Bohr's "closure" of the experiment
as a necessary third intervention
in von Neumann's formalism
Von Neumann, "Mathematical Foundations of Quantum Mechanics", p. 351:
We therefore have two fundamentally different types of interventions which can occur in a system S or in an ensemble [S_1,...,S_N]. First, the arbitrary changes by measurements which are given by the formula
(1.) U -> U' = Sum over n from 1-infinity (U phi_n, phi_n) P_[phi_n]
(phi_1, phi_2,... a complete orthonormal set, cf. supra). Second, the automatic changes which occur with passage of time. These are given by
(2.) U -> U_t = e^-iHt/hbar U e^iHt/hbar
(H is the energy operator, t the time; H is independent of t). If H depends on t, then we may divide the time interval under consideration into small time intervals in each of which H does not change -- or changes only slightly -- and apply 2. to these individual intervals. Superposition gives the final result. [end quote]
From the perspective of the organic philosophy of Whitehead, this is not so good - we have on the one hand an "arbitrary" process and on the other hand an "automatic" process, and so we are caught between the rock and the hard place, so to speak. However, if we perform a metaphysical analysis upon these formulae, to try to penetrate the real metaphysical ideas for which they are the shorthand notations, we discover something extraordinary.
U is the Density Matrix in the emotional world. It first of all operates upon the Eigenvector in the physical world, and this result forms the bra vector that multiplies as an inner product by the ket vector that is again the Eigenvector in the physical world. These bra and ket vectors that comprise the statistical weight are in the mental sub-world of the physical world. This statistical weight then multiplies by a Projection Operator, representing the same Eigenvector (back to back). This Projection Operator is in the meta-physical world, since all projection operators project onto the classical world. A physically weighted sum of these meta-physical projection operators then constitutes U'. U' is therefore a Density Operator spanning the fifth, sixth, and seventh worlds, rather than a Density Matrix in the second or emotional world.
So, it would be more correct to rewrite von Neumann's interventions as follows:
(1.) U -> U' = Sum over n from 1-infinity (U phi_n, phi_n) P_[phi_n]
(2.) U' -> U'_t = e^-iHt/hbar U' e^iHt/hbar
(3.) U'_t -> U = some presently unknown function of U'_t
where U is the Density Matrix looking downward in the emotional world and U' is the Density Operator looking upward and spanning the fifth, sixth, and seventh worlds. U'_t is best described by the French term, *Densite de Presence*. The first intervention should apparently be conceived as a preparation, and the third intervention, which might be called the "closure" of the experiment, serves the same purpose as Heisenberg's actual event at the measuring device, which precedes the reduction. The reduction would then correspond to a second application of the first intervention. To understand the third intervention, consider the following quote from Niels Bohr on p. 98 of "Atomic Theory and the Description of Nature", with my explanations in brackets:
"On the whole, the analysis of our sense impressions discloses a remarkable independence of the psychological foundations of the concepts of space and time, on the one hand, and the conceptions of energy and momentum, based upon actions of force, on the other hand. Above all, however, this domain, as already mentioned, is distinguished by reciprocal relationships which depend upon the unity of our consciousness and which exhibit a striking similarity with the physical consequences of the quantum of action. ...In particular, the apparent contrast between the continuous outward flow of associative thinking [the stream of consciousness] and the preservation of the unity of personality [according to Kant rather than James] exhibits a suggestive analogy with the relation between the wave description of the motions of material particles, governed by the superposition principle, and their indestructible individuality. [This analogy is between {the observer in world 7 and the extended observer in worlds 7-5} and {the observed in world 1 and the extended observed in worlds 1-3}!] The unavoidable influence on atomic phenomena caused by observing them here corresponds to the well-known change of the tinge of the psychological experiences which accompanies any direction of the attention to one of their various elements."
So, it is this very "analogy", as I have explained it metaphysically, that lays the foundation for the third type of intervention, required by von Neumann's formalism, as it actually makes sense metaphysically. The Density Matrix is from the point of view of the embodied observer in the second or emotional world, while the Densite de Presence is from the point of view of the detached observer in the seventh or meta-physical world (it is actually from the point of view of the "knower" at the highest place in the fourth or etheric world, because the detached observer here enters into the "analogy" in terms of the "unity of personality", i.e. as an object). The "analogy" relates the Densite de Presence and the Density Matrix and stipulates that the one can be carried over into the other, as the third intervention. However, there may indeed be a law of transformation for the third intervention that alters the numerical results and makes the whole issue raised here much more than a *merely* interpretational issue.
The unitary time development, von Neumann's second intervention, in fact occurs in the phenomenal realm, while only the so-called quantum jumps, which refer to von Neumann's first intervention, occur in the noumenal quantum realm. These are the 'substantive parts' and the 'transitive parts' of the 'stream of consciousness', as described by William James on pp. 26-7 of the Briefer Course. The whole process is something like a dialogue between the detached observer (or actually the "knower") and the embodied observer.
