make any sense to think of that third dimension as somehow rolled up into the two dimensions of the painting?  No, it doesn't.  The third dimension is orthogonal to the other two dimensions.  It's kind of what orthogonal means--the new dimension does not align with the other two.  There is no overlap between the new and old dimensions.  Similarly, if the fourth spatial dimension is orthogonal to the first three, then I think it makes precisely as much sense to discuss its size in those original three dimensions as it actually takes up in those dimensions:  None at all.

I'm determined it's deterministic (maybe)

Okay, here's a silly but profound rant, just to get it out of my head.  Seeing as how it has been rattling around in there in one form or another for over two decades now, maybe this will satisfy the internal monologuist and reduce the noise level a bit.

Though I don't think I'd claim to have strong convictions about any particular interpretation of physical reality, the idea that it is potentially deterministic has long been attractive to me for some reason.  The idea that there might actually be some pervasive order underlying the apparent chaos just appeals to me.

Then quantum phenomena and Bell's inequality come along and mess things up, with most people interpreting these as implying that god does play with dice, and that no hidden variables--no underlying deterministic set of rules--can account for easily observable quantum effects.  Certainly, experimental evidence of nonlocality has been with us since Aspect's experiments in the 1980s, which have been reproduced (at greater distance) a number of times since.

But Bell's theorem only places limits on correlation for local hidden variables.  Basically, the "local realism" that entangled particles violate is predicated on purely local hidden variables.  Given the demonstrated nonlocality of quantum entanglement and the substantial number of additional dimensions posited by some modern theories of physics (11 in M-theory), the idea of non-local hidden variables doesn't seem all that far-fetched.

Granted, nonlocality is normally thought of as contrary to hidden variables and determinism.  But if there are actually more dimensions than 4 (3 space plus time), then two points that are nonlocal in our limited view of space-time may very well be local in a higher-dimensional space-time.  And hidden variables may themselves operate in a non-local fashion.  Problem solved.  Reality can be deterministic, as long as it can be described using both local and non-local variables.

The non-local hidden variables may emerge from a dimensionality greater than 4 or they may be intrinsically non-local, independent of the number of physical dimensions.  All that is required is that they appear to operate in a non-local fashion from our 4-D view of space-time.  This kind of non-locality satisfies Bell's inequality without abandoning determinism.  (In fact, if the hidden variables are actually local in those higher dimensions, it might relax the inequality completely.)  It also resolves the Einstein-Podolsky-Rosen paradox, making Einstein happy on the determinism front, though probably not on the non-locality front (anything having an effect faster than the speed of light was verboten).

Et voila, a deterministic universe.

Disclaimer:  I am not a physicist, but I do look like one:   :)