Stapp quotes Mohrhoff (1): "an algorithm for assigning probabilities to the possible results of possible measurements cannot also represent an evolving state of affairs"

Stapp: "But a successful probability algorithm must have a basis in a state of affairs. A theory that provides an explanation of that basis, or at least a rationally coherent possible explanation of that basis, is more satisfactory than just the algorithm alone, because an explanation can point beyond what is currently known. That is why many scientists seek not just algorithms but also explanations and understanding."

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We interpret Mohrhoff as saying that a Dirac superposition of possible states does not describe actual states. The superposition depends on the choice of basis set. By the Wittgensteinian phrase "state of affairs," Mohrhoff means a "fact," citing the dictionary definition - "a thing that is known to have occurred, to exist, or to be true; a datum of experience; an item of verified information; a piece of evidence."

The proper basis for making experimental predictions depends on the "free choice" (Stapp calls it the Heisenberg Choice) of the experimenter as to "which question to ask of Nature" (which experiment to do). And Stapp accepts that the answer that Nature provides is indeterministic, the result of Nature's "Dirac choice," involving the random collapse of the wave function.

Mohrhoff is correct that we must distinguish possibilities, with their probabilities that quantum mechanics helps us to calculate, and the actuality of an ontological fact. Mohrhoff knows that ontological facts are objective and independent of any observer, whereas epistemological facts are subjective and depend on observers.

Mohrhoff: Stapp capitalizes on von Neumann’s formulation and interpretation of QM as a theory of the objective world interacting with human consciousness. The unobserved world evolves according to a dynamical equation such as the Schrödinger equation, while observations cause “a sudden change that brings the objective physical state of a system in line with a subjectively felt psychical reality”. This makes QM “intrinsically a theory of mind–matter interaction,” and more specifically a theory “about the mind–brain connection.”

Stapp quotes Mohrhoff (2.1): "The introduction of consciousness... [is] gratuitous.”

Stapp: The empirical basis of science consists of relationships between our conscious experiences. Thus an essential part of any physical theory is a description of the connection between the mathematical formulas and the conscious experiences that are both their empirical basis and the link to possible applications. For quantum theory, as formulated by its founders, the most profound departure from prior science was the introduction of ‘the observer’ into the theory in a nontrivial way. The founders certainly would have avoided this radical innovation if they had been able to conceive of a satisfactory way to do so. But they could not. The introduction into the theory of the experiences of the observer seemed to be needed to define the ‘facts’ that science had to deal with.

Stapp quotes Mohrhoff (2.5): “If the answer (to the question does physics presuppose conscious observers) is negative for classical physics then it is equally negative for quantum physics.”

Stapp: Our conscious experiences play no dynamical role in classical physics: they enter only as passive witnesses to events that are determined by local physical laws. Whether the same is true in the quantum universe cannot be inferred from analogy to the classical approximation. For there is no analog in the classical approximation to the lack of determination by contemporary laws of quantum theory of which question will be posed, or put to nature. That is, there is in quantum dynamics not only the indeterminateness associated with the familiar stochastic element, but also the need to define, in connection with each actual fact, a particular question that was put to nature. This question is not fixed by the known laws of quantum theory. So this issue of the ontological character of the ‘facts’, and of the process that fixes them, makes quantum physics potentially ontologically different from classical physics: ideas suggested by the classical approximation need not suffice in the real world.

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Stapp is correct that all human knowledge is based on observations (by conscious observers). But this does not mean that the universe is dependent on conscious observers for everything that happens. Many "facts" - the origin of the universe, the origin and evolution of our sun and planets, the beginning of life - were ontological and objective long before human observers made them subjective and epistemological.

No knowledge can be gained by a "conscious observer" unless new information has already been irreversibly recorded in the universe. That information can be created and recorded in either the target quantum system or the measuring apparatus. Only then can it become knowledge in the observer's mind

Stapp quotes Mohrhoff (3.1): “A possibility is not the kind of thing that persists and changes in time.”

Stapp: But a propensity, or disposition [my words] can be a function of time. And the propensities for various events to occur can change when some event occurs: the propensity for an earthquake to occur is higher when an earthquake has very recently occurred. In a universe (or theory) with stochastic elements the notion of time-dependent propensities can make sense.

Stapp quotes Mohrhoff (3.2): “the "third error... is a category mistake. It consists of ... treating possibilities as if they possessed an actuality of their own.”

