Skip to main content

How long is a piece of string?

String theory is something that I've been highly sceptical about for some time, influenced by books like Not Even Wrong and The Trouble with Physics. This meant that a recent book, Why String Theory? by Joseph Conlon has proved a very interesting read to provide an explanation for the popularity of string theory among physicists, despite its apparent inability to make predictions about the real world.

I can't say the new book has won me over (and I ought to stress that, like Not Even Wrong, it's not an easy read), but what I do now understand is the puzzle many onlookers face as to how physicists can end up in what appears to be such an abstruse and disconnected mathematical world to be able to insist with a straight face and counter to all observation that we need at least 10 and probably 11 dimensions to make the universe work.

It seems that string theory emerged from an attempt to explain the strong force back in the late sixties, early seventies. The idea of particles as tiny strings, rather than point particles, seemed to provide an explanation for the strong force, however the only way to make it work required the universe to have 26 dimensions (25 spatial, one of time). This was all looking quite good (if weird, but quantum theory has showed us that weird is okay), until the new collider experiments showed the sort of scattering you'd expect from particles, not strings - and along came quantum chromodynamics, requiring only the standard 4 dimensions, blowing string theory out of the water.

However, the more mathematically-driven physicists loved string theory because it was elegant and seemed to hold together unnaturally well, even if it didn't match the real world. They continued to play around with it and eventually massaged it from what was intended as a description of the strong interaction into a mechanism for quantum gravity (or more precisely several mathematical mechanisms). The good news was that this did away with the 26 dimensions, though the bad news was it still required at least 10. Again, there was no experimental justification for the mathematics, but in its new form, mathematical things started to click into place. There was a surprising effectiveness and fit to other mathematical structures. The approach even fitted a number of oddities of the observed particle families. So the abstruse mathematics felt right - and that, essentially is why so many theoretical physicists have clung onto string theory even though it has yet to make new experimentally verifiable predictions, and has so many possible outcomes and all the other problems those books identify with it.

What Why String Theory? isn't very good at, is giving a feel for what is going on in the brains of the physicists in the way ordinary folk can understand (the author is himself a theoretical physicist), so I thought it might be useful to share an analogy that seemed to fit well for me. We're going to do a thought experiment featuring a civilisation that does mathematics to base 5, rather than the familiar base 10. So they count 1, 2, 3, 4, 10, 11, 12, 13, 14, 20, 21... For some obscure reason they use the same numbers as us, but only have 0, 1, 2, 3 and 4. Now these people have come across some textbooks from our civilisation. And they see all those numbers, which make a kind of sense, except there's some weird extra symbols.

Before I go into what they do, I ought to defend the base 5 idea, in case you're wondering why any civilisation would not sensibly realise they could count on the digits of both hands, but rather stuck to the 5 fingers and a thumb of a single hand. This isn't because the civilisation has a strange one armed mutation, it's because they were cleverer than us. How many can you count to on your two hands? Ten. But my civilisation can count to 30. This is because they don't regard their left and right hands as equivalent, but as two totally separate things with different names. The left hand has five digits. But the right hand has five handits. (Bear with me.) When they count on their fingers, they go up the digits of the left hand just as we do. But when the pinkie goes up, they close the whole left hand and raise the pinkie of their right hand, representing five. They then count up on the left again, but when they get a full hand they raise the second finger on their right hand, and so on. Instead of just working linearly across their fingers and thumbs, by working to base 5 their hands become a simple abacus.

So, back to interpreting our base 10 documents. Some rather wacky mathematicians in this society start playing with using bigger bases than base 5. There's no reason why, no application. It's just interesting. And when they happen on base 10 - so they're counting 1, 2, 3, 4, A, B, C, D, E, 10, 11, 12, 13, 14, 1A, 1B... they get a strange frisson of excitement. This isn't the same as the system used in our documents, where the 12th character in the list is 7, rather than C. But suddenly the two kinds of mathematics start to align. Calculations that didn't make any sense suddenly start to click.

In a hugely simplified analogy, this seems a bit like the string lovers' reason for sticking with their theory. It has that same kind of neat mathematical fit. It seems to work too well to be just coincidence. All those extra dimensions and intricate mathematical manipulation don't seem natural, any more than working to base 10 seems natural when you think of left and right hands as totally different things. But it doesn't mean there's not something behind it. I hope the analogy helps you - it certainly helped me to devise it!

Comments

Popular posts from this blog

The Feed (SF) - Nick Clark Windo ****

Ever since The War of the Worlds, the post-apocalyptic disaster novel has been a firm fixture in the Science Fiction universe. What's more, such books are often among the few SF titles that are shown any interest by the literati, probably because many future disaster novels feature very little science. With a few exceptions, though (I'm thinking, for instance, The Chrysalids) they can make for pretty miserable reading unless you enjoy a diet of page after page of literary agonising.

The Feed is a real mixture. Large chunks of it are exactly that - page after page of self-examining misery with an occasional bit of action thrown in. But, there are parts where the writing really comes alive and shows its quality. This happens when we get the references back to pre-disaster, when we discover the Feed, which takes The Circle's premise to a whole new level with a mega-connected society where all human interaction is through directly-wired connections… until the whole thing fails …

The Bastard Legion (SF) - Gavin Smith *****

Science fiction has a long tradition of 'military in space' themes - and usually these books are uninspiring at best and verging on fascist at worst. From a serious SF viewpoint, it seemed that Joe Haldeman's magnificent The Forever War made the likes of Starship Troopers a mocked thing of the past, but sadly Hollywood seems to have rebooted the concept and we now see a lot of military SF on the shelves.

The bad news is that The Bastard Legion could not be classified as anything else - but the good news is that, just as Buffy the Vampire Slayer subverted the vampire genre, The Bastard Legion has so many twists on a straightforward 'marines in space' title that it does a brilliant job of subversion too.

The basic scenario is instantly different. Miska is heading up a mercenary legion, except they're all hardened criminals on a stolen prison ship, taking part because she has stolen the ship and fitted them all with explosive collars. Oh, and helping her train her &…

Euler's Pioneering Equation - Robin Wilson ***

The concept of a 'beautiful equation' is a mystery to many, but it seems to combine a piece of mathematics that expresses something sophisticated in relatively few terms and something that looks satisfying. The equation that has proved standout amongst mathematicians, as by far the most beautiful (and is only placed second to Maxwell's equation amongst physicists) is Euler's remarkable eiπ+1 = 0. What seems remarkable to me about this is that it just seems bizarre that this combination of things produces such a neat result. (Incidentally, as far as I can see, the only reason for the 'pioneering' in the title was to enable the fancy graphic on the cover of the book.)

Getting popular maths books right is incredibly difficult. When I started reading this book, I really thought that Robin Wilson had cracked it. After an introduction, he gives us a chapter on each of the elements of the equation (except the plus and equals signs), from the more basic aspects like 1 a…