In my conversation with Jonathan Gorard about the founding of the Wolfram Physics Project (listen to the audio ⋅ watch the video), I said that I don’t like String Theory.
Now, I’ll admit, I don’t really understand String Theory.
It’s highly mathematical. And I’m not much of a mathematician. Actually, that’s an understatement. I’m not a mathematician at all.
So if there’s a problem in the relationship between String Theory and me, it might not be String Theory, it might be me.
Sadly, admitting that I might be part of the problem doesn’t change anything between us. I still don’t like String Theory.
Here’s why.
Fluffy ontology
String Theory models elementary particles such as electrons and quarks as one-dimensional objects called strings.
You can think of them as tiny threads, some of them open, some of them closed loops, floating through the universe.
So you can think of the universe as a tumble dryer with a dodgy lint filter, so that all those tiny threads remain suspended in the drum after you’ve removed your clothes.
If the universe is that ugly, then I want out.
I mean, seriously, the universe is little bits of fluff floating around?
When Jonathan Gorard told me that he doesn’t consider string theory a plausible ontology for reality, I think he meant that he, too, finds it hard to imagine that the universe is really little bits of fluff floating around.
Mathematical conceit
According to String Theory, the vibrations of each of these tiny threads determine the mass, charge and all the other properties of the elementary particle it models.
There’s no denying it, the mathematics of these vibrations yields some compelling results in physics. In particular, one of the vibrational states of the strings can be taken to correspond to the graviton, giving us a theory of quantum gravity.
The trouble is, mathematics has a habit of misleading us if we take it too literally.
Vibrational states? The mathematics of vibrations is so basic that we see it everywhere.
It models the passage of sound through the air, for example, but that doesn’t mean that the air is made of string.
It models the orbit of an electron around a proton according the Schrödinger equation, another example, but that doesn’t mean that atoms are made of string.
So it models gravitons in a way that’s consistent with quantum mechanics? That’s interesting, but it doesn’t mean that the universe is made of string.
Physicists v Mathematicians
Which brings us to the core of the problem: the tension between mathematics and physics.
Jonathan Gorard, a self-confessed mathematician, told me that he tends to appraise theories according to their mathematical and philosophical elegance.
Whereas I, a would-be physicist, tend to appraise theories according to their physical and philosophical elegance.
I like theories that stem from beautiful, simple, physical insights.
Relativity is a good example. Einstein began with beautiful, simple, physical insights, such as that the laws of physics are the same everywhere, and that the speed of light is the same everywhere. From such basic postulates, Einstein conceived the special and general theories of relativity.
Sure, mathematics came along for the ride: Minkowski space, Riemannian manifolds, the Cartan-Karlhede algorithm, and all the rest. But the physics came first.
Despite having been responsible for much of the mathematical complexity, Einstein famously quipped: “Since the mathematicians have invaded the theory of relativity, I do not understand it myself any more.”
It seems to me that String Theory is the reverse of relativity in this respect.
With relativity, the physics came first, and mathematics came along for the ride.
With String Theory, the mathematics came first, and physics came along for the ride.
Back to reality
In our conversation, Jonathan Gorard described String Theory as a beautiful collection of mathematical ideas that have had a profound influence on complex geometry, algebraic geometry, differential geometry.
As mathematics, maybe, it’s sublime.
As physics, however, it seems unable to offer true insights into the nature of reality.