In his 1999 article, "The Physics of Interactionism," Mohrhoff investigated "another hard problem" (beyond David Chalmers's consciousness), namely "how anything material can have freedom." He says:

By 'freedom' I mean a person's ability to behave in a purposive, non-random fashion that is not determined by neurophysiological structure and physical law. I do not mean the absence of other determining factors, as this would render freedom synonymous with randomness...

Physics has been invoked both to refute and to support psycho-physical interactionism, the view that mind and matter are two mutually irreducible, interacting domains. Thus it has been held against interactionism that it implies violations of the laws of physics, notably the law of energy conservation. I examine the meaning of conservation laws in physics and show that in fact no valid argument against the interactionist theory can be drawn from them. In defence of interactionism it has been argued that mind can act on matter through an apparent loophole in physical determinism, without violating physical laws. I show that this argument is equally fallacious.

This leads to the conclusion that the indeterminism of quantum mechanics cannot be the physical correlate of free will; if there is a causally efficacious non-material mind, then the behaviour of matter cannot be fully governed by physical laws. I show that the best (if not the only) way of formulating departures from the 'normal', physically determined behaviour of matter is in terms of modifications of the electromagnetic interactions between particles. I also show that mental states and events are non-spatial, and that departures from the 'normal' behaviour of matter, when caused by mental events, are not amenable to mathematical description.

(The Physics of Interactionism, Journal of Consciousness Studies, 6, No. 8-9, 1999, p.165)

The absence of causal primaries is often called 'the causal closure of the physical world', where 'physical' means 'non-mental' rather than 'governed by the laws of physics'.

Causal closure is used by Jaegwon Kim to deny downward causation and the possibility of a non-reductive physicalism.

This causal closure is a trivial consequence of the lack of scientific interest which results from being unable to identify causal primaries. What is causally closed is the scientifically known world, not the world as such. Yet there are many philosophers who look upon causal closure as an ontological truth and go on to invoke it as an argument against interactionism, the doctrine that mind and matter are two mutually irreducible, interacting spheres. Interactionists as I understand them are motivated primarily by a desire to make room for free will, the denial of which is both counterintuitive and at odds with notions (moral and otherwise) that are central to the fabric of our active lives. While repudiating the causal closure of the physical world, interactionists nevertheless shrink from contesting the validity of the laws of physics, not realizing that this is contingent on the presumption of causal closure.

Quantum-mechanical indeterminism is not a "loophole" but an irreducible component
of standard quantum physics.
It is difficult to integrate into interactionism because it threatens to make actions random, as Mohrhoff notes.

That is how we come to witness futile fights between philosophers of mind who reject interactionism on the ground that it is incompatible with the laws of physics and, in particular, the law of the conservation of energy, and interactionists who meekly defend their position, claiming that, by exploiting the loophole of quantum-mechanical indeterminism, non-material mind is capable of influencing matter without violating conservation laws. Both the charge and the defence are misconceived. The law of energy conservation is either true by virtue of the meaning of 'energy', and therefore is not threatened by interactionism, or it is contingent upon the causal closure of the physical world, and therefore is no threat to interactionism. The loophole hypothesis, on the other hand, violates basic physical laws other than the law of energy conservation.

If causal primaries "freely" generate new (non-material) ideas in the mind, and if an adequately determined "will" follows one idea by moving the body, such an interaction violates no physical law.

This should not come as a surprise. To be causally efficacious, mental events that are causal primaries must make a difference to the behaviour of matter and thus to the behaviour of its constituent particles. The effects of such events on the behaviour of particles have to be expressed in the language of physics, for this is the only language suitable for describing the behaviour of particles. But the laws of physics presuppose causal closure and describe the behaviour of matter in the absence of causal primaries. Hence it follows that the behaviour of matter in the presence of a causally efficacious non-material mind cannot be fully governed by those laws.

(The Physics of Interactionism, p.166)

Mohrhoff attempts to show that mind is "not spatial" and that makes it not amenable to a mathematical description (for example, one describable in terms of electromagnetic fields with conservation of energy and momentum). He reaches the following conclusions:

(1) The conservation of energy and momentum is a consequence of the homogeneity of time and of space. This is warranted for systems that are causally closed. As to material systems that are open to causal influences from non-material mind, either energy/momentum is/are ill-defined or there is no reason why it/they should be conserved.

(2) Assuming that part but not all of matter is causally open to non-material mind, it makes sense to attribute (non-conserved) energy and momentum even to physical systems that interact with non-material mind.

(3) The causal efficacy of non-material mind implies departures from the statistical laws of quantum physics. These departures are capable of being formulated in terms of modifications, by the conscious self, of the electromagnetic interactions between particles; and they are more consistently formulated in this manner.

