%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% On the Work of Henry P. Stapp. %%% quant-ph/0311158 %%% November 2003 %%% %%% %%% Plain TeX, 14 pages %%% %%% Matthew J. Donald %%% %%% web site: http://people.bss.phy.cam.ac.uk/~mjd1014 %%% %%% e-mail : mjd1014@cam.ac.uk %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\count17=0 %%to use pdfTeX comment out this line and uncomment the next \count17=1 \pdfoutput=\count17 %%to use plain TeX comment out this line %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% and uncomment the previous %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \ifnum\count17=1 \def\cmykBlue{1 1 0 0} \def\cmykBlack{0 0 0 1} \def\Blue{\pdfsetcolor{\cmykBlue}} \def\Black{\pdfsetcolor{\cmykBlack}} \def\pdfsetcolor#1{\pdfliteral{#1 k}} \def\setcolor#1{\mark{#1}\pdfsetcolor{#1}} \def\maincolor{\cmykBlack} \pdfsetcolor{\maincolor} \pdfinfo { /Title (On the Work of Henry P. Stapp.) /Author (Matthew J. Donald) /CreationDate (November 2003) /ModDate (\number\year/\number\month/\number\day) /Subject (mind and interpretation of quantum theory.) /Keywords (quantum theory, mind, brain)} \pdfcompresslevel=9 \fi \magnification=1200 \hsize=13cm \def\newline{\hfil\break} \def\newpage{\vfil\eject} \def\proclaim#1#2{\medskip\noindent{\bf #1}\quad \begingroup #2} \def\endproclaim{\endgroup\medskip} \def\tr{{\rm tr}} \def\parasign{\S} \def\dsize{\displaystyle} \abovedisplayskip=3pt plus 1pt minus 1pt \belowdisplayskip=3pt plus 1pt minus 1pt \def\hcrh{\hfill \cr \hfill} \def\crh{\cr \hfill} \def\hcr{\hfill \cr} \font\brm=cmbx12 \def\tilbf{\lower 1.1 ex\hbox{\brm \char'176}} \font\trm=cmr12 \def\tilrm{\lower 1.1 ex\hbox{\trm \char'176}} \topskip10pt plus40pt \clubpenalty=30 \ifnum\count17=1 \def\link#1#2{\leavevmode\pdfstartlink attr{/Border [0 0 0]} goto name{#1}\setcolor\cmykBlue #2\pdfendlink\setcolor\cmykBlack} \def\name#1{\pdfdest name{#1} xyz} \def\outlink#1#2{\leavevmode \pdfstartlink attr{/Border [0 0 0]} user{/Subtype /Link /A << /S /URI /URI (#1) >>} \setcolor\cmykBlue #2\pdfendlink\setcolor\cmykBlack} \def\pdfeject{\eject} \else \def\link#1#2{{#2}} \def\outlink#1#2{{#2}} \def\name#1{} \def\pdfeject{} \fi \headline={\hfil} \footline={\hss\tenrm\folio\hss} {\bf \centerline{\ \ On the Work of Henry P. Stapp. \link{*}{*}\footnote{}{\tenrm * \outlink{http://arXiv.org/abs/quant-ph/0311158}{quant-ph/0311158}, November 2003.}} \medskip \centerline{Matthew J. Donald} \medskip \centerline{The Cavendish Laboratory, JJ Thomson Avenue,} \centerline{Cambridge CB3 0HE, Great Britain.} \smallskip \centerline{ e-mail: \quad mjd1014@cam.ac.uk} \smallskip {\bf \hfill web site:\quad \catcode`\~=12 \outlink{http://people.bss.phy.cam.ac.uk/~mjd1014} {http://people.bss.phy.cam.ac.uk/\tilbf mjd1014} \hfill }} \medskip For many years, Henry Stapp and I have been working separately and independently on mind-centered interpretations of quantum theory. In this review, I discuss his work and contrast it with my own. There is much that we agree on, both in the broad problems we have addressed and in some of the specific details of our analyses of neural physics, but ultimately we disagree fundamentally in our views on mind, matter, and quantum mechanics. In particular, I discuss our contrasting opinions about the nature and randomness of quantum events, about relativity theory, and about the many-minds idea. I also suggest that Stapp's theories are inadequately developed. The theoretical analysis of the idea that there might be a link between quantum mechanics and consciousness begins with the famous book by \link{rffour}{von Neumann (1932)}. von Neumann proposed a mathematical formalism according to which there were two distinct ways in which a quantum system could change with time. On the one hand, there were abrupt indeterministic ``quantum events'' due to ``measurement'', in which, with appropriate probability, one of the possible results of the measurement appears. On the other hand, for isolated and unmeasured systems, there was just the continuous deterministic change described by the Schr\"odinger equation. This proposed duality in dynamics immediately raises the question of what distinguishes ``measurements'' from other physical processes. von Neumann argued that measurement involved a chain of physical processes in which the physical system to be measured interacts with a physical measuring device, which ultimately interacts with light, which in turn interacts with the eye of an observer. Eventually information is carried to the brain of the observer. This suggests the possibility that it is only when that information becomes conscious that something has occurred which can make ``measurement'' different in kind from any other physical process. Stapp and I have both attempted to investigate this possibility by proposing theoretical \name{*}analyses to make sense of our conscious observations of the world in the light of the evidence for quantum theory. We have both tried to understand the duality of quantum events and the Schr\"odinger equation. We both agree that brain processes are fundamentally decoherent and that brain states should be analysed as mixtures of essentially classical states (\link{ref}{Donald 1990}, \link{rftwo}{1992}, \link{rffive}{Stapp 2000a, 2000b}). We have both noted the extent to which brains are unstable and unpredictable dynamical systems (\link{ref}{Donald 1990}, \link{rftwo}{2002}, \link{rffive}{Stapp 1993 chapter 6}, \link{rffive}{1999 Appendix A}). Both of us argue that neural uncertainties are ultimately ``quantum'' in origin. This leads both of us to stress the multiplicity of quantum events which must be ``decided'', or of ``choices'' or ``measurements'' which must be ``made'', at every moment in normal brain functioning. Beyond these basic agreements, there are however very significant differences in our proposals. According to my analysis, the abrupt indeterministic quantum events are not physical occurences in a conventional observer-independent sense. They correspond rather to the steps in the development of the mental structures of individual observers. My aim has been to provide an explicit abstract characterization of the structure of an observer and to argue that human beings can be described as possessing such structures. These structures