by Jack Sarfatti
Introduction.
Bohm was one of Oppenheimer's students and was driven from America by Senator Joe Mc Carthy. He wound up in Brasil in 1952 where he wrote:
"Proof That Probability Density Approaches |psi|^2 in Causal Interpretation of the Quantum Theory"
(Physical Review,Vol 89, Jan 15, 1953)
Bohm's meta-theory replaces Bohr's meta-theory. Bohr's meta-theory, called the Copenhagen interpretation, requires that the quantum wave function (i.e., psi) is a complete description of individual events in quantum reality. Bohm, in agreement with Einstein, says that the wavefunction is an incomplete description of individual events that requires, in addition, the initial position of the actual material particle which is guided by (but does not directly affect) its wavefunction. The actual individual particle is not required in Bohr's meta- theory.
One of the defects of Bohr's Smoky Dragon meta- theory is that it is not clear how the actual matter we experience directly in so-called classical reality emerges from the quantum wave function, which in Bohr's view is implicitly more "mental" than "material" because the wave function is basically a pragmatic rule or algorithm that enable us to compute numbers for our expectations to observe particular results of experiments. Bohr's meta-theory is "epistemological". In contrast, Bohm's meta-theory is "ontological". Not only that, Bohm's meta-theory has a self-referential Godel "strange loop" in which it is not only a meta-theory, but is also it's own object, i.e., the very theory described by the meta-theory.
Bohr's meta-theory requires two separate ways for the wave function to evolve in time. In the first way, the wave function evolves as an isolated system between measurements in what is called a "unitary" way. The second way is the "measurement" which is a "nonunitary collapse" the wavefunction into an "eigenfunction" of the "observable" operator defined by the "total experimental arrangement". Bohm's theory does not need the second way of "collapse". In this respect, Bohm's theory is like the "many worlds" meta-theory of quantum reality.
Unitarity means that the total probability is conserved as the isolated system evolves. The system is no longer isolated when it is being measured. It doesn't even have its own wave function any more. The collapse is in the new larger combined wave function of both the original system and the measuring apparatus. The total probability of the combined system is not conserved in the collapse. Therefore, the process is called "nonunitary". The recent fashion is to attribute this collapse to quantum connections with the rest of the universe called "the environment". We shall see that Bohm's theory has "collapse without collapse" -- to coin a new Wheelerism.
Bohm, in his first papers on his new "hidden variable" theory, showed that if one simply assumed Born's formula for the probability density at an initial time, then the time evolution preserves the formula. In this 1953 paper he shows that "random collisions" quickly damp any distortion P of Born's formula |psi|^2 back to it. Bohm wrote:
... because those discrepancies have been shown to die out as a result of collisions, we can expect thatunder normal conditions the difference between P and |psi|^2 would be negligible. Conditions are suggested, however, in which this difference might be appreciable...
It is Brian Josephson's and Henry Stapp's idea (developed independently) that the essential difference between living an nonliving matter is that "this difference" is "appreciable".
Let us recall that Eberhard's theorem shows that Born's formula |psi|^2 prevents any use of the nonlocal quantum connection as a faster-than-light practical communication channel. As soon as P - |psi|^2 differs from zero, it is a new ball game.
Section II of Bohm's paper is a very long esoteric mathematical argument that cannot be summarized in a popular way without a lot more effort on my part. It shows the incredible analytical power of Bohm's mind when he was young over forty years ago. It is interesting that Bohm's only acknowledgement is to discussions with Richard Feynman.
Section III is much more physical and easy to understand. It clearly demonstrates the economy of hypotheses and intuitive superiority of Bohm's meta-theory over Bohr's on the level of individual quantum events. Bohm treats two uranium nuclei with the same wavefunction today one of which decays tomorrow and the other in two billion years from tomorrow. The two nuclei are connected in a more elaborate Schrodinger Cat set up so that the decay of the individual nucleus will trigger a large thermonuclear explosion. Bohr's meta theory says that it is impossible in principle to imagine any physical difference between the two nuclei. Bohm's theory enables us to imagine a very vivid difference in terms of the initial positions of the nucleons inside each nucleus even though they have the same initial wave function.
One final point. If you read the Landau-Lifshitz books on quantum physics based on Bohr's meta theory one sees an emphasis on the two very different kinds of statistics needed. Both kinds are combined in the impure density matrix which is a classical statistical distribution of pure states. Each pure state has a kind of quantum statistics that is different in kind from the classical. Bohm points out that in his theory there is only one kind of statistics as well as only one kind of time evolution provided that one assumes definite paths in space for actual particles in which their instantaneous velocity is proportional to the gradient of the phase of the wavefunction. Born's formula is the result of a large number of random collisions experienced by the members of the statistical ensemble with their environment. The technology of the 90's is very advanced compared with the technology of the 50's. It is now possible to damp out the random collisions and work with individual atoms even individual electrons. One can now test Bohm's ideas. In addition, I, building on ideas of Penrose and Hameroff, have offered some biological mechanisms in microtubules of the living cell that damp out random collisions of what may be the Eccles Gates that connect mind to matter -- in which mind is conceived as a quantum wavefunction of the system of single electrons that control the conformation of dimer proteins that cover the microtubules like the kernels on an ear of corn.