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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Einstein, Podolski, Rosen

Demystifying quantum mechanics VI

When one says that one wants to demystify quantum mechanics, then it may create the false impression that there is nothing strange about quantum mechanics. Well, that would be a misleading notion. Quantum mechanics does have a counterintuitive aspect (perhaps even more than one). However, that does not mean that quantum mechanics need to be mysterious. We can still understand this aspect, and accept its counterintuitive aspect as part of nature, even though we don’t experience it in everyday life.

The counterintuitive aspect of quantum mechanics is perhaps best revealed by the phenomenon of quantum entanglement. But before I discuss quantum entanglement, it may be helpful to discuss some of the historical development of this concept. Therefore, I’ll focus on an apparent paradox that Einstein, Podolski and Rosen (EPR) presented.

They proposed a simple experiment to challenge the idea that one cannot measure position and momentum of a particle with arbitrary accuracy, due to the Heisenberg uncertainty. In the experiment, an unstable particle would be allowed to decay into two particles. Then, one would measure the momentum of one of the particles and the position of the other particle. Due to the conservation momentum, one can then relate the momentum of the one particle to that of the other. The idea is now that one should be able to make the respective measurements as accurately as possible so that the combined information would then give one the position and momentum of one particle more accurately than what Heisenberg uncertainty should allow.

Previously, I explained that the Heisenberg uncertainty principle has a perfectly understandable foundation, which has nothing to do with quantum mechanics apart from the de Broglie relationship, which links momentum to the wave number. However, what the EPR trio revealed in their hypothetical experiment is a concept which, at the time, was quite shocking, even for those people that thought they understood quantum mechanics. This concept eventually led to the notion of quantum entanglement. But, I’m getting ahead of myself.

John Bell

The next development came from John Bell, who also did not quite buy into all this quantum mechanics. So, to try and understand what would happen in the EPR experiment, he made a derivation of the statistics that one can expect to observe in such an experiment. The result was an inequality, which shows that, under some apparently innocuous assumptions, the measurement results when combine in a particular way must always give a value smaller than a certain maximum value. These “innocuous” assumptions were: (a) that there is a unique reality, (b) that there are no nonlocal interactions (“spooky action at a distance”) .

It took a while before an actual experiment that tested the EPR paradox could be perform. However, eventually such experiments were performed, notably by Alain Aspect in 1982. He used polarization of light instead of position and momentum, but the same principle applies. And guess what? When he combined the measurement result as proposed for the Bell inequality, he found that it violated the Bell inequality!

So, what does this imply? It means that at least one of the assumption made by Bell must be wrong. Either, the physical universe does not have a unique reality, or there are nonlocal interactions allowed. The problem with the latter is that it would then also contradict special relativity. So, then we have to conclude that there is no unique reality.

It is this lack of a unique reality that lies at the heart of an understand of the concept of quantum entanglement. More about that later.

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What is your aim?

The endless debate about where fundamental physics should be going, proceeds unabated. As can be expected, this soul searching exercise includes many discussions of a philosophical nature. The ideas of Popper and Kuhn are reassessed for the gazillionth time. Where is all this leading us?

The one thing I often identify in these discussions is the narrow-minded view people have of the diversity of humanity. Philosophers and physicists alike, come up with all sorts of ways to describe what science is supposed to be and what methodologies are supposed to be followed. However, they miss the fact that none of these “extremely good ideas” have any reasonable probability to be successful in the long run.

Why am I so pessimistic? Because humanity has the ability to corrupt almost anything that you can come up with. Those structures and systems that exist in our cultures that actual do work are not the result of some “bright individuals” that decided on some sunny day to suck some good ideas out of their thumbs. No, these structures have evolved into the forms that they have today over a long time. They work because they have been tested over generations by people trying to corrupt them with the devious ideas. (It reminds me that cultural anthropology is, according to me, one of the most underrated fields of study. The scientific knowledge of how cultures evolve would help many governments to make better decisions.)