are based on the idea of a temporal pattern of elementary abstract quantum events which I call ``switchings'' (``determinations'' in \link{rftwo}{Donald 1999}). I propose that there are no other quantum events. Thus, in my proposal, the problem of the characterization of consciousness and the problem of the interpretation of quantum theory are both solved together. \link{rffive}{Stapp (1993, \S 6.7.4)}, by contrast, proposes that quantum events are physical and occur in inanimate objects as well as in the brains of observers. This means that he encumbers himself with the necessity of providing a characterization of the inanimate occurences of the events if he is to complete his interpretation. Were he to succeed in doing this, he would already have managed to solve what is often seen as the central problem in the interpretation of quantum theory, and his comments on consciousness would seem to many (although not to me) to be extraneous. Stapp and I also disagree at a fundamental level about the randomness of quantum events. In \link{rffive}{Stapp (1993, \S 7.6)}, for example, he writes that, ``it is an absurdity to believe that the quantum choices can appear simply randomly `out of the blue', on the basis of absolutely nothing at all.'' Presumably because he believes that reality is not absurd, Stapp uses this first claim to argue that consciousness intervenes in quantum events to influence outcomes. This second claim is bold, but in \link{rfsix}{Stapp (2001a)}, he moves toward the even bolder third claim, which he attributes to both Copenhagen and von Neumann quantum theory, that ``the choice of which question will be put to nature, is not controlled by any rules that are known or understood within contemporary physics''. Again, in \link{rffive}{Stapp (2000b)}, he writes ``there is one element that [is] not governed by any known law of physics, namely the choices to consent or not consent at time $t$ to putting to nature the question associated with the possible experience $E(t)$''. As far as the first claim is concerned, it is hard to avoid the idea that in physics ultimately everything just does appear ``out of the blue''. In classical mechanics, for example, physics does not explain the initial conditions, but merely provides the laws by which those initial conditions develop. One of the attractions of a many-minds approach, in my opinion, is that it allows us to avoid the ``absurdity'' of requiring the entire observed future to be encoded into the initial state of the universe. Instead, as I discuss in section 9 of \link{rftwo}{Donald (1999)}, it is possible to suppose that the initial state of the universe is a simple state -- perhaps even a vacuum state in the ultimate theory of everything -- and to suppose that all the remaining information which constructs our apparent individual reality is individually-observed information. This information is determined in our personal observations of the genuinely-random, ``out of the blue'', outcomes of the quantum events which make up our mental structures. Stapp's second and third claims would seem to suppose that consciousness is an extra-physical actor; directing physical dynamics by making choices. I find Stapp's position on this issue rather confusing. In section 6.7.2 of \link{rffive}{Stapp (1993)}, he rejects the somewhat similiar proposals of \link{rftwo}{Eccles (1986)} as being explicitly dualistic and introducing a ``homunculus''. The proposals of \link{rfseven}{Walker (2000)} are also similar, and I have criticized them on the same grounds in \link{rftwo}{Donald (2001b)}. So Stapp and I apparently agree that it is essential to avoid the idea of a little man inside the brain directing the brain's thinking. However the lesson of modern neurophysiology seems to me to be that everything we experience is directly reflected in the functioning and structure of our nervous system. Here ``everything we experience'' includes not only our thoughts and feelings, but also our thoughts about our thoughts. According to this neurophysiological hypothesis, every human thought and action, including choices, decisions, and self-analysis, can be explained in terms of the functioning of the evolved physical brain. One day, I choose to take dessert because the firing from my appetite centers dominates the firing from my prefrontal cortex and I say, ``I'll have the chocolate mousse, please'', rather than, ``Nothing for me, thank you''. Another day, I will myself to abstain, because I have been sufficiently disturbed by not being able to get my old trousers to fasten, that thoughts of consequences outweigh thoughts of pleasure. The ability of a brain to talk about and apparently to decide its own behaviour is not paradoxical, because it is limited, and because of the parallel and modular structure of neural processing. It is easy to understand why such an ability should have evolved because it allows efficient analysis, planning, and communication. Stapp and I seem to agree that the evolved physical brain, as studied by neurophysiologists, is not a deterministic machine. Stapp proposes that aspects of the random events which affect the path of the machine can be chosen. Yet, in \link{rffive}{Stapp (2000b)}, he writes, ``I do not intend to speculate at this point about how the evaluation that lies behind this choice is carried out. At the present early stage in the development of the science of the mind-brain system that question remains a project for future research.'' If he is not simply invoking an extra-physical homunculus at this point, however then at least we can ask whether choices are supposed to be made using conventional neural circuitry -- in which case, it is certainly not clear to me where the requisite circuitry is supposed to be -- or whether some other type of physical process is supposed to be involved. The events which initiate randomness in the brain include quantum spreading in the paths of calcium ions (\link{rffive}{Stapp 1999}). Clearly there is no neural circuitry which is capable of analysing those paths directly. Instead, Stapp's suggestion, at least in his earlier papers, seems to be that the brain state becomes a superposition or mixture of different developing possibilities until consciousness is reached, a choice occurs, and