Stapp: Sir Karl Popper and Werner Heisenberg both recommended treating quantum probabilities as propensities: i.e., as absolutely existing tendencies or ‘potentia’ for quantum (actualization) events to occur. This notion has a long history in philosophy that dates back to Aristotle.

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Stapp is right that possibilities and probabilities change with time. This does not make them actualities. When one possibility becomes actuality, the probabilities for all the other possibilities go instantaneously to zero in all the parts of space where an instant earlier they had definite values. [Note that in quantum mechanics these are complex probability amplitudes with both positive and negative values, allowing them to create interference with themselves.]

Stapp quotes Mohrhoff (4): “the erroneous notion that possibilities are things (“propensities”) that exist and evolve in time.”

Stapp: Within von Neumann’s formulation of quantum theory the quantum probabilities can be consistently interpreted as propensities that exist and evolve in time.

Mohrhoff: It is well known that the statistical regularities with which QM is concerned are consistent with SR, while von Neumann’s interpretation of states as evolving, collapsible states of affairs is not. Stapp tries to reconcile SR with von Neumann’s interpretation by giving “special objective physical status” to a particular family of constant-time hypersurfaces: State reductions occur globally and instantaneously with respect to this family of hypersurfaces. He offers two arguments purporting to support the existence of a “dynamically preferred sequence of instantaneous ‘nows’ ”. The first invokes astronomical data that, incontestably, indicate the existence of a (cosmologically) preferred sequence of “nows.”

Stapp quotes Mohrhoff (5) : “astronomical data...support the existence of a historically preferred family of hypersurfaces, but not of a dynamically preferred one.”

Stapp: The empirically preferred surfaces are generally believed to be created by ‘inflation’, which is a dynamical process.

Stapp quotes Mohrhoff (7): “fallacious... proof of... faster-than-light information transfers of information.”

Stapp: Mohrhoff’s description of my proof bears little resemblance to my proof itself: there is no buttressing: no second proof. There is one concise and rigorous proof.

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There are instantaneous changes in probability amplitudes (wave functions) in nonlocality demonstrations (see EPR). But there is no physical transfer of material or energy when wave functions collapse. Only abstract information changes (see collapse of the wave function). Mohrhoff: According to Stapp, granting free will to experimenters leads to a physical reality inconsistent with the “block universe” of special relativity (SR), a reality that unfolds in response to choices. This is one (ε₈) of a cluster of misconceptions arising from the erroneous notion that the experiential now, and the temporal distinctions that we base on it, have anything to do with the physical world (ε₉). Objectively, the past, the present, and the future exist in exactly the same atemporal sense. There is no such thing as “an evolving objective physical world” (ε₁₀), and there is no such thing as an objectively open future or an objectively closed past (ε₁₁). The results of performed measurements are always “fixed and settled.” What is objectively open is the results of unperformed measurements.

Stapp quotes Mohrhoff (8.1): “granting free will to experimenters” does not lead “to a physical reality inconsistent with the ‘block universe’ of SR.

Stapp: By free will I mean the freedom to will ourselves to act ‘now’ either in some particular way, or not in that way. The existence of freedom in this sense is incompatible with the ‘block universe’ of SR, which says that the whole universe is laid out for all time in the way that SR (classical special relativity theory) ordains, i.e., such that given the physical state of the universe for very earlier times there is no possibility of choosing now to act in some way or to not act in that way. But the laws of quantum mechanics, being dynamically incomplete, do not entail a block universe in the way that the deterministic and complete laws of SR do. The generally accepted application of the requirements of the theory of relativity to quantum theory is to its predictions: they must conform to the no-faster-than-light requirements of the theory of relativity. This is exemplified by Tomonaga-Schwinger relativistic quantum field theory, which is completely compatible with instantaneous collapses along spacelike surfaces, and in fact demands such collapse to the extent that one accepts the existence of von Neumann’s Process I. The laws of quantum theory lack the coercive quality of the classical laws that entail the block universe.

Stapp quotes Mohrhoff (8.2): ”if the possibility of foreknowledge does not exist,..I can actually be a free agent.”

Stapp: Not in the sense that I have described, in a universe in which the deterministic laws of SR hold. For being free in that sense means being free to act in either one of two different ways in a universe with a given fixed past. No such freedom exists in a universe that obeys the deterministic laws of special relativity. What the person knows, or does not know, is not pertinent to that conclusion.

Stapp quotes Mohrhoff (8.3): “The fact that the future in a sense ‘already’ exists is no reason why choices made at an earlier time cannot be partially responsible for it.”

