A mechanism for quantum collapse

It is argued that the current impasse in fundamental physics is at least partially caused by the fact that there does not exist a credible understanding of the process of quantum collapse. This argument begs the question of those interpretations of quantum mechanics that incorporate quantum collapse. Therein lies a dilemma: interpretations of quantum mechanics are generally non-scientific – except for a few special cases – interpretations of quantum mechanics are not falsifiable. Therefore, even if we were able to come up with a mechanism for quantum collapse, it would not form part of our scientific understanding because it would not allow falsification.

However, there are interpretations of quantum mechanics that do not involve quantum collapse. They present a possible way out of this dilemma. Whatever reason one would have to introduce the notion of quantum collapse in the first place, must somehow be reproduced in those interpretations of quantum mechanics that do not explicitly contain it. In other words, the observable phenomena that suggest a collapse mechanism, must somehow be reproduced in interpretations without quantum collapse. The explanation of any mechanism that would reproduce such phenomena would therefore provide a kind of mechanism for quantum collapse without quantum collapse. In this case, the falsification takes on the lesser form of a retrodiction where the observed phenomena are explained in term of a successful theory. That successful theory is standard quantum mechanics. In other words, what we’ll do is to use standard quantum mechanics without introducing quantum collapse to explain those phenomena that seem to require quantum collapse.

If we do not want to introduce quantum collapse we inevitably employ an interpretation of quantum mechanics that does not involve quantum collapse. The one that we use is the so-called many worlds interpretation. However, we first need to review it to remove some misconceptions. In effect, we’ll use a modified version of the many worlds interpretation.

The many worlds interpretation is often associated with a multi-verse that is produced by the constant branching of a universe due to the quantum interactions that take place in that universe. This notion is misleading. Taking a good hard look at the quantum mechanics formalism, one should realize that it does not support the idea of a multi-verse produced by constant branching. Instead, there is just one universe, but with an infinite multiple of “realities” that are associated with the infinite number of elements in the basis of the Hilbert space of this universe. The number of these realities never change – there is no branching. Instead, the basis always consist of an infinite number of discrete elements. The only effect of quantum interactions is to change their relative probabilities. So, the many worlds (or the multiple realities) correspond to the terms in the superposition of all these basis elements forming the state of the universe. This state evolves in a unitary fashion that incorporates all the interactions that take place in the universe and thereby produces a constant variation over time in the coefficients of the terms in the superposition.

With this picture in mind, we can consider what it means to have quantum collapse, or to understand any physical process that seems to suggest quantum collapse. As a first example of such a physical process, we use a historically relevant example presented by Albert Einstein during the 5th Solvay conference, which was held in Brussels in 1927. [For a transcript of the discussions at the 5th Solvay conference, see G. Bacciagaluppi and A. Valentini, Quantum Theory at the Crossroads, Reconsidering the 1927 Solvay Conference, Cambridge University Press (2009); arXiv:0609184.] At this conference, which played a prominent role in the development of quantum mechanics and the Copenhagen interpretation, Einstein described a scenario where an electron propagates toward a screen on which it is registered as a single point of absorption on the screen. He then presented two possible ways to view the process that takes place, exemplifying the problem of maintaining energy conservation without introducing action at a distance. This example is an apt demonstration of one of the key problems with the notion of quantum collapse.

Attendants of the Fifth Solvay Conference
Attendants of the Fifth Solvay Conference

Before we deal with the understanding of this process in the context of multiple realities, we first need to remove an unfortunate tacit assumption that we find in the discussions of such experimental scenarios. It mentions a particle. What particle? Or perhaps one should ask what is meant by the term particle? Does is refer to a localized lump of matter (or a dimensionless point) traveling on a world line? Or is it a more abstract notion associated with a finite mass and a discrete charge, without localization? I suspect, that the former is implies in these discussions, because it would help to explain the localization of the observed absorption. However, what we see is a localized absorption and not a particle. The notion of something that is itself localized is not the only possible explanation for the localization of an absorption process. The latter can simply be the result of a localized mechanism for the absorption process. In the scenario, the screen is assumed to be a photographic material, presumably consisting of little silver crystals that can register the electron.