the possibilities are reduced to a single outcome. The trouble with this idea is that the state becomes a mixture of different neural firing patterns rather than a neural firing pattern analysing a mixture. The self-analysis of such a mixture would require not just an entirely new type of neurophysiology, but an entirely new type of physics. \proclaim{example}{} Suppose, as a result of quantum spreading, that in one branch of the total quantum state of a brain the initiation of a single neural firing is delayed, compared to another branch, by a mere $10^{-5}$s relative to some other neural firing. Because of the metastability of neural firing, even a delay as short as this, on the millisecond firing timescale, could be long enough to trigger radical changes in the ultimate outcome of the developing neural response. Yet $10^{-5}$s is macroscopic on the picosecond timescale of molecular vibrations in the warm wet brain. This means that just this initial difference is sufficient to make these branches of the total state almost instantly become mutually decoherent. They can then be assigned their own separate density-matrix quantum states, which we shall denote by $\rho_1$ and $\rho_2$. So, in this situation, the relevant part of the total state, by the time the firing patterns have developed sufficiently for a choice between the outcomes to be possible in conventional terms, will be a mixture of approximate form $\rho = p_1 \rho_1 + p_2 \rho_2$ where $p_1$ and $p_2$ are the conventional probabilities of the two possibilities. The notation here supresses important dependencies. In non-relativistic quantum mechanics, which is sufficient for our present purposes, $\rho$ depends on time and on a choice of the space of operators considered relevant to the situation, while in relativistic quantum field theory the time will itself be specified by the space of operators. However, at any time on the conventionally-recognised timescale of conscious processing and for any space of operators localized within the brain of the individual considered, $\rho$ will have a decoherent decomposition of the suggested form. It follows that no conventional physical process within the brain will be able to cause a (generalized) ``collapse'' from $\rho$ to either $\rho_1$ or $\rho_2$. Because of decoherence, $\rho_1$ and $\rho_2$ have become dynamically independent. The splitting into decoherent states is a locally irreversible process due to the dissipation of information. \endproclaim In his earlier papers (\link{rffive}{1982}, \link{rffive}{1993 chapter 6, 1995}), Stapp seems to suggest that somehow the structure of $\rho$, or possibly of $\rho_1$ or $\rho_2$, directs the collapse. How this is supposed to work is not explained. In his later papers (\link{rffive}{1999, 2000a,} \link{rfsix}{2001a}), Stapp suggests the quantum Zeno process as the mechanism. This suggestion has been picked up by Jeffrey M. Schwartz (\link{rffour}{Schwartz and Begley 2002}). In his treatment of obsessive-compulsive disorder patients, Schwartz appeals to Stapp's work, along with the Buddhist concept of mindfulness, to argue for the reality of free will. Nothing I say here should be taken as a criticism of Schwartz's plausible and apparently-successful treatment, which involves patients learning to challenge their intrusive thoughts. Nor do I criticize the wealth of interesting evidence reviewed by Schwartz and Begley about the possibility, throughout life, of quite large-scale changes in neural connectivity. This evidence allows them to justify a strong form of the conclusion that, ``it is the life we lead that creates the brain we have''. I only disagree with the framework which Schwartz uses to explain the meaning of challenging one's own thoughts. \link{rfthree}{Johnjoe McFadden (2000)} has independently invoked the quantum Zeno effect in an attempt to solve problems in biological science. In \link{rftwo}{Donald (2001a)}, I criticise McFadden's work on the grounds that, in as far as the Zeno effect (or ``inverse Zeno effect'' to use McFadden's language) is a physical effect, it can occur only in very carefully established circumstances, precisely set up in order to achieve a given end. Suppose, in the notation of the example above, that $\rho_2$ represents the outcome which is to be chosen. Then, as I explain in \link{rftwo}{Donald (2001a)}, the Zeno effect does provide a dynamics formed using a sequence of carefully chosen projections, corresponding to von Neumann's quantum events, which, with probability one, will drive the total state towards the state $\rho_2$. That dynamics, however, is not the well-understood biologically-evolved dynamics produced by the interactions of the ions and atoms and molecules and electric fields of the human brain. It is a purely theoretical dynamics which depends on working towards the desired outcome right from the start of the initial quantum spreading. How and when the choice is supposed to result in the construction and action of the projection operators still has to be explained. The projections need to be defined to the precision of an individual wavefunction. Above atomic scales, no biological mechanism can control or even repeat states at this level of precision. If we want to observe the quantum Zeno effect in the laboratory, then we need to build an apparatus (e.g.~\link{rfthree}{Itano et al.\ 1990}). Using von Neumann's idea of ``measurement'' as a chain of physical processes, it would seem that such a physical apparatus will itself have a dynamics which can be understood in terms of the conventional laws of physics described by the Schr\"odinger equation, and which can be used to explain the observed effects. Models of this type are discussed in chapter 8 of \link{rfthree}{Namiki, Pascazio, and Nakazato (1997)}, in section 3.3.1 of \link{rfthree}{Giulini et al.