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Quantum theory is a theory which produces probabilities, but it is not entirely clear what precisely those probabilities are probabilities of. If, as is often suggested, they are probabilities of observations, then perhaps we need to be able to distinguish observations from other classes of events. We might be able to do that by understanding and characterizing observers. But if observers really constitute a special class of entity, then perhaps that is because they are the entities which have, or which are, minds.
In the course of developing the theory, I showed, mainly in unpublished work, that many of its earlier versions were untenable. For example, I once considered a definition for a complex structure which I hoped would characterize observers, but which turned out to be satisfied by the pattern formed by the leaves of a tree blowing in the wind.
It is also, of course, possible that quantum mechanics does not apply to macroscopic objects. Experimental evidence for this has long been sought. Maybe one day it will be found.
Refutability is important for scientific theories, but it is not the only mark of virtue. Science is too broad an enterprise for any single criterion to provide an adequate measure of interest. Explanatory power and consistency are also important. The aim of my theory is a coherent explanation of how the empirical evidence and the mathematical structure of quantum theory can be consistent with our individual subjective experiences.
There have been many suggestions about what quantum theory might tell us about the nature of reality. Some of these suggestions are hopelessly vague. Trying to build a vague idea into a technically-consistent framework is a powerful way of understanding what it might really mean, whether it can really work, and what its consequences might really be. It will also involve answering specific questions which may be of wider relevance.
I start with the vague idea of the many-worlds interpretation and the vague idea that quantum measurements might have something to do with observers. I translate this into the idea that all quantum possibilities are observed possibilities and that what can be observed depends on the structure of observers. So then I need to produce technical analyses of “observer structures” and of “quantum possibilities”. Some of the specific question I address include:
In the context of local quantum field theory, how might definite information-bearing structures be constituted in the warm wet brain? (Donald 1990)
What combinatorial structures can be used to express the causal relations between a finite family of spacetime sets? (Donald 1995)
Is it plausible that consciousness could supervene merely on the instantaneous state of a brain? (Donald 1997)
Can probabilities for the experiences of an individual observer be defined? Is such a definition compatible with our observations? (Donald 1999)
Is it necessary to specify the concept of a “world” in a many-worlds theory? (Donald 2002)
What is the role of infinitary mathematics? (Donald 2003)
A form of idealism is among the consequences which I see as ultimately stemming from the vague ideas with which I started. I also conclude that this makes it necessary for there to be laws defining the nature of observers. These laws seem necessarily to be both quite complicated and somewhat arbitrary (Donald 1999). Another conclusion is that, at a fundamental level, time is an aspect of our structure as individual observers, rather than a co-ordinate of a fixed observer-independent spacetime.
No. I not believe that there is any evidence or necessity for such coherence. In particular, as I discuss here, I do not believe that the brain has somehow evolved any special capacities which make it in any way like a “quantum computer”.
Instead my starting point is the idea that we seem to be able to experience only that limited subset of all possible quantum states which correspond to our being aware of single (unsuperposed) definite answers to suitable empirical questions. (Is that spot on that photograph here or there? Is that cat dead or alive?)
I therefore begin, in Donald 1990, with an analysis of how we ought to describe a brain which is processing definite information. According to conventional neurophysiology, a brain which is processing definite information is, essentially, a brain which has a definite pattern of neural firing. Adapting this description to the context of a universal quantum theory, involves expressing it in abstract terms and developing, in Donald 1995, a concept of a definite pattern of information within the mathematics of quantum theory. This does require an analysis at sub-neural length scales, and ultimately leads to some radical metaphysics, but it does not require innovations in neurophysiology.
The problem of the unity of consciousness, sometimes referred to as the binding problem, has two aspects. The ontological aspect is concerned with the individuation and wholeness of separate minds while the psychological aspect concerns the perceptions of those minds.
I propose a solution to the problems of quantum theory which solves the binding problem, not by large scale quantum coherence, but by putting individual minds and their structures at the forefront of ontology. My focus in considering the mind-body problem is on trying to specify the “body” which forms the structure of a particular “mind”. This is a far from trivial task given the extent to which quantum theory calls the nature of all physical systems into question. The outcome of my analysis yields a description, in Donald 1999, of individuated structures which grow in an organic fashion, filling-in and completing themselves as they do so. These self-completing structures are abstract reflections of the total pattern of an individual's neural firings, interpreted by conventional neuropsychology as a representation of that individual's perceptions.
