Quantum Mechanics and Its Interpretations: A Defense of the Quantum Principles

Abstract

One of the most striking features of the epistemological situation of Quantum Mechanics is the number of interpretations and the many schools of thought, with no consensus on the way to understand the theory. In this article, I introduce a distinction between orthodox interpretations and heterodox interpretations of Quantum Mechanics: the orthodox interpretations preserve all the quantum principles while the heterodox interpretations replace at least one of them. Then, I argue that we have strong empirical and epistemological reasons to prefer orthodox interpretations to heterodox interpretations. The first argument is that all the experiments on the foundations of Quantum Mechanics give a high degree of corroboration to the quantum principles and, consequently, to the orthodox interpretations. The second argument is that the scientific progress needs a consensus: this consensus is impossible with the heterodox interpretations, while it is possible with the orthodox interpretations. Giving the preference to the orthodox interpretations is a reasonable position which could preserve both a consensus on quantum principles and a plurality of views on Quantum Mechanics.

Appendix: Examples of Interpretations

In order to illustrate the distinction between orthodox and heterodox interpretations, I will give examples of the two types of interpretations. Because one interpretation can have different variants, the following presentation will depend on the choosen variants. This is not a problem because my goal is only to illustrate the distinction between the two strategies, it is not to discuss any particular version and all its variants. Furthermore, I choose some versions because they are useful to illustrate the distinction. I don’t want to deny that each of them may have its own difficulties and that its advocates have to solve some conceptual or physical problems. Once again, my goal is only to illustrate the distinction between orthodox and heterodox interpretations of Quantum Mechanics.

First I will give four examples of orthodox interpretations of Quantum Mechanics, that is to say four examples of quantum versions that keep the quantum principles but change the domain of validity of one (or more) of them.

The first example is Bohr’s interpretation of Quantum Mechanics ([6]). He opposes microscopic and macroscopic levels and said that quantum mechanics concerns only the microscopic level, where the Planck constant cannot be neglicted. On the contrary, macroscopic phenomena should be described by classical physics, not by Quantum Mechanics, because the Planck constant can be neglected for macroscopic phenomena. In other words, Bohr limits the domain of validity of all the quantum principles to microscopic level. In this approach, the Measurement Problem has no reason to appear. Indeed the second description of a quantum measurement in the Measurement Problem supposes that a measurement apparatus can be treated as a quantum system. Yet a measurement apparatus is a macroscopic system. So, according to Bohr’s interpretation, its behavior should not be described by the quantum laws and it should not be any Measurement Problem.

The propensionist interpretation developed by Karl Popper ([25]) is also an example of orthodox interpretation. This interpretation is a realist interpretation of the quantum principles. One of the key features of this interpretation is that the state function that is associated with a system doesn’t represent the physical state of this system but only the propensions attached to the system (and to the whole physical situation). Thus the Scrödinger equation does represent the evolution of the state of the system, but only of the propensions. According to this interpretation, the contradiction between Principle III and Principle IV is supposed to disappear because these principles don’t have the same meaning: one is about the state of the system, the other is about the propensions. Thus, during a measurement, the physical state of the system is described by Principle III, and only by it. The description of a quantum measurement by the Principle IV is meaningless in this interpretation.

A third example of an orthodox interpretation is given by Rovelli’s interpretation [27]. According to this interpretation, the two descriptions involved in the Measurement Problem are not seen from the same point of view. Each of them is true relatively to its proper observer. The key of this approach is to consider that each description is dependent of a specific observer, that is to say: the descriptions are not “observer independent” and depend on two different observers. The use of Principle 3 (first description) or the use of Principle 4 (second description) are thus governed by the reference to an observer (or a point of view). This regulation tries to solve the problem: there are two different descriptions that are not true within the same conditions. We do not have to reject any of the quantum principles, we have to specify the conditions to which we can use it⁵.

The pragmatist approach [4] is also an example of orthodox interpretation. This interpretation tries to make explicit the pragmatic meaning of the terms used by the researchers in microphysics and to give them a pragmatic definition, based on human action. Besides, this interpretation divide any experiment into four chronological phases: the preparation (wich is a set of sequences of precise and controlled experimental operations), the intermediate phase (during this phase, the prepared system is free to evolve without any experimental operation), the measurement (which is a set of experimental operations producing a macroscopic event), and the observation and the statement of the outcome. According to this interpretation, the pragmatist meanings of all the important terms of the theory are sufficiently determined to make the difference between all the phases and to know when the evolution is driven by Principle IV (as in the second phase) or by Principle III (as in the third phase). In terms of human actions, we know when we do a measurement and must use only Principle III. Thus, according to this interpretation, the contradiction of the Measurement Problem is supposed to disappear.

The previous examples illustrate the orthodox interpretations. Now I will give three examples of heterodox interpretations. A first example is given by Bohm’s interpretation [5]. In this interpretation, the physical matter is supposed to be composed of particles that have determined position and velocity at any moment. A first modification to the mathematical formalism concerns Principle 1: a system S is not only associated to a state vector $\vert \varPsi \rangle$ but also to a function x(t) which represents the position of the system S. Futhermore, the position of a particle is supposed to be guided by a pilot wave (as in De Broglie’s version). Thus a second modification of the mathematical formalism is made: a new equation, called “guiding equation”, that described the evolution over time of the positions of every particles, is added to the standard formalism.

A second example is given by Everett’s interpretation [9] and its variants. According to the Everett’s interpretation, the Principle III is removed and the right description of a quantum measurement is the description given by Principle IV. We must not consider that only one outcome: all the possible outcomes are superposed. Because Principle III is removed, the contradiction of the Measurement Problem doesn’t exist anymore. The variants of Everett’s interpretation (like [7]) tries to explain why we observe only one result by saying that the possible outcomes don’t occur in the same “world” (or “universe”). For example, if we measure the spin of an electron, in a branch we will find the result "$+$" and in another branch we will find the result "−". contrary to Principle 3, all the possibilities are realized but not in the same “world” (or “universe”).

We can also try to replace Principle 4 (the Schrödinger’s equation) by another equation. This way was proposed by Ghirardi et al. [13]. In this version, the fundamental idea consists in supposing that spontaneous collapses can occur randomly for any particle that compose a quantum system. “Spontaneous” means that it can occur without any interaction with another system. “Collapse” means that the concerned particle becomes localised in a small region of space. This hypothesis leads to modify the standard Schrödinger’s equation. Without entering too technical aspects, we can say that the standard Schrödinger’s equation can be written for the density operator $\rho$ as follow: $\frac{d \rho (t)}{d t} = - \frac{i}{ \hbar } [H,\rho ]$ (this formula is equivalent to $P_4$). In the GRW version, for a system composed of several particles, it is replaced by: $\frac{d \rho (t)}{d t} = - \frac{i}{ \hbar } [H,\rho ] - \displaystyle \sum _{k=1}^{n}{\lambda _{k} (\rho - T_{k}(\rho ))}$, where $\lambda _{k}$ is a numerical parameter and $T_{k}(\rho )$ expresses mathematically the spontaneous localisation process of the $k^{th}$ particle. $T_{k}(\rho )$ has the effect to change a pure state into a mixed state, that is to say: a state without quantum interferences. For a microscopic system, the probability of a spontaneous collapse is very low. But for a macroscopic system, because of the number of particles, the probability is very high. This is why, according to this interpretation, neither a macroscopic system nor a measured system (that is to say: a system in interaction with a measurement apparatus), are in entangled state: spontaneous collapses occur with a probability almost equal to one and the system is supposed to in a classical state.