So, a slightly different picture from that which was put forward by Einstein emerges. The electron is now represented by a wave function (not a particle) that propagates toward the screen. The screen contains numerous little crystals that can register the electron. However, assuming that the wave function represents only one electron, one would find only one such absorption event (otherwise we’ll have the problem of violating conservation principles). In terms of multiple realities, many of these crystals could serve to perform the absorption process. Each reality would correspond to a different crystal receiving the electron.

But how does the situation within a particular reality manages the localize the electron wave function without causing action at a distance? Remember that the different realities are associated with the different basis elements in the Hilbert space. The basis of the Hilbert space is not unique. One can define infinitely many different basis, each of which is related to any other basis by a unitary transformation. In general, there is nothing special about any particular basis. In other words, the separation of the wave function of the universe into a superposition of different realities can be changed via unitary transformation into another set of realities, each of which is a combination of the previous set of realities. However, when it comes to a specific interaction process, such as the absorption of an electron by a specific crystal, then there is a special basis that would clarify the process. This basis corresponds to the measurement basis of the crystal.

To understand what this measurement basis is, one can determine what electron wave function would have been radiated by the crystal if the absorption process is inverted as the adjoint process. At the fundamental level, all processes are invertible. It is just that the probability for the required initial conditions to produce a specific inverted process may be vanishingly small. We can nevertheless assume that these required conditions exist so that it would produce the radiated wave function. The conjugate of the radiated wave function would describe the ideal measurement basis element for the absorption of an electron by this crystal. In effect, nature transforms the basis (the realities) into the measurement basis for the absorption of electrons by the crystals. All the different realities now correspond to different basis elements, each of which is associated by the absorption of the electron by a different crystal.

Obviously all these basis elements are localized at the their associated crystals. This localization is accomplished purely through a unitary transformation without any funny action at a distance. The way that the unitary transformation accomplishes this localization is through constructive and destructive interference among the elements of any other basis that may initially have represented the multiple realities.

The different realities in the localized measurement basis have different coefficients associated with them in the superposition. Some of these coefficients would be larger than others, indicating which crystal is most likely to absorb the electron. It may be that one specific reality has a coefficient that completely dominates. In that case, although there are multiple realities, one specific reality would dominate. This dominant reality may be the one that we perceive as the single reality in our experience.

Hopefully, this understanding gives a feasible picture of the process whereby quantum collapse seems to take place. More can be said about this topic, but since this discussion has already been rather long, I’ll postpone further discussions for another day.

 

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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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Transcending the impasse, part III

Many-worlds interpretation

In my series on the impasse in physics and how to transcend it, I previously discussed the issue of classical vs quantum physics. Here, I want to talk about the interpretations of quantum mechanics.

There is much activity and debate on these interpretations. Part of it is related to the measurement problem. Is there such a thing as quantum collapse? How does it work?

David Mermin once said in an article in Physics Today that new interpretations are added every year and none has ever been ruled out. If this is true, then it indicates that the interpretations of quantum mechanics is not part of science, and therefore also not part of physics.

I am not going to say one should not work on such interpretations and try to make sense of what is going on, but the scientific method does not seem to help us here. Perhaps people will eventually come up with experiments to determine how nature works. I’ve seen some proposals, but they are usually associated with some new mechanisms, which in my view are unlikely to be correct.

It occurs to me that while we cannot say which of the interpretations are correct, we may just as well just pick one and work with that. So I pick the simplest one and when I want to figure out how things will work out in one of these experiments, then I can just consider how things will work according to this interpretation. If such a prediction turns out to be wrong, it would show that this interpretation (and all those that made the same prediction) is wrong after all.

The simplest interpretation according to me is the many-world interpretation. It is simple because it does not require the weird unexplained notion of quantum collapse. People don’t like it, because it seems to require such a lot of different worlds. For that reason it is also associated with the idea of a multiverse.

