Review: October 2022

This blog is intended to

• Help organise and develop my thinking on quantum mechanics, the role of probability, and the ontological status of particles and states.
• Examine and develop ontologies in other areas.

 My guiding principle is that entities have properties and interactions that are independent of whatever anyone or anything knows about them. Experiments are for finding out about the physical world not for instantiating it. That is, the physical world is there even when no one is looking. So far, the discussion has engaged with ontologies that deal with an autonomous physical world independent of considerations of what is known about the system or who is interfering with it. There are quantum theories that focus on what can be known about a physical system rather than what the systems behaviour is per se. The original Copenhagen interpretation of quantum mechanics falls into this category, but a more recent approach is Quantum Bayesianism. Commonly shortened to QBism, it interprets the quantum state as capturing a degree of belief. There are questions about the ontological assumptions associated with the theory, with options ranging from a form of idealism to "participatory realism". I will return to this in future posts.  

This blog has inherited a lot of material from a draft paper I prepared on ontology and quantum mechanics. The substance of that paper has now been captured as a set of blog posts. One reason for putting aside the draft paper was the recognition of the further reading on ontology that I needed to do. At the time of moving from the academic paper format to the blog, I had only started to delve into the New Ontology by Nicolai Hartman [1]. What I won from Hartmann was a structure of ontological strata and spheres of being. This structure is much richer than Karl Popper's three-world ontology [2]. An academic paper is appropriate once all the problems with concepts have been addressed or at least clarified, whereas a blog is more flexible and informal and that should help in developing my ideas.

Critical ontology

I have taken the title of the blog from a earlier paper by Hartmann: Wie ist kritische Ontologie überhaupt möglich?. Critical ontology implies, in this blog, a constructive but forensic attitude to concepts and theories in science and philosophy whether I am initially sympathetic to them or not. This is an attitude that I think is consistent with both Hartmann's and Popper's approach to philosophy.

Quantum chance

A major challenge, and focus so far, is how to include objective probabilities in an ontology for quantum mechanics. Popper's proposal for a propensity interpretation introduced a dispositional model for objective chance but its ontological status remains ambiguous with its presentation strongly dependent on artificial experimental arrangements rather than the situations in which physical entities mostly find themselves. Popper's intent seems to be to reduce quantum indeterminacy to classical probability with a dispositional interpretation. I do not think that can be directly achieved. 

In previous posts not enough emphasis was given to explaining the special status of quantum chance. The use of the letter p to represent the quantum state should not be taken to imply that quantum mechanics has been reduced to classical probability. There are major differences, such as interference terms, as shown in the mathematical presentation.

Here I want to explain another major difference. Classical probability theory has its origins in the analysis of games of chance and statistics was initially developed to deal with the vast quantities of data associated with entities of interest to the state.  In games of chance the numbers on dice or patterns of playing cards are actual but hidden. Similarly in the use of statistics by the state, members of the population are actual, and while not hidden, the state needs to work with averages and distributions. In quantum chance the probabilities are not merely a means of dealing with hidden or irrelevant variables. It is known from the work of Kochen and Specker [3] that in general the quantum variables are not actual. The electron does not have an actual spin value that is unknown because in general its spin value is only a potential value. This means that the dispositional powers that lead to quantum chance are fundamental.

A consideration that requires further work is the mechanism for property values to become actual that is not tied to a measurement. There are proposals for spontaneous wavefunction reduction but if they only decrease the variance (or some other measure of the spread) of the wavefunction this only reduces the number of possibilities without selecting one to be actualised. This seems to me to indicate a major open problem.

These considerations indicate the need for a theory that recognises dispositions as fundamental properties of physical entities. The concepts developed by Alexander Bird [4] show promise although it is a still open to investigation how widely ranging dispositional properties are in nature. 

Ontological status of mathematics and physical theories

 The ontological status of mathematical representations in physical theories also needs further development. In Hartmann's ontological structure pure mathematics belongs to the ideal rather than the real sphere. Physical theories seem to fit better objectivated mode belonging to the spirit stratum of the real sphere, but they apply structures with an origin in pure mathematics and provide a description of aspects of the inorganic stratum of the real sphere. This means it is necessary to understand to what extent mathematical entities belong to the ideal rather than the real sphere and what the interaction is between the ideal sphere, the spirit stratum, and the inorganic stratum in the real sphere. Whereas Hartmann goes back to Aristotle to develop an ontology that includes ideal and real spheres of existence, an Aristotelean ontology that places mathematics in the real sphere is also a possibility. Franklin [5] has developed a version of this.

Next steps

My next task is to absorb the content of books like those of by Franklin and Bird, and capture what I learn in future posts. It is hoped that my earlier posts in this blog will then be developed, clarified, and improved. In addition, I will examine and discuss the proposals for gravity induced state reduction [6], event-oriented theories [7], and quantum Bayesian approaches.

[1] Hartmann, N., New Ways of Ontology, Taylor and Francis, 2017 (translated from Hartmann, N., Neue Wege der Ontologie, W Kohlhammer, 1949)

[2] Popper, K. R., Objective Knowledge, Oxford: Clarendon Press, 1972

[3] Kochen, S. & Specker, E. P., The Problem of Hidden Variables in Quantum Mechanics, 

J. Math. & Mech., 1967, 17, 59 

[4] Bird, A., Nature’s Metaphysics, Oxford University Press, 2007

[5] Franklin, J., An Aristotelian Realist Philosophy of Mathematics, Palgrave Macmillan UK, 2014

[6] Penrose, R., Shadows of the Mind, Oxford University Press, 1994

[7] Fröhlich, J. & Pizzo, A., The Time-Evolution of States in Quantum Mechanics according to the ETH-Approach, Communications in Mathematical Physics, 2021