~(1996)}, and in \link{rfthree}{Gurvitz (2002)}. According to this picture, Stapp needs to tell us what apparatus biology has built into our brains which allows us to use the quantum Zeno effect to make choices. Otherwise, he would seem to be supposing that brains are somehow physically special and that, for some reason, they cannot themselves be analysed by external observers. He would have invented a homunculus with access to a space of projection operators defined on an atomic scale. How is that homunculus supposed to choose which projection he wants to employ next? How does he control individual wavefunctions or the projections which correspond to them? von Neumann's abrupt changes seem to require the choice of a question; the choice of what is to be measured. At the heart of Stapp's work is the idea that making that choice is what consciousness does. However, I believe that when we make a choice we are doing mental work involving ordinary physical neural processing; just as when we express a question in words we use the linguistic mechanisms which are available in our brains as a result of the life we have led. In my opinion, despite the interesting ideas of William James (\link{rffive}{Stapp 1993}) and Harold Pashler (\link{rfsix}{Stapp 2001a}), neurophysiology is more fundamental than psychology. My basic objection to Stapp's work is that he does not appear to have made any connection between the representation of choices by physical neural processing -- or indeed any other cellular process -- and their representation as projection operators to be measured. Only for an extra-physical homunculus, does the consideration of a choice not involve physical operations. And however the choices are made, the ultimate purpose of choosing must lie in the physical consequences of the choice; in other words in the change in the global quantum state. Stapp has not explained how he supposes such changes are limited. Why should they be restricted to changes within a brain? If mental forces can effectively decide the trajectories of atoms or molecules inside a brain, why can they not decide the trajectories of electrons in a laboratory or of prey in the ocean? What determined the point in evolutionary history when brains are supposed to have started to be able to make choices? And finally, even if we do suppose that mind is some sort of extra-physical homunculus, we have only managed to introduce a new mystery. If there is a problem of free will, then it will still be there if we can ever get to the point of analysing the operations of the homunculus. As I see it, the central problem of the interpretation of quantum theory is to explain and characterize the existence, or apparent existence, of ``quantum events'', or, in other words, of the process referred to as state ``collapse'', or ``wave-packet reduction'', or ``von Neumann's process 1''. How is it, for example, that an electron, despite going through a double slit as an extended wave, always appears to make a well-localized impact on a screen at only one of many possible places, so that the extended wave apparently ``collapses'' to a localized state? A characterization of collapse should tell us what possibilities arise -- this is ``the preferred basis problem''. The characterization should be well-defined and unambiguous. It should be explained how one collapse leads on to the next and the probability of a given collapse should also be well-defined. With such a theory, it will no longer be possible to invoke the quantum Zeno effect as a clever trick by which arbitrary sequences of collapses can be used to attain any desired outcome. Instead, there will be specific circumstances in which the effect, or the appearance of the effect, will arise as a consequence of the specific collapses which actually occur, or which appear to occur. Just as one of the most fundamental questions in the philosophy of mind is whether mental events are merely how neurophysiological events appear, so one of the most fundamental questions in the philosophy of quantum theory is whether von Neumann's indeterministic events are merely how the continuous changes appear in specific circumstances. My starting point is to answer both questions affirmatively, and therefore I have tried to develop a theory characterizing ``appearance''. Stapp certainly answers the second negatively and therefore owes us an analysis of quantum events. He is ambiguous about the first. In \link{rffive}{Stapp (1993 \S 7.5)}, he claims that there is, ``An isomorphic connection [\ ] between the structural forms of conscious thoughts, as described by psychologists, and corresponding actualized structural forms in the neurological patterns of brain activity, as suggested by brain scientists.'' On the other hand, on the same page, he claims to have provided for, ``A mechanical explanation of the efficacy of conscious thoughts''. I have no idea to what this is supposed to refer. In \link{rffive}{Stapp (1993 \S 1.10)}, Stapp states that his theory ``makes consciousness causally effective, yet it is fully compatible with all known laws of physics, including the law of conservation of energy.'' Stapp does not justify this statement. In general, energy is not conserved in individual quantum jumps. Average total energy may be conserved if the projections involved commute with the global Hamiltonian. Leaving aside the commutation question, however, this would require that ``causal effectiveness'' produces the same averages as conventional quantum probabilities. In \link{rffive}{Stapp (1995)}, Stapp admits that, ``No attempt is made here to show that the quantum statistical laws will hold for the aspects of the brain's internal dynamics controlled by conscious thoughts''. While it may be appropriate, as he suggests in the same paper, to make an assumption of ignorance about the external causes of external events, it would be absurd to suppose that conscious thoughts can be efficacious but without external consequences. The suggestion mentioned above that the initial state of the universe might be a vacuum state is certainly not compatible with the idea that energy is conserved (or appears to be conserved) in individual quantum events (or observed events). Stapp suggests that state collapse is driven by conscious choice, but does not explain what conscious choice involves. \link{rfthree}{Ulrich Mohrhoff (2001)} criticizes Stapp's work and is replied to by \link{rfsix}{Stapp (2001b)}. In my opinion, Mohrhoff's proposals are at least as weak as Stapp's. Mohrhoff agrees with Stapp that, ``the choice of which question will be put to nature \dots is not governed by the physical laws of contemporary physics'', but he bases his analysis of quantum