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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Testable proposals for the measurement problem

In a previous post, I made the statement: “Currently, there are no known experimental conditions that can distinguish between different interpretations of quantum mechanics.” Well, that is not exactly true. Perhaps one can argue that no experiment has yet been performed that conclusively ruled out or confirmed any of the interpretations of quantum mechanics. But, the fact is that recently, there has been some experimentally testable proposals. Still, I’m not holding my breath.

Recently, seeing one such proposal, I remembered that I also knew about another testable proposal made by Lajos Diósi and Roger Penrose. The reason I forgot about that is probably because it seems to have some serious problems. At some point, during a conversation I had with Lajos, I told him I have a stupid question to ask him: does quantum collapse travel at the speed of light? His response was: that is not a stupid question. So, then I concluded that it is not something that any of the existing collapse models can handle correctly. In fact, I don’t think any such model will ever be able to handle it in a satisfactory manner.

Thinking back to those discussions and the other bits and pieces I’ve read about the measurement problem, I tend to reconfirm my conviction that the simplest interpretation of quantum mechanics (and therefore the one most likely to be correct) is the so-called Many Worlds interpretation of quantum mechanics. However, the more I think about it, the more I believe that “many worlds” is a misnomer. It is not about many worlds or many universes that are constantly branching off to become disjoint universes.

Perhaps one can instead call it the “multiple reality” interpretation. But how would multiple realities be different from “many worlds”? That fact is that these realities are not disjoint, but form part of the unitary whole of a single universe. These realities can be combined into arbitrary superpositions. What more, these realities are not branching of to produce more realities. The number of realities remains the same for all time. (There are actually an infinite number of them, but the cardinality of the set remains the same.) The interactions merely change the relative complex probability amplitudes of all the realities. 

Anyway, just thought I should clear this up. I don’t see myself ever writing publication on this topic.

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The problem with the measurement problem

It is not really a topic I want to discuss. In fact, I don’t think it is worthy of including under my Demystifying Quantum Mechanics series. However, since even physicists don’t seem to get it, it is necessary to clarify a few things.

So the argument seems to go that even of one were to consider a completely mixed quantum states with equal probabilities for different outcomes then a measure would convert this mixed state into one with only one outcome and zero for all other outcomes. This transformation is then interpreted as a quantum collapse and the fact that this process is not understood is called the measurement problem.

The problem with this interpretation of the situation is just that: it is an interpretation. So it falls under the general topic of interpretations of quantum mechanics. Currently, there are no known experimental conditions that can distinguish between different interpretations of quantum mechanics. As such it is not physics, because it is not science. It falls under philosophy. As a result, it would not be possible to solve the so-called measurement problem.

Just in case you are wondering whether this measurement scenario can be interpreted in any other way that does not involve collapse, the answer is yes. The obvious alternative is the Many World interpretations. In terms of that interpretation the mixed quantum state describes the different probabilities for all the different world in which measurement are to be performed. If one would restrict the quantum state to any one of these worlds (or realities) then it would have 100% probability for a specific outcome even before the measurement is performed. Hence, not collapse and no measurement problem.

So, yes indeed, the measurement problem is a pseudo-problem. It is not one that can (or need to be) solved in physics.

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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 VI

A little bit of meta-physics

Anyone that has read some of my previous posts may know that I’m not a big fan of philosophy. However, I admit that philosophy can sometimes have some benefits. It occurs to me that, if we want to transcend the impasse in fundamental physics, we may need to take one step back; stand outside the realm of science and view our activities a bit more critically.

Yeah well flippiefanus, what do you think all the philosophers of science are doing? OK, maybe I’m not going to be jumping so deeply into the fray. Only a tiny little step, just enough to say something about the meta-physics of those aspects most pertinent to the problem.

So what is most pertinent to the problem? Someone said that we need to go back and make sure that we sort out the mistakes and misconceptions. That idea resonates with me. However, it is inevitable in the diverse nature of humans to do that anyway. The problem is that if somebody finds something that seems incorrect in our current understanding, then it is generally very difficult to convince people that it is something that needs to be corrected.

What I want to propose here is a slightly different approach. We need to get rid of the clutter.

Clutter in our theory space

There is such a large amount of clutter in our way of looking at the physical world. Much of this clutter is a kind of curtain that we use to hide our ignorance behind. I guess it is human to try hiding one’s ignorance and what better way to do that by dumping a lot of befuddling nonsense over it.

Take for instance quantum mechanics. One often hears about quantum weirdness or the statement that nobody can really understand quantum physics. This mystery that anything quantum represents is one such curtain that people draw over their ignorance. I don’t think that it is impossible to understand quantum mechanics. It is just that we don’t like what we learn.

So what I propose is a minimalist approach. The idea is to identify the core of our understand about a phenomenon and put everything else in the proper perspective without cluttering it with nonsense. The idea of minimalism resonates with the idea of Occam’s razor. It states that the simplest explanation is probably the correct one.

To support the idea of minimalism in physics, we can remind ourselves that scientific theories are constructs that we compile in our minds to help us make sense of the physical world. One should be wary of confusing the two. That opens up the possibility that there may always be multiple theoretical constructs that successfully describe the same physical phenomena. Minimalism tells us to look for the simplest one among them. Those that are more complicated may contain unnecessary clutter that will inevitably just confuse us later.

To give a concrete example of this situation, we can think of the current so-called measurement problem. Previous, I explained that one can avoid any issues related to the measurement problem and the enigma of quantum collapse by resorting to the many-worlds interpretation. This choice enforces the principle of minimalism by selecting the simplest interpretation. Thereby, we are getting rid of the unnecessary clutter of quantum collapse.

This example is somewhat beyond science, because the interpretations of quantum mechanics is not (currently?) a scientific topic. However, there are other examples where we can also apply the minimalist principle. Perhaps I’ll write about that some other day.

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