There has been this nagging feeling that something is not quite right with the current flavor of fundamental physics theories. I’m not just talking about string theory. All the attempts that are currently being pursued share this salient property, which, until recently, I could not quite put my figure on. One thing that is quite obvious is that the level of mathematics that they entail are of a extremely sophisticated nature. That in itself is not quite where the problem lies, although it does have something to do with it.
Then, recently I looked at a 48 page write-up of somebody’s ideas concerning a fundamental theory to unify gravity and quantum physics. (It identifies the need for the “analytic continuation of spinors” and I thought it may be related to something that I’ve worked on recently.) It was while I read through the introductory parts of this manuscript that it struck me what the problem is.
If we take the standard model of particle physics as a case in point. It is a collection of theories (quantum chromodynamics or QCD, and the electro-weak theory) formulated in the language of quantum field theory. So, there is a separation between the formalism (quantum field theory) and the physics (QCD, etc.). The formalism was originally developed for quantum electro-dynamics. It contains some physics principles that have previous been established as scientific principles. In other words, those principles which are regarded as established scientific knowledge are built into the formalism. The speculative parts are all the models that can be modeled in terms of the formalism. They are not cast in stone, but the formalism is powerful enough to allow different models. Eventually some of these models passed various experimental tests and thus became established theories, which we now call the standard model.
What the formalism of quantum field theory does not allow is the incorporation of general relativity or some equivalent that would allow us to formulate models for quantum theories of gravity. So it is natural to think that what fundamental physicists should be spending their efforts on, would be an even more powerful formalism that would allow model building that addresses the question of gravity. However, when you take a critical look at the theoretical attempts that are currently being worked on, then we see that this is not the case. Instead, the models and the formalisms are the same thing. The established scientific knowledge and the speculative stuff are mixed together in highly complex mathematical theories. Does such an approach have any hope of success?
Why do people do that? I think it is because they are aiming high. They have the hope that what they come up with will be the last word in fundamental physics. It is the ambitious dream of a final theory. They don’t want to be bothering with models that are built on some general formalism in terms of which one can formulate various different models, and which may eventually be referred to as “the standard model.” That is just too modest.
Another reason is the view that seems to exist among those working on fundamental physics that nature dictates the mathematics that needs to be used to model it. In other words, they seem to think that the correct theory can only have one possible mathematical formalism. If that were true the chances that we have already invented that formalism or that we may by chance select the correct approach is extremely small.
But can it work? I don’t think there is any reasonable chance that some random venture into theory space could miraculously turn out to be the right guess. Theory space is just too big. In the manuscript I read, one can see that the author makes various ad hoc decisions in terms of the mathematical modeling. Some of these guesses seem to produce familiar aspects that resemble something about the physical world as we understand it, which them gives some indication that it is the “right path” to follow. However, mathematics is an extremely versatile and diverse language. One can easily be mislead by something that looked like the “right path” at some point. String theory is an excellent example in this regard.
So what would be a better approach? We need a powerful formalism in terms of which we can formulate various different quantum theories that incorporate gravity. The formalism can have, incorporate into it, as much of the established scientific principles as possible. That will make it easier to present models that already satisfy those principles. The speculations are then left for the modeling part.
The benefit of such an approach is that it unifies the different attempts in that such a common formalism makes it easier to use ideas from other attempts that seemed to have worked. In this way, the community of fundamental physics can work together to make progress. Hopefully the theories thus formulated will be able to make predictions that can be tested with physical experiments or perhaps astronomical observations that would allow such theories to become scientific theories. Chances are that a successful theory that incorporates gravity and at the same time covers all of particle physics as we understand it today will still not be the “final theory.” It may still be just a “standard model.” But it will represent progress in understanding which is more than what we can say for what is currently going on in fundamental physics.