events on the idea of the existence of definite ``facts'' and he explicitly denies that ``facts'' can be characterized. In my own work, I have attempted to give an {\it abstract\/} characterization of ``facts''. Thus, instead of trying to define a particular set of projection operators giving rise to the observed collapses, I have defined an abstract pattern of projection operators which is capable of expressing the observed information. Such a pattern can be constituted by many possible sets of projections, and the entire set of these sets for a given pattern is central to the definitions I provide. By working at a high level of abstraction in this way, it is possible to avoid much arbitrariness in the definitions. I propose that each of us exists as an individual developing pattern of information. The development is stochastic, with probabilities defined by quantum mechanical laws. According to these laws, the experience of each individual observer is the experience of observing a particular, identified, discrete stochastic process. While I work at a high level of abstraction, I work with simple elements. In other words, I have built up patterns of information using projections considered as yes-no questions. This is speculation. It is just a hypothesis that information in the brain is constituted as a pattern of yes-no questions. Making a specific hypothesis, however, does allow specific technical questions to be addressed and allows a theory to be developed and its defects to be revealed. My theory is a many-minds theory. This means that each of us has our own pattern of observed ``quantum events''. Consistency between mutually-aware observers is a consequence of the nature of quantum probability. My theory is dualistic in the sense that there are physical laws and there are observers, but there are no mental computations without observable physical structure. My theory is epiphenomenalistic in the sense that a mind does not direct a pattern of observed physical events, rather it has to make sense of such a pattern as it unfolds. Ultimately, however, my theory should probably be considered as idealistic because, in its final form, the central structures in the theory are mental structures. Physics just supplies the probabilities by which those mental structures change. Mental structures give meaning to their realities by understanding themselves in terms of observable physical structures and observed physical events. I propose that, with an appropriate definition of mental structure, the nature of quantum probability will make it likely that if awareness is attained, it will understand itself in such terms. The centrality of mind allows the often-asked question of how an epiphenomenal consciousness could have evolved, to be side-stepped. Instead, I suggest that we should look for the most likely way in which a structure sufficiently complex to be self-aware could appear to have arisen under simple natural laws. Relativity is another major issue which has led Henry Stapp and I to take very different paths. With the extension to relativistic quantum field theory, the continuous deterministic unitary change at the heart of quantum theory does become manifestly compatible with the theory of special relativity. Abrupt events however are much more problematic. Special relativity requires that no change can be communicated at a speed faster than that of light. Yet von Neumann's abrupt events apparently happen instantaneously across the entire universe. Moreover, there seems to be considerable empirical evidence for instantaneous non-local changes in a rather peculiar form of correlation information about what might happen under various independent choices. Stapp has generated much debate (e.g.~\link{rfseven}{Unruh 1997}, \link{rfthree}{Mermin 1997}) by arguing that quantum mechanics is therefore non-local (\link{rffive}{Stapp 1993 chapter 1}, \link{rffive}{1997, 2000c}, \link{rfsix}{2002}). Interesting as the subleties of this debate may be, the most direct way to resolve the problem that it addresses is to assume that the symmetry of special relativity is broken by some objective sequence of hypersurfaces of simultaneity. This is the assumption that \link{rffive}{Stapp (1993 \S 4.5.13}, \link{rffive}{1997,} \link{rfsix}{2001a}) makes. Citing \link{rfseven}{Tomonaga (1946)} and \link{rffive}{Schwinger (1951)}, \link{rfsix}{Stapp (2001a)} claims that this assumption ``does not disrupt the covariance properties of the {\sl empirical predictions\/} of the theory'' [his italics]. The precise relevance of these old papers, the technical validity of which has been called into question by \link{rfseven}{Torre and Varadarajan (1998)}, is not entirely clear to me. The arguments of Tomonaga and Schwinger are concerned with generalizing the Schr\"odinger equation to allow for arbitrary spacelike hypersurfaces, rather than with an analysis of individual quantum events. A more modern approach to relativistic quantum field theory uses the language of local algebraic quantum field theory (\link{rfthree}{Haag 1992}). According to this theory, empirical predictions made in two spacelike-separated regions $\Lambda_1$ and $\Lambda_2$ can be expressed by commuting projection operators $P_1$ and $P_2$. Then, if $\rho$ is the initial quantum state, the probability of the result corresponding to $P_1$ being seen in $\Lambda_1$ and the result $P_2$ being seen in $\Lambda_2$ is given by $\rho(P_1 P_2)$ in the notation used by mathematicians. (Physicists would think of $\rho$ as a density matrix and would write $\tr(\rho P_1 P_2)$.) In this context, following the observation in $\Lambda_1$, von Neumann's abrupt event would correspond to the replacement of $\rho$ by $\rho_1 = P_1 \rho P_1/ \rho(P_1)$ and then, if the observation in $\Lambda_2$ is considered to be subsequent, $\rho_1$ would be replaced by $\rho_{12} = P_2 \rho_1 P_2/ \rho_1(P_2) = P_2 P_1 \rho P_1 P_2/\rho(P_1 P_2)$. As $P_1$ and $P_2$ commute, this is symmetric under interchange of $1$ and $2$, and so, consistent with Stapp's claim, does not depend on the ordering of spacelike separated events. Apart from the question, raised above, of whether the probabilities of events in Stapp's theory are equal to the conventional quantum probabilities given by