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Status of the Wave Function of Quantum Mechanics, or, What is Quantum Mechanics Trying to Tell Us?

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The most debated status of the wave function of Quantum Mechanics is discussed in the light of the epistemological vs ontological opposition.

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Acknowledgements

It is a pleasure to thank Br. G.-M. Grange, O.P. for a careful reading of the manuscript.

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Authors and Affiliations

  1. Couvent Saint Etienne, Jerusalem, Israel

    D-M. Cabaret

  2. Université Côte d’Azur, Institut de Physique de Nice, UMR CNRS 7010; 1361 routes des Lucioles, 06560, Valbonne, France

    T. Grandou

  3. Université catholique de Toulouse, 1, Impasse Lacordaire, Toulouse, 31400, France

    E. Perrier

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  1. D-M. Cabaret
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Appendix

Appendix

Against the dominant interpretations of the wave function in QM which are focused on the knowledge/reality gap, this paper has argued that two facts are central to understand the nature of the wave function: One is the real linear combination of possibilities, the other is the unitary evolution and the collapse into actual states. These facts involve three notions which need to be explained and defined: Possibility, actuality and reality. These notions have received considerable attention since Aristotle first showed their universal importance in the \(\Lambda \)-Book of his Metaphysics. However, this is not the place to enter into those complex discussions. Instead, we provide here an analogy which can help to understand what the wave function of QM shows us: The seed analogy.

Tree seeds offer a relevant analogy of the distinction between reality, possibility and actuality. First, a seed is real, it has an existence of its own, with material constituents, organs and functions. Now, in a seed, a whole panel of grown up trees are contained in an inchoative manner. Even though, a given seed will ever produce a unique tree out of the whole set of possible trees. There is, then, a clear distinction between the tree seed and the grown-up tree. What is to be stressed here, is the opposition between a determined actual state (the tree), and the fact that this actual/realised state was present already in the whole set of possibilities the real seed entailed. The seed exhibits a mode of reality which is plainly real though not actual, being a whole set of possible actualisations, one of which only will get realised. As the seed itself, this potentiality must be regarded as real. In particular, it departs from a pure imaginary picture one could form concerning the possibilities the seed comprises. In the seed in effect, an infinity of other possibilities are excluded. The range of possibilities is a constrained range, real, even though a mere potentiality with respect to any of the full possible actualisations. This case, familiar of metaphysical considerations, exhibits two states of one and the same entity, its potential state and its actual or realised state. It may be helpful to get a bit more accustomed to a mode of reality which physics so far has excluded from its analyses, as stated in our Conclusion. The seed, however, offers only an analogical instance of the act/potency distinction.

A crucial difference with the wave function is that in the seed the potentialities disappear to give way to one, and only one, actual state, through a temporal process of growing. It is proper to quantum objects, and this puts them apart from entities studied by other sciences, that their potentiality is so much ingrained in what they are, that their actualisation has a very peculiar relation to time, as explained in Sect. 5.

From this viewpoint, the wave function encompasses the following assessments about reality, potentiality and actuality:

  • Being potential is not opposed to being real. In that a possibility reflects an indetermination, it can result from the unknowability of the cause which determines (like the possibility of winning in a lottery), or from the indifference to actual reality (as with mathematical hypotheses). But possibilities can also be real. It is the case when a reality virtually contains all of the possible outcomes that it is capable of. And this is the kind of possibilities that the wave function correlates about a given system.

  • Being potential is opposed to being actual. It is necessary to distinguish between the combination of all possible states of a quantum system, and the actual state taken by that same system: both are real, but not in the same manner. And the mathematical tour de force of the wave function formalism is that it is able to express both the real potency or the real actuality of a system.

  • A wave function can describe the same quantum objects when being in potency, and when being in act. In a given linear superposition or in an actual state resulting from its collapse, there is but one and the same subject of superposition and collapse. Unitarity is the conservation of the overall probabilities of all the possible realisations a quantum subject is capable of. Once a given realisation comes about, a formal discontinuity takes place as the series of complex-valued probability amplitudes gets reduced to a unique real-valued coefficient of 100%. This discontinuity however does not compromise the continuity/conservation of the underlying subject, since on the contrary, it is in this way that the latter is asserted through the passage of potential to actual.

  • Being potential and being actual are mutually exclusive for any quantum object. The wave function describes states that are either potential or actual, but the formalism excludes that the real potentiality of a given system could coexist with the actual state of the same system, at the same time and under the same assessment.

  • Actual states realise potential states. The wave function is able to represent the potentialities of a given system and its collapse into an actual state. Therefore, actual states can only be conceived and performed by getting out of potential states.

  • Potential states are apprehended as qualified actual states. Potentialities are construed by the mathematical formalism as could-be actualities, and they are “measured” through the measurement process that gets them out of their potential state. It can then be stated in general that our intelligence needs actuality to apprehend potentiality.

  • Even when in potency, quantum objects are actual in some part. Wave functions deal with determined objects (e.g. photons, electrons, quarks...), even if some of their properties are in potency. In the extreme case, if those objects were deprived of any determination at all, they would be in potency to everything. That is to say, the more the real is potential, the more it is undetermined, the more it is in potency to any actual state, the more it escapes characterization by determined nouns and properties, and the more it is unknowable in itself.

  • Something in act is needed to get a quantum object out of its initial degree of potency. A reality in a given state of potentiality does not leave this state of potentiality on its own. An action is needed, operating upon it, so as to induce such a transition. There is, then, a difference between an actual collapse of the wave function when a measure is performed on a given system, and what has been unduly called a ‘collapse’, when no measure is performed (see the examples in Sect. 2).

These points are illustrated through the eight revisited cases of Sect. 6.

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Cabaret, DM., Grandou, T. & Perrier, E. Status of the Wave Function of Quantum Mechanics, or, What is Quantum Mechanics Trying to Tell Us?. Found Phys 52, 58 (2022). https://doi.org/10.1007/s10701-022-00574-w

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