a new mental dynamics description of quantum mechanics
in this paper i seek to develop a new description of quantum mechanics, using the notion of a mental dynamics as a central aspect of the theory. unlike other notions of mental dynamics, i abandon the strongest notion of the supervenience of mental upon physical states. this move produces a simpler and less ad-hoc mental dynamics, and is justified by the nature of the supervenience that does still remain, as well as an investigation of a naive empiricist version of the theory.the structure of quantum mechanics
what follows is a brief account of the structure of quantum mechanics, but it is not sufficient as a complete account; i assume throughout that the reader is familiar with the structure of the theory. here, i retell the story, so to speak, in order to acquaint the reader with my manner of speaking, and give a certain spin to the interpretation of the theory.quantum mechanics provides us with a formalism to answer questions about what will be the results of particular experiments. similarly, classical mechanics is also a formalism to allow the prediction of particular experiments. at a basic level then, quantum mechanics and classical mechanics both fill a similar niche. however, the details of how the prediction rules operate in quantum mechanics will cause serious problems when the mechanics is taken not merely as a method of predicting experiments, but as a complete description of the manner of operation of the universe.
first i will describe the basic operation of the experiment-predicting formalism of quantum mechanics. an experiment is a system, some subset of the universe as a whole, which we isolate from as many interactions with other parts of the universe as we can. this simplifies the number of considerations we must take into account. we start with the system in some known state, and then we manipulate the system in some way. finally, we measure the final state of the system. the job of a physical theory, in its experiment-predicting aspect, is to accurately predict what the final state will be from the known initial state, the residual interactions with other parts of the universe which we were unable to eliminate, and the deliberate manipulations of the system.
as noted by Karl Popper and others, the experimental setup is not theory neutral: the experimental results to some extent presuppose an understanding of the initial state and the nature of the manipulations. this is a pregnant philosophical issue, but it does not raise practical difficulties for either quantum mechanical or classical predictions of experimental results. a successful theory, in its experiment-predicting mode, must give rules for constructing experiments, reducing residual interactions, understanding manipulations, and so forth. these rules are not the source of the difficulty for quantum mechanics, and in fact are essentially identical for both classical and quantum physics.
in classical physics, the final state of the experimental set-up is measured by some measuring device; this measuring device can in principal be made arbitrarily perfect, and we can in principle measure the final state as accurately as we like. the measuring device becomes correlated in its state to a particular state of the experimental set up, such that it points at a number indicating the speed of some object, for example.
in classical physics, the states of the measuring apparatus are directly related to the posited physical states of the system in a simple way. typically there is a straightforward correspondence between, say, pointer positions and physical states. the physical rules for predicting experiments are then just descriptions of how the states change over time. the result of the experiment, given by the measuring apparatus, is a straightforward reflection of the predicted final state.
the quantum mechanical formalism also gives rules for understanding the evolution of the system under various manipulations, which experimenters can provoke, and then describes a final state of the system. however, the measuring device does not simply track the final state. indeed, it is impossible to build a measuring device which would track the final state.
a state in quantum mechanics is expressed by a vector in a certain complex valued vector space. the details of the vector space do not concern us here. however, what is significant is that we cannot directly measure the value of the state vector. instead, a measuring device is described in the formalism by some basis on that vector space. each possible state of the measuring device is represented by one of the orthogonal vectors in the space.
the rules for the evolution of the system describe the changes in the vector in accord with a unitary linear dynamical law. the rules for predicting experiments then come apart into two pieces: first, this linear dynamics, and then second, a rule for how the states of the system are reflected in terms of the possible measurement outcomes.
this final rule is probabilistic; the rule is to project the vector onto the basis that describes the measuring device; the probability of a particular measurement result is the square of the norm of the projection onto that basis component.
if we have an ensemble of particles known to be in an identical state, we can measure that state as accurately as we like by making many measurements; because decomposition into any basis is unique, we can determine as accurately as we like the state by the statistical predominance of particular results. indeed, this is the way experiments in quantum mechanics typically proceed: a large number of nearly identical particles are put through the same experimental setup, and the statistical predominances of various outcomes are recorded.
at first glance, this appears not terribly different from classical mechanics. understood as a set of rules for predicting experimental outcomes, the two formalisms operate in similar manner, but for atomic experiments, give quite different predictions, and in every experiment, the quantum mechanical formalism gives entirely correct predictions, and the classical formalism gives incorrect, or even wildly wrong predictions. from this standpoint then, quantum mechanics is a resounding success. we shall see, however, that the presence of these two different rules in quantum mechanics causes major problems for the interpretation and understanding of the theory.
