25 June 2011

Super duper super strings

I just finished reading The Elegant Universe by Brian Greene, which attempt to explain the newest bit of theoretical physics, Superstring Theory, to non-physicists. The elegance in the title comes from the fact that the real quest of superstring theory is to combine general relativity and quantum mechanics in one elegant theory, instead of the messiness of currently having two not-quite-reconcilable ones. I think the book succeeded at this goal, in fact this post is mostly about my reactions to the content of the book rather than a critique of the book itself.

One reason the book was very satisfying to me is because ever since I learned about the lengthening list of so-called elementary particles (bosons, muons, etc.) my first thought has been, "hey, you don't really understand this yet, and when you do, that list suddenly all turn out to be something simpler."

That's exactly what string theory purports to do. It posits that everything is made up of tiny (but not infinitely tiny) loops of string, and that the different forms of matter can all be derived by looking at the different fundamental vibration modes of the string. Just as a guitar string when plucked has a fundamental, first harmonic, second harmonic, and so forth, these hypothesized tiny strings can only give rise to a finite number of expressions. Due to a mathematical trick involving nearly-self-canceling probability waves, the string theorists are able to show they can rise to expressions that look like quite a number of the basic particles in the catalog .

This also resonates (get it?) with me. Another of my thoughts way back was that particles would all turn out to be just periodic waves. String theory is actually a lot better than that (the fact that string are not infinitely small but rather just small helps with a lot of things in quantum mechanics that are otherwise mathematically intractable) but it's at least along the same lines.

Quite aside from the string theory portion of the book, it's also a good explanation of the basic of 20th century physics, namely relativity and quantum mechanics. In particular, while I spent time in college calculating Lorentz contractions and time dilations for homework assignments, I never encountered as satisfying an explanation as Greene's of exactly how to think about both Lorentz contraction and time dilation as simple consequences of treating time as a fourth dimension.

So far so good. However, there are several other qualities of string theory as explained in the book that make one go "Eh?"

The big one (which to his credit Greene does not shy away from or obscure) is that we have no idea if string theory is correct or not. The math is so complicated that there aren't many ways that scientists can actually calculate the predicted properties of string theory with enough precision to verify that it's a complete explanation of previous observations (more about why the math is so complex in a minute). As Greene says after spending an entire chapter showing how five competing. branches of string theory actually are just the same theory expressed in different math - a happy conclusion that was greatly to the relief of all involved - he points out, "of course, we still have no proof any of these theories describe the world we live in."

Related to this is the fact that string theory has so far failed to be able to make any predictions about the world that we don't already know. That is, string theorists are busily working away trying to advance the math to the point where they can explain all the measurements of the world that have already taken place. However, so far they haven't been able to use it to make a verifiable prediction about anything we haven't measured yet. Greene points out how this predictive ability was a big factor in making both relativity (with the prediction of light rays being bent by gravity) and big bang theory (being ably to accurately predict the at-that-time unmeasured strength of cosmic background radiation) turn into accepted knowledge.

Finally, string theory as currently formulated contains one of those "Eh?" moments that's so strong you have to ask for the evidence again (and as mentioned previously the evidence is not yet forthcoming). Namely, current string theory posits that the world is 11-dimensional (10 dimensions of space plus time). Why does the world seem three-dimensional in space to us?

To even explain the answer I have to make use of Greene's excellent analogy from the book. Suppose a tiny snail-like creature lives entirely on the surface of a garden hose. The surface of a garden hose is two-dimensional, that is, it takes a minimum of two numbers to explain where on the garden hose the snail is: one giving where the snail is along the length of the host and one giving where the snail is around the circumference of the hose.

However, unlike x, y, and z in our world, the two dimesions of the snail's existence are very different from each other. The distance around the circumference of the hose wraps back on itself, so if the snail travels in the direction around the hose they get back to where they started.

So, now we go back to why we don't see the other dimensions of our world. The answer according to string theorists is that the other dimensions are firstly, curled up like the circumference of the garden hose, and secondly are very very small (i.e., the radius of the equivalent of the garden hose is very small) and so we haven't seen them yet.

Frankly, "Oooooohhhhhhhkaaaaaaayyy..... Ssssssuuurrrrreee." is a pretty reasonable reaction to that. However, implausibility doesn't make a theory wrong either (let's remind ourselves we're in the same discipline as general relativity and quantum mechanics here). However, it does make you long for some actual predictions about the world that would make this theory testable. Since unlike quantum mechanics (which for all it's implausibility has actually succeeded in predicting stuff that goes on at the micro-scale pretty well) we don't have a lot of predictions out of string theory yet, skepticism is still justifiable.

And this cuts to the biggest worry I have about string theory after reading the book. In a lot of ways string theory is very elegant - it derives all of the fundamental particles rather than taking them as assumptions. If correct it will provide an integrated theory for understanding both microscopic and cosmological phenomena. And scientists and engineers both really like elegant theories.

But elegant theories can be wrong in sufficiently complex systems. Actual systems have a way of requiring somewhat inelegant solutions. But the intellectual appeal (and mental convenience) of elegant theories still gives them a powerful appeal. While my elegance-admiring side (which I am as prone to as anyone else) revels in the possibility of string theory explaining everything, my experience with humans suggest we would pursue this theory vigorously even if it was wrong because of its elegance.

I hope the string theorists do keep going, and it will be neat if they're right. I'm all for it! But... Let's just say that after reading this book, I'm even more convinced that there is no pressing need to spend billions and billions building the Superconducting Supercollider just yet. This feels like an area where we need the theory to advance quite a bit before it will have any impact on the world outside of intellectual stimulation.

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