Lisa Randall is a rare specimen: a renowned cosmologist who happens to be female. We listened to her give a talk the other night based on her 2005 book Warped Passages, about the possibility of "hidden" dimensions in space-time.
Randall explained that the investigations into additional dimensions are triggered by the desire to make quantum theory consistent with relativity theory. The existence of higher dimensions may explain apparent inconsistencies. One thing that was striking is how the mathematics drives the investigation. For example, "there is nothing in the mathematics that rules out the existence of other dimensions." It reminds me of another talk we went to--last year, I think--where the scientist talked about how there is nothing in the math of physics to explain why we can go forward in time but not backward.
So the work is to a considerable extent mathematical rather than physical (though this is physics). But there's nothing particularly new about that--Einstein used mathematics, too, and it was a long time before his theories could be proved empirically.
Randall claimed that the theories about higher dimensions may well be proved (or disproved) by experiments at the new CERN hadron collider in Switzerland, starting next year.
It is exceedingly hard to imagine higher spatial dimensions, though Randall tried her darnedest to help us do so. She explained that it is much easier to imagine them mathematically than visually. After her talk, I wondered if the whole question of what higher dimensions would look like is meaningless--as the cosmologist Rocky Kolb once said my question--what existed before the universe?--was meaningless after one of his lectures. We can't picture higher dimensions anymore than a point can picture a line. I wondered if the best way to think about dimensions is as projections. For example, you can look at a point as the one-dimensional projection of a line; a square is the two-dimensional projection of a cube; so a cube would be a three-dimensional projection of a four-dimensional object.
Which means there are hidden worlds we can't perceive directly. But that's not new, is it? The microscopic world--was largely hidden from us for most of human history, and even now some of what we know about this world is due to inference rather than direct observation. You could say something similar about the astronomical world.
Anyway, it was all very interesting and thought provoking. One of these days I'll try reading Randall's book, which I bought in 2005 but haven't gotten to yet.