state expectation values, there are two problems with Stapp's reliance on this argument. The first is with the assumption that all quantum events can be divided into classes associated with some foliation of spacetime into spacelike hypersurfaces. In relativistic quantum field theory, events are associated with spacetime regions rather than with spacetime points. If there are too many events too close together, then there may be no simple way of ordering the corresponding regions. This is why, in my work (\link{rftwo}{Donald 1995}), I use the full causal structure of the relations between spacetime sets in which events occur. The second problem is with the identification of the ``initial quantum state'' -- the state $\rho$. Suppose that I try to model my observations of some particular local macroscopic system by associating a quantum state $\sigma_1$ with that system. $\sigma_1$ will depend on my observations and my knowledge of the system. This means that $\sigma_1$ will already be a ``collapsed'' state, like $\rho_1$, rather than ``uncollapsed'', like $\rho$. Indeed, the only truly ``uncollapsed'' state would be the actual initial state of the universe, which is the state Everett refers to as the universal wavefunction. $P_2 P_1 \rho P_1 P_2/\rho(P_1 P_2)$ may be symmetric under interchange of $1$ and $2$, but it does still depend on $P_1$. If Stapp's suggestions are correct, $\sigma_1$ will depend on the time in the universal clock defined by Stapp's objective sequence of hypersurfaces of simultaneity and on non-local events at arbitrary distances; involving perhaps, conscious observers in other galaxies. Without a complete theory describing the nature of quantum events, it is difficult to decide on the significance of this dependence of local observed states on the supposed external events. Relativistic quantum field suggests that correlations between distant events are ever-present (\link{ref}{Clifton and Halvorson 2000}). Many of these correlations may be individually negligible, but if instantaneous action at a distance is allowed, then, at any moment, the effect of infinitely many distant events may need to be taken into account. In particular, this might make it surprising that the passage of time on Stapp's universal clock, if it existed, should not have been observed through some sort of frame-dependent effect on system dynamics. An alternative way of looking at this issue would be to suppose that in some region $\Lambda_1$ (the ``external'' region) there is a range of possible results, corresponding to projections $(P_1^n)_{n=1}^N$. As long as $\sum_{n=1}^N P_1^n = 1$, result $P^n_1$ will have probability $\rho(P^n_1)$ in a global state $\rho$, and the expected state in a spacelike-separated region $\Lambda_2$ will be $\sum_{n=1}^N \rho(P^n_1) P^n_1 \rho P^n_1/\rho(P^n_1) = \sum_{n=1}^N P^n_1 \rho P^n_1$. As $P_1^n$ commutes with every operator local to $\Lambda_2$, this expected state is equal to $\rho$ on $\Lambda_2$. This indicates that external events have no average effect in $\Lambda_2$. However, going from this argument to the conclusion that even infinitely many individual choices of projections like $P^n_1$ acting on the state $\rho$ will have no observable effect within $\Lambda_2$ seems rather like imagining that it would help a seasick man to be told that the average height of the sea is constant. It is not straightforward to reconcile the apparent empirical evidence for instantaneous non-local changes in correlation information with the apparent evidence for the Lorentz invariance of physical processes. My own approach takes as fundamental the information possessed by individual localized observers. Each observer assigns, to any system, the expected quantum state given the information s/he currently possesses. In general, these states are not compatible. Although Alice may know that her distant colleague Bob will have performed an experiment and will have found a result, she can only assign to the system which he is observing a state which expresses her ignorance until such time as she learns what experiment he chose to perform and what results he found. This has suggested to many (e.g. \link{rfseven}{Wolfe 1936, Wigner 1961}, \link{rffour}{Peierls 1991}, \link{rftwo}{Fuchs 2002}) that quantum states are merely states of knowledge. Unfortunately, such a position becomes problematic when we try to understand psycho-physical parallelism (\link{rftwo}{Donald 2002}). Quantum states seem to play two roles; on the one hand describing how things are, and on the other describing what we know about how things are and about how they might be. Alice and Bob assign different states to each other in ways which suggest that, for Alice, Bob's existence has to be as indefinite as her knowledge of his observations. This provides a primary motivation for a many-minds approach. If individual local observers are considered separately, then we can suppose that for Alice, all of Bob's possibilities will continue to exist until she is in a position to see his results for herself. By this means, the problem of compatibility between special relativity and quantum theory can be reduced from dealing with events which are supposed to occur instantaneously across the entire universe, to dealing with events which occur within the structure of individual observers (cf.~\link{rfsix}{Tipler 2000, Timpson and Brown 2002}). Of course, no single observer should be singled out. If Alice believes that all of Bob's alternative possibilities continued to exist after the instant of Bob's observation, then she should also be prepared to allow that all of her own alternative possibilities will also have continued to exist. Stapp has always rejected many-worlds interpretations. He claims that such interpretations have many technical problems to overcome (\link{rffive}{Stapp 1993, \S 1.13}). In \link{rfsix}{Stapp (2001c)}, for example, he reviews some of the well-known problems with the simplistic idea of a many-worlds theory which depends on a specific preferred orthonormal basis. It was precisely in order to avoid the kind of problem which he discusses in that paper that I developed a theory in terms of abstract patterns of information expressed not by a precise choice of wavefunction basis, but by ranges of properties of density matrices (\link{ref}{Donald 1986, 1990}). Stapp also raises metaphysical problems with many-worlds interpretations; in particular problems concerning the nature of probabilities. For example, in \link{rffive}{Stapp (1999)} he writes, ``In the evolving wave function of Everett the various branches do evolve independently, and hence might naturally be imagined to have different `minds' associated with them, as Everett suggests. But these branches, and the minds that are imagined to be properties of these branches, are all simultaneously present. Hence there is no way to give meaning to the notion that one mind is far more likely to be present at some finite time than the others.''