(4) Because the electromagnetic field is a summary representation of effects on the motion of particles, the effects caused by mental events are necessarily among the effects represented by it. It is not that one cannot formulate the effects of the self in terms of a separate probability field, to use Margenau's (1984) term. The point is that this field would be indistinguishable from a contribution to the electromagnetic field, which makes it obvious that departures from the laws of physics are involved. Thinking of the effects of the self as contributions to the electromagnetic field is preferable for two reasons. First, it eschews the contentious notion that measurement-like events take place in the unobserved brain. Second, it leads to a more unified treatment of causality. There is no reason whatever for having probabilities determined twice over, once during their deterministic evolution by the physically determined vector potential, and once at the end through a superimposed probability field generated by the self.

(5) Quantum-mechanical indeterminism cannot be the physical correlate of free will. Free will implies departures from the laws of physics.

(6) Mind is non-spatial. There is no point in attributing positions to mental states and events.

(7) The departures from the physical laws caused by non-physical mental events are not amenable to mathematical description. It is worth emphasizing that they are not therefore random. They could be necessitated by something of a primarily qualitative nature, something that manifests itself in quantitative, spatio-temporal terms but is not reducible to these terms.

(The Physics of Interactionism, pp.181-82)

...proceeds from the recognition that the fundamental theoretical framework of physics is a probability algorithm, which serves to describe an objective fuzziness (the literal meaning of Heisenberg's term 'Unschärfe', usually mistranslated as 'uncertainty') by assigning objective probabilities to the possible outcomes of unperformed measurements. Although it rejects attempts to construe quantum states as evolving ontological states, it arrives at an objective description of the quantum world that owes nothing to observers or the goings-on in physics laboratories. In fact, unless such attempts are rejected, quantum theory's true ontological implications cannot be seen.

("The Pondicherry Interpretation of Quantum Mechanics," PRAMANA journal of physics, Indian Academy of Sciences Vol. 64, No. 2, February 2005 pp. 171-185)

Quantum mechanics gives us probability amplitudes, of course. Probabilities, being always positive, cannot interfere with one another

Quantum mechanics, the fundamental theoretical framework of contemporary physics, is a probability algorithm. This serves to assign, on the basis of outcomes of measurements that have been made, probabilities to the possible outcomes of measurements that may be made. The inevitable reference to 'measurement' in all standard axiomatizations of unadulterated quantum mechanics was famously criticized by John Bell: "To restrict quantum mechanics to be exclusively about piddling laboratory operations is to betray the great enterprise." The search for more respectable ways of thinking about measurements began early. Since the discovery of special relativity in 1905, physicists had become used to calling them 'observations', and in 1939 London and Bauer [16] were the first to speak of 'the essential role played by the consciousness of the observer'.

Over the years, this red herring has taken many forms. To a few [Wigner], it meant that the mind of the observer actively intervenes in the goings-on in the physical world, to some (e.g. [D'Espagnat]), it meant that science concerns our perceptions rather than the goings-on 'out there', while to most (e.g. [Fuchs, Peres, Petersen, Peierls]), it meant that quantum mechanics concerns knowledge or information about the physical world, rather than the physical world itself.

It is not hard to account for the relative popularity of the slogan 'quantum states are states of knowledge' [Fuchs on decoherence]. The fundamental theory of the physical world is a probability algorithm, and there is a notion that probabilities are inherently subjective. Subjective probabilities are ignorance probabilities: they enter the picture when relevant facts are ignored. Because we lack the information needed to predict on which side a coin will fall, we assign a probability to each possibility. Subjective probabilities disappear when all relevant facts are taken into account (which in many cases is practically impossible).

The notion that probabilities are inherently subjective is a wholly classical idea. The very fact that our fundamental physical theory is a probability algorithm tells us that the probabilities it serves to assign are objective. The existence of objective probabilities (not to be confused with relative frequencies) is due to the fact that even the totality of previous measurement outcomes is insufficient for predicting subsequent measurement outcomes with certainty. The 'uncertainty principle' (the literal meaning of Heisenberg's original term, fuzziness principle, is more to the point), guarantees that, unlike subjective probabilities, quantum mechanical probabilities cannot be made to disappear. If the relevant facts are sufficient to predict a position with certainty, there are no facts that would allow us to predict the corresponding momentum. What matters are facts, not what we can know about them.

("The Pondicherry Interpretation of Quantum Mechanics," p. 173)

Then take a look at our critical comparison of their questions and answers. See "The Mohrhoff-Stapp Debate."

The World According to Quantum Mechanics: Why the Laws of Physics Make Perfect Sense After All (Second Edition Kindle eBook. 2018)

Objective probability and quantum fuzziness 2009 (PDF)

Quantum Mechanics Explained 2006 (PDF)

Pondicherry Interpretation of Quantum Mechanics 2005 (PDF)

This Quantum World - Mohrhoff's website/blog

Mohrhoff's Papers and Presentations

Quantum Theory and the Role of Mind in Nature

The World According to Quantum Mechanics (Or, the 18 Errors of Henry P. Stapp) (Mohrhoff on Stapp)

The 18-Fold Way (Stapp on Mohrhoff)

"Manifesting the Quantum World" (Foundations of Physics, 2014)

"Quantum mechanics in a new light" (Foundations of Science, 2016)

"Niels Bohr, objectivity, and the irreversibility of measurements" (Quantum Studies: Mathematics and Foundations, 2019):