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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Discreteness

Demystifying quantum mechanics V

Perhaps one of the most iconic “mysteries” of quantum mechanics is the particle-wave duality. Basically, it comes down to the fact that the interference effects one can observe implies that quantum entities behave like waves, but at the same time, these entities are observed as discrete lumps, which are interpreted as particles. Previously, I explained that one can relax the idea of localized lumps a bit to allow only the interactions, which are required for observations, to be localized. So instead of particles, we can think of these entities as partites that share all the properties of particles, accept that they are not localized lumps. So, they can behave like waves and thus give rise to all the wave phenomena that are observed. In this way, the mystery of the particle-wave duality is removed.

Now, it is important to understand that, just like particles, partites are discrete entities. The discreteness of these entities is an important aspect that plays a significant role in the phenomena that we observe in quantum physics. Richard Feynman even considered the idea that “all things are made of atoms” to be the single most important bit of scientific knowledge that we have.

Model of the atom

How then does it happen that some physicist would claim that quantum mechanics is not about discreteness? In her blog post, Hossenfelder goes on to make a number of statements that contradict much of our understanding of fundamental physics. For instance, she would claim that “quantizing a theory does not mean you make it discrete.”

Let’s just clarify. What does it mean to quantize a theory? It depends, whether we are talking about quantum mechanics or quantum field theory. In quantum mechanics, the processing of quantizing a theory implies that we replace observable quantities with operators for these quantities. These operators don’t always commute with each other, which then leads to the Heisenberg uncertainty relation. So the discreteness is not immediately apparent. On the other hand, in quantum field theory, the quantization process implies that fields are replaced by field operators. These field operators are expressed in terms of so-called ladder operators: creation and annihilation operators. What a ladder operator does is to change the excitation of a field in discrete lumps. Therefore, discreteness is clearly apparent in quantum field theory.

What Hossenfelder says, is that the Heisenberg uncertainty relationships is the key foundation for quantum mechanics. In one of her comments, she states: “The uncertainty principle is a quantum phenomenon. It is not a property of classical waves. If there’s no hbar in it, it’s not the uncertainty principle. People get confused by the fact that waves obey a property that looks similar to the uncertainty principle, but in this case it’s for the position and wave-number, not momentum. That’s not a quantum phenomenon. That’s just a mathematical identity.”

It seems that she forgot about Louise de Broglie’s equation, which relates the wave-number to the momentum. In a previous post, I have explained that the Heisenberg uncertain relationship is an inevitable consequence of the Planck and de Broglie equations, which relate the conjugate variables of the phase space with Fourier variables. It has nothing to do with classical physics. It is founded in the underlying mathematics associated with Fourier analysis. Let’s not allow us to be mislead by people that are more interested in sensationalism than knowledge and understanding.

The discreteness of partites allows the creation of superpositions of arbitrary combinations of such partites. The consequences for such scenarios include quantum interference that is observed in for instance the Hong-Ou-Mandel effect. It can also lead to quantum entanglement, which is an important property used in quantum information systems. The discreteness in quantum physics therefore allows it to go beyond what one can find in classical physics.

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Partiteness

Demystifying quantum mechanics IV

Yes I know, it is not a word, at least not yet. We tend to do that in physics sometimes. When one wants to introduce a new concept, one needs to give it a name. Often, that name would be a word that does not exist yet.

What does it mean? The word “partiteness” indicates the property of nature that it can be represented in terms of parties or partites. It is the intrinsic capability of a system to incorporate an arbitrary number of partites. In my previous post, I mentioned partites as a replacement for the notion of particles. The idea of partites is not new. People often consider quantum systems consisting of multiple partites.

What are these partites then? They represent an abstraction of the concept of a particle. Usually the concept is used rather vaguely, since it is not intended to carry more significance than what is necessary to describe the quantum system. I don’t think anybody has ever considered it to be a defining property that nature possesses at the fundamental level. However, I feel that we may need to consider the idea of partiteness more seriously.

