Open Letter to Henry Stapp
The following is concerned with your groundbreaking 1979 paper, "Whiteheadian Approach to Quantum Theory and the Generalized Bell's Theorem", which of course has relevance to your most recent work, "Bell's Theorem Without Hidden-Variables", LBNL-46942, June 18, 2001.
You start with the algorithm, comprised of Density Operator, Rho_A, for the preparation, Alphapoint Time Development Operator, U, Omegapoint Time Development Operator, U^-1, and Density Operator, Rho_B, for the observation. The probability of the given preparation leading to the given observation is then given by P(A, B) = Tr U Rho_A U^-1 Rho_B. Now, I think there is alot of subtlety hidden here in the real meaning of these "operational specifications", A and B, as you call them. It seems to me, for instance, that there is quite a big difference ontologically between a preparation and an observation. A preparation is like an action, which must have causal efficacy, while the observation is like a perception, which is essentially phenomenal.
The algorithm just mentioned, which you describe as the whole content of the pragmatic approach, takes place (like all algorithms) at the classical level, von Neumann's III, which I assign to the three higher worlds: phenomenal, causal, and meta-physical or classical proper. My seven-world system is just based on the subject/object dualism, but reiterated as mental/physical in the lower octave and meta-physical/phenomenal in the higher octave. The intermediate etheric world then divides the lower octave from the higher octave, while the emotional world divides the mental world from the physical world and the causal world divides the meta-physical world from the phenomenal world. I maintain that this metaphysical structure is essential for understanding even the formulas and procedures of the pragmatic approach, since it is the inherent structure of all our experience and of nature.
Now, you specify that:
"Quantum theory is not a comprehensive, unified theory of nature: The completeness claimed by Bohr was of a limited kind. Bohr stressed that quantum theory rests on an apparent contradiction between the demands that the quantum system must interact with the surrounding environment (i.e., with the measuring devices) to be prepared and observed, but must be isolated from the environment to be defined. That is, the quantum nature of the interaction between the quantum system and measuring system makes it impossible to consider the quantum system as a separately existing system: It must be regarded as an integral part of the whole experimental arrangement. On the other hand, in order to represent the quantum system by a wave function, governed by the Schrodinger equation, this system must be idealized as a separate system. And for this idealization to work, the quantum system must be effectively isolated from quantum interactions with the surrounding environment.
"To resolve these conflicting demands, quantum theory must in principle be applied to situations that conform to the format shown in Fig. 1. The spacetime region R_A of the preparation is separated from the spacetime region R_B of the observation. The gap between them is bridged by the quantum system, which must be effectively isolated from the environment during the passage from R_A to R_B. If the quantum system were not effectively isolated from the environment during this interval, then it could not be idealized as a separate system, and its quantum theoretical description in terms of a wave function that develops in time according to the Schrodinger equation appropriate to that system would lose its validity: The intrusion of the environment would cause quantum jumps.
"This isolation requirement, and the consequent limitation on the scope of quantum theory, arises from the need, within the pragmatic framework, to treat the measuring devices and the surrounding environment classically, i.e., in terms of operational specifications."
Now, I would like to make the case that Leon Rosenfeld makes, namely that the so-called pragmatic approach is already adequate and does not need another interpretation added to it. I believe that is because the pragmatic approach is already, in essence, both ontological and metaphysical. Your Fig. 1,
which is a bit better when it is connected with the appropriate lines, is, I would suggest, an archetypal and metaphysical diagram, existing in metaphysical space. The regions, R_A and R_B, are NOT, in essence, spacetime regions, as you specify, but metaphysical regions. R_A signifies the seventh or meta-physical world, while R_B signifies the fifth or phenomenal world. The introverted and transcendental intentional experience of the classical observer in R_A prepares the system in the first or physical world by virtue of its oroboric connection to that world, and the extroverted and phenomenal representational experience of the classical observer then observes the total Quantum System, conceived in terms of its causal properties and hence raptured into the causal world, in the phenomenal world, signified by R_B.
Now, you hesitate to call this isolated system a noumenal *potentia* in nature, which term you would rather reserve for the world as a whole, and not just the world in the backward light cone of the mental pole of an Actual Entity, as Whitehead would do, but the whole world that has already settled from the perspective of the preferred frame of reference established by the cosmological solution to Einstein's equation (Godel's idea) *or* the cosmic background radiation (your more recent idea). Question: Can these be shown to be the same?
In any case, your reasoning here seems to me like a throwback to classical thinking. Apparently, it seems obvious to you that the whole world is a noumenal reality and an ontological *potentia*, while individual atomic elements are just abstractions. But, IMHO, the very essence of quantum theory is that the opposite of this classical intuition is correct. It is interesting that not only James and Whitehead seemed to understand this, but also Marx and Engels. The latter made clear that by "materialism" they did not refer to matter as a whole, which was but an abstraction, but rather to the individual embodiments of matter.
So, your metaphysical assumptions, it seems to me, are questionable and must be examined. What are the simple facts of phenomenological and ontological reality? I think they are these: The whole ontological framework can be well conceived in terms of the subject/object Observer/Observed framework. The Observed must always be some isolated element under observation and it must be conceived as an *individual* noumenon. The horizon of all such Observed noumenal elements is the whole world, but the whole world is not itself an Observed noumenal element. Even as the Observed noumenal elements emerge from the horizon of the whole world, so the Observer emerges from its own internal and transcendental noumenal essence. This internal noumenal essence is discovered through the phenomenological reduction and of course it is complementary to the external noumenal essence of Observed elements in nature. Either you have the transcendental ego, grounded in its internal noumenal essence, and the whole world outwardly, or you have von Neumann's abstract "ego" (Husserl's *natural ego*) as the Observer and some individual Observed element as the external noumenal essence. The former state of affairs constitutes the phenomenological system of worlds, while the latter state of affairs constitutes the ontological system of worlds. These two systems of worlds are transformable, one into the other, through a rotation in metaphysical space.
So, based on these considerations, I doubt that it is correct to say that the whole world can be regarded as obeying the Schrodinger Equation. What I think Whitehead intended is that the mental pole of an Actual Entity, which is in an atomic region that approximates to a point-instant, becomes the microscopic or quantum subject or "observer" establishing either the State Vector description or the Actual Event prehension of other Concrescences in the future or the past, respectively. State Vector Substance therefore represents the forward lightcone, with its origin at the mental pole of the present Actual Entity and its forward expanse in the emotional world of prehensions (feelings). Similarly, Potential Actual Event represents the backward lightcone, making accessible to the mental pole of the present Actual Entity the Superject as Potential of each Concrescence in the emotional world or "Actual World" of its backward lightcone. Whether Whitehead is correct in identifying the emotional world of the backward lightcone with the Actual World is dubious. Again, one might rather identify the term Actual World with the whole world as the physical horizon of all externally or ontologically physical noumenal reality. This Actual World is then realized through the phenomenological reduction, which is identifiable with the State Vector Reduction. From Heisenberg's point of view, the whole world becomes involved in the latter stages of an actual event at a measuring device, which in turn leads to the reduction.
The thing that is different between this and Heisenberg's perspective is that he imagined the State Vector Substance and the Potential Actual Event as representing the interaction (action and back-action) of the functionally classical measuring device with the noumenal quantum system. The interpretation of State Vector Substance and Potential Actual Event as lightcones only makes sense from the perspective of a microscopic or quantum subject or "observer". This is a profoundly different situation than a lab scale classical observer relating to a noumenal quantum system through a mediating functionally classical measuring device.
These are just some preliminary considerations. Let me know if they make sense to you, so far.