The deceptive lure of a final theory

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.

Adrift in theory space

It is downright depressing to think that after all the effort to understand the overlap between gravity and quantum physics there is still no scientific theory that explains the situation. For several decades a veritable crowd of physicists worked on this problem and the best they have are conjectures that cannot be tested experimentally. The manpower that has been spent on this topic must be phenomenal. How is it possible that they are not making progress?

I do understand that it is a difficult problem. However, the quantum properties of nature was also a difficult problem, and so was the particle zoo that led to quantum field theory. And what about gravity, which was effectively solved singled-handedly by just one person? There must be another reason why the current challenge is evidently so much more formidable, or why the efforts to address the challenge are not successful.

It could be that we really have reached the end of science as far as fundamental physics is concerned. For a long time it was argued that the effects of the overlap between gravity and quantum physics will only show at energy scales that are much higher than what a particle collider could achieve. As a result, there is a lack of experimental observations that can point the way. However, with the increase in understanding of quantum physics, which led to the notion of entanglement, it has become evident that it should be possible to consider experiments where mass is entangled, leading to scenarios where gravity comes in confrontation with quantum physics at energy levels easily achievable with current technology. We should see results of such experiments in the not-too-distant future.

Another reason for the lack of progress is of a more cultural nature. Physics as a cultural activity that has gone through some changes, which I believe may be responsible for the lack of progress. I have written before about the problem with vanity and do not want to discuss that again here. Instead, I want to discuss the effect of the current physics culture on progress in fundamental physics.

The study of fundamental physics differs from other fields in physics in that it does not have an underlying well-establish theory in terms of which one can formulate the current problem. In other fields of physics, you always have more fundamental physical theories in terms of which you can model the problem under investigation. So how does one approach problems in fundamental physics? You basically need to make a leap into theory space hoping that the theory you end up with successfully describes the problem that you are studying. But theory space is vast and the number of directions you can leap into is infinite. You need something to guide you.

In the past, this guidance often came in the form of experimental results. However, there are cases where progress in fundamental physics was made without the benefit of experimental results. An prominent example is Einstein’s theory of general relativity. How did he do it? He spent a long time think about the problem until he came up with some guiding principles. He realized that gravity and acceleration are interchangeable.

So, if you want to make progress in fundamental physics and you don’t have experimental results to guide you, then you need a guiding principle to show you which direction to take in theory space. What are the guiding principles of the current effort? For string theory, it is the notion that fundamental particles are strings rather than points. But why would that be the case? It seems to be a rather ad hoc choice for a guiding principle. One justification is the fact that it seems to avoid some of the infinities that often appear in theories of fundamental physics. However, these infinities are mathematical artifacts of such theories that are to be expected when the theory must describe an infinite number of degrees of freedom. Using some mathematical approach to avoid such infinities, we may end up with a theory that is finite, but such an approach only address the mathematical properties of the theory and has nothing to do with physical reality. So, it does not serve as a physical guiding principle. After all the effort that has been poured into string theory, without having achieved success, one should perhaps ponder whether the departing assumption is not where the problem lies.

The problem with such a large effort is the investment that is being made. Eventually the investment is just too large to abandon. A large number of very intelligent people have spent their entire careers on this topic. They have reached prominence in the broader field of physics and simply cannot afford to give it up now. As a result, they drag most of the effort in fundamental physics, including a large number of young physicists, along with them on this failed endeavor.

There are other theories, such as loop quantum gravity, that tries to find an description of fundamental physics. These theories, together with string theory, all have it in common that they rely heavily on highly sophisticated mathematics. In fact, the “progress” in these theories often takes on the form of mathematical theorems. It does not look like physics anymore. Instead of physical guiding principles, they are using sets of mathematical axioms as their guiding principle.

To make things worse, physicists working on these fundamental aspect are starting to contemplate deviating from the basics of the scientific method. They judge the validity of their theories on various criteria that have nothing to do with the scientific approach of testing predictions against experimental observations. Hence, the emergence of non-falsifiable notions such as the multiverse.

In view of these distortions that are currently plaguing the prevailing physics culture, I am not surprised at the lack of progress in fundamental physics. The remarkable understand in our physical world that humanity has gained has come through the healthy application of the scientific method. No alternative has made any comparable progress.

What I am proposing is that we go back to the basics. First and foremost, we need to establish the scientific method as the only approach to follow. And then, we need to discuss physical guiding principles that can show the way forward in our current effort to understand the interplay between gravity and quantum physics.

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