As a theorist, I may have misled some people into thinking that I don’t care much for experimental work. In particle physics, there tend to be a clear separation between theorists and experimentalists, with the phenomenologists sitting in between. Other fields in physics don’t have such sharp separations. However, most physicists lean toward one of the two.

Physics is a science. As such, it follows the scientific method. That implies that both theory and experiment are important. In fact, they are absolutely essential!

There are people that advocate, not only the suspension of experimental work in particle physics, but even that the methodology in particle physics be changed. What methodology in particle physics needs to be changed? Hopefully not anything related to the scientific method! To maintain the scientific method in particle physics, people need to keep on doing particle physics experiments.

There was a time when I also thought that the extreme expense in doing particle physics experiments was not justified by the results obtained from the Large Hadron Collider (LHC). However, as somebody explained, the results of the LHC are not so insignificant. If you think about it, the “lack of results” is a fallout of the bad theories that the theorists came up with. So by stopping the experimental work due to the “lack of results,” you would be punishing the experimentalists for the bad work of the theorists. More importantly, the experimentalists are just doing precisely what they should be doing in support of the scientific method: ruling out the nonsense theories that the theorists came up with. I think they’ve done more than just that. Hopefully, the theorists will do better in future, so that the experimentalists can have more positive results in future.

I should also mention the experimental work that is currently being done on neutrinos. It is a part of particle physics that we still do not understand well. These results may open the door for significant improvements in our theoretical understanding of particle physics.

So, please keep on doing experimental work in particle physics. If there is an methodological changes needed in particle physics, then that is limited to the way theorists are doing their work.

Somebody once explained that when a theory is shown to be wrong, its proponents will keep on believing in it. It is only when they pass away that the younger generation can move on.

None of this applies to string theory. To be shown to be wrong there must be something to present. The mathematical construct that is currently associated with string theory is not in any form that can be subjected to any scientific testing.

What was shown to be wrong is supersymmetry, which is a prerequisite for the currently favored version of string theory – super string theory. (The non-supersymmetric version of string theory fell into disfavor decades ago.) The Large Hadron Collider did not see the expected particles predicted by supersymmetry. Well, to be honest, there is a small change that it will see something in the third run which has just started, but I get the feeling that people are not exactly holding their breath. I’m willing to say supersymmetry is dead and therefore so is super string theory.

Another reason why things are different with string theory is because the proponents found a way to extend the postmortem activity in string theory beyond their own careers. They get a younger generation of physicists addicted to it, so that this new generation of string theorist would go on working in it and popularizing it. What a horrible thing to do!

Why would the current string theorists mislead a younger generation of physicists to work on a failed idea? Legacy! Most of these current string theorists have spent their entire careers working on this topic. Some of them got very famous for it. Now they want to ensure that they are remembered for something that worked and not for something that failed. So it all comes down to vanity, which I’ve written about before.

String theory was already around when I was still a student several decades ago. I could have decided to pursue it as a field of study at that point. What would I have had to show for it now? Nothing! No accomplishments! A wasted career!

There was a time when you couldn’t get a position in a physics department unless you were a string theorist. As a result, there is a vast population of string theorists sitting in faculty positions. It is no wonder that they still maintain such a strong influence in physics even though the theory they work on is dead.

Sometimes an idea runs away from us. It may start in a certain direction, perhaps to achieve a certain goal, but then at some point down the line it becomes something else. It may be an undesirable situation, or it may be a new opportunity. Often, only time will tell.

Quantum mechanics is such an idea. It is ostensibly a subfield of physics, but when we take a hard look at quantum mechanics, it looks more and more like mathematics. It has taken on a life of its own, which often seems to have very little to do with physics.

To be sure, physics would not get far without mathematics. However, mathematics has a very specific role to play in physics. We use mathematics to model the physical world. It allows us to calculate what we expect to see when we make observations of the phenomena associated with that model.

Quantum mechanics is different from other physical theories. While other physical theories tend to describe very specific sets of phenomena associated with a specific physical context, quantum mechanics is more general in that is describes a large variety of phenomena in different contexts. For example, all electric and magnetic phenomena provide the context for Maxwell’s theory of electromagnetism. On the other hand, the context of quantum mechanics is any phenomenon that can be found in the micro world. As such quantum mechanics is much more abstract.

We can say that quantum mechanics is not a theory, but instead a formalism in terms of which theories about the micro world can be formulated. It is therefore not strange that quantum mechanics looks more like mathematics. It even has a set of postulates from which the formalism of quantum mechanics can be derived.

But quantum mechanics still needs to be associated with the physical world. Even if it exits as a mathematical formalism, it must make some connection to the physical world. Otherwise, how would we know that it is doing a good job? Comparisons between predictions of theories formulated in terms quantum mechanics and experimental results of the physical phenomena associated with those theories show that quantum mechanics is very successful. However, in the pursuit of understanding the overlap between quantum physics and gravity in fundamental physics, the role of quantum mechanics needs to be understood not as a mere mathematical formalism, but as a fundamental mechanism in the physical world.

