Causation and chance in quantum mechanics

The competing and complementary concepts of causality within the dispositional or powers approach is already quite intricate, as indicated by a previous post.  There are also concepts of causality that do not follow a dispositional approach and are in fact better known.

For a concise and balanced overview of the status see Anjum and Mumford Causality, Oxford 2014. My previous post provided a commentary on Chapter 3 of "What Tends to Be the Philosophy of Dispositional Modality", which examined a dispositional ontological for objective probability. In Chapter 4 of the same book Anjum, Mumford and Andersen examine how a dispositional theory of causality stands up against the ontological challenges of quantum mechanics. 

 The understanding of causality that is still the most influential can be traced back to David Hume's sceptical analysis and Emmanuel Kant's response. In A Treatise of Human Nature (1973, Book I, Part III, Section VI) Hume argued that all that can be observed in nature is a series of events. One thing happens and then another, and then another, and so on. Whether any of those events are causally connected is not itself part of experience of events. For example, a match is struck and then almost immediately that same match lights, but what is not observed is that the striking of the match caused it to light. If there is cause and effect, then it is not known through direct observation of events. But what do our physical theories tells us? In Newtonian physics one thing happens followed by another but that following is determined by the laws of physics. The state of the world at one time determines the state of the world later. That this seems not to be the case in a world described by quantum mechanics leads to claims that causality no longer holds. In standard quantum mechanics a later state does follow deterministically from an earlier state but measurement breaks the causal link.

Heisenberg and Bohr (Walter Heitler and Léon Rosenfeld in the background), in the mid 1930s 

Now let's look at those features of classical causation that were explicitly discussed by Bohr and Heisenberg: necessitation, determinism, predictability, and separability.

Classical causation

Hume was sceptical about a necessary connection between cause and effect because none can be known from experience. However, the intuition that a cause necessitates an effect is strong and led Kant to formulate causal necessity as a precondition for science.  It may seem strange that the radical empiricist, Hume, is seen to be undermining the scientific enterprise but his analysis, according to Kant, denies the possibility of scientific explanation. Kant, in the Critique of Pure Reason, states:

[T]he very concept of a cause so obviously contains the concept of a necessity of connection with an effect and a strict universality of rule that it would be entirely lost if one sought, as Hume did, to derive it from a frequent association of that which happens with that which precedes and a habit (thus a merely subjective necessity) of connecting representations arising from that association.

Kant's influence was strong, especially in Germany, and Heisenberg felt compelled to respond given the empirical success of quantum mechanics. In the lectures "Physics and Philosophy" he uses the radioactive decay of the radium atom as an example in which there is no predictability of the timing of a decay event.  There is no decay event that follows through necessity from the prior state of the atom. There is no quantum law that necessarily connects the state of the radium atom with the decay event. However, quantum theory does predict the probability of a decay event per unit time. There is no determinacy. If necessity and determinism are characteristic of a cause, then causality does not hold in quantum mechanics. 

Heisenberg, in agreement with Bohr argues that causality is needed but only as a classical concept for interpreting experiments. This is because we do not directly observe the decay but use a detector and it is taken as a rule that the decay causes a chain of events that result in what is detected or measured. 

The question remains whether necessitation and determinism are characteristic of all theories of causality. A further question is whether it is coherent to have classical causal laws holding in interpreting measurements but not in atomic physics.

Without determinism and necessitation at the fundamental level, the same event would not always follow from two identical sets of initial conditions or states. Predictions in the quantum realm, prior to detection, are probabilistic in general and this provides a reason for rejecting a classical causal interpretation of quantum mechanics.

The connection between determinism and prediction is that the former provides the metaphysical ground for the later.

In addition, the classical theory of causation has the cause and the effect as two distinct things. How distinct must these two things be? The predictions of quantum mechanics, in addition to being indeterministic, do not, according to Bohr (Causality and Complementarity, Philosophy of Science, Vol. 4, No. 3, 1937), allow the separation of the microscopic quantum system and the measuring apparatus. This gives rise to the notion that the act of measurement is in part responsible for the measured result. Cause and effect cannot be separated and so there is no clear demarcation between them. Classical causality breaks down again.

In the same paper Bohr insists that "the concept of causality underlies the very interpretation of each result of experiment, and that even in the coordination of experience one can never, in the nature of

things, have to do with well-defined breaks in the causal chain."

So, for Bohr there is a theory of atomic and sub-atomic physics, quantum mechanics, but there is no separable cause and effect in that theory. After an event is detected by the measuring apparatus then classical cause and effect come into play.

