3. Thoughts Within the Quantum FrameworkSarfatti Note: This is all true but it applies equally to both dead and living organizations of matter. The essential difference between the dead and the living, is that in a living system the structure of the Heisenberg operators of the top-level observables of the brain are modified by the actual jumps or wave function collapses. This modification is the quantum mechanism of learning and memory without which consciousness is not possible. In Bohm's theory this is feedback from the particle to its wave function. In David Albert's theory it is the Godelian strange loop of self-measurement.Let us consider now how the brain would be simulated by a set of parallel computers when the brain is treated as a quantum system. To make this description clear to every reader, particularly those with no familiarity with quantum theory, I shall start again from the classical description, but spell it out in more detail by using some symbols and numbers.
We introduced a grid of points in the brain. Let these points be represented by a 'set' (i.e., '{ }') of vectors {xi}, where i ranges over the integers from 1 to N. At each point xi there was a set of fields {Fj(xi)}, where j ranges from 1 to M, and M is relatively small, say ten. For each of the allowed values of the pair (i,j) the (field) quantity Fj(xi) will have (at each fixed time) some value taken from the set of integers that range from -L to +L, where L is a very large number. There is also a grid of temporal values tn, with n ranging from 1 to T.
The description of the classical system at any time tn, is given, therefore, by specifying for each value of i in the set {1, 2,..., N} and each value of j in the set {1,2,..., M} some value of (the field) Fj(xi) in the set {-L,..., +L}. We would consequently need, in order to specify this classical system at one time, tn, NM "registers" or "boxes", each of which is able to hold an integer in the range {-L,..., +L}.
We now go over to the quantum mechanical description of this same system. It is helpful to make the transition in two steps. First we pass to the classical statistical description of the classical system. This is done by assigning a probability to each of the possible states of the classical system. The number of possible states of the classical system (at one time) is (2L + l)^NM (That is (2L + 1) raised to the NM power.) If the probability assigned to each of the possible classical systems is one of K possible values then the statistical description of the classical system at one time requires (2L + 1)^NM registers, each with the capacity to distinguish K different values. This can be compared to the number of registers that was needed to describe the classical system at one time, which was NM registers, each with a capacity to distinguish (2L + 1) different values.
If the (new) index m runs over the (2L + 1)^NM possible classical system (states or configurations) then a probability Pm is assigned to each value of m, where Pm >=0, and the sum over all Pm = 1.
The quantum-mechanical description is now obtained by replacing each Pm by a complex number
Pm -> Rm(cos@m + isin@m),
where Rm = squareroot of Pm, @m is an angle, cos@ and sin@ are the cosine and sine functions, and i = square root of - 1.
This replacement might seem an odd thing to do, but one sees that this description does somehow combine the particle-like aspect of things with a wavelike aspect: the probability associated with any specific classical state m is Rm^2 = Pm, and an increase of @m gives wavelike oscillation.
I am not trying to explain here how quantum theory works: I am merely describing the way in which the description of the computer/brain system changes when one passes from the classical description of it to the quantum description.
For the classical description we needed just NM registers, but for the quantum description we need 2(2L + 1)^NM registers. Thus the information contained in the quantum mechanical description is enormously larger. We need a value of Rm, and of @m for each of the possible states of the entire classical system, where the specification of the state of the classical system includes, simultaneously, a value of Fj(xi) for each allowed combination of values of i and j. That is, for each conceivable state of the entire classical system one needs two separate registers.
Consider again a belief. As before, a belief would correspond physically to some combination of values of the fields (i.e., Fj(xi)) at many well-separated field points xi. In the classical computer model of the brain there was no register that represented, or could represent, such a combination of values, and hence we were led to bring in an "external knower" to provide an adequate ontological substrate for the existence of the belief. But in the quantum-mechanical description there is such a register. Indeed, each of the 2(2L + 1)^NM registers in the quantum mechanical description of the computer/brain corresponds to a possible correlated state of activity of the entire classically-conceived computer/brain.
Consequently, there is no longer any need to bring in an "external observer": the quantum system itself has the requisite structural complexity.