. This is a much discussed problem (\link{rfthree}{Loewer 1996}, \link{rfseven}{Vaidman 1996}, \link{rffour}{Saunders 1998}). My response is to emphasize the primacy of the experience of probability. Life is a game of chance. If we can give any meaning to probability at all, then we can give meaning to the notion that we are far more likely to observe one possible future event than another. In other words, if, as Stapp and I both propose, we accept that consciousness is a significant aspect of reality, then we should be prepared to examine the idea of ``simultaneous presence''. Although, of course, there is a sense in which other branches are present, only my current branch is present to me. Probability is something which, according to my theory, is experienced in individual branches. The experience of an individual branch is genuinely unpredictable. I would similarly emphasize the importance of the experience of free will. \link{rffour}{Schwar\-tz and Begley (2002)} suggest that free will is incompatible with determinism, but whe\-ther all your actions have already been forseen by some omniscient deity, or whether your brain is abuzz with quantum jumpings has no relevance to your apparent ability to decide whether to call heads or tails when a coin is tossed. Until you call, you know you are free to change your mind. In my opinion, the lesson of Zeno's original classical paradoxes is that it is a mistake to attempt to use metaphysics to foreclose options in theoretical physics. Stapp and I agree that normal neural functioning provides a stream of quantum events. In my view, the die roll for each of us as each of our quantum events occurs. My primary goal has been to understand the technical problems of how to define such events (\link{ref}{Donald 1990}) and patterns of them (\link{rftwo}{Donald 1995}), and of how to define probabilities for these events in a way compatible with the mathematics of quantum theory and the assumption that our observations are typical (\link{ref}{Donald 1986}, \link{rftwo}{1992, 1999}). If that task has been successfully completed, then it is time to turn metaphysician and investigate what might be implied about the nature of reality. Of course, the implications may be strange or even disturbing, and may give us reason to prefer an alternative theory if we have one, but I do not believe that metaphysics by itself can provide a convincing refutation. Refutation, for the sort of theory I am proposing, would, I believe, require flaws in the technical details, as discussed in section 1 of \link{rftwo}{Donald (1999)}, or empirical evidence that quantum theory does not apply at the macroscopic level. There may be many other reasons, such as the speculative nature of the theory and its complexity, to prefer an alternative theory, but it is hard to know how seriously these reasons should be taken if the alternative has not reached a similar level of development. It is precisely because of the importance and difficulty of constructing a complete theoretical structure that it is so disappointing that Stapp fails to provide more than sketches of his ideas about the mathematical structure of thought (\link{rffive}{Stapp 1993 Appendix}), about selection of top-level codes (\link{rffive}{Stapp 1982}) and selection processes (\link{rffive}{Stapp 1995}), about the role of the electromagnetic field (\link{rffive}{Stapp 1999}), and about the quantum Zeno effect (\link{rffive}{Stapp 1999, 2000a,} \link{rfsix}{2001a}). \ \name{ref} \ \proclaim{References}{} \endproclaim {\frenchspacing \parindent=0pt \everypar={\hangindent=0.75cm \hangafter=1} Clifton, R. and Halvorson, H. (2000) ``Entanglement and open systems in algebraic quantum field theory.'' {\sl \outlink{http://arXiv.org/abs/quant-ph/0001107}{quant-ph/0001107}}. Printed: {\sl Stud. Hist. Philos. Mod. Phys. \bf 32}, 1--31 (2001). Donald, M.J. (1986) ``On the relative entropy.'' {\sl Commun. Math. Phys. }{\bf 105}, 13--34. Donald, M.J. (1990) ``Quantum theory and the brain.'' {\sl Proc. R. Soc. Lond. \bf A 427}, 43--93. \pdfeject \name{rftwo} Donald, M.J. (1992) ``A priori probability and localized observers.'' {\sl Found. Phys. \bf 22}, 1111--1172. Donald, M.J. (1995) ``A mathematical characterization of the physical structure of observers.'' {\sl Found. Phys. \bf 25}, 529--571. Donald, M.J. (1999) ``Progress in a many-minds interpretation of quantum theory.'' {\sl \outlink{http://arXiv.org/abs/quant-ph/9904001}{quant-ph/9904001}} Donald, M.J. (2001a) ``A review of Johnjoe McFadden's book {\sl Quantum Evolution}.'' {\sl \outlink{http://arXiv.org/abs/quant-ph/0101019}{quant-ph/0101019}} Donald, M.J. (2001b) ``A review of Evan Harris Walker's book {\sl The Physics of Consciousness}.'' \outlink{http://www.theassc.org/vol_7_2001}{{\sl Psyche \bf 7}} Donald, M.J. (2002) ``Neural unpredictability, the interpretation of quantum theory, and the mind-body problem.'' {\sl \outlink{http://arXiv.org/abs/quant-ph/0208033}{quant-ph/0208033}} {\hfill Papers and related material of mine are also available on my web site\hfill} {\hfill {\catcode`\~=12 \outlink{http://people.bss.phy.cam.ac.uk/~mjd1014} {http://people.bss.phy.cam.ac.uk/\tilrm mjd1014} \hfill}} \smallskip Eccles, J.C. (1986) ``Do mental events cause neural events analogously to the probability fields of quantum mechanics?'' {\sl Proc. R. Soc. Lond. \bf B 227}, 411--428. Fuchs, C.A. (2002) ``Quantum mechanics as quantum information (and only a little more).'' {\sl \outlink{http://arXiv.org/abs/quant-ph/0205039}{quant-ph/0205039}} \name{rfthree} Giulini, D., Joos, E., Kiefer, C., Kupsch, J., Stamatescu, I.