Quantum coherence merely allows certain dynamical processes on certain state spaces. It has been suggested that the binding problem would somehow be solved were such processes to exist on a sufficiently large scale in the brain. I do not believe that they do.
Occam's razor is the idea that entities should not be multiplied without necessity.
The necessities that drive many-minds interpretations are compatibility with physical theory and the avoidance of solipsism.
The many-minds idea allows us to make sense of the Schroedinger cat problem by permitting certain events to lead to multiple observed futures. It allows us to make sense of the quantum locality problem by permitting two distant observers (“Alice” and “Bob”) to make independent local choices between different localized measurements with different sets of independently observed local futures. The independence implies that when Alice and Bob eventually meet they may encounter any of several of the other's possibilities. Avoiding solipsism requires that we assign consciousness (or reality) to everyone we could meet who is sufficiently similar to ourselves. So Alice should assign reality to each of Bob's possible futures, and, by symmetry, to each of her own.
More generally, Occam's razor refers to a principle of parsimony in physical theories. Many-minds theories are parsimonious in that they do not require every detail of future reality to be fixed by the initial state of the universe. That state can be taken to be simple. The complexity we observe is then a reflection of our individual experiences of outcomes of stochastic events. Complexity only exists for the observers who have experienced it.
Realism: in the sense that I believe that our possible experiences and their probabilities are determined by truths about reality which are independent of our abilities to know or verify them.
Not Relativism: scientific and logical truths are the same for everyone. However, I think that morality is partly learned, partly reasoned, and partly innate.
Not Pragmatism: scientific laws are not true because they are useful. However, I believe that the nuture, the acceptance, and the imposition of moral responsibility are all justified on pragmatic grounds.
Physicalism: only in the sense that I believe that the truths about reality which determine our possible experiences and their probabilities are mathematical laws which include, and extend, the laws of physics. I am not a materialist, although, as I note in my summary,
In much of my writing, there is a tension between a final fully-consistent but highly abstract analysis and a preliminary analysis posed in comprehensible terms. The preliminary analysis may describe, for example, a quantum state for a physical brain in the sort of physical world that we see around us. Ultimately, however, this is to be superseded by an understanding of such apparent worlds as mere appearance; merely a reflection of the abstract information-bearing structures which constitute our minds.
Dualism: in the sense that I believe in the existence both of minds and of the laws which determine their possible experiences. I also believe that probabilities exist and are experienced.
Not Platonism: mathematical truths are simply necessary logical consequences. Scientific laws however are contingent. Those which happen to be true are therefore special and can be said to “exist”.
Idealism: in the sense that I believe that the material world is mere appearance and that law-obeying minds are the fundamental entities. In as far as initial conditions are required, I believe that they are simple and can be subsumed into the laws.
Epiphenomenalism: only in the sense that I believe that consciousness has no power over the course of events. I believe that free will is an illusion, albeit a necessary one.
Not Functionalism: I believe that consciousness must obey specific laws which restrict the nature of its (apparent) physical substrate. Patterns of (apparent) behaviour, either actual or possible, are not sufficient.
Not Solipsism: in the sense that I think it most likely that all possible lawful mental histories exist, each with its own probability. And yet I also believe that every mind is an experience of one of the ways in which your own life might have developed.
Scepticism: about our abilities to discover the most fundamental scientific truths and about my own beliefs.
The situation of split-brain patients illustrates some fundamental issues about the nature of consciousness.
In order to develop a solution to the problem of the interpretation of quantum theory, I set out to provide a characterization of an “observer”. Having done this, I have a theory which purports to provide an identification of those entities which have minds. This theory can be tested for plausibility by considering if it identifies as having minds those entities which we imagine do have minds and if does not identify as having minds those entities which we imagine not to have minds.
Unfortunately, however, it is impossible to test such an identification directly, for exactly the same reasons that it is impossible to claim with certainty that any particular person or machine has, or is, a mind; whether or not that person is behaving in some particular way. Even self-identification can be problematic. In my view, quantum theory calls the existence of all physical objects, including brains, into question, and points us towards an alternative ontology according to which it is minds which exist rather than brains. This means that mind is a form of being rather than an access to self-knowledge. My consciousness is what I am. My communicable understanding of my consciousness through what I say, or think, or believe need not necessarily be complete or correct.
