I’ve been reading up on quantum physics lately, and I’m confused. The first book I read, written in 1994, said that quantum superstrings can only vibrate in the tenth and twenty-sixth dimensions. It wa very clear on that point- only those two, and no one knows why.
It also said that there was some string mathatical problem that they couldn’t solve because there were hundreds of possible answers and they couldn’t tell which one was right.
Fast foward to the next book, written by the same guy around 2007. It seems that the solutions to the aforementioned mathimatical problem have been narrowed down to five that work. Which is still too many for scientists’ liking. But aha! While the five solutions were meant to apply to tenth dimensional vibrations, if you solve for eleven dimensions, they unify into the same principle. Or something. I know this isn’t very helpful, but presumably someone who knows about string theory would know what I’m talking about.
So, my question is: how can these equations apply in eleven dimesions when strings are supposed to vibrate only in ten and twenty six dimensions?
(Sure there must be someone who knows about quantum hanging around on the Dope, right?)
I’m guessing the 1994 book you read was Hyperspace by Michio Kaku which was my intro to string theory too. I think the science in that book is pretty stale nowadays.
The number 26 came out of so-called bosonic string theory, which (as the name suggests) was only able to handle bosons, not fermions, and thus described only forces, not matter, which is somewhat lacking (it’s also unstable on top of that). The five types of string theory being studied (mainly) nowadays are known as I, IIa, IIb, and two heterotic types (commonly called HO and HE). Each of those have 10 spacetime dimensions. Between these types there exist certain correspondences, known as dualities, which provided the first clue that they might not all be different theories. Now, in the low energy limit, these five string theories can be described by (10 dimensional) supergravity theories, i.e. theories which combine general relativity with supersymmetry, which essentially means that each bosonic particle has a fermionic superpartner and vice versa. However, those theories are dimensionally reduced versions of 11d supergravity, which had been an early candidate for a theory of everything. The conjecture, then, is that in the same way string theories in the low energy limit become (10d) supergravity theories, this 11d-supergravity might itself just be the low-energy limit of some more fundamental theory, dubbed ‘M-theory’ for dubious reasons (some say that Ed Witten, who more or less came up with this, just inverted the W of his last name).
At least, that’s as far as my sketchy knowledge on the topic will take me. I can make some more vaguely mumbling noises that there also exists a 12-dimensional F-theory, F standing for father where M stands for mother, and I believe there have been suggestions for 12 dimensional theories with two timelike dimensions, but I’m really not up to date with that stuff.
If you’ve got some time to spare, you could do a lot worse than checking out the NOVA programme The Elegant Universe, which gives a good outline of the topic, or, if you’re more pressed for time, check out Brian Greene’s TED talk based in part on the programme.
First of all, the five different formulations of the string model are not the same thing as the googols of possible solutions to the string model. The five formulations are basically just different ways of writing down equations to describe the same physical phenomena, though it wasn’t realized until a few years ago that they did describe the same phenomena. Any one of those notational methods, though, will admit of an insane number of solutions (“googols” in my first sentence was actually a significant understatement), which basically means that there are that many different sets of laws of physics that could be derived from the string model. This is very bad, for something that purports to be a scientific theory, because it means that the string model is essentially useless for making predictions: No matter how many observations you make, there are always going to be many possible outcomes for the next observation that are all consistent with the model and the observations you’ve made so far.
Oh, you’ll also note that I refer to it as “string model”, not “string theory”. This is an important distinction: Because of the lack of predictability I mentioned above, it is not a theory.
I’d be very curious how they can manage to get this to work. Any model with other than one timelike dimension (or alternately, one spacelike dimension and all the rest timelike, but that’s exactly equivalent) starts getting some really wonky properties-- For one thing, causality becomes pretty much meaningless.
Well, I know little more about it than just that it exists, but the leading proponent of the theory appears to be one Itzhak Bars; here’s an overview of his (mostly, at least) work, and here he is at arXiv. A mathematician, George A. Sparling, even proposes two extra timelike dimensions (here, for instance). Interestingly, both seem to come from a Twistor theory background.