Classical optics diffraction pattern

Let’s see if we can make the concept of a partite a little more precise. It is after all the key property that allows nature to transcend its classical nature. It is indeed an abstraction of the concept of a particle, retaining only those aspects of particles that we can confirm experimentally. Essentially, they can carry a full compliment of all the degrees of freedom associated with a certain type of particle. But, unlike particles, they are not dimensionless points traveling on world lines. In that sense, they are not localized. Usually, one can think of a single partite in the same way one would think of a single particle such as a photon, provided one does not think of it as a single point moving around in space. A single photon can have a wave function described by any complex function that satisfies the equations of motion. (See for instance the diffraction pattern in the figure above.) The same is true for a partite. As a result, a single partite behaves in the same way as a classical field. So, we can switch it around and say that a classical field represents just one partite.

The situation becomes more complicated with multiple partites. The wave function for such a system can become rather complex. It allows the possibility for quantum entanglement. We’ll postpone a better discussion of quantum entanglement for another time.

Multiple photons can behave in a coherent fashion so that they all essentially share the same state in terms of the degrees of freedom. All these photons can then be viewed collectively as just one partite. This situation is what a coherent classical optical field would represent. Once again we see that such a classical field behaves as just one partite.

The important difference between a particle and a partite is that the latter is not localized in the way a particle is localized. A partite is delocalized in a way that is described by its wave function. This wave function describes all the properties of the partite in terms of all the degrees of freedom associated with it, including the spatiotemporal degrees of freedom and the internal degrees of freedom such as spin.

The wave function must satisfy all the constraints imposed by the dynamics associated with the type of field. It includes interactions, either with itself (such as gluons in quantum chromodynamics) or with other types of fields (such as photons with charges particles).

All observations involve interactions of the field with whatever device is used for the observation. The notion of particles comes from the fact that these observations tend to be localized. However, on careful consideration, such a localization of an observation only tells us that the interactions are localized and not that the observed field must consist of localized particles. So, we will relax the idea that fields must be consisting of localized particle and only say that, for some reason that we perhaps don’t understand yet, the interaction among fields are localized. That leaves us free to consider the field as consisting of nonlocal partites (thus avoiding all sort of conceptual pitfalls such as the particle-wave duality).

Hopefully I have succeeded to convey the idea that I have in my mind of the concept of a partite. If not, please let me know. I would love to discuss it.

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What particle?

Demystifying quantum mechanics III

The notion of a particle played an important role in our understanding of fundamental physics. It also lies at the core of understanding quantum mechanics. However, there are some issues with the notion of a particle that can complicate things. Before addressing the role that particles play in the understanding of quantum mechanics, we first need to look at these issues.

Particle trajectories detected in a high energy experiment

So what is this issue about particles? The problem is that we don’t really know whether there really are particles. What?!!! Perhaps you may think that what I’m referring to has something to do with the wave-particle duality. No, this issue about the actual existence of particles goes a little deeper than that.

It may seem like a nonsense issue, when one considers all the experimental observation of particles. The problem is that, while the idea of a particle provides a convenient explanation for what we see in those experiments, none of them actually confirms that what we see must be particles. Even when one obtains a trajectory as in a cloud chamber or in the more sophisticated particle detectors that are used in high energy particle experiments, such as the Large Hadron Collider, such a trajectory can be explained as a sequence of localized observations each of which projects the state onto a localize pointer state, thus forcing the state to remain localized through a kind of Zeno effect. It all this sounds a little too esoteric, don’t worry. The only point I’m trying to make is that the case for the existence of actual particles is far from being closed.

Just to be on the same page, let’s first agree what we mean when we talk about a particle. I think it was Eugene Wigner that defined a particle as a dimensionless point traveling on a world line. Such a particle would explain those observed trajectories, provided one allows for a limited resolution in the observation. However, this definition runs into problems with quantum mechanics.

Consider for example Young’s double slit experiment. Here the notion of a particle on a world line encounters a problem, because somehow the particle needs to pass through both slits to produce the interference pattern that is observed. This leads to the particle-wave duality. To solve this problem, one can introduce the idea of a superposition of trajectories. By itself this idea does not solve the problem, because these trajectories must produce an interference pattern. So one can add the notion (thanks to Richard Feynman) of a little clock that accompanies each of the trajectories, representing the evolution of the phase along the trajectory. Then when the particle arrives at the screen along these different trajectories the superposition together with the different phase values will determine the interference at that point.

