The way forward

It is a new year. Time to look ahead, having completed a project toward the end of last year. Well, it still has some things I can look at, but I did make a bit of a breakthrough (if removing an error that resolved an annoying divergence can be called a “breakthrough”). Now, it is natural to look further ahead and ask oneself where one is heading.

In my case, I still hope to develop a formalism that is powerful enough to formulate fundamental theories that incorporate the dynamics of the standard model with gravity. But wait, isn’t that what they are trying to do with string theory and all those other theories?

No, there is a difference. The idea is not to build the speculative aspects of a new theory into the formalism itself. It seems to me that all the currently popular attempts to formulate theories of fundamental physics incorporate speculative ideas into the mathematics of the formalism itself. If they fail, the whole thing fails and there is nothing to salvage.

The only physics that should be built into the formalism is physics that has been established as scientific knowledge. That is the situation with quantum field theory. It has special relativity built into it, because that has been confirmed experimentally. Thus it allows speculative new theories to be formulated.

The inclusion of special relativity may also be the reason why quantum field theory cannot model gravity, which goes beyond special relativity. The obvious thing is then to modify the part that involves the special relativity and to replace it with general relativity. Well that has been tried and did not work.

I think the reason why the obvious extension of quantum field theory to incorporate gravity did not work is because it does not incorporate the formulation of states. Gravity depends on the nature of states. Therefore, my idea is to replace the path integral formulation with a functional phase space. Such a functional phase space formulation allows the definition of arbitrary complicated states. Such a functional phase space formulation is an idea that has been bounced around in the literature, but I have not seen a complete formulation that can handle gravity.

Transcending the impasse, part V

Beauty as a guiding principle

Proceeding with the series on Transcending the impasse in fundamental physics, I like to address some of the issues that has been proposed as reasons for the current impasse. One such issue is the methods by which theorists come up with their theories in fundamental physics. Sabine Hossenfelder, for example, feels strongly that one should not use beauty in the mathematics as a guide to what could be a potential theoretical explanation for fundamental phenomena.

What am I talking about? Perhaps the idea that beauty can have anything to do with fundamental physics sounds ridiculous anyway. Well, beauty, as they say lies in the eyes of the beholder. To a theoretical physicist, the notion of beauty may refer to a different experience than to an artist or a lover. Potential salient aspects of the concept of beauty that would be relevant for all those that experience beauty may include things like symmetry, balance, consistency, etc.

However, it is not my intention here to philosophize about beauty and what it is. The fact of the matter is that physicist do sometimes use their notion of beauty to guide them in how they construct their theories, or in what they consider to be the correct theory. One example that springs to mind is the relativistic equation of the electron of Paul Dirac. It is said that Dirac was guided in its derivation by the beauty in the mathematics.

Paul Dirac, who apparently used beauty as a guide to derive the relativistic electron equation

The issue of whether one should use beauty, or for that matter anything else, as a guide in the construction of fundamental theories reveals a deeper issue at stake here. First, we need to identify a difference between fundamental theoretical physics and other fields of physics. I hasten to add that this is not to be interpreted as a distinction between what is inferior and what is superior.

Other fields of physics usually have some underlying scientifically established physical theory in terms of which investigations are (or can be) done. For example, in classical optics, the fundamental theory is electromagnetism. If all else fails, one can always start with electromagnetism and derive the theoretical description of a phenomena rigorously from Maxwell’s equations for electromagnetism. If the phenomenon includes quantum effects, one may need to fall back on quantum electrodynamics (QED) for this purpose.

In fundamental physics, one does not have this commodity. In most cases one can be lucky to have some experimental results to work with. Sometimes, the only guide is a nagging feeling that the current theories are not adequate. This is the case with quantum gravity. There are some conceptual arguments why general relativity cannot explain everything, but there are no experimental observations showing that something is missing.

How does one approach such a problem? One needs some form of inspiration. Different people tend to use different forms of inspiration. Some use the beauty in mathematics as their inspiration. Perhaps too many theorists have done that and ended up with unsuccessful theories. Hence, the reaction against it.

The point is, we need to remember what it takes to arrive at a scientifically established physical theory. Regardless of what method or form of inspiration or guiding principle one uses, the resulting theory can only become a scientific theory once it has survived experimental testing. In other words, the theory must be able to make predictions that can then be compared with actually observations and then be shown to agree with such observations.

So, in the end, whatever method theorists use to produce their theories is of no consequence, as long as it can succeed as a scientific theory. To put restrictions on the guiding principles, be it beauty or whatever else, makes no sense. Instead, one should allow the diversity of perspectives and freedom in thought to come up with potential theoretical explanations, and leave it to the rigors of the scientific method to sort out the successful theoretical descriptions from those that are to be discarded.

I do not believe that the use of beauty as a guiding principle is responsible for the current impasse in fundamental physics. That dubious honor belongs to a much more inimical phenomenon. But that is a topic for another day.

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