Vanity and formalism

During my series on Transcending the impasse, I wrote about Vanity in Physics. I also addressed the issue of Physics vs Formalism in a previous post. Neither of these two aspects are conducive to advances in physics. So, when one encounters the confluence of these aspects, things are really turning inimical. Recently, I heard of such a situation.

In an attempt to make advances in fundamental physics, the physics community has turned to mathematics, or at least something that looks like mathematics. It seems to be the believe that some exceptional mathematical formalism will lead us to a unique understanding of the fundamentals of nature.

Obviously, based on what I’ve written before, this approach is not ideal. However, we need to understand that the challenges in fundamental physics is different from those in other fields of physics. For the latter, there are always some well-established underlying theory in terms of which the new phenomena are studied. The underlying theory usually comes with a thoroughly developed formalism. The new phenomena may require a refinement in formalism, but one can always check that any improvements or additions are consistent with the underlying theory.

With fundamental physics, the situation is different. There is no underlying theory. So, the whole thing needs to be invented from scratch. How does one do that?

Albert Einstein

We can take a leave out of the book of previous examples from the history of physics. A good example is the development of general relativity. Today there are well established formalisms for general relativity. (Note the use of the plural. It will become important later.) How did Einstein know what formalism to use for the development of general relativity? He realized that spacetime is curved and therefore need a formalism that can handle curved spacetime metrics. How did he know that spacetime is curved? He figured it out with the aid of some simple heuristic arguments. These arguments led him to conceive of a fundamental principle that would guide him in the development of the theory.

That is a success story. Now compare it with what is going on today. There are different formalisms being developed. The “fundamental principle” is simply to get a formalism that can handle curved spacetime in the context of a quantum field theory so that the curvature of spacetime can somehow be represented be the exchange of particles. As such, it goes back to the old notions existing before general relativity that regarded gravity as a force. According to our understanding of general relativity, gravity is not a force. But let’s leave that for now.

There does not seem to be any new physics principles that guide the development of these new formalisms. Here I exclude all those so called “postulates” that have been presented for quantum mechanics, because those postulates are of a mathematical nature. They may provide a basis for quantum mechanics as a mathematical formalism but not for the physics associated with quantum phenomena.

So, if there is no fundamental principle driving the current effort to develop new formalisms for fundamental physics, then what is driving it? What motivates people to spend all the effort in this formidable exercise?

Recent revelations gave me a clue. There was some name-calling going on among some of the most prominent researcher in the field. The proponents of one formalism would denounce some other formalism. It is as if we are watching a game show to see which formalism would “win” at the end of the day. However, the fact that there are different approaches should be seen as a good thing. It provides the diversity that improves the chances for success. More than one of these approaches may turn out to be successful. Here again an example from the history of science can be provided. The formalisms of Heisenberg and Schroedinger both turned out to be correct descriptions for quantum physics. Moreover, there are more than one formalism in terms of which general relativity can be expressed.

So what then is really the reason for this name-calling among proponents of the different approaches to develop formalisms for fundamental physics? It seems to be that deviant new motivation for doing physics: vanity! It is not about gaining a new understanding. That is secondary. It is all about being the one that comes up with the successful theory and then reaping in all the fame and glory.

The problem with vanity is that it does not directly address the goal. Vanity is a reward that can be acquired without achieving the goal. Therefore, it is not the optimal motivation for uncovering an understanding of fundamental physics. I see this as one of the main reasons for the lack of progress in fundamental physics.

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Canada in my garden

The seasons are opposite in the Northern and Southern hemisphere. So, while the Northern hemisphere is moving into autumn (or “fall”), we are having spring down here in the Southern hemisphere.

Therefore, I am glad to see the leaves coming out on the trees. The world is beautiful. It makes the neighborhood looks like an urban jungle.

I have a favorite tree in my garden. Not sure what kind of tree it is. Perhaps some kind of maple tree? In autumn its leave turn red. That makes me remember Canada.

Mu favorite tree

Most trees don’t turn red. Some even remain green right through winter.