It is therefore not sufficient to provide mathematical postulates for the derivation of quantum mechanics as a mathematical formalism. What we need are the physical principles of nature at the fundamental level that leads to quantum mechanics as seen in quantum physics.

Principles differ from postulates. They are not expressed in terms of mathematical concepts, but rather in terms of physical concepts. In other words, instead of talking about non-commuting operators and Hilbert spaces, we would instead be talking about interactions, particle or fields, velocities, trajectories and things like that.

Another important difference is the notion of what is more fundamental than what. In mathematics, the postulates can be combined into sets of axioms from which theorems are derived. It would mean that the postulates are more fundamental. However, they may not be unique in the sense that different sets of axioms could be shown to be equivalent. In physics on the other hand, the principles are considered to be more fundamental than the theories in terms of which physical scenarios are modeled. There may be a cascade of different theories formulated in terms of more fundamental theories. Since, these theories are formulated in terms of mathematics, it can now happen that the axioms for the mathematics in terms of which some of these theories are formulated, are not fundamental from a physics point of view, but a consequence of more fundamental physical aspects.

An example is the non-commutation of operators in quantum mechanics. It is often considered as a fundamental aspect of quantum mechanics. However, it is only fundamental from a purely mathematical point of view. From a physical point of view, the non-commutation follows as a consequence of more fundamental aspects of quantum physics. Ultimately, the fundamental property of nature that leads to this non-commutation is the Planck relationship between energy (or momentum) and frequency (or the propagation vector).

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.

Recently, the number of preprints that contain theorems with proofs in the arXiv under quantum physics has increased drastically. I’ve also noticed that some journals in this field tend to publish more such papers, even though they are not ostensibly mathematical physics journals. It seems to suggest that theoretical physics needs to look like mathematics in order to be taken seriously.

Theorems with proofs are not science. Physics, which is a science, is about getting agreement between predictions and experimental observations. So, what is the role of mathematics in physics?

For the physicist, mathematics is a tool, often an indispensable tool, but still, just a tool. When Feynman invented his version of quantum field theory in terms of the path integral, he provided a means to compute predictions for the scattering amplitudes in particle physics that can be compared with the results from high energy particle physics experiments. That was the whole point of this formulation. From a mathematical perspective, the path integral formulation was a bit crude to say the least. It presented a significant challenge to come up with a rigorous formulation of the measure theory that would be suitable for the notion of a path integral.

These days, there seems to be much criticism against quantum field theory. The Haag theorem indicates some inconsistencies in the interaction picture. I also saw that Ed Witten is taking issue with the process of quantization that is used in quantum field theory because of some inconsistencies and he tries to solve these problems with some concepts taken from string theory.

I think these criticisms are missing the point. The one thing that you can take from quantum field theory is this: it works! There is a very good agreement between the predictions of the standard model and the results from high energy physics experiments. So, if anybody thinks that quantum field theory needs to be reformulated or replaced by a better formulations then they are missing the point. The physics is only concerned with having some mathematical procedure to compute predictions, regardless of whether that procedure is a bit crude or not. It is just a tool. Mathematicians may then ask themselves: why does it work?

Mathematics is extremely flexible. There are usually more than one way to represent physical reality in terms of mathematical models. Often these different formulations are completely equivalent as far as experimental predictions are concerned. For this reason, one should realize that physical reality is not intrinsically mathematical. Or stated differently, the math is not real (as Hossenfelder would like us to believe). Mathematical models exist in our minds. It is merely the way we represent the physical world so that we can do calculations. If we come up with a crude model that serves the purpose to perform successful calculations, then there are probably several other less crude ways to do the same calculations. However, it is the amusement of the mathematician to ponder such alternatives. As far as the physicist is concerned, such alternatives are of less importance.

Having said that, there is one possible justification for a physicist to be concerned about the more rigorous formulation of mathematical models. That has to do with progress beyond the current understanding. It may be possible that a more rigorous formulation of our current models may point the way forward. However, here the flexibility of mathematics produces such a diverse array of possibilities that this line of argument is probably not going to be of much use.

Consider another example from the history of physics. Newtonian mechanics was developed into a very rigorous format with the aid of Hamiltonian mechanics. And yet, none of that gave any indication of the direction that special and general relativity took us in. The mathematics turned out to be completely different.

So, I don’t think that we should rely on more rigor in our mathematical models to point the way forward in physics. For progress in physics, we need to focus on physics. As always, mathematics will merely be the tool to do it. For that reason, I tend to ignore all these preprints with their theorems and proofs.