For the people who appear to others to be split-brain patients, the obvious question is whether they exist as one mind or as two. This question might have no answer, but it does according to my theory. Leaving to one side the technicality that the theory actually associates each of “us” with a cloud of minds, the answer is that split-brain patients are essentially single minds. This follows from the ideas in sections 3 and 4 of Donald 1999.
I do not view this consequence of my proposals as being either particularly plausible or particularly implausible. In either case, we could try to imagine what it would like to be such a mind. In the single mind case, for example, there would no longer be the usual “natural” consistency in experiences at any moment. As a split-brain patient, this would leave someone with the possibility of being simultaneously aware both of a toad and of a stool, but with no direct awareness of the simultaneity or of any inconsistency.
What my work on the many-minds interpretation of quantum theory suggests to me in this context is
that reality is very different from appearance,
that brains and minds are distinct; indeed that the brain is but a shadow of the mind,
that our possibilities and their probabilities are determined by objective and impersonal physical laws,
that apparent physical brain structure represents the way that every detail of consciousness is a consequence of the workings of those laws,
that we should not think of our lives as merely threescore years and ten but as a vast range of possibilities branching out from each moment.
As answers, the third and fourth statements say no while the last says that perhaps it may not matter as much as one might think.
At present, I have no plans to place these papers in the print literature. They are freely available from here and from the physics e-print archive. They can be cited by their quant-ph numbers. For example, “Progress in a Many-Minds Interpretation” can be cited as “quant-ph/9904001”.
I write my papers using Plain TeX. TeX is a wonderful and very widely-used mathematics typesetting system. A program for processing TeX will convert the “TeX source” versions of the papers into typeset mathematics. This is how my “pdf” versions are produced. There are several free programs for processing TeX available on the web. I currently use TeXShop on my Mac. I have also used MiKTeX on a PC. A good starting-point is the TeX Users Group.
In elementary courses on quantum theory, one is introduced to the idea of wave-functions. The wave-functions are the “pure quantum states” or the “coherent quantum states”. But these are not the only kinds of quantum state. There is also a well developed mathematical theory of “mixed quantum states”. This applies to situations in which a classical probabilistic structure is added to a quantum structure, so that one can speak, for example, of a state as being wave-function Psi with probability p and wave-function Phi with probability q. The mathematics of these mixed states is identical to the mathematics which describes the restriction to a subsystem of a state of a compound system. These restrictions of states are the “decoherent quantum states”.
A decoherent quantum state is like a mixture of pure states. In decoherence theory, it is argued that typical quantum states of physical systems in their normal environments are like mixtures (with appropriate probabilities) of quasi-classical quantum states. A quasi-classical quantum state is the sort of quantum state which one would build if asked to describe the world as observed at the present instant — in other words, it is a state in which quantum effects are microscopic; in which, subject to the uncertainty principle, macroscopic objects have well-defined positions and momenta; and in which any cat has well-defined viability.
The crucial problem which this leaves unsolved is what it means for a state to be “like” a mixture. Decoherence is approximate. The decomposition into quasi-classical states is not unique. “Quasi-classical” may be an idea which we can understand for all practical purposes, but it is no less vague than the Copenhagen interpretation idea of a “measurement”. The identification of the fundamental subsystems, or the splitting between system and environment, is also left vague.
The purpose of an interpretation of quantum theory is to explain how solutions to the Schroedinger equation relate to the everyday world we see around us. The many-worlds idea is that solutions to the Schroedinger equation split into quasi-classical parts and that our everyday world is described by one of those parts. Decoherence theory confirms that such splittings exist for all practical purposes at the level of the local density matrix of typical physical systems in their normal environments. But there is no canonical or fundamental version of the splitting. In particular, the eigenfunctions of realistic density matrices need not be quasi-classical. (They also need not be unique and can be unstable under small perturbations in the density matrix.)
Suppose that we choose a density matrix which we think would be a reasonable description of some system were it not to be observed for some period of time. Thus we look for the density matrix of the system which would result at the end of the period if we began the period with an appropriate quasi-classical state both for the system and for its environment and then we let that combined state develop under the universal Hamiltonian. Of course we really should consider the state of the world as it would be had it never been observed, but the problems for the many-worlds interpretation are apparent even if we assume that we have already identified this planet and most of its contents.
