On the Nature of Circular Dimensions...

In order to try to visualize more dimensions than we humans are normally accustomed to, physicists will typically have you imagine a universe on a plane or even on a line, and then have you imagine what the "extra" dimension(s) might seem like to some creature living in this stunted universe. What does the second dimension look like to a creature of "Lineland"? What was Homer's reaction when he experienced the mythical "third dimension" (being, as he was, a creature of "Flatland")? That is useful, but of course, only takes you so far.

Imagine now, a universe on a garden hose. A little like Flatland, this imaginary 2-dimensional universe, but with a twist (or a circle, if you will). Now imagine seeing it from a long way away (like hundreds of miles away). This universe now appears to be 1-dimesional and an entity on it seems to be an entity existing on a one-dimesional universe. But close up (from just inches away), the nature of this unverse becomes clearer - its a 2-dimensional space (the surface of the hose) with a single dimension traversing length-wise and another dimension that is circular. So, for each point in the 1-dimensional space (from far away) there is a second, circular dimension that has length, but that exhibits the "curious" property that, if you travel far enough in that dimension, you end up where you started.

Now scale that up.

We appear to live in a 3-dimensional universe (3 spatial dimensions anyway). But what if we actually lived on a 3-dimensional garden hose however from very close up (close to the Plank length) other (circular) dimensions became apparent? This is (in part) what String theory proposes.

There could be (in scales we cannot directly see or experience) circular dimensions that add to the three apparent dimentions in which we live - dimensions which are folded or curled up on themselves such that, if you were to travel along them for some length, you would wind up back where you started. (In fact they dont actually have to be "circles" per se, just so long as they are closed loops of some variety) String theory (the mathmatics of it anyway) proposes that there are actually six additional dimensions that are not apprent to us in our everyday worlds. In fact that maybe we might live in a 9-spatial (+1 temporal) -dimension universe... With 6 of the unseen dimensions existing at scales beyond our ability to directly experience. What would that look like? Well apparently (according to the math) the six circular dimentions might look very much like this picture except at distace scale far too small to be "seen". We are talking Plank length, so something just over 10^-35 meters here. That is 0.00000000000000000000000000000000001 meters. Small. Very VERY small.

So. Assuming this were a possibility... Now imagine that one of these "extra" circular dimensions is, in fact, a time dimension. What if one or more of those tiny circular dimentions were actually temporal in nature? How would that appear to us in the macro-world? What would that mean to sub-atomic particle theory? How would that affect your life if, say, you were a photon or an electron? Or even a muon?

In a scaled up way, I think it might appear something like this: No matter where you would go or what you would do, the same moment would keep coming back around and you would find yourself at the same point again. Movement in that dimension would be forever forward (as it is in the familiar time dimension) and forever repeating itself. So in much the same way that despite what we do with ourselves throughout the week, Friday continues to come around and we find ourselves at Red Hook, drinking beer. In so much as it really does come down to how each of our individual perceptions decide to experience the universe, I choose to experience the universe as having a circular temporal dimension with a radius of 168 hours, at which time t₀ is 5:30pm PST on Fridays. :-)

Eh, eh? (Beer + Physics) * Geeks = ??

(Note: A universe on a garden hose as a visualization construct is Brian Greene's. A universe with a circular temporal dimension of radius 7 days is mine. :-) Check out this.)