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.

Guiding principles I: substructure

Usually the principles of physics are derived from successful scientific theories. For instance, Lorentz invariance which can be seen as the underlying principle on which special relativity is based, was originally derived from Maxwell’s equations. As we learn more about the universe and how it works, we discover more principles. These principles serve to constrain any new theories that we try to formulate to describe that which we don’t understand yet.

It turns out that the physics principles that we have uncovered so far, don’t seem to constrain theories enough. There are still vastly different ways to formulate new theories. So we need to do something that is very dangerous. We need to guess some additional physics principles that would guide us in the formulation of such new theories. Chances are that any random guess would send us down a random path in theory space with very little chance of being the right thing. An example is string theory, where the random guess was that the fundamental objects are strings. It has kept a vast number of researchers busy for decades without success.

Instead of making a random guess, we can try to see if our existing theories don’t perhaps already give us some additional hints at what such a guiding principle should be. So, I’ll share my thoughts on this for what it is worth. I’ll start with what our current theories tell us about substructure.

The notion of a substructure can already be identified in the work of Huygens, Fresnel, etc. on interference . It revealed that light is a wave. The physical quantity that is observed is the intensity, which is always positive. However, we need to break the intensity apart into amplitudes that can have negative values to allow destructive interference. In this very simple sense, the amplitude (which is often modeled as a complex valued function) serves as a substructure for that which is observed.

Interference

It is not a big leap from interference in classical light to come to the interference in quantum systems. Here the observation is interpreted as a probability, which is also a positive quantity. In quantum mechanics, the notion of a probability is given a substructure in the form of a probability amplitude which can be negative (or complex) to allow interference phenomena.

The concept of a substructure is today perhaps mostly associated with the notion of constituent particles. We know now that the proton is not a fundamental particle, but that it has a substructure consisting of fundamental particles called quarks, bound together via the strong force. Although it is not currently considered to be the case, these quarks may also have some substructure. However, the concept of this substructure may be different from the way it appears in protons.

A new idea that is emerging is the idea that spacetime itself may have a substructure. Ever since the advent of general relativity, we know that spacetime is affective by gravity. In our current formulation of particle physics, spacetime is the backdrop on which all the particle fields perform their dance. But when gravity is added, spacetime joins the dance. It makes the formulation of fundamental theories very complicated. The difference between the particles and spacetime becomes blurred. This leads to the idea that spacetime itself may have a substructure. In this way, it combines the two different ways to look at substructure. On the one hand it may be divided into two parts, perhaps to separate chirality, much in the way intensity separates into an amplitude and its complex conjugate. On the other hand the separation of spacetime may give some substructure to the particle fields, being described in terms of fluctuations in spacetime’s substructure.

Caution is necessary here. Even if these ideas turn out to be valid, they still leave much detail unspecified. It may not be enough to regard the idea of substructure as a physics principle. The importance it to keep to the standard practice in physics: mathematics is merely used to formulate and model the physics universe. It does not tell us something new about the universe unless this is somehow already logically encoded in what we start off with.

Perhaps an example would help to explain what I mean. Einstein formulated general relativity (GR) after he figured out the equivalence principle. So everything that we can learn from GR follows as inevitable logical consequences from this principle. It tells us that the mass-energy distribution curves spacetime, but it does not tell us how this happens. In other words, the mechanism by which mass curves spacetime is not known because it is not a logical consequence of the equivalence principle.

So, the idea is to come up with a general mathematical formalism that is powerful enough to model this kind of scenario without trying to dictate the physics. Remember, quantum field theory is a formalism in terms of which different models for the dynamics in particle physics can be modeled. It does not dictate the dynamics but allow anything to be modeled. Another example is differential geometry which allows the formulation of GR but does not dictate it. Part of the reason why string theory fails is because is a mathematical formulation that also dictates the dynamics. The formulation of a quantum theory for gravity requires a flexible formalism that does not dictate the dynamics.

In defense of particle physics experiments

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.

CMS detector at LHC

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.

The nerds and the jocks, the saga continues

Recently, after reading another blog, I was reminded of this issue. There are jocks and there are nerds. The jocks are popular and influential. They like to run the show and order others around. Nerds, on the other hand, are not popular. They are not good at running the show, but they make everything else runs smoothly. They tend to be the backroom boys and the behind-the-scene people that make sure things work.

Image from Revenge of the Nerds movie

The one place where the nerds use to hold their own was the academic world. They are particularly excellent at figuring out how things work and therefore they thrived in the sciences. Much of what we know about the physical world is thanks to the nerds who passionately, tenaciously and meticulously studied the physical phenomena.

That was how things were up until roughly the second world war. Then their knowledge started to have a big enough impact that they appeared on the radar screen of the jocks. So, the jock said to themselves, “Wait a minute, what is going on here? Why are we not aware of this?” And so the jocks started to infiltrate the academic scene.

Today the situation is very different. The jock are running the show in the academic world. They are involved in academic research. The most prominent academic are, with almost no exception, all jocks.

Make no mistake, the jocks are not stupid. They are good enough to maintain successful academic programs. In fact, the way that currently works has to a large extent been invented by the jocks. The funding process, the way academics are currently recruited, and even the way publications are evaluated and judged for suitability are based on the methods typical of the way that jocks would run things. It’s all based on popularity, impact and influence.

However, the jock are not as good at academic research as the nerds are. The consequences can be seen in the lack of progress in fundamental research. You see, jocks are more concerned about their egos and they are only doing this research thing for the fame and glory that first popped onto their radar at the time of the second world war. They are not primarily interested to gain an understanding. No, it is all about the glory. Ostensibly, the goal is still to gain the understanding, and for that the reward comes with all the fame and glory. However, when the reward and goal is not one and the same thing, it is always possible to reap the reward without achieving the goal. This is something I call rewardism.

For the nerds, the understanding itself is the reward. Anything less is simply not good enough. Sure, it is good to receive recognition, but that is not the reason for getting up in the morning.

So, the more I think about the situation in fundamental physics, the more convinced I become that the reason for the lack of progress is at least partly due to the bloated egos of those people running the show there. There may still be some nerds that are actively trying the figure out how nature works, but they are marginalized to the point of being totally ignored. Instead, we have all these people with their crazy predictions and unjustified inventions, that has reached the point where they even consider dispensing with the scientific method itself.

I don’t see how this will ever change. Perhaps several generations need to pass to weed out the jocks by depriving them of the fame and glory that they were hoping for. Then the nerds can come back and pick up where they left off. Who knows? I won’t be around by then.

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Postulates or principles?

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).