Why not an uncertainty principle?

It may seem strange that there are no fundamental physical principle for quantum physics that is associated with uncertainty among those that I have proposed recently. What would be the reason? Since we refer to it as the Heisenberg uncertainty principle, it should qualify as one of the fundamental principles of quantum physics, right? Well, that is just it. Although it qualifies as being a principle, it is not fundamental.

It may help to consider how these concepts developed. At first, quantum mechanics was introduced as an improvement of classical mechanics. Therefore, quantities like position and momentum played an important role.

A prime example of a system in classical mechanics is the harmonic oscillator. Think of a metal ball hanging from a spring. Being pulled down and let go, the ball will start oscillating, moving periodically up and down. This behavior is classically described in terms of a Hamiltonian that contains the position and momentum of the metal ball.

In the quantum version of this system, the momentum is replaced by the wave vector times the Planck constant. But position and the wave vector are conjugate Fourier variables. That is the origin of the uncertainty. Moreover, it also leads to non-commutation when position and momentum are represented as operators. The sum and difference of these two operators behave as lowering and raising operators for quanta of energy in the system. The one reduces the energy in discrete steps and the other increases it in discrete steps.

It was then found that quantum mechanics can also be used to improve classical field theory. But there are several differences. Oscillations in fields are not represented as displacements in position that is exchange into momentum. Instead, their oscillations manifest in terms of the field strength. So, to develop a quantum theory of fields, one would start with the lowering and raising operators, which are now called creation and annihilation operators or ladder operators. Their sum and difference produce a pair of operators that are analogues to the position and momentum operators for the harmonic oscillator. In this context, these are called quadrature operators. They portray the same qualitative behavior as the momentum and position operators. They represent conjugate Fourier variables and therefore again produce an uncertainty and non-commutation. The full development of quantum field theory is far more involved then what I described here, but I only focused on the origin of the uncertainty in this context here.

So, in summary, uncertainty emerges as an inevitable consequence of the Fourier relationship between conjugate variables. In the case of mechanical systems, these conjugate variables come about because of the quantum relationship between momentum and wave vector. In the case of fields, these conjugate variables comes from the ladder operators, leading to analogues properties as found for the formal description of the harmonic oscillator. Hence, uncertainty is not a fundamental property in quantum physics.

The collective

Let’s for the moment imagine that humanity can avoid a fall of civilization. Then one may ponder where humanity is heading to. There are some very strong hints.

Despite laws that prohibit the use of a cell phone while driving a car, I often see people busy typing on their cell phones while they are supposed to be focussing on the road. I’ve also often seen couples or groups of people sitting at tables in restaurants typing on cell phones instead of talking to each other. Why do people behave this way? And what does it have to do with where humanity is heading?

It reveals a very strong urge lying within the human psyche. Humans like to interact with other humans. Social media provide them with this capability on a scale that far exceeds the usual level of interaction. They become so attached to this new thing that they cannot stop interacting via social media to do mundane tasks such as driving cars. They would also rather interact via social media with a large number of “friends” than face-to-face with a few individuals.

Many years ago there was a TV series called Star Trek. One of the antagonists introduced in this series was the Borg. It consisted of a hive of mentally interconnect individuals – a group mind. It was know as the Collective. Its mode of operation was to attack civilizations and then absorb the individuals from those civilizations into itself. It would say “resistance is futile, you shall be assimilated.”

The Brog from Star Trek

So, when I see how attached people become to social media, I get the feeling humanity is becoming a collective. We are turning into the Borg. There is no fighting it. Unless this process is halted by a fall of civilization, humanity will eventually be a single being consisting of mentally interconnected individuals.

Perhaps such a state of existence is not a bad thing. I can think of a few benefits. Most people are generally more happy when they have constant interaction with other people. There are exceptions of course (like me). But there always need to be those that keep the systems running.

Speaking of which, those that develop technology should keep in mind this tendency toward the development of a collective. For one thing, it would help if the need to be connected to the collective does not interfere with mundane tasks. It would be better if cars can drive themselves. However, there are other tasks that cannot be delegated. For that purpose, cell phones need to be replaced by wearable devices. The screen can become a heads-up display in goggles that can be integrated into glasses if necessary. The keyboard needs to become integrated into gloves that sense finger motion. Or the keyboard can be dispensed with if voice-to-text technology matures. Then the microphone needs to be replaced by a ultra-sonic sensor that images the mouth cavity to determine what is being said. This way, people would not need to talk out load. With such technology, you can stay connected to the collective while doing your shopping.

At the end of the cold war, one would have expected that humanity would have pulled out all stops to develop space travel and colonize the moon and the other planets. Instead, technology shifted to the development of communication in the form of cell phones and the internet. That brought us to where we are today. The one recent exception to this trend was Elon Musk who developed space travel into a commercial enterprise. But now he is buying Twitter. Go figure!

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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Principles of quantum physics

Previously, I argued for principles rather than postulates. Usually, principles are added to a field of study only after some progress have been made with the theories in that field. However, sometimes these principles are required ahead of the time to make progress in a field. That may be the case in fundamental physics where such principles can be used as guiding principles. However, in the latter case such principles may be just guess-work. They may turn out to be wrong.

Quantum physics has been around for a long enough time to justify having its own set of principles. There are postulates for quantum mechanics, but as I explained, they are like a set of axioms for the mathematical formalism and therefore don’t qualify as principles. Principles are statements phrased in terms of physical concepts and not in terms of mathematical concepts.

Here, I want to propose such principles. They are a work in progress. Those that I can state are not extremely surprising. They shouldn’t be because quantum physics has been investigated in so many different ways. However, there are some subtleties that need special attention.

The first principle is simply a statement of Planck’s discovery: fundamental interactions are quantized. Note that it does not say that “fields” or “particles” are quantized, because we don’t know that. All we do know is what happens at interactions because all our observations involve interactions. Here, the word “quantized” implies that the interacting entities exchange quantized amounts of energy and momentum.

What are these interacting entities? Usually we would refer to them as particles, but that already makes an assumption about their existence. Whenever we make an observation that would suggest that there are particles, we actually see an interaction. So we cannot conclude that we saw a particle, but we can conclude that the interaction is localized. Unless there is some fundamental distance scale that sets a lower limit, the interaction is point-like – it happens at a dimensionless point. The most successful theories treat these entities as fields with point-like interactions. We can therefore add another principle: fundamental interactions are localized. However, we can combine it with the previous principle and see it as another side of one and the same principle: fundamental interactions are quantized and localized.

The next principle is a statement about the consequences of such interactions. However, it is so important that it needs to be stated as a separate principle. I am still struggling with the exact wording, so I’ll just call it the superposition principle. Now, superposition is something that already exists in classical field theory. In that case, the superposition entails the coherent additions of different fields. The generalization that is introduced by quantum physics is the fact that such superpositions can involved multiple entities. In other words, the superposition is the coherent addition of multiple fields. The notion of multiple entities is introduced due to the interactions. It allows a single entity to split up into multiple entities, each of which can carry a full compliment of all the degrees of freedom that can be associated with such an entity. However, due to conservation principles, the interaction sets up constraints on the relationship among the degrees of freedom of the different entities. As a result, the degrees of freedom of these entities are entangled, which manifests as a superposition of multiple entities.

Classical and quantum superpositions

We need another principle to deal with the complexities of fermionic entities, but here I am still very much in the dark. I do not want to refer to the anti-commuting nature of fermionic operators because that is a mathematical statement. Perhaps, it just shows how little we really know about fermions. We have a successful mathematical formulation, but still do not understand the physical implications of this formulation.

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).