Hugh Everett III, the person that invented the many-worlds interpretation

Well no, those ideas are anyway misleading. In quantum mechanics, all interactions are described by unitary evolution. The picture that it represents is that there is a set of states that the universe can take on. One can think of each such state as a different description of the world. Hence “many worlds.” However, the actual state of the universe is a quantum superposition of all the possible worlds. In the superposition each world is associated with a complex probability amplitude. It means that some worlds are more likely than others. During interactions these probability amplitudes change.

That is the whole idea of unitary evolution. All the possibilities are already present right from the start. The only thing that interactions do is to change the probability amplitudes that are associated with the different worlds. During the evolution in time the different worlds in the superposition can experience constructive or destructive interference, which would change their probability amplitudes, making some less or more likely that they were before.

The number of worlds (number of terms in the superposition) stays the same. They don’t increase as a result of interactions. How many such worlds are there? Well, if we look at the properties of the set of such basis states, then it is often assumed to be a countable infinite number. However, it may turn out to be uncountably infinite, having what is called the cardinality of the continuum.

What is more is that these different worlds are not distinct unique worlds. One can redefine the basis set of worlds by forming different superpositions of the worlds in the original set to get a new set in which the worlds now look different.

How does all this relate to what we see? The dynamics of the universe causes the interferences due to the unitary evolution to favor a small set of worlds that look very similar. This coherence in what the world looks like is a result of the constructive interference produced by the dynamics.

So the world that we see at a macroscopic level is not just one of these worlds. It is, in a sense, a conglomeration of all those worlds with large probability amplitudes. However, the differences among all these worlds are so small that we cannot notice it at a macroscopic level.

OK, not everything I said here can be confirmed in a scientific way. I cannot even proof that the many-worlds interpretation is correct. However, by thinking of it in this way, one can at least get some idea of it that makes sense.

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Wisdom is the path to knowledge

As a physicist, I cherish the freedom that comes with the endeavor to uncover new knowledge about our physical world. However, it irks me when people include things in physics that do not qualify.

Physics is a science. As a science, it follows the scientific method. What this means is that, while one can use any conceivable method to come up with ideas for explaining the physical world, only those ideas that work survive to become scientific knowledge. How do we know that it works? We go and look! That means we make observations and perform experiments.

That is the scientific method. It has been like that for more than a few centuries. And it is still the way it is today. All this talk about compromising on the basics of the scientific method is annoying. If we start to compromise, then eventually we’ll end up compromising on our understanding of the physical world. The scientific method works the way it works because that is the only way we can know that our ideas work.

Some people want to go further and put restrictions on how one should come up with these ideas or what kind of ideas should be allowed to have any potential to become scientific knowledge even before it has been tested. There is the idea of falsifiability, as proposed by Karl Popper. It may be a useful idea, but sometimes it is difficult to say in advance whether an idea would be falsifiable. So, I don’t think one should be too exclusive. However, sometimes it is quite obvious that an idea can never be tested.

For example, the interior of a black hole cannot be observed in a way that will give us scientific knowledge about what is going on inside a black hole. Nobody that has entered a black hole can come back with the experimental or observational evidence to tell us that the theory works. So, any theory about the inside of a black hole can never constitute scientific knowledge.

Now there is this issue of the interpretations of quantum mechanics. In a broader sense, it is included under the current studies of the foundations of quantum mechanics. A particular problem that is much talked about within this field, is the so-called measurement problem. The question is: are these scientific topics? Will it ever be possible to test interpretations of quantum mechanics experimentally? Will we be able to study the foundations of quantum mechanics experimentally? Some aspects of it perhaps? What about the measurement problem? Are these topics to be included in physics, or is it perhaps better to just include them under philosophy?

Does philosophy ever lead to knowledge? No, probably not. However, it helps one to find the path to knowledge. If philosophy is considered to embody wisdom (it is the love of wisdom after all), then wisdom must be the path to knowledge. Part of this wisdom is also to know which paths do not lead to knowledge.

It then follows that one should probably not even include the studies of foundations of quantum mechanics under philosophy, because it is not about discovering which paths will lead to knowledge. It tries to achieve knowledge itself, even if it does not always follow the scientific method. Well, we argued that such an approach cannot lead to scientific knowledge. I guess a philosophical viewpoint would then tell us that this is not the path to knowledge after all.