The scientific method is one such cultural system that has evolved over many centuries. The remarkable scientific and technological knowledge that we posses today stand as clear evidence of the robustness of this method. There is not much, if anything, to be improved in this system.

However, we do need to understand that one cannot obtain all possible knowledge with the scientific method. It does have limitations, but these limitations are not failing of the method that can be improved on. These limitations lie in the nature of knowledge itself. The simple fact is that there are things that we cannot know with any scientific certainty.

What is your reward?

So, the current problem in fundamental science is not something that can be overcome by “improving” the scientific method. The problem lies elsewhere. According to my understanding, this problem has one of two possible reasons, which I have discussed previously. It is either because people have lost their true curiosity in favor of vanity. Or it is because our knowledge is running into a wall that cannot be penetrated by the scientific method.

While the latter has no solution, the former may be overcome if people realize that a return to curiosity instead of vanity as the driving force behind scientific research may help to adjust their focus to achieve progress. Short term extravagant research results do not always provide the path to more knowledge. It is mainly designed to increase some individual’s impact with the aim to obtain fame and glory. The road to true knowledge may sometimes lead through mundane avenues that seem boring to the general public. Only the truly passionate researcher with no interest in fame and glory would follow that avenue. However, it may perhaps be what is needed to make the breakthrough that would advance fundamental 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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Demystifying quantum mechanics I

Feynman’s statement

In one of his books, The Character of Physical Law (MIT Press: Cambridge, Massachusetts, 1995), Richard Feynman stated: “I think I can safely say that nobody understands quantum mechanics.”¬†Apparently, he also said “If you think you understand quantum mechanics, you don’t understand quantum mechanics”¬†in a talk with the same title as the book.

Richard Feynman

So it is quite clear that Feynman strongly believed that quantum mechanics is fundamentally incomprehensible. Who can argue with Feynman? He was a genius. If he said nobody can understand it, then nobody can understand it, right?

Genius or not, Feynman was just a human being. One should not elevate any person to such a level that their statements are considered to be cast in stone.

I don’t think that quantum mechanics is fundamentally incomprehensible. It is just that we don’t like what we learn. The way nature behaves at the fundamental level seems to contradict our intuition because it is so different from what we experience in our daily lives.

To be sure, there are things about the micro world that we simply cannot know. We know that atoms radiate photons, and that the atoms change their states when this happens. But we don’t know the exact mechanism by which such a photon is created.

The amazing thing about quantum mechanics is that it allows us to make reliable calculations without knowing these details. It is a way to encapsulate our ignorance and renders it innocuous, allowing us to use the little that we can know to make useful predictions.

Quantum mechanics is not the only scientific approach that allows one to make useful calculations amidst ignorance. Statistical analysis does the same. It also ignores the ignorance about the details and allows useful calculations exploiting the little that we do know.

What makes quantum mechanics more mysterious is that the part that we can know includes aspects that are strange to say the least. This strangeness has many manifestations, variously referred to as “the wave-particle duality,” “quantum uncertainty,” “quantum tunneling,” “quantum entanglement,” and many others.

A thorough understanding of these various aspects of quantum mechanics removes some of the strangeness. One can often identify the mechanisms with similar mechanisms in non-quantum scenarios without any strangeness.

However, within this understanding there usually remains an aspect that does not have any equivalent aspect in non-quantum scenarios. Distilling out this one aspect that makes things seem weird, one can refer to it as the notion of multiple realities.

People don’t like this idea of multiple realities. So they invented the idea of quantum collapse. However, there is no observable confirmation of quantum collapse. One can even argue that it is in principle impossible to observe quantum collapse, because it would have to be intrinsically involved in the process of observations. So this led to the so-called “measurement problem.”

The very fact the there are people that try to solve the measurement problem shows that they don’t buy into Feynman’s statement. They invest a significant amount of time and effort to understand something that Feynman believed could not be understood.

I don’t think the idea of multiple realities needs more understanding. It is the way it is, even if we don’t like it. I intend to say a bit more about it later.

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