the solopsist empiricist
the problem occurs when we attempt to take our physics as a complete description of physical reality. the first step towards developing a complete description of physical reality, given a physical theory which predicts the results of experiments, is to create broader meta-experiments, in which the primary experiments are themselves the subjects of a broader experiment. i call this the meta-experimental method.in classical physics this procedure is entirely satisfactory. we obtain a broader theory, which tells us how our pointers and telescopes work. similarly, we can build a quantum mechanical description of pointers and telescopes and Geiger counters and the like. however, the resulting description will tell us always only how the states themselves change, what the states look like for the measuring apparatus, and so forth.
but in quantum mechanics, the meta-experimental method can never tell us about the operation of the norm-squared rule. we would see that the rule functions, but there is no physical aspect of the system which behaves according to the norm-squared rule as contrasted with the linear dynamics.
in every experiment, there is always an apparatus and an observer; the apparatus follows the linear dynamics and has quantum mechanical states φ, and then the observer looks and sees a state m which is probabilistically obtained from the final state φ according to the norm-squared rule. when we construct a meta-experiment, we now consider the inner experiment purely with the linear dynamics, and only when the meta-experimenter looks do we apply the norm-squared rule. this is the procedure of quantum mechanics. for it to work, certain conditions on the linear dynamics must apply, but they do in fact apply. these conditions amount to the reality of the measurements φ and the stability of their relationships to states m.
we find that we cannot eliminate the role of the observer as we could for classical mechanics. we can never treat the observation as merely part of the total physical system, because the physics only tells us how complete experiments work, and they always involve an intrinsic separation between apparatus and onlooker. in the classical theory, a measurement device never tells us the exact state of the system, but we can in principle reduce the error as much as we please. but in the quantum theory, the measurement device in principle is incapable of measuring the state. at best, we can only measure the state of a large ensemble of identical systems.
there is a viewpoint for which none of this is a problem. it takes the sole role of physics to be the predicting of experiments, and not also the complete description of reality.
we proceed by treating all of experience as a single experiment. from that standpoint, the rules for predicting experiments, as given by quantum mechanics, correctly describe all the experience a subject sees. however, from within that standpoint, there is no way at all for the observing subject to regard themselves as a part of the universe, because the same dynamical laws that apply to the rest of the world do not apply to their process of observation.
thinking of human observers, we are then forced to drop the supervenience of mental states on brain states. the brain, as a physical object in the world, has a state φ, but the observer always sees states m, which are a subset of the possible states φ.
thus, a naive empiricistic view results in a profound dualism, and even a sort of solopsism. whatever it is that our subject's mind does, in observing the world, is something that no other person, whatsoever, seems to do (from the subject's point of view). the subject's observations are of a world that exactly follows the linear dynamics, and then when he looks at things, he sees always eigenstates.
most understandings of quantum mechanics are unhappy with the dualism implied by this naive empiricistic view. they generally operate in one of two ways. either they say that the actual states sometimes behave non-linearly (von Neumann, grw) or they deny the need for any states m at all (the bare theory, the many worlds interpretation).
if we are unhappy with solopsism, then we might try and expand this model of the world into one which has multiple minds. my goal is to elaborate what that will result in; i believe we will see a significantly interesting understanding of quantum mechanics result.
mental dynamics
one way of understanding the solopsistic empiricist theory is to see it as involving two sets of dynamical rules, corresponding to the two parts of the empiricist's world. first, there are the usual linear dynamics of quantum mechanics, which apply to the external universe, and second, there is a special dynamical rule which describes the content of the observer's mind.
the first rule is the linear dynamics, and the second rule is the norm-squared rule. The linear dynamics apply to the whole world, including the observer's mind, and the norm-squared rule tells us what the mental state of the observer is: it is some state μ chosen from the possibilities given by φ in accordance with the norm-squared rule.
one additional step must be added, however: the observer's memory must also correctly track the results of the previous observations. as a result, once the observer sees the measurement pointer to be in a particular state φ, chosen from the superposition in accordance with the mental dynamics, future mental events must consider only that term of the superposition; all others are forever dropped. this additional requirement is similar to the collapse dynamics in the von Neumann formalism, but here is not a physical process, but rather a process in the mental dynamics necessary to establish diachronic consistency.
what we seek, in developing a non-solopsist understanding, is to see how to generalize this to a situation with multiple observers. again, the diachronic consistency requirement between observers must be maintained. so we will now posit the existence of many minds, all observing events. again, the linear dynamics will apply to all the observers, including their brains, and we need a mental dynamics that describes what their mental states are.
