In preparing my presentation for the next lecture in the LRC Public Lecture Series, I came across a video of a talk given by Nima Arkani-Hamed, of the Institute for Advanced Studies at Princeton, entitled “Fundamental Physics in 2010.” I recognized it as a video I had started to watch once before, but became impatient with before it was over. Too bad, because it’s really good.
He explains the “crises and paradoxes” that current fundamental physics faces as well, or better even, than anyone else I’ve seen. He even explains why theorists find that space-time is emergent, something I had looked for in vain a while back. It turns out to be quite simple. Just like the 20th Century discovery of the uncertainty principle stood classical physics on its ear, because both position and momentum, which are the heart and soul of classical physics, can’t be specified to an arbitrary precision in quantum mechanics, the new crisis stands quantum mechanics on its ear, because distances smaller than the Planck length can never be observed, since doing so would require so much energy that it would warp spacetime into a black hole at that scale.
This means that, at singularities, such as black holes and the big bang, the breakdown of the spacetime fabric creates a need for a replacement of some kind. The break down of the spacetime equations at singularities means that physicists can’t speak of a time before the big bang, since it makes no sense to do so. Arkani-Hamed says, “Our theories simply break down when gravity and quantum mechanics both become important. Cool stuff.”
But then he goes on to explain how, initially, string theory was thought to be a way to get around the problem since the smallest strings were considered to be around 10-31cm, which were too big to be swallowed up by the black hole at 10-33cm. However, in 1995 it was found that strings could be points, strings or even membranes and could have any size. This was “probably, the most important theoretical development in the last twenty years,” says Hamed. “The whole dichotomy between particles and strings has disappeared…particle theories and string theories can be different facets of exactly the same thing.”
I thought this would be a really good seqway into the lecture I was preparing, so I used it. Or at least I started out to use it. By the time I was finished, it was hard to tell that the current idea of emergent spacetime was at the core of the presentation. In fact, in the end, I ended up talking more about dimensions in general, the 26 dimensions of string theory, the 10 dimensions of superstring theory, and, finally, 11 dimensions of M-theory, all of which lead to the theories of Arkani-Hamad et al (ADD theory) and Lisa Randall et al (RS theory), known generally as theories of large extra dimensions.
The reason they are called large extra dimensions is because, with M-theory, the extra dimensions of string theory no longer need be compactified to make them fit into the 1+ 3 dimensions of observed reality, but they may be as large as the universe; that is a closed loop of string, like an over inflated inner tube, may morph into a membrane and the 1+ 3 dimensions may be on its surface, with open ended strings attached like leeches, unable to escape, while closed strings easily drift off into the interior bulk of the membrane. Since closed strings are gravitons in string theory, this provides ADD theories with an alternate way to explain the relative weakness of gravity, which does not require the unification of gravity at the planck scale, at 10-33cm, but only at the much more manageable electroweak unification scale at 10-17cm. The RS theory is a variation of this where the gravitons live on another brane, the scale of which is much larger than the scale of the 1+ 3 brane, providing a warped transition for gravitons that reduces their strength.
However, you can probably imagine the difficulty of explaining all this in less than one hour, while at the same time trying to provide enough background to motivate it all. It’s one tall order and I’m not sure how well I succeeded, but in the end I tried to show how young Heisenbergs might fiddle around with dimensions themselves by taking a fresh look at the meaning of dimensions in the tetraktys, in the Grassmann numbers of Clifford algebra, and in geometry. If you’re wondering how I did justice to all that in a presentation of less than one hour, you’ll soon realize that I couldn’t.
What I hoped to show, though, was that it’s possible to see how the 26 dimensions of string theory reduce to the 10 dimensions of superstring theory, by simple inspection of the tetraktys, through the principle of duality. I didn’t even come close to doing that, but, hopefully, I managed to open the door to their curiosity enough to give them a peek at this marvelous mystery.
For those who might be interested, I will try to explain it more completely tomorrow on the New Math blog.