Extra dimensions
Last night at a jazz club I was talking to a graduate student at the UofC Divinity School, trying to explain the concept of extra dimensions of spacetime. The possibility of extra dimensions is one of the most exciting ideas in modern physics, but also the one I've had the most trouble elucidating to non-experts. (For noble attempts, see

here,

here,

here,

here,

here.) I'm not completely sure why this is the one thing that is hardest to understand.

How do we know there are three dimensions of space? The simplest way is to take a set of meter sticks and tie them together, such that every one is perpendicular to every other one. What is the largest number of sticks for which you can do that? Three. If we lived in a world with two spatial dimensions, it would only be two, but if there were extra large dimensions it would be some bigger number. Given that we have developed mathematical techniques for describing the geometry of one-dimensional curves, two-dimensional surfaces, and three-dimensional spaces (not to mention four-dimensional spacetime), it shouldn't be too surprising that we can straightforwardly generalize to higher numbers of dimensions. But people who spend their free time doing something other than studying mathematics don't want to hear that -- they want to know how you can

*visualize* all these extra dimensions. We try our best, but ultimately you can't really do it, and you have to resort to metaphor.

When trying to explain extra dimensions, there are a few standard analogies we always trot out. One is a straw, or garden hose. We can idealize a straw as a two-dimensional cylinder, but if you look at it from very far away it looks essentially one-dimensional. This is supposed to capture the idea that there can be extra compact dimensions at each point in space. I think this analogy is perfectly transparent, and everyone who hears it should instantly comprehend this otherwise difficult concept. But the actual reactions run the gamut from blank stares to gently-furrowed brows. (A very tiny gamut.) When I'm trying to explain this in a radio interview, it's even worse, as the complete lack of visual aids renders me helpless. Is there some better metaphor lurking out there?

If string theory is right and there are seven extra dimensions curled up at every point in our apparently three-dimensional space, we are actually smeared out uniformly throughout these dimensions. This smearing can ultimately be traced back to our status as relatively low-energy phenomena in the universe. Something physicists take for granted is the connection between energy and distance: to access phenomena at very small scales (like a tiny curled-up extra dimension) requires the focusing of extremely high energies. That's why we're hoping to find evidence for extra dimensions at particle accelerators. It's a long shot, though; we're gradually increasing our reach in energy, but it wouldn't be a surprise if the extra dimensions were well beyond our currently conceivable experiments.

Probably the best way to explain extra dimensions is to imagine that there were fewer dimensions, and how inhabitants of these lower-dimensional worlds could be convinced of the existence of three spatial dimensions. This was the strategy taken in Edwin Abbott's classic social satire

Flatland. Let's not forget, however, that once the protagonist is convinced of the existence of extra dimensions and starts spreading the word, he's thrown into jail for his subversive ideas.

Although I didn't really succeed in conveying much understanding about extra dimensions, I did learn something about the divinity school: many, if not most, if its faculty members don't believe in God. "Pretty skeptical about religion" was the description offered. I wonder if this phenomenon is widespread in divinity schools elsewhere?