believable theories of everything

A few years ago I got about half way through The Elegant Universe by Brian Greene, which is a classic introduction to superstring theory. I'd like to think I gave up because of intellectual skepticism, but I think I just ran out of steam. But now I'm cruising through Lee Smolin's The Trouble with Physics. Both books are written by experts in "theories of everything," but they line up on opposite sides of one of the great debates. Namely, whether superstring theory is terribly clever and exciting or whether it's Not Even Wrong.

Greene is known for his ability to popularize what is in reality a ludicrously arcane mathematical theory. The motivation behind this blog is the notion that synthesizing scientific concepts and trying to present them intuitively to a lay audience is an extremely worthwhile exercise. Science becomes a beautiful aesthetic experience when something messy can be described by an elegant theory. Such a theory may perhaps still contain technically difficult mathematics, but if it proposes a model of reality that gives us insight at some intuitive level, then it can be appreciated by scientist and layperson alike. Also, it becomes intuitively believable. This follows the principle of the medieval scholar William of Ockham, who proposed that the theory that explained the most by way of the least knobs and twiddles is to be preferred. For example, proposing that the earth and other planets orbited the sun led to way fewer twiddles in describing the motion of those other planets viewed from the earth.

Then there is the aesthetic of finding a theory that provides a more unified explanation of nature. A good example is Maxwell's theory of electromagnetism. The equations can look a bit daunting to a layperson but there is certainly something very elegant here. There is a nice symmetry to the way the electric and magnetic fields enter the equations. There is incidentally a lack of symmetry in that electric charges are incorporated into the model, but the magnetic equivalent - magnetic "monopoles" - are conspicuously absent. But when we just look at the fields, Maxwell's equations predict the propagation of an electromagnetic wave at a speed that can be calculated from two properties - one electric, the other magnetic - of a vacuum. And this speed is exactly the speed of light (in a vacuum). This implies that the speed of light is fixed, regardless of the speed of any observer, and this, of course, was Einstein's starting point for his theory of special relativity.

The "theory of everything" physicists are continuing this tradition of trying to unify areas of physics. Faraday showed experimentally that electricity and magnetism were connected, and Maxwell finished the job off mathematically. This led to Einstein's special relativity, which unified space and time, and also mass and energy. Oh, and he showed even more deeply than Maxwell how electricity and magnetism are in fact the same thing, only viewed at different relative velocities. Then came Einstein's theory of general relativity, which unifies gravitation with acceleration, and hence explains the equivalence of gravitational and inertial mass, while also demonstrating that matter influences the geometrical properties of space.

Although few of us have much grasp of general relativity, we know that there is something elegant about it. But as one reaches out in an attempt to unify ever more diverse phenomena, one's theories may of course develop an alarming number of knobs and twiddles. And in fact, things have become quite messy. There are three forces that affect elementary particles, and then there is gravity, which is only noticeable when there are vast numbers of elementary particles grouped into astronomical sized objects. Not surprisingly, gravity has always been hard to connect up with the other three forces, which are part of the quantum mechanical world of subatomic particles. So let's keep gravity out of it for now. This leaves us with the Standard Model of particle physics, which is a weird combination of elegance and messiness, as some deep symmetries of nature have been "spontaneously broken" while others remain intact.

We live in a world where different kinds of matter share some properties but not others. Some carry electrical charge, and so are sensitive to electromagnetism. Some carry the nuclear charge called color, and so are sensitive to the strong nuclear force. And all carry weak isospin and hence are all affected by the weak force. In their respective domains, these charges are conserved, corresponding to underlying symmetries. But electrons are fundamentally different from the quarks that make up protons and neutrons, the different quarks have different masses, and all of this represents a breaking of symmetries.

Similarly the three forces are carried by particles that are very different from each other. The familiar photon that carries the electromagnetic force is massless, as is the gluon that carries the strong force, whereas the weak force is carried by three very massive (and shortlived) particles. And yet, the photon and weak force carriers can be shown to be beautifully related in a unified "electroweak" theory that also connects electrons to neutrinos and explains how neutrons can change "flavor" and turn into protons during radioactive decay.

Needless to say, force particles are different from matter particles. Yet superstring theory aims to connect even these aspects of reality together in an overarching theory that combines all four forces of nature and all flavors of matter together. This makes Maxwell's synthesis of electricity and magnetism seem quite modest. Modest yet elegant has been superceded by extremely ambitious and extremely messy.

This may sound like an excuse, but I think the reason I stopped reading The Elegant Universe was that I knew that Greene was having to hide all that messiness under the rug in order to convince me of the elegance. And so I couldn't even begin to judge the believability of any of it. I feel more comfortable with Smolin's skeptical approach, and I've finally caught the theory of everything bug.