-O., and Zeh, H.D. (1996) {\sl Decoherence and the Appearance of a Classical World in Quantum Theory} (Springer). Gurvitz, S.A. (2002) ``Quantum description of classical apparatus: Zeno effect and decoherence.'' {\sl \outlink{http://arXiv.org/abs/quant-ph/0212155}{quant-ph/0212155}} Haag, R. (1992) {\sl Local Quantum Physics.} (Springer) Itano, W.M., Heinzen, D.J., Bollinger, J.J., and Wineland, D.J. (1990) ``Quantum Zeno effect.'' {\sl Phys. Rev. \bf A 41}, 2295--2300. Loewer, B. (1996) ``Comment on Lockwood.'' {\sl Brit. J. Phil. Sci. \bf 47}, 229--232. McFadden, J. (2000) {\sl Quantum Evolution: Life in the Multiverse.} (HarperCollins) Mermin, N.D. (1997) ``Nonlocal character of quantum theory?'' {\sl \outlink{http://arXiv.org/abs/quant-ph/9711052}{quant-ph/9711052}}. Printed: {\sl Amer. J. Phys. \bf 66}, 920--924 (1998). Mohrhoff, U. (2001) ``The world according to quantum mechanics (or, the 18 errors of Henry P. Stapp).'' {\sl \outlink{http://arXiv.org/abs/quant-ph/0105097}{quant-ph/0105097}}. Printed: {\sl Found. Phys. \bf 32}, 217--254 (2002). \name{rffour} Namiki, M., Pascazio, S., and Nakazato, H. (1997) {\sl Decoherence and Quantum Measurements} (World Scientific). von Neumann, J. (1932) {\sl Mathematische Grundlagen der Quantenmechanik} (Springer) English translation (1955) {\sl Mathematical Foundations of Quantum Mechanics} (Princeton). Peierls, R. (1991) ``In defence of `measurement'.'' {\sl Physics World}, January 19--20. Saunders, S. (1998) ``Time, quantum mechanics, and probability.'' {\sl Synthese, \bf 114}, 373--404. {\sl \outlink{http://arXiv.org/abs/quant-ph/0111047}{quant-ph/0111047}} Schwartz, J.M. and Begley, S. (2002) {\sl The Mind and the Brain: Neuroplasticity and the Power of Mental Force.} (HarperCollins) \vfill \eject \name{rffive} Schwinger, J. (1951) ``The theory of quantized fields, I.'' {\sl Phys. Rev. \bf 82}, 914--927. Stapp, H.P. (1982) ``Mind, Matter, and Quantum Mechanics.'' {\sl Found. Phys. \bf 12}, 363--399. Reprinted as chapter 4 of Stapp (1993). Stapp, H.P. (1993) {\sl Mind, Matter, and Quantum Mechanics.} (Springer). A new edition of this book has been announced. Stapp, H.P. (1995) ``Chance, choice, and consciousness: The role of mind in the quantum brain.'' {\sl \outlink{http://arXiv.org/abs/quant-ph/9511029}{quant-ph/9511029}} Stapp, H.P. (1997) ``Nonlocal character of quantum theory.'' {\sl Amer. J. Phys. \bf 65,} 300--304. Stapp, H.P. (1999) ``Quantum ontologies and mind-matter synthesis.'' \newline {\sl \outlink{http://arXiv.org/abs/quant-ph/9905053}{quant-ph/9905053}}. Printed in {\sl Quantum Future,} eds. P. Blanchard and A. Jadczyk, (Springer 1999). Stapp, H.P. (2000a) ``Decoherence, quantum Zeno effect, and the efficacy of mental effort.'' {\sl \outlink{http://arXiv.org/abs/quant-ph/0003065}{quant-ph/0003065}} Stapp, H.P. (2000b) ``The importance of quantum decoherence in brain processes.'' {\sl \outlink{http://arXiv.org/abs/quant-ph/0010029}{quant-ph/0010029}} Stapp, H.P. (2000c) ``Bell's theorem without hidden variables.'' {\sl \outlink{http://arXiv.org/abs/quant-ph/0010047}{quant-ph/0010047}} \name{rfsix} Stapp, H.P. (2001a) ``Quantum theory and the role of mind in nature.'' \newline {\sl \outlink{http://arXiv.org/abs/quant-ph/0103043}{quant-ph/0103043}}. Printed: {\sl Found. Phys. \bf 31}, 1465--1499 (2001). Stapp, H.P. (2001b) ``The 18-fold way.'' {\sl \outlink{http://arXiv.org/abs/quant-ph/0108092}{quant-ph/0108092}}. Printed: {\sl Found. Phys. \bf 32}, 255--266 (2002). Stapp, H.P. (2001c) ``The basis problem in many-worlds theories.'' {\sl \outlink{http://arXiv.org/abs/quant-ph/0110148}{quant-ph/0110148}}. Printed: {\sl Can. J. Phys. \bf 80}, 1043--1052 (2002). Stapp, H.P. (2002) ``A Bell-type theorem without hidden variables.'' \newline {\sl \outlink{http://arXiv.org/abs/quant-ph/0205096}{quant-ph/0205096}}. {\hfill Papers and related material by Henry Stapp are also available on his web site\hfill} {\hfill {\catcode`\~=12 \outlink{http://www-physics.lbl.gov/~stapp/stappfiles.html} {http://www-physics.lbl.gov/\tilrm stapp/stappfiles.html} \hfill}} \smallskip Timpson, C.G. and Brown, H.R. (2002) ``Entanglement and relativity.'' \newline {\sl \outlink{http://arXiv.org/abs/quant-ph/0212140}{quant-ph/0212140}}. To appear in {\sl Understanding Physical Knowledge,} eds V. Fano and R. Lupacchini. Tipler, F.J. (2000) ``Does quantum nonlocality exist? Bell's theorem and the many-worlds interpretation.'' {\sl \outlink{http://arXiv.org/abs/quant-ph/0003146}{quant-ph/0003146}} \name{rfseven} Tomonaga, S. (1946) ``On a relativistically invariant formulation of the quantum theory of wave fields.'' {\sl Prog. Theor. Phys. \bf 1}, 27--42. Torre, C.G. and Varadarajan M. (1998) ``Functional evolution of free quantum fields.'' {\sl \outlink{http://arXiv.org/abs/hep-th/9811222}{hep-th/9811222}}. Printed: {\sl Class. Quant. Grav. \bf16,} 2651--2668 (1999). Unruh, W.G. (1997) ``Is quantum mechanics non-local?'' {\sl \outlink{http://arXiv.org/abs/quant-ph/9710032}{quant-ph/9710032}} Vaidman, L. (1996) ``On schizophrenic experiences of the neutron.'' \newline {\sl \outlink{http://arXiv.org/abs/quant-ph/9609006}{quant-ph/9609006}}. Printed: {\sl Int. Stud. Phil. Sci. \bf 12}, 245--261 (1998). Walker, E.H. (2000) {\sl The Physics of Consciousness: The Quantum Mind and the Meaning of Life.} (Perseus) Wigner, E.P. (1961) ``Remarks on the mind-body question.'' In {\sl The Scientist Speculates,} ed. I.J. Good, 284--302. (Heinemann) Wolfe, H.C. (1936) ``Quantum mechanics and physical reality.'' {\sl Phys. Rev. \bf 49}, 274. } \proclaim{Note Added.} \endproclaim After this review of his work appeared on quant-ph, Henry Stapp posted an e-mail with a series of comments on his web site: {\hfill {\catcode`\~=12 \outlink{http://www-physics.lbl.gov/~stapp/stappfiles.html} {http://www-physics.lbl.gov/\tilrm stapp/stappfiles.html} \hfill}} I reproduced those comments, quoting the points to which he had replied and giving my subsequent responses to him. Following correspondence, and with some editing from us both, this has developed into a multi-stage debate which is available on my web site at {\quad {\catcode`\~=12 \outlink{http://people.bss.phy.cam.ac.uk/~mjd1014/stappr.html} {http://people.bss.phy.cam.ac.uk/\tilrm mjd1014/stappr.html} }} \end