Sharp Blue: String theory, aesthetics and experiment

Gautam mused:

Physicists don’t postulate ten unobservable dimensions for fun - they do it because that’s where the math takes them. They create this math in order to describe (very real) experimental results. This isn’t arm-waving.

Actually, this isn’t really true. There are no current experimental data that General Relativiy or the Standard Model of particle physics (or minor variations thereof) can’t explain. The impulse that drives some physicists into the realms of superstring theory and M theory and other exotic theories is largely aesthetic. The problem as they (and I) see it is that we have not one but two seemingly fundamental theories of physics (the aforementioned General Relativity and the Quantum Field Theory of which the Standard Model is an application) and this is an affront to our ideas of beauty and elegance.

To make things worse, the domains which these two theories describe don’t overlap within the scales of energy and momentum (or, equivalently, time and space) that our experiments can probe. This means that the search for a theory that subsumes both cannot be guided, as physics almost always has been, by experiment but must instead draw on our sense of what must be true. This is, needless to say, a dangerous business. Worse still is the fact that the mathematics of string theory is so arcane that it’s proven nearly impossible to extract physical predictions from it at all, so we don’t even know for sure that it reduces to our current theories in the relevant limits. In a way, the most fundamental physics being studied today has more in common with the approach taken by the ancient Greeks than it does to physics during its “Golden Age” in the 20th century.

There is a famous precedent for great physicists trying to advance in conceptual bounds beyond the frontiers probed by experiments: Einstein himself. The theory of General Relativity, unlike the earlier theory of Special Relativity, was not intended to explain any puzzling experimental anomalies. Einstein was driven instead by a passion for conceptual simplicity and unity. In that case, he got lucky: after the theory was formulated he extracted predictions from it, and these were supported by experiment. (One of the triumphs of GR was the explanation of the precession of the orbit of Mercury which had been observed prior to the formulation of the theory, but this problem wasn’t a motivation for the search for a relativistic theory of gravitation.)

However, the very triumph of General Relativity led Einstein astray. He spent the last few decades of his life in a quest for a “Unified Field Theory” that would combine gravitation and electomagnetism into a single geometric theory. Needless to say, he failed to find such a unified theory, and after General Relativity produced little of enduring value. I sometimes worry that the string theorists are heading along the same road. The mathematics might be alluring and the feeling of closing in on a “Theory of Everything” might be thrilling, yet still they could be on entirely the wrong track and not even know it.

(There’s a cute link between string theory and the quest of Einstein and his coworkers: the idea of hidden extra dimensions is common to both. The idea was first proposed by Kaluza and Klein, whose famous theory of five-dimensional general relativity with a single compactified dimension yielded the equations of electromagnetism [and of a scalar field] in addition to the field equations for gravitation.)