Stapp: The ‘choices’ actually made at an earlier time can certainly be partially responsible for what happens later. But in a world that conforms to the deterministic laws of classical of SR, and with a fixed early universe, that ‘choice’ made at the earlier time is not ‘free’: it could not go in either one of two different ways. “Freedom”, in this sense is not compatible with the block universe of SR, but it is compatible with von Neumann quantum theory, due to the indeterminacy within that theory of which question will be put to nature.

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Mohrhoff and Stapp appear to be talking at cross purposes here? Mohrhoff: Causality, as Hume discovered two and a half centuries ago, lies in the eye of the beholder. While classical physics permits the anthropomorphic projection of causality into the physical world with some measure of consistency, quantum physics does not. Trying to causally explain the quantum-mechanical correlations is putting the cart in front of the horse. It is the correlations that explain why causal explanations work to the extent they do. Stapp’s attempt to involve causality at a more fundamental level (ε₁₂) depends crucially on his erroneous view that the factual basis on which quantum-mechanical probabilities are to be assigned is determined by Nature rather than by us (ε₁₃).

Stapp quotes Mohrhoff (12): The “attempt to involve causality at a more fundamental level” is an error. “While classical physics permits the anthropomorphic projection of causality into the physical world with some measure of consistency quantum physics does not.”

Stapp: I am not projecting the intuition of the causal power of our thoughts into the world to explain the deterministic aspect of nature associated with the Schroedinger equation. I am concerned rather with explaining how our thoughts themselves can be causally efficacious. The mathematical fact is that the quantum laws allow this, by virtue of the indeterminacy associated with von Neumann’s Process I, (The freedom of choice in which question to pose — i.e., the basis problem) whereas the classical laws do not provide or allow an analogous causal efficacy. In classical theory the future is determined by the past by LOCAL laws, whereas in quantum theory a present choice of which question to pose is not determined by the local laws of contemporary physics.

Stapp quotes Mohrhoff (13): “Error 12 depends crucially upon ...[the] erronous view that the factual basis on which quantum probabilities are to be assigned is determined by Nature rather than by us.”

Stapp: One of my very chief points is that quantum theory is incomplete because the equations of quantum theory do not specify which question is put to Nature, i.e., which apparatus is put in place, which ‘basis’ is used to determine a ‘fact’. That role is given to us, the observer/participants, by Copenhagen quantum theory. In von Neumann’s formulation this choice is bound up in the psycho-physical event specified by Process I. That this freedom of choice of basis, is given to “us”, is the key point that I exploit to explain how mental effort can influence brain activity. Mohrhoff and I seem to be in basic agreement on this essential point.

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So Stapp does not in fact take the "opposite" position from Mohrhoff on everything. What Stapp sometimes calls the "Heisenberg Choice" is a free act. (Von Neumann's Process 1, which Stapp calls the "Dirac Choice," the choice made by Nature, is indeterminate.) It is not clear that either Stapp or Mohrhoff see clearly how - first - quantum indeterminism, then - second - an "adequate" determinism combine to make human freedom possible. Mohrhoff: Stapp’s account of mental causation, and a number of further errors (not all enumerated) are pointed out, such as: The objective brain can (sometimes) be described as a decoherent mixture of “classically described brains” all of which must be regarded as real (ε₁₆).Crucial to Stapp’s account is the metaphor of the experimenter as interrogator of Nature. Within the Copenhagen framework, which accords a special status to measuring instruments, this is a fitting metaphor for a well-defined scenario. In Stapp’s framework, which accords a special status to the neural correlates of mental states, it is not (ε₁₇). Its sole purpose is to gloss over the disparity between physical experimentation and psychological attention. Once this purpose is achieved, the metaphor is discarded, for in the end Nature not only provides the answers but also asks the questions. The theory Stapp ends up formulating is completely different from the theory he initially professes to formulate (ε₁₈), for in the beginning consciousness is responsible for state vector reductions, while in the end a new physical law is responsible, a law that in no wise depends on the presence of consciousness.

Stapp quotes Mohrhoff (15): “freedom to choose is a classical phenomenon.”

Stapp: Mohrhoff’s argument is based on his idea that mental choice and effort must be coercive, rather than dispositional. But quantum theory allows dispositional causes. And within classical physical theory there is no possibility of freedom of the kind that I have described above. But von Neumann quantum theory does allow that sort of freedom.