the rule must look something like the following: each observer must see a perceptual state μ corresponding to the physical state φ, chosen in accordance with the norm-squared rule, and maintaining diachronic consistency for that observer. but this is not itself sufficient; an additional consistency requirement arises from the multiplicity of observers.
suppose two observers look at the same measurement pointer which is in some quantum state φ. the observers brains become correlated with the different positions of the pointer, and with each other. it will not do, however, if the different observers mental states choose different possible μ. see why, as follows. suppose observer 1 looks at state φ, and his mental state becomes μ1 in accord with the norm-squared rule. Observer 2 looks at the same state φ but her mental state becomes μ2. observer 1 asks observer 2: do you see the pointer? where is it? simultaneously, observer 1 applies a sophisticated brain scanning device to observer 2's head.
because of the correlation established in the value of φ, observer 1 knows that what he sees in observer 2's head will match what he sees when looking at the pointer; this is guaranteed by the linear dynamics. So observer 2's brain, as witnessed by observer 1, must report it's pointing at 1. if, therefore, observer 2's mental state is μ2, then we can only conclude that either brains are not really physical objects, or that there is no connection at all between a person's reports and their mental states. neither of these alternatives are palatable.
accordingly, we must adopt an additional consistency requirement on the mental dynamics. different minds making related measurements (measurements in which their brains become correlated) must experience norm-squared results μ consistently with each other and the nature of the physical correlation of their brain states φ. this is similar in nature to the diachronic consistency we must have for even a single observer; i will call in the requirement of synchronic consistency.
incorporating as much supervenience of mental states on physical as we can, the mental dynamics then looks as follows. When an observer's brain is in physical state φ, their mental state is μ, where μ corresponds to one term of the superposition φ chosen in accord with the norm-squared rule, and with the requirements of diachronic consistency the observer's past, and synchronic consistency with other minds. the alert reader wonders what basis we are expanding φ in to make this choice. more on that later.
dualism and solopsism
at this point, i have presented two views, one strongly solopsistic, and the other apparently strongly dualistic. dualism is objectionable to most modern-minded philosophers, who might therefore be inclined to object to the mental dynamics model i give.this would be a mistake. first, note that the solopsistic model is also strongly dualistic, as any form of solopsism probably must be. it is no good to accept a solopsistic dualist account to avoid the dualism of a realistic dualist account.
but more importantly, supervenience saves us. in my model, mental states do supervene on brain states in all the right ways. unlike, for example, the bare theory, my model gives mental states which properly supervene on physical brain states. the only aspect of traditional supervenience which is missing in my model is that one cannot read off the mental state from a complete knowledge of the current physical state.
however, even that is not a serious problem: if one actually reads the physical state of a subject's brain, that is, knows it by anything approaching normal knowledge, then indeed, one does know the corresponding brain state. the brain one is reading is in a superposition, and one's own brain then enters a correlated superposition, but one's mind (in accord with the mental dynamics) encounters a determinate answer, which (by synchronic consistency) tells you the mental state of the subject.
However, by means of a so-called a-type measurement, one can in principle directly measure the superposition in the subject's brain, knowing that it is in a certain superposition. in that case, one knows exactly the subject's brain state, but still not her mental state, and the preceding argument is of no avail. what are we to make of this?
there must be some determinate measurement basis, so the argument usually goes, in which the subject's brain records information and which (by supervenience) corresponds to mental predicates. i am not so sure of this; supervenience would only seem to require a fairly weaker relation between mental states and brain states: that any mental state corresponds to some physical eigenstate. but there is no reason immediately apparent that different mental states should each correspond to eigenstates of some single basis. if one takes mental states seriously, then it is logically conceivable some that mental state μx corresponds to x-spin up and some other mental state μz corresponds to z-spin down. the emphasis in the literature on the basis in which beliefs are recorded amounts to a presumption that mental states cannot have the kind of real independence from physical states that my single-mind theory gives them.
there is a relationship between a brain state φ and a mental state μ. however it does not follow that the state μ must correspond to some eigenvalue of φ in some basis. Indeed μ is a mental state, described by a mental predicate like sees the pointer at position 1.
we can still predict experiments under this model. our brain sees a measurement pointer, and enters brain state φ, which is some superposition of visual cortex sees pointer at position 1 and visual cortex sees pointer at position 2. the mental dynamics tells us we will enter mental state μ1 or μ2, which correspond to the mental correlates of those statements about the visual cortex: experimenter sees the pointer at position 1 and experimenter sees pointer at position 2. by synchronic consistency, we know that other experimenters whose brains are correlated with the same setup will enter consistent mental states.