For some reason, I was worried that it would die during winter. Therefore, I was very happy to see that it is sprouting new leaves.

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The role of mathematics in 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?

Mathematics

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.

No to science pledge

As a physicist, I understand what science is about. I have a good understanding of the scientific method and what science has achieved. But, unlike many other physicists it seems, I also know about the limits of science.

So, recently, I saw this “pledge for science” where people are asked to add their support to say that they put their trust in science. Unfortunately, I could not find a fully worded statement of this pledge to understand exactly what is meant by it. What does it mean to put your trust in science?

To be honest, I think I know where this is coming from. With all the anti-vaxxers, followings on the heals of global warming denial, and all those kinds of trends and misinformation that is being spread via social media, it is not surprising that some reaction would follow from the scientific community. However, one needs to guard against an over-reaction.global-warming-effects-1576273649696

Science does not have a clean track record. It is unfortunately responsible for several serious problems in our world today. Take for instance global warming. It does not take much to realize that in as far as it is caused by human activity, it is with the aid of scientific development that this human activity is able to cause global warming.

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Another example is weapons of mass destruction. Through scientific investigation humanity achieved the point where it can cause unprecedented death and destruction. Not exactly a highpoint in human cultural achievement. Once this door was opened, nothing could close it again. Forever, humanity will have this sword having over its head.

One can proceed to list other negative effects of scientific development such as pollution and the hole in the ozone layer, but I think the message is clear by now. An unconditional trust in science is a very dangerous thing. Instead, one should rather support an effort to get people educated and informed, not only about science and the scientific method, but also about other aspects of culture. For instance, if people have better knowledge of history, they would have a better understanding of how ignorance can lead to terrible things.

Let me emphasize then, I do not support an unconditional pledge to put my trust in science. In fact, it is a dangerous thing to put one’s unconditional trust in any specific thing on this earth.

Humanity vs the human

The world is in the grip of a pandemic. In many ways, it tests the systems that have come into existence through the cultural development of humanity. To some extent, it may even be testing its survivability.

If humanity were still in the process of biological evolution, the outcome of the test would simply be determined by the survival-of-the-fittest criterium. But humanity has moved beyond mere biological evolution. It has developed culture.

Culture provides a mechanism that can circumvent the threats posed by the environment, even when humans are not the “fittest.” A culture can adapt much faster than the genome. The pandemic is testing the fitness of culture as a mechanism for survival.

The world consists of many different cultures. Each culture provides various systems, including those responsible for government, finance, education, health and so forth. All these systems must work together to provide the protection for the people of these cultures during times such as these.

We live in a time where the cultures of the world have started to merge. The information obtained through research and the technologies that are developed are shared among all the cultures. The benefit of cooperation is obvious. For any single culture to survive, it is necessary that all of humanity survives.

While the picture of the world in terms of cultures may give a positive view of humanity’s prospects, it does not reveal the negative side. For this picture to prevail, these cultures need to be healthy. Here lies the problem.

A culture transcends the mechanism of biological evolution in that it cares for the individual members of the culture. The golden rule “do unto others as you would have them do unto you” forms the foundation for civilization. It allows people to live and work together to enable the development of culture and to achieve the great works that are associated with it.

At some point, it was decided that the golden rule is not enough. Individuals need more protection. So people introduced the notion of “human rights” and even call them “fundamental.” The idea makes sense, but begs the question of a culture that is at least moderately civilized. Within the context of the golden rule the concept of human rights can work.

But the world contains many communities where the cultural development is either lacking or has decayed to the point where the golden rule is not part of culture. In such situations, human rights provides a platform from which a community can be terrorized. The individual is elevated above the community. The result is a general breakdown of culture and a return to the survival of the fittest scenario.

Examples of this breakdown becomes prevalent. People oppose the attempts of governments to contain the spread of the virus. In some cases, these situations become violent. It threatens the culture’s ability to protect.

Human rights have a place in culture, but it must be placed in balance with the protection of the community. The individual human is not more important than all of humanity. How this balance should work and be implemented is not clear to me at the moment. But I’m sure the thinkers of our time can come up with some ingenious ideas.

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