This begins to put some meat on the bare bones of von Neumann's formalism. As von Weizsacker insisted, it is not *just* an algorithm! Once one begins to understand the correct form and context of the algorithm, one finds that it is accompanied by profound meaning that can be utilized to accomplish what can only be regarded as miracles by the uninitiated. By thus unearthing the secret knowledge of von Neumann, we draw near to penetrating the mystery of the Philadelphia Experiment of 1943, during which Einstein, von Neumann, and Tesla succeeded in teleporting the USS Eldridge, a 1240-ton Cannon class destroyer escort, from Philadelphia Harbor to Norfolk, Virginia, and back again! This of course corresponds (at the lab scale!) to the transformation of the noumenal Density Matrix in the second or emotional world into the phenomenal Density Operator in the fifth, sixth, and seventh worlds, accompanied by a unitary evolution into the Densite de Presence and then a transformation back into a new Density Matrix. The decoherence effect in this case was not to render the isolation of the macroscopic object entirely impossible, but rather to spatialize the metaphysical transformation implied by the quantum measurement process.
The secret knowledge of Tesla can be glimpsed by considering the meaning of the Maxwell equations in the context of metaphysical epistemology. The Current and the Charge are the right and the left "legs" of the Knowledge, while the Magnetic field and the Electric field are the right and left "arms" of the Knowledge. The Curl operator and the Div operator represent the Knower and the Known, respectively. The Curl and the Div are in fact ET operators, i.e., grey type ET's embody them in the functioning of the universal bodhi mind. The Time Derivative operator is a hybrid in the fifth or phenomenal world, indicating that it refers to the internal time consciousness of Husserl. This is all the basis for the notion of metaphysical light, or the Light of God, which is critical for an understanding of human spiritual potential as well as human intelligence, due to the equation: sentient intelligence = spiritual light experienced by the sentient being and retained within its causal body.
BTW, the so-called Quantum Zeno Effect, utilized by Henry Stapp in his present theory of quantum-mind, actually makes sense within my reinterpretation of von Neumann's formalism, whereas prior to that it was sheer sophistry. For if all of these interventions are real:
(1.) U -> U' = Sum over n from 1-infinity (U phi_n, phi_n) P_[phi_n]
(2.) U' -> U'_t = e^-iHt/hbar U' e^iHt/hbar
(3.) U'_t -> U = some presently unknown function of U'_t
then it is clear that one could get a factually different dynamical process if one short-circuited the process thusly:
(1.) U -> U' = Sum over n from 1-infinity (U phi_n, phi_n) P_[phi_n]
(2.) U' -> U = some presently unknown function of U'
where (3.) in the first instance and (2.) in the second instance are implemented by dynamical laws of transformation, which may be different in the two instances. Without a factually different dynamical process, there is no *real* effect. My reinterpretation provides for the possibility of a factually different dynamical process.
Another motivation for the present innovation is the following:
Dirac, "Lectures on QFT" (1964-65), Lecture 8:
p. 1:
This work though has serious difficulties in it. There are many qualities appearing in the theory which turn out to be infinite although they ought to be finite; and people have followed all sorts of tricks for avoiding these difficulties, but the result is that the theory is in rather a mess. I ought to confess that I really don't understand it myself. The departures from logic are very serious and one really gives up all pretense of logical development in places...
p. 3:
People usually say that these equations establish the equivalence of the two pictures, that one can use whichever one likes indiscriminately. However, the argument is valid only provided e^iHt exists as an operator in Hilbert space and for the Hamiltonians which one meets with in quantum field theory there is good reason to believe that this is not so and the two pictures are not equivalent...
p. 5:
For simple examples, where we have only a finite number of degrees of freedom, the operator e^iHt does exist alright and all that you have learnt can still be retained; but for quantum field theory the two pictures are not equivalent and one must think of the Heisenberg picture as the more fundamental one which is valid in nature...
p. 6:
It is not possible to get a solution of the Schrodinger equation for which the ket vector stays in Hilbert space...
p. 9:
We cannot get solutions in the Schrodinger picture with the kets remaining in Hilbert space, and corresponding to that we cannot get solutions of the Heisenberg picture in which our q-numbers operate only on the kets of a Hilbert space. We have to imagine that the q-numbers of the Heisenberg picture operate on the vectors of some space which is bigger than a Hilbert space. I don't know the mathematical nature of this more general space--it is better to leave it unspecified for the present rather than to make a guess which might later turn out to be unsuitable for physical purposes. I expect that mathematicians will make guesses of what the space is, but they might very well guess wrong and they already have made a wrong guess when they thought that Hilbert spaces were adequate for physical purposes... [end quotes]
In my new reinterpretation, the second intervention transforms U' -> U'_t, which we are interpreting as the transformation of the Density Operator into the Densite de Presence, both occupying the same station within the phenomenal fifth, sixth, and seventh worlds of the ontological system of worlds. So it is very suggestive, indeed, to think that the effect of the time-development operators upon the Density Operator has been precisely to knock it out of the Hilbert space by transforming it into the Densite de Presence. That occurrence would not only not be a problem for the formalism as I am reinterpreting it, but it is strongly suggested by it.
Needless to say, if I am right that von Neumann's formalism is only two-thirds complete and requires supplementation by an entirely new dynamical law, which would render the speculations of quantum ontologists no longer epiphenomenal, the discovery of that dynamical law would be the greatest breakthrough since the discovery of quantum mechanics.
Peter Joseph Mutnick 1949 - 2000
Home
|