we can also understand the entire universe as a whole. mental states like beliefs are related to physical states in a certain way; the details of brain biology are uninteresting here. it is a precondition that the connection between mental and physical states be such as to render the subject capable of accurate perception, which in this context means that if the pointer is in a near-eigenstate of position, the mental state is correctly correlated; if it's in a superposition of near-eigenstates, then the mental state is in one or the other, according to the norm-squared rule.
more on synchronic consistency
a great deal of work is being done in my model by the synchronic consistency requirement. above i produce it as a simple deduction from two premises, one that the normal linear dynamics of quantum mechanics is correct, and second, that a subject's reports of basic phenomenal experience can be correlated to the subject's experience.synchronic consistency is a logical requirement, forced upon us by the assumption that different minds see a single objective world, and that their observation and reports are sufficiently accurate to permit shared experience and communication.
however, it might appear that synchronic consistency violates the principles of special relativity, and this should be a worry. indeed, if synchronic consistency is violated, then the result would be for the possibility of superluminal communication.
but this is not a real worry. first, synchronic consistency is a mental fact; a fact about mental objects. the violation of relativity happens only if the mental objects are able to communicate. (that is, if you violate synchronic consistency, and also get rid of the mental objects entirely, you have the bare theory, which does not permit superluminal communication.) this means that the second premise above is a reasonable one; to deny it really amounts to a denial that we are talking about minds in the usual sense.
one might wonder how the various minds communicate to arrange the consistency, but this is to assume that the mental states must somehow be physical. it is already an antecedent property of the mental dynamics i propose that the mental states cannot simply be identified with particular physical states in a naive fashion. minds do not have physical locations. one basic possibility, which i call the direct divine action hypothesis, would say that God simply arranges for mental states to correspond to physical states without any mechanical process at all.
if synchronic consistency were some kind of communication between minds, we would have a problem, for supervenience, plus direct communication between minds whose associated brains are at some remove, produces a violation of special relativity. but special relativity only restricts what minds can do subject to the supervenience they have. synchronic consistency is an antecedent requirement of making the supervenience relation work, but it is not any kind of method that the minds have of communicating aside from the usual physical mechanisms of communication. (this exactly corresponds to the no-signaling theorem of traditional quantum mechanics.)
comparisons with other accounts
one might wonder whether a hard-boiled physicalist should be happy with this account. if one is suspicious about language that suggests the existence of minds independent in some way from physical objects, one might find the mental dynamics questionable.remove the mental dynamics from the theory, and what remains is the bare theory. indeed, the bare theory has trouble accounting for subjective features of experience, but this should be no trouble for the convinced disbeliever in the mental. i have no objection to the bare theory as a description of the physical, but it seems to me to be unable to account for the behavior of minds.
unlike von Neumann collapse dynamics, grw, and such, i accept here the wave function and the linear dynamics as a complete description of physical states and evolution. the many-worlds theory suffers from many problems; but at the least its extravagant ontology is avoided by my account. similarly the many-threads theory involves an extra needless ontology.
obviously this account is very close to the single- and many-minds theories. it differs from many-minds theories of course in having only one mind to a person rather than a large number. the single-mind q theory lacks an account of synchronic consistency. in addition, these theories need an account of a preferred basis. as pointed out above, the present theory does not involve a necessarily preferred basis.
the single-mind q theory supposes there to be some basis for a given mind, which determines which physical attributes correspond to mental predicates. because the theory lacks an account of synchronic consistency, it has a serious problem when one considers the possibility of a different physical brain setup which uses a markedly different basis. if two different observers, with different bases q see a similar set up, it is unclear how they are to relate in the single-mind q theory.
by contrast, my account has no particular trouble. the synchronic consistency requirement expresses the observed fact that different minds see the same things. it is a logical consistency requirement which presumes the objectivity of observation and observational reports and requires consistency in descriptive accounts from different observers.
in conclusion
whether this account is superior to others depends on what is being looked for in a physical theory. if the desire is to account for the results of experiments, then the solopsistic account is good enough.if however one wants an account which could accurately describe the entire universe, including its observers, and account for their experience, we must do better. to the extent one sees one's self as part of the natural world, an account which cannot adequately describe experience will not do.
the bare theory, together with the simplest notion of supervenience is strictly adequate here, but it forces us to think about there being superpositions of mental states, and not just the associated brain states. i know of no direct argument against this position, but for many people it contradicts what they claim to know of the nature of their own mind.
i object to the ontological extravagance of the many worlds, many minds, and many threads theories; in addition, they seem to my eyes to be irrealistic. clearly the single-mind theory is closest to my account, but the chief differences lie in the ability to avoid any need for a preferred basis for the mind. in addition, i place heavy stress on the need for synchronic consistency as a logical requirement.