Stapp quotes Mohrhoff (16): It is erroneous to claim that “The objective brain can (sometimes) be described as a decoherent statistical mixture of ‘classically described brains’ all of which must be regarded as real.”

Stapp: By the objective brain I mean the quantum state defined by taking the trace of the state (density matrix) of the universe over all variables other than those that characterize the brain, and my claim is merely that interaction with the environment converts this state to a form that can be roughly described as a mixture of states each of which approximates a classical state of the brain, in the sense that in the position-bases the states are approximately localized. This mixture includes ALL of these states, not just one of them, or some small subset that are all observationally indistinguishable. There is therefore the problem of relating this state to observation. This is achieved, within the von Neumann formulation, by a psycho-physical event described by Process I. This approach can be described as taking the mathematics of quantum theory to give valid information about the structure of reality, and making our idea of nature, and the facts that define it, conform as closely as possible to that mathematical description.

Stapp quotes Mohrhoff (17): “The metaphor of experimenter as interrogator of Nature [is fitting] within the Copenhagen framework, which accords special status to measuring instruments, [but is not fitting] in Stapp’s scenario, which accords special status to neural correlates of mental states.”

Stapp: In the Copenhagen interpretation ‘the measuring instruments and the participant/observer’ stand outside the system that is described by the quantum mathematics, and they are probing some property of a ‘measured system’, which is part of an imbedding quantum universe. In the von Neumann formulation the role of ‘the measuring instruments and the participant/ observer’ is transferred to the ’abstract ego’, and the measured system whose properties are being probed is the brain of the observer.

The need for the outside ‘observer’, which includes the measuring devices, is to specify a definite question, which is represented by a projection operator P acting on the state of the ‘measured system’, even though nothing about that system itself— or even the whole of the quantum-described universe— defines that particular operator P, or specifies when that question is ‘put to Nature.’

A key technical question now arises: To what extent does the natural Schroedinger evolution of the brain, abetted by the Environment-Induced- Decoherence (EID), already decompose the quantum state of the brain into orthogonal branches that correspond to distinguishable ‘facts’? The EID tends to create ‘coherent states’, which have exponential tails, and are not mutually orthogonal. In fact, it is impossible in principle for a Schroedinger evolution to define the projection operators P that are needed in the von Neumann formulas. That fact is undoubtedly why von Neumann introduced his Process I as a basic process not derivable from the Schroedinger Process II. There is no way to get the needed projection operators out of Process II. A projection operator defines, and is defined by, a subspace. That means that the definition of a projection operator P must distinguish every vector in the subspace from vectors that lie outside that subspace and differ from that vector by infinitesimal amounts. The Schroedinger evolution of an isolated system could define and preserve energy eigenstates, but there is no way that the Schroedinger evolution of a brain interacting with its environment could specify subspaces associated with experientially distinct facts without some extra rule or process not specified by the Schroedinger Process II itself. This fact is the technical basis of von Neumann’s theory. It is this need for some outside process to fix the content of the facts, and their times of coming into being, that opens the door to the efficacy of experience.

Stapp quotes Mohrhoff (17.1): “The questions the mind can put to the brain, by choosing where to fix its attention, are always compatible, for the mind does not have to choose between incompatible experimental arrangements.”

Stapp: But it does have to define an operator P, or, equivalently, a subspace of the Hilbert space associated with the brain, and this subspace is not specified by the prior (quantum) state of the brain or the universe.

Stapp quotes Mohrhoff (17.2): “If attention is drawn to the highest bidder, the highest bidder is not a component of a mixture of CDBs (Classically Described Brains), but one among several neural events or activities competing for attention in one and the same CDB.”

Stapp: The various CDBs are overlapping (non-orthogonal), and the function of Process I is to pick out of this amorphous mass of possible states some well defined subspace associated with a distinct experience. Our ruminations about possible choices can run over various consciously experienced possibilities, but each such experience is associated with a selection of a subspace from the amorphous collection of overlapping possibilities that constitutes the state of the brain at that moment. The Schroedinger Process II cannot by itself unambiguously decompose the state of the brain into well defined orthogonal branches corresponding to distinct CDBs. [Note that Stapp now calls von Neumann Process II the Schrödinger process.]

Mohrhoff: Stapp presents a simple dynamical model of mind– brain interaction in which “the ‘best possible’ question that could be asked by the individual at time t,” given the state S(t) of the universe at this time, is the question P_max that maximizes Tr[PS(t)]. This question is posed when the probability of a positive answer reaches a relative maximum.

