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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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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Lockdown fits me like a glove

Previous posts not withstanding, now that I’ve been living in this state of lockdown for more than a month, I realize that it is not so bad. In fact, when I hear how others are freaking out and protesting the current situation, my reaction is something like “really??!!”. Then I remember that, when it comes to normal humanity, I’m probably a bit of an outsider.

It helps to be an introvert, which means that alone-time is always valued much higher than time with people. Make no mistaken, I do enjoy the occasional social time with friends or family, but too much of that drains my energy and makes me feel awkward.

However, being an introvert is not enough to help one enjoy lockdown. There is this one dangerous condition called boredom that afflicts most people in lockdown, leading to cabin fever and then to all sorts of other things that we need not elaborate on.

Boredom

So what would be an effective way to counter boredom? One would need lots of things to do. Many people perform what they call “spring cleaning.” (However, if you think about it, cleaning during lockdown is the opposite of spring cleaning.)

There are other activities that one may become involved with due to the lockdown such as cooking. However, if cooking was not part of you daily routine and if it does not suddenly become a new found passion, then it can soon develop into a onerous chore. The same applies to many other chores that are suddenly imposed on one by the lockdown situation.

So what would then be an effective activity to counter boredom? The answer is flow. You need something that you are passionate about, something that involves activities that challenge you, but for which you are capable to meet these challenges. It can keep you busy for hours. While you are doing it, you enter a state of flow; you don’t even realize that time is flying by. Instead, you are completely focussed on what you are doing. And you enjoy it!

My passion is theoretical physics research. When I’m busy performing those calculations or developing those derivations, I am almost unaware of anything else going on in the world. The activity puts me in a positive frame of mind and keeps me there for the duration of the activity.

It is a good thing that I have embarked on a particular challenging project just before lockdown started. There are times that I don’t have anything interesting and challenging to work on, but now I do. My setup at home is perfectly geared to perform this work. In fact, it is even better than at work. So, I’m glad for the opportunity that lockdown provides me to do this work. I hope I can finish it before lockdown is lifted to the point where I need to go back to work.

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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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Consequences of lockdown

It is now just over a week since we entered lockdown. The statistics of the number of known COVID-19 cases seemed to have flattened off, but the authorities warn that there may be many more people that are infected that we don’t know about yet.

don’t panic, don’t panic

So, here we are going about our business in as far as one can go about one’s business sitting at home. Of course we need to stay positive. This is especially important for those of us living alone. As a result, I find myself thinking about the situation, observing how things develop and trying to think what it will lead to. I came to the conclusion that the world will probably never be the same again. Even assuming we get through this (and I guess one must hold onto the conviction that we will get through it), there are certain things that (I think) will change forever.

What does the future hold?

Perhaps you’ve already heard that one of the effects of lockdown is that more people will start to work from home. Video conferencing will become more prevalent. So will online file-sharing facilities and all that kind of stuff. (Let’s just hope the internet keeps on working.) However, I think there is another consequence that has been largely ignored. It is something I call the collective impetus.

So, what is this collective impetus? A long long time ago there was this TV series called Star Trek. It actually spawned several different series. One of the iconic antagonists that appeared in many of these series, but especially in Star Trek Voyager is the Borg, a cybernetic hive mind that called itself the Collective. It would inform its victims: “Resistance is futile. You will be assimilated.”

Some time ago I started to see a resemblance between the Collective (the Borg) and those people that are constantly on their cellphones. It occurred to me that the obsession of these people to be in contact with others (so much so that they even do that while driving a car) effectively means that they are gradually becoming part of a collective hive mind.

Enter lockdown. Now, what little face-to-face interaction people had is drastically reduced. As a result, more people are forced to keep contact with one another via cellphones. Hence the collective impetus. The society that will emerge after the lockdown may look significantly more like a collective than before the lockdown.

Is this what cellphones will look like in the future?

One can even imagine that cellphones will eventually start to look like the devices on the heads of people in the Borg. Perhaps this is the next phase in the evolution of the universe. Perhaps people will lose their individuality and the whole collective hive mind will start to act like a single organism. What about those of us that refuse to become part of this collective?

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