Those quirky fermions

All of the matter in the universe is made of fermions. They are for this reason one of the most abundant things in the universe. Fermions have been the topic of investigation for a long time. We have learned much about them. However, what we do know about them is encapsulated in the formalisms with which we deal with them in our theories. Does that mean we understand them?

Let’s think about the way we treat fermions in our theories. Basically, we represent them in terms of creation and annihilation operators, which are used to formulate the interactions in which they take part. These operators are distinguished from those for bosons by the anti-commutation relations that they obey.

To the uninitiated, all this must sound like a bunch of gobbledygook. What are the physical manifestations of all these operators? There are none! These operators are just mathematical entities in the formalism for our theories. Although these theories are quite successful, it does not reveal the physical machinery at work on the inside. Or does it?

Although a creation operator does not by itself represent any physical process, it distinguishes different scenarios with different arrangements of fermions. Starting with a given scenario, I can apply a fermion creation operator to introduce a new scenario which contains one additional fermion. Then I can apply the operator again, provided that I am not trying to add another fermion with the same degrees of freedom, it will produce another new scenario.

Here is the strange thing. If I change the order in which I added the two additional fermions, I get a scenario that is different from the one with the previous order. I can contrast this to the situation with bosons. Provided that I don’t try to add bosons with the same degrees of freedom, the order in which I add them doesn’t matter. What it tells us is that bosons with different degrees of freedom don’t effect each other. (We need to be careful about the concepts of time-like or space-like separations, but for the sake of this argument, we’ll assume all bosons or fermions are space-like separated.)

The fact that the order in which we place fermions in our scenario (even when they are space-like separated) makes a difference tells us something physical about fermions. They must be global entities. The entire universe seems to “know” about the existence of each and every fermion in it.

How can that be possible? I can think of one way: topological defects. This is not a new idea. It pops up quite often in various fields of physics.

Topological defect

Why would a topological defect explain the apparent global nature of fermions? It is because all kinds of topological defects can be identified with the aid of an integral that computes the winding number of the topological defect. This type of integral is evaluated over a (hyper)surface that encloses the topological defect. In other words, the field values far away from the defect are included in the integral and not the field value at the defect. Therefore, knowledge about the defect in encoded in the entire field. It therefore suggest that fermions can behave as global entities if they topological defect. This is just a hypothesis. It needs more careful investigation.

Calling all cultural anthropologists

Once I’ve pick up a book at one of these book sales that book stores sometimes have. The topic did not fall in my immediate field of interest, but for the sake of “broadening my horizons” I decided to buy the book. The idea that something one reads in a book can change one’s life is perhaps rather far fetched, but this book came close. It definitely changed the way I look at the world and people.

The book I picked (mine is the 6th edition)

The book is about cultural anthropology, a topic which, until I’ve pick up that book, I did not know exists. It is not a topic that one hears about much. There are no big breakthroughs in cultural anthropology that appear in the news headlines. I don’t ever hear about excited young students that want to study cultural anthropology, but often hear about them wanting to study medicine or engineering. And yet, when I look at the world and what is going on, I realize that cultural anthropology is what we desperately need.

A cultural anthropologist studies cultures and tries to understand how they evolve. Cultures are complex emergent phenomena; a product of the highly evolved human mind and psyche. It is culture that makes humans different from animals. Our cultures protect us in hostile changing environments. People often think it is our technology that does that, but technology is just part of our cultures. Without culture, we won’t have technology.

Humanity has become progressively more complex and interconnected. It is one thing to have a culture when it evolves in isolation with occasional contact with other cultures. However, through colonization and modern technology, cultures at very different levels of development have been brought in close contact. The consequences are often devastating. Modern communication technology, which drives social media, also has severe unintended consequences. While each culture tends to develop its own unique morality, the intense interaction among different cultures causes morality to become diluted. One would think that this interaction would give rise to a unified morality for the world, but instead what we see is a general loss of moral behavior. It is as if the realization of the relativity in morality instills a disrespect of the very concept of right and wrong. This is not a good situation.

The problem is that we do not understand these effects. We do not have the knowledge to predict the consequences or, if possible, come up with solutions; the necessary actions that need to be taken. Governments take action to compensate for situations that occur in their countries, but when it comes to these cultural effects, they act in apparent complete ignorance of the consequences of their actions. There are countries with populations consisting of people with different cultures at vastly different levels of development. The governments of these countries are trying to manage this situation with complete ignorance of how to handle the situation, often with devastating consequences.

Clearly there is a desperate need for better knowledge about how cultures evolve and how they interact; the cultural dynamics. What is the effect of mixing people with vastly different cultural development levels? This is the topic of cultural anthropology. We need more cultural anthropologists.

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.

This image has an empty alt attribute; its file name is 1C7DB1746CFC72286DF097344AF23BD2.png