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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