Here Stapp introduces a new physical law, specifying which question Nature will ask herself next and when she will do so. Stapp thus effectively proposes a new theory, as different from standard QM as nonlinear adulterations of QM. The theory which he ends up formulating is completely different from the theory he initially professes to formulate, for in the beginning consciousness is responsible for state vector reductions, while in the end a new physical law is responsible — a law that in no wise depends on the presence of consciousness.

Thus in the end Stapp, like Eccles, fails to account for mental causation without implying “violations” of the laws of contemporary physics. Eccles did not introduce a new physical law, but he allowed the mind to load the quantum dice in the process of exocytosis, and this is tantamount to postulating mentally generated local modifications of physical laws . Stapp introduces a new physical law specifying which questions Nature asks herself, and when, and he allows the mind to modify the rates at which Nature interrogates herself. This, too, is tantamount to postulating mentally generated local modifications of a physical law — the very law Stapp himself has introduced.

Stapp quotes Mohrhoff (18): “The theory Stapp ends up formulating is completely different from the theory that he initially professes to formulate, for in the beginning consciousness is responsible for state vector reduction, whereas in the end a new physical law is responsible, a law that in no wise depends on consciousness.”

Stapp: That example is not my final theory. It was put forward as a simple model to show how one could, within the general von Neumann framework that I have developed, produce a dynamically complete theory. It does this by postulating a new law that resolves in a certain definite way the dynamical freedom that I have used to make consciousness efficacious.

Mohrhoff suggests that this model violates the quantum laws, but that is not true: the extra postulated law controls which questions are asked, and when they are asked, and these are precisely the elements that are not controlled by the standard quantum laws, and whose indeterminacy, with respect to those laws, provides the opening for efficacious minds within contemporary basic physical theory.

The key issue is whether consciousness itself enters the dynamics. This devolves to the question: What is the ontological source or basis of the coercive quality of the laws of nature?

My answer is that with respect to the local dynamical process governed by the Schroedinger equation this question is not worth pursuing: it is the existence of that mechanical law that matters to us, and inquiry into what gives that law its coercive quality is unduly speculative. But the same question is far from meaningless in connection with the collapse process that is associated with a human conscious experience. This is because the experiences associated with these collapses are known to us, and are in fact the only things really known to us. Thus they are proper elements of science, and are, in fact, the basis of science.

I have thus emphasized that the resetting (of the state of the brain) associated with a conscious human experience is mathematically and dynamically different from the local mechanical (Schroedinger) process, and I now suggest that the coerciveness of the laws that govern the creation of a stream of consciousness comes in part from the experiences that constitute that stream: that the experiential realities are actually doing something that is not done by the local mechanical laws. Why else would they exist?

Thus I have noted that some process beyond the local mechanical process described by the Schroedinger equation is needed to complete basic contemporary physical theory, and tie it to the empirical facts, and I am suggesting that the conscious experiences that emerge in this process are essential causal elements of a nonlocal evaluative process that is needed to complete the quantum dynamics.

In summary, local mechanical process alone is logically incapable picking the question (choosing the basis) and fixing the timings of the events in the quantum universe. So there is no rational reason to claim that the experiential reality that constitutes a stream of consciousness is not a causal aspect of the dynamical process that prolongs or extends this reality, yet lies beyond what the local quantum mechanical process is logically able to do.

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What Stapp's argument comes down to is that Nature alone can never choose a basis set on its own. This he reserves to the power of conscious observers who can exercise their free (Heisenberg) choices.

Henry Stapp has been generous in answering Mohrhoff's biting criticism with a fine sense of humor. He takes Mohrhoff's 18 error claims as generating a Buddhist "18-fold way" which result in 18 questions with 18 possible right (Yes/No) answers. Stapp worries that he has only one chance in 250,000 of getting the answers all right (2^-18).

These long odds (probabilities) might be the case if

1. we see Mohrhoff as exercising his free (Heisenberg) choice of the questions to put to Stapp (Nature), and

2. we see Stapp using a random Dirac choice to provide the answers instead of his own free will and reasoning powers!

But these are two intelligent scientists, and we hope that Stapp is right that each answer will add one bit of information to our quantum universe that helps us explicate the role of quantum physics in mental causation.

We can look forward to the Stapp-Mohrhoff discussions at the June 2013 conference in Milan "Quantum Physics Meets the Philosophy of Mind."

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