Moreover if we accept von Neumann's (and Wigner's(7)) suggestion that the Heisenberg quantum Jumps occur precisely at the high level of brain activity that corresponds to conscious events then there is an "actual happening" (in a particular register, m) that corresponds to the occurrence of the conscious experience of having an awareness of this belief. This happening" is the quantum jump that shifts the value of Rm associated with this register m from some value less than unity to the value unity. This jump constitutes the Heisenberg actualization of the particular brain state that corresponds to this belief. Jumps of this general kind are not introduced merely to accommodate the empirical fact that thoughts exist. Instead, they are already an essential feature of the Heisenberg description of nature, which is the most orthodox of the existing quantum mechanical descriptions of the physical world. Thus in the quantum mechanical description of the brain no reference is needed to any "ghost behind the machine": the quantum description already has within itself a register that corresponds to the particular state of the entire brain that corresponds to the belief. Moreover, it already has a dynamical process for representing the "occurrence" of this belief. This dynamical process, namely the occurrence of the quantum jump (reduction of wave packet), associates the thought with a choice between alternative classically describable possibilities, any one of which is allowed to occur, according to the laws of quantum dynamics. Thus the dynamical correlates of thoughts are natural parts of the quantum-mechanical description of the brain, and they play a dynamically efficacious role in the evolution of that physical system.Sarfatti Note, Murray Gell-Mann in his book, The Quark and the Jaguar calls this position of Stapp's "Flapdoodle" because Murray considers any one who does not use the many- worlds interpretation of quantum mechanics to be essentially a crackpot distorting the story. You see Stapp's position that there is an actual world requires spooky action at a distance which severely disturbs Gell-Mann's sense of reality. Heisenberg would also be in the Flapdoodle Camp of potty physicists along with Penrose and Bohm. In the many worlds theory of quantum reality the feeling that there is an actual universe with a unique history is an illusion. In one universe O J is innocent, in another he is guilty, in still another Nicole and Ron are still alive, and so on. David Albert has shown that if the many worlds theory is really true that we can literally "photograph" these other worlds! Many worlds or spooky telepathic action at a distance faster than the speeding photon - make your choice. Either way it's a weird weird world we live in! :-)
The essential point, here, is that the quantum description is automatically wholistic, in the sense that its individual registers refer to states of the entire brain, whereas the individual registers in the classically conceived computer/brain represent only local entities. Moreover, the quantum jump associated with the thought is a wholistic entity: it actualizes as a unit the state of the entire brain that is associated with the thought.Sarfatti Note. Stapp is obviously on the Righteous Path to Buddhahood. I am still wrestling with harmonizing his picture of the quantum solution to the mind-matter mystery with my own. Like Heisenberg versus the Schrodinger versions of quantum mechanics in the 1920s they must be two sides of the same coin. Stapp, coming from Heisenberg's idealistic view, sees the wave function as fundamental and complete with no hidden variables. Matter is the expression of the deterministically evolving, but highly nonlocal, wave function. Our experiences, our inner thoughts, the aha of discovery, our feelings of pleasure and pain are all quantum jumps of the wave function of our entire brain in Stapp's theory. In contrast, I, coming from Bohm's materialism, with hidden variables, obviously see the hidden variable elementary particles and their local force fields as matter with the nonlocal spooky acting quantum goo connecting it all into a unitary whole as the mind-stuff. This is apparently diametrically opposite to Stapp's picture! Yet there are also significant similarities. Stapp has a criterion for going beyond orthodox theory in which the top- level observables of the brain are modified by the quantum jumps of the collapsing wave functions. This is the essence of his July 1994 Physical Review A paper on what is essentially a model for the backwards in time psychokinesis reported in a paper by Helmut Schmidt that Stapp cites. Bohm has an equivalent criterion in which the hidden variable particle acts back on its mindlike nonlocal quantum spooky goo. Both of these pictures, in turn, correspond to David Albert's strange loop of self-measurement. Stapp's quantum jump does correspond to Bohm's particle falling into an attractor created by the local classical potential fused with the nonlocal quantum potential. Finally, we have Penrose's OR process beyond the ordinary quantum jump which is also another way of describing how the Heisenberg operators are changed by the jump. All of this was described mathematically by Steven Weinberg who lost his nerve and rejected his own equations because they were too weird (e.g. Dreams of a Final Theory).The fundamentally wholistic character of the quantum mechanical description of nature is perhaps its most basic and pervasive feature. It has been demonstrated to extend to the macroscopic (hundred centimeter) scale in, for example, the experiments of Aspect, Grangier, and Roger (8). In view of the fact that the wholistic character of our thoughts is so antithetical to the principles of classical physics, it would seem imprudent to ignore the wholistic aspect of matter that lies at the heart of contemporary physics when trying to grapple with the problem of the connection of matter to consciousness.