Potentiality

Heisenberg was not content to leave atomic physics inexplicable and so proposed an ontology at the atomic level with substance in isolation understood as pure potentiality

All the elementary particles are made of the same substance, which we may call energy or universal matter; they are just different forms in which matter can appear. If we compare this situation with the Aristotelian concepts of matter and form, we can say that the matter of Aristotle, which is mere ‘potentia’, should be compared to our concept of energy, which gets into ‘actuality’ by means of the form, when the elementary particle is created. (Heisenberg 1959)

Every time a potency gets actualised, causation happens and that is due to isolated substance encountering actualised matter. In mentioning particle creation Heisenberg has moved from quantum mechanics to field theory and his claim 'poentia' are energy like can only be sustained in an Aristotelian sense that has little to do with the concept in physics. As will be explained below, potentiality can be introduced within quantum mechanics using the theory outlined in the previous post. The idea is that objects behave the way they do, not because of some external laws that determine what happens to them, but because of their own intrinsic dispositions and their interactions. Let's follows Anjum and Mumford and call such a theory of causality neo-Aristotelian.

Neo-Aristotelian causality does not invoke necessitation. Instead, there are irreducible tendencies. It adopts dispositional modality rather than conditional necessity. A tendency is less than necessity, so the effect is not guaranteed by its cause.

As described in the previous post, a typical example of a probabilistic disposition is the 50:50 propensity of a fair coin to land heads or tails if tossed, while a non-probabilistic disposition could be the propensity of a vase to break if dropped onto a firm surface.

Neo-Aristotelian causation is not a relation between two separate events or objects, but is a continuous, unified process that typically takes time to unfold. One way to understand an event as stochastic is that there is some objective probabilistic element involved. In other words, a chance event. This is an ontological interpretation of probability, which contrasts with the purely epistemic notion of credence or subjective probability. An individual event could therefore still be caused, in the neo-Aristotelian sense, even if it is random to some degree and not predictable. Typically, this type of causation takes place when the possibilities exist, when the effect is enabled by the right stimulus and under the right conditions. Neo-Aristotelian causation happens once the disposition manifests itself. 

An object with the potentiality to manifest as possible events will find itself in a situation where there are enabling dispositions and interfering dispositions. For example, firewood is disposed to ignite but the process leading up to it burning requires the presence of manifestation partners: a suitable site, proper ignition, enough oxygen, and so on, and that inhibitors such as dampness are not too strong. The firewood, its enablers and its inhibitors are all active in the cause of the effect. No ontological distinction is drawn between properties belonging to the object undergoing change and the contextual properties in this process. They are all, in a general sense, causes of the specific outcome. Depending on the balance the firewood may

• Burn brightly and sustainably
• Burn but go out quickly
• Smolder and smoke
• Fail to light at all.

In summary, neo-Aristotelian causation

• Involves irreducible tendencies
• Is not deterministic, although some process can be close to deterministic
• Supports predictions of what tends to happen, not what will happen with certainty
• Is a unified process, not a relationship between two distinct events.

A sketch of quantum causation

Take the electron as a typical quantum object. We need to identify what possibilities it can potentially manifest and what is needed to enable that manifestation.

The possible manifestations of the electron are as values of position, momentum, spin, charge, and mass. At this level of description charge and mass are classical properties. The others are potential properties and from quantum theory there is structure to and constraints on how the other properties can appear. This is captured in the formulation of quantum mechanics favoured in this blog that uses the generalisation of probability to a \(\sigma\)-complex.

As indicated, at this stage I only propose a sketch of how this may work. Developing the detail and confirming whether the proposed process is correct will require much more work.

For the potentiality to manifest the electron cannot be isolated. It therefore interacts with other objects. It is proposed that the interaction selects one \(\sigma\)-algebra from the complex. That is, the context will be for certain spin values or position or momentum to manifest. This provides a preliminary selection of a \(\sigma\)-algebras from the complex and therefore standard probability description of the tendency of the electron properties to manifest. Now this manifestation takes place via a Monte-Carlo selection process from the probability distribution associated with the selected \(sigma\)-algebra. This provides a model of the causal chain from potentiality to actuality in the quantum domain.

To make this more concrete consider the analysis of the double slit experiment.  In the initial version discussed previously the slits split the quantum state to produce an interference effect. The context is already selecting position and therefore one probability distribution from those possible. At the detecting screen the position of the electron is made actual through Monte-Carlo selection from the probability distribution.

Now consider the addition of a pointer immediately after the double slit. The pointer tends to point towards the electron. The pointer description is purely quantum and is not a measurement apparatus. As my earlier analysis shows the presence of the pointer eliminates the interference effect and selects a probability distribution for the electron position that is a normalised sum of the distributions that would obtain if the electron only passed through one slit. Again, the context has selected the probability distribution over position and at the detecting screen the position of the electron is made actual with a Monte-Carlo selection from the probability distribution.