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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Transcending the impasse, part VIII

… or not?

In this final posting in the series on transcending the impasse in fundamental physics, we need to consider the possibility that we may never be able to transcend the impasse. Perhaps this is it as far as our scientific understanding of fundamental physics in concerned. Perhaps our ability to probe deeper into the unknown ends here.

Why would that be? Perhaps the theory that would correctly explain what happens above the electroweak scale would need observations at an energy scale that is too high to reach with conceivable colliders. Without such observations, the theory may remain in the status of a hypothesis and never become part of our scientifically established knowledge.

It seems that collider physics has run its course. The contributions to our scientific knowledge made with the aid of colliders are truly remarkable. But, at increasing higher energies, it runs into a number of serious challenges. At such high energies, a collider needs to be very large and extremely expensive. As a result, it becomes impractical and financially unjustifiable.

Even if such a large expensive collider does become a reality, the challenges do not end there. The scattering events produced in such a collider become increasingly complex. Already at the Large Hadron Collider, the scattering events look more like the hair on a drag queen’s wig. The amount of data produced in such events is formidable. The rate at which the data is generated become unmanageable.

Even if one can handle that much data, then one finds that the signal is swamped by background noise. At those high energies, particles are more unstable. It means that their peaks are very broad and relatively low. So it becomes that much harder to see a new particle popping up in the scattering data.

There are suggestions of how scientific observations can be made to support high-energy physics without the use of colliders. One such suggestion is based on astronomical observations. There are high energies generated in some astronomical events. However, such events are unpredictable and the information that can be extracted from these event is very limited compared to what is possible with the detectors of colliders.

Another suggestion is to use high precision measurements at lower energies. It becomes a metrology challenge to measure properties of matter increasingly more accurate and use that to infer what happens at high energies.

Whether any of these suggestions will eventually be able to increase our knowledge of fundamental physics remains to be seen. But I would not be holding my breath.

Perhaps it sounds like that old story about those 19th century physicists that predicted the end of physics even before the discoveries of relativity and quantum mechanics. Well, I think the idea that a steady increase in our physical understanding in perpetuity is equally ludicrous. At some point, we will see a slow-down in the increase of our understanding of fundamental physics, and even in physics in general. However, applied physics and engineering can proceed unabated.

We are already seeing a slow-down in the increase of our understanding of fundamental physics. Many fields of physics are already mostly devoted to applied physics. Very little is added in terms of new fundamental understanding of our physical universe. So, perhaps the impasse is simply an inevitable stage in the development of human culture, heralding to maturity of our knowledge about the universe in which we live.

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