Potentiality, possibility, and probability

In the previous post I returned to Heisenberg and his discussion of potentia in quantum theory and examined Barbara Vetter's modal metaphysics of potentiality in that context. The intention being to relate this metaphysics to the formulation of quantum mechanics as a \(\sigma\)-complex of potentiae, that captures the possible manifestations of quantum objects. The occurrence of actual events is then governed by the probability of actualisation, which depends on the physical context that the object finds itself.

Heisenberg's book on the philosophy of quantum mechanics is well known and I may have missed some recent work by others that is inspired by or develops his thinking.  A search found a number of papers but one, "Taking Heisenberg’s Potentia Seriously" by R. E. Kastner, Stuart Kauffman and Michael Epperson [1], provided an analysis that is close to the position that I have arrived at 5 years later and goes further in working out some consequences for our understanding of quantum theory. 

To better compare my position with that of Kastner et al, here is a brief list of my main points:

1. Physics is about the physical and not about, information, knowledge, or psychology (of course physics is knowledge and provides information.)
2. Ontology needs to encompass potentiality so that the dispositional nature of quantum processes can be captured in a physical theory
3. The quantum state is represented by a complex of probability models (modified Kochen formulation) and is not merely statistical
4. The manifestation (or actuality) of quantum events depends on the physical context (the mechanism for this is the outstanding puzzle)
5. The process of going from the potential to the actual is a probabilistic transition
6. Measurment is a physical process but there are physical events in the absence of measurement that the theory must be able to describe
7. The mathematical structure of quantum theory can provide important clues to the underpinning ontology.

The main points extracted from Kastner et al are:

1. A realist understanding of quantum mechanics calls for the metaphysical category of res potentia
2. Res potentia and res extensa are interdependent modes of existence
3. Quantum states instantiate in quantifiable form res potentia; ‘Quantum Potentiae’
4. Quantum Potentiae are not spacetime objects, and they do not obey the Law of the Excluded Middle or the Principle of Non-Contradiction.
5. Measurement is a real physical process that transforms Quantum Potentiae into elements of res extensa, in a non-unitary, acausal process
6. Spacetime (the structured set of actual events) emerges from a quantum substratum
7. Spacetime is not all that exists
8. There is a mathematical theory covering the above.

Although the above only provides the briefest summary of both points of view, the similarities should be obvious. 

The modifications I made to Kochen's formulation, although modest, were aimed at eliminating any temptation to think that we are dealing with some non-standard logic. So, point 4 by Kastner et al poses a problem and I don't think that it is well argued in the paper that potentiae do not obey the Law of the Excluded Middle or the Principle of Non-Contradiction (I note that in her book [2] Ruth Kastner makes no mention of this point). I think the appropriate logic for potentiality is far better captured in the proposal of Barbara Vetter. However, within point 4 the proposal that potentiae are not space-time objects is interesting and potentially fruitful. However, it does indicate an ontology that may be as extravagant as the multiverse interpretation. In mitigation the ontology captures a rich substratum of all possibilities rather than infinity of actual universes. 

Where they clearly go beyond my points is with their point 9. Whereas I have been comparing and contrasting standard quantum theory, the propensity interpretation, Kochen's reformulation, various Bohmian proposals, GRW collapse theories, the multiverse interpretation, and Fröhlich's ETH research project; Ruth Kastner has developed a specific theory of quantum potentiality [2]. She starts with an interpretation that I have neglected so far; the Transactional [3]. It is an interpretation that gives physical importance to an aspect of the mathematical formulation that is usually considered a mere calculation device. In the Dirac notation, for standard quantum mechanics, a state \(\Psi\) is denoted by the ket \(|\Psi>\). The observables, represented by Hermitian operators, act on the ket as follows \(\Omega |\Psi>\) and in standard theory it is simply a calculation device to gain the expected value of the observable in the state to use the complex conjugate of the state, the bra, \(<\Psi|\Omega |\Psi>\).

However, in the transactional interpretation \(<\Psi|\) gains a physical significance. It is the confirming echo from the absorber (or detector) to the emitter's potential for observable properties to become actual. Despite this attractive proposal Cramer's original formulation has some issues. There is backward causation. This is what many would consider anti-causation because the effect precedes the effect. There are some other issues that Ruth Kastner proposes a solution for in her book and we will examine later. She takes Cramer's formulation and, building on other work, develops a relativistic formulation. She shows that this is needed to avoid some of Cramer's difficulties. 

I now believe that Kastner's formulation and ontology provides a very promising approach to gaining a deeper understanding of the quantum domain and it will therefore provide the focus of the coming posts. Even if it turns out to have some flaw the analysis should rewarding.

Some of the points I address will be presentation and terminology. For example, Vetter's metaphysics indicates a process going from potential to possibility and (through weighting) probability. So, for me quantum states will represent potentiality with the set of possible events represented by the spectrum of the associated observables. The probabilities are gained by decomposing the potentiality in the basis associated with a particular observable. I will als try to eliminate reference to the wave concept. I will stick by my preference for a Heisenberg picture because the wave concept to too closely tied to the space-time continuum.

1. Ruth  E. Kastner, Stuart Kauffman and Michael Epperson, Taking Heisenberg’s Potentia Seriously, International Journal of Quantum Foundations, March 27, 2018, Volume 4, Issue 2, pages 158-172
2. Ruth E. Kastner, The Transactional Interpretation of Quantum Mechanics - A Relativistic Treatment, Cambridge University Press, 2nd edition 2022
3. J. G. Cramer, (1986). The transactional interpretation of quantum mechanics, Reviews of Modern Physics 58, 647–88.