Why the QM-models are explanatory

Since the mechanistic, the causal-interventionist and the causal ancestry account of explanations do not fit what happens in the QM explanation, the question arises whether QM provides any causal explanation at all. In the literature it appears that there is no consensus about whether or not quantum mechanics is compatible with our views on

causality26_{. Instead of arguing that QM-models are causal explanations or non-causal}

explanation, I would like to start from the question: if QM models are not causal, can they still be explanatory?

In order to answer this question, I focus on plain explanation-seeking questions, for instance:

Why is lithium a good electrical conductor? I will come back to the resemblance questions in 6.7.

The QM-model answers this question by referring to the electron configuration: The good electric conductivity of lithium physically depends on its electron configuration, viz. 1s²2s.

One might argue that this is an example of purely derivational unification, but it is not. On the contrary, I will argue that it is purely ontological.

First, the chemical properties cannot be directly derived from the electron configuration. As seen in section 6.3.:

There is a problem with the claim that the periodic table is deductively explained by quantum mechanics. A feature that seems to generally go unnoticed is the need to assume the empirical order of shell filling rather than trying to derive it from the theory. The order in which orbitals are occupied with electrons is not derived from first principles. It is justified post facto and by some complex calculations. (Scerri, 2007, p. 237)

That the QM models do not provide a full deductive account, might be a problem for physics, but it does not need to be a problem for the explanatory status of QM-models. Deductive information can be relevant in certain explanations, but it is not what makes an explanation explanatory. As I have written in Chapter 5, it is the mirroring of deductive relations to physical dependency relations that make a derivation explanatory. Dependencies always guide us towards explanations, derivations do not. (Woodward, 2003, p. 203).

The idea is that these derivations trace or mirror the relations of physical dependency that hold between the explanans conditions and the explananda phenomena-relations that would be revealed if, for example, we were to physically intervene to alter the explanans conditions. (2003, p. 201)

Throughout the dissertation I have used this criterion of representing physical dependency relations as the demarcation between an explanation and a description that is non-explanatory. Nowhere in Woodward’s criterion is the condition that these relations need to be causal:

The underlying or unifying idea in the notion of causal explanation is the idea that an explanation must answer a what-if-things-had-been-different question, or exhibit information about a pattern of dependency. (2003, p. 201; italics added)

Causality is not a criterion for the representation of physical dependency relations, it is the other way around. If we accept that the QM models mirror such physical dependency relations, they can be classified as explanatory according to Woodward’s view. More generally, in order to accept QM derivations as explanations we have to accept claims of the following format:

Chemical property X of atoms of type Y physically depends on their typical electron configuration.

The constituents that form the base of the QM explanation of the periodic law, the electrons, obey three organizational principles: the Aufbau principle (Mandelung rule), Hund’s rule and the Pauli Exclusion Principle. These principles can be seen as pure mathematical rules. For instance, the Pauli Exclusion Principle can be formulated as: no two electrons can have four identical quantum numbers. Usually the principle is formulated making also an ontological claim such as: no two electrons can simultaneously occupy the same quantum state with respect to orbital and spin. Concepts such as ‘occupy’, ‘quantum state’ and ‘orbital spin’ suggest more than pure mathematical constraints of behavior. They tell us something about how electrons can behave, about certain characteristics they may have. Quantum mechanics not only provides useful mathematical tools but also makes ontological claims:

Quantum mechanics neatly accommodates the existence of particles that are indistinguishable in principle: we simply construct a wave function that is noncommittal as to which particle is in which state. […] This is the famous Pauli

exclusion principle. It is not (as you may have been led to believe) a weird ad hoc assumption applying only to electrons, but rather a consequence of the rules for constructing two-particle wave functions, applying to all identical fermions. (Griffiths, 2005, p. 204)

Quantum mechanics does tell us something about relations of physical dependency. However, section 6.4 and 6.5 suggest that if there is such a physical dependency, it is a bit spooky: it is not causal dependence (unlike what is the case in causal network unification and mechanism unification) and it does not supervene on causal relation (unlike what is the case in optimality explanations). So, in line with the idea that physical dependencies can be non-causal, I define structural explanations as follows:

An explanation is structural if and only if the explanandum physically depends, in a non-causal way, on the micro-structure described in the explanans.

With this definition in place, the derivations from the QM models may be called structural explanations.

Some people may say that structural explanations as I define them cannot exist, because they reject the idea of “physical dependency in a non-causal way” as spooky metaphysics. In their view all physical dependency relations are causal or supervene on causal relations. If the QM-models are non-causal, they would consider them as non- explanatory.