As we are interested in our everyday world, we should consider a bounded system which includes our own body (or at least our own brain). Random radiative scattering carries lots of information across and out of such a system, so a minimum time period on which mixing occurs, for a system of human scale, would be no more than long enough for light to pass across the system. More significant mixing occurs, particularly in liquid and gaseous phases, with every particle-particle collision and scattering. In air, there are around 10^34 such collisions per cubic metre per second. In each one, the angle of scattering is not precisely predictable and the state becomes less quasi-classical. By the time a new-made cup of coffee would have cooled sufficiently to be drinkable, Hamiltonian interactions within the system and with its environment will have led to a great deal of mixing as the system approaches thermal equilibrium on short distance scales. Moreover, given the natural thermally-driven small-scale dynamical instability of the functioning human brain, even such a short time will be enough for the state to include a mixture of different thought patterns and their consequences. The longer we wait, the more mixed the state becomes and the closer we approach to the correct starting point for a many-worlds theory.
There are many different decompositions of the resulting density matrix into quasi-classical states which each provide accurate descriptions of the system as we might see it at an instant. For example, we can change the extent to which we describe individual particles as being localized, either in position or in momentum. Indeed we can use more or less refined descriptions for any aspect of the system of which we are not directly aware; including details of the localization of water molecules in the brain. We can even change precisely what we include in the system, whether we describe it in terms of a specified set of molecules, or whether we prefer a description in terms of local density operators. Any of these changes in description may make a radical difference to the probability of the corresponding quasi-classical states.
Despite the fact that many of these decompositions are mutually incompatible, it may seem that this extravagant vagueness makes little difference to the many-worlds idea as a picture of reality at an instant. Nevertheless, without a resolution of the vagueness, it is impossible to see how the apparent temporal progression of our everyday world is to be explained or what meaning can be attached to probability. Continuity clearly does not pick out a unique future description when continuous variation is possible in the instantaneous description.
I posted the two previous answers to the newsgroup sci.physics.research in response to a question about the status of the combination of the many-worlds interpretation with decoherence theory. Here is some of the dialogue that followed.
According to the conventional interpretation, the outcome of a “measurement” is always one of the eigenvalues of “the measured operator”, and the probability of a specific outcome is determined by transition probabilities between the current wavefunction and the eigenfunctions of that operator. As a result of the measurement, the current wavefunction is replaced by the outcome eigenfunction.
On a technical level, the main problem, as far as I can see, with the Bohm interpretation is compatibility with special relativity theory.
Another issue has to do with quantum field theory. In conventional quantum field theory, “second quantization” gives a well-defined mathematical framework within which both quasi-classical particle-like states and quasi-classical field-like states exist. These states can be used, in the appropriate contexts, to describe the same physical objects. Correspondingly, there are two forms of the Bohm interpretation; one in which the fundamental entities are quasi-classical particles and one in which they are quasi-classical fields. These fundamental entities are “piloted” by a wave function, which is Everett's non-collapsing “universal wave function”. Unfortunately, in Bohm theory, the two types of fundamental entity would seem to be totally irreconcilable. They cannot be both used for the same objects in different circumstances.
Non-locality is also much more difficult to make sense of in Bohm theory than in a many-minds interpretation.
Yet another problem is with the understanding of psycho-physical parallelism. This last problem I discuss briefly in this section of Donald 2002.
Nevertheless, the Bohm interpretation is a serious and interesting attempt to answer the fundamental ontological problems raised by quantum theory.
It is possible that there may be more than one radically-different way in which quantum theory could be understood and each of these ways might be just as compatible with empirical evidence. In my opinion, we should pursue all such ways. We may not be able to learn the truth, but we can at least circumscribe different possibilities.
If you have a consistent set of histories then the theory tells you the probability of each element of that set. However, the theory does not provide an unambiguous determination of any fundamental consistent set. This is the “set selection problem”. If consistent histories theory is to be more than merely a classification of frameworks which allow an uncharacterized external observer to make conventional probabilistic statements, then the set selection problem is crucial and, in my opinion, any attempt to solve it will be at least as involved as my attempt to provide an unambiguous characterization of an “observer”.
It does make a serious attack on the ambiguity problems of many previous interpretations by explicitly defining its quasi-classical domain (“characterizing observers”). It is also compatible with special relativistic quantum field theory.
Leaving aside the possibility that the theory fails to achieve what it claims to achieve and the fact that special relativistic quantum field theory is clearly not the ultimate theory of everything, many of the remaining open problems are aesthetic or metaphysical.
Back to the papers.