Although the construction thus obtained can explain what is being seen, it remains a hypothesis. We run into the frustrating situation that nature does not allow us any means to determine whether this picture is correct. Every observation that we make just gives us the same localized interaction and there is no way to probe deeper to see what happens beyond that localize interaction.

So, we arrive at the situation where our scientific knowledge of the micro-world will always remain incomplete. We can build strange convoluted constructs to provide potential explanations, but we can never establish their veracity.

This situation may seem like a very depressing conclusion, but if we can accept that there are things we can never know, then we may develop a different approach to our understanding. It helps to realize that our ignorance exactly coincides with the irrelevance of the issue. In other words, that which we cannot know is precise that which would never be useful. This conclusion follows from the fact that, if it could have been useful, we would have had the means to study it and uncover a true understanding of it.

So, let’s introduce at a more pragmatic approach to our understanding of the micro-world. Instead of trying to describe the exact nature of the physical entities (such as particles) that we encounter, let’s rather focus on the properties of these entities that would produce the phenomena that we can observe. Instead of particles, we focus of the properties that make things look like particles. This brings us to the notion of a party or a partite.

But now the discussion is becoming too long. More about that next time.

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Particle physics impasse

Physics is the study of the physical universe. As a science, it involves a process consisting of two components. The theoretical component strives to construct theoretical models for the physical phenomena that we observe. The experimental component tests these theoretical models and explores the physical world for more information about phenomena.

Progress in physics is enhanced when many physicists using different approaches tackle the same problem. The diversity in the nature of problems need to be confronted by a diversity of perspectives. This diversity is reflected in the literature. The same physical phenomenon is often studied by different approaches, using different mathematical formulations. Some of them may turn out to produce the same results, but some may differ in their predictions. The experimental work can then be used to make a selection among them.

That is all fine and dandy for physics in general, but the situation is a bit more complicated for particle physics. Perhaps, one can see the reason for all these complications as the fact that particle physics is running out of observable energy space.

What do I mean by that? Progress in particle physics is (to some extent at least) indicated by understanding the fundamental mechanisms of nature at progressively higher energy scales. Today, we understand these fundamental mechanisms to a fairly good degree up to the electroweak scale (at about 200 GeV). It is described by the Standard Model, which was established during the 1970’s. So, for the past 4 decades, particle physicists tried to extend the understand beyond that scale. Various theoretical ideas were proposed, prominent among these were the idea of supersymmetry. Then a big experiment, the Large Hadron Collider (LHC) was constructed to test these ideas above the electroweak scale. It discovered the Higgs boson, which was the last extent particle predicted by the standard model. But no supersymmetry. In fact, none of the other ideas panned out at all. So there is a serious back-to-the-drawing-board situation going on in particle physics.

The problem is, the LHC did not discover anything else that could give a hint at what is going on up there, or did it? There will be another run to accumulate more data. The data still needs to be analyzed. Perhaps something can still emerge. Who knows? However, even if some new particle is lurking within the data, it becomes difficult to see. Such particles tend to be more unstable at those higher energies, leading to very broad peaks. To make things worse, there is so much more background noise. This makes it difficult, even unlikely, that such particles can be identified at these higher energies. At some point, no experiment would be able to observe such particles anymore.

The interesting things about the situation is the backlash that one reads about in the media. The particle physicists are arguing among themselves about the reason for the current situation and what the way forward should be. There are those that say that the proposed models were all a bunch of harebrained ideas that were then hyped and that we should not build any new colliders until we have done some proper theoretical work first.

See, the problem with building new colliders is the cost involved. It is not like other fields of physics where the local funding organization can support several experimental groups. These colliders require several countries to pitch in to cover the cost. (OK, particle physics is not the only field with such big ticket experiments.)

The combined effect of the unlikeness to observe new particles at higher energies and the cost involved to build new colliders at higher energies, creates an impasse in particle physics. Although they may come up with marvelous new theories for the mechanisms above the electroweak scale, it may be impossible to see whether these theories are correct. Perhaps the last energy scale below which we will be able to understand the fundamental mechanisms in a scientific manner, will turn out to be the electroweak scale.

Glad I did not stay in particle physics.