Realist Interpretations of Non-collapse Quantum Mechanics

It is sometimes thought, in line with the earlier-mentioned notion that quantum physics is an inherently instrumentalist field of research, that there are no realist inter­pretations of quantum mechanics.

In fact there are quite some realist interpretations of non-collapse quantum mechanics: hidden variables interpretations a la Bohm (1952), Goldstein (2016), many worlds interpretations Vaidman (2016); Wallace (2012), modal interpretations Dieks and Vermaas (1998), Bub (1997), Lombardi and Dieks (2016) and consistent histories interpretations Griffiths (2014) are only the more obvious ones. Whether the Copenhagen interpretation of Bohr belongs to this class of non-collapse realist interpretations is more controversial Dieks (2017), Faye (2014), as is the question of the status of versions of the Copenhagen interpretation proposed by others, like Heisenberg.

In most interpretations the mathematical structure of quantum mechanics is con­strued as a description of one single physical world, in which we find ourselves, but the many worlds interpretation is notorious for its assumption that in a measurement interaction all possible measurement results are actually realized in non-interacting different worlds—so that in a measurement interaction the world can be imagined to branch into many copies that differ from each other in the result of the measurement.

The just-mentioned difference (many versus one world) is already well-suited to illustrate how different interpretations of the quantum mechanical formalism may agree in their predictions of measurement results and still give rise to very different pictures of what the universe is like. In the many worlds interpretation all possible outcomes of a measurement are realized when a measurement is performed; but each one is realized in only one world. Because the epistemic access of observers is con­fined to a single world, each observer will empirically find only one single outcome. Of course, because of the branching that took place in the measurement, there is a copy of the observer in all other worlds, and each one of these “clones” will find a dif­ferent outcome—unbeknownst to our original observer. The single worlds by them­selves are governed by the usual laws of quantum mechanics, and each observer-copy will only make contact with his own world.

Modal interpretations, by contrast, are based on the idea that there exists only one actual world. This world has a quantum character and therefore should be described by means of non-classical properties; the task is to define these properties in such a way that on the level of macroscopic observations the standard quantum mechani­cal predictions are reproduced. As in the many worlds interpretation, these standard predictions are not supposed to appear as subjective impressions of observers but are realized as objective properties of measuring instruments (pointers indicating a certain position on a dial, etc.). These macroscopic properties are part of a network of properties that extends also to the micro-realm, so that all physical systems at all times possess well-defined albeit nonclassical physical characteristics. It is for this reason that the scheme may be called realist. The exact details of the property assign­ment depend on the version of the modal scheme that one considers Bub (1997), Lombardi and Dieks (2016).

It is instructive to look at Bohm’s theory in some detail to illustrate why, and to what extent, this theory can be said to reproduce the standard predictions of quan­tum mechanics. According to Bohm, quantum objects like electrons are localized particles that at each instant of time possess a definite spatial position, and therefore also a definite velocity. Here we already recognize that the Bohmian world is dras­tically different from the world pictured in other quantum accounts: most of these other accounts abide with Bohr’s complementarity, and Heisenberg’s uncertainty relations, according to which a quantum system cannot possess a precise value for both velocity and position. In addition to the particles the Bohm‘scheme works with the wavefunction, whose evolution is always governed by the Schrodinger equation, in exactly the same way as in all non-collapse schemes. This wavefunction, according to Bohm, defines the probability that a particle will find itself at a certain position, via the equation P(x) = | ¥(x) |²; P(x) is the probability that the particle is at posi­tion x and ¥(x) is the value of the wavefunction at that spot.^[117] Particles will move in such a way that the probability law P(x) = |¥(x)|² will be satisfied at all times.^{[118] [119] [120] [121] The wavefunction evolves in the standard Schrodinger way, which means that in a mea­surement an entangled state will be formed of object plus measuring device, includ­ing the part of the device that eventually indicates the outcome (the pointer). As in all non-collapse interpretations, the final state will be a superposition in which |T|2 will have non-vanishing values for all position configurations of the combination of particle and device-plus-pointer, in which the pointer indicates one of the possible outcomes.}

This illustrates the way in which the Bohm scheme reproduces the standard pre­dictions of quantum mechanics. The crux here, as in all non-collapse schemes, is that the evolution of the wavefunction is taken over, in unmodified form, from the standard quantum formalism. So ¥(x) and the probabilities |¥(x)|² are always the same as in the standard formalism. But the associated picture is quite different from the usual one: in Bohm’s theory all objects always possess definite positions and fol­low well-defined trajectories through space. The probabilities in Bohmian quantum mechanics represent our ignorance about the actual positions of particles; but this ignorance also reflects an objective “chaos” in the world that makes it impossible to improve on the probabilistic quantum predictions. Indeed, according to Bohm there is a basic lack of controllability and repeatability in the world, which makes the use of probabilities unavoidable. For example, when we repeat a measurement of the kind just described, we cannot arrange for it that the incoming particle starts at the same position as in the previous run of the experiment. In fact, in many repetitions of the experiment the initial particle positions will be distributed according to the values of |¥(x)|². So although in each run of the experiment everything happens according to a deterministic law of motion, which fully determines the outcome given the ini­tial conditions, we cannot fully predict that outcome because the initial conditions themselves are uncontrollable and only open to a probabilistic treatment.

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