Sketch of Solution to Stapp's 3 Problem's for MWI
(From "The Basis Problem in Many-Worlds Theories", Sept. 18, 2001, LBNL-48917, at http://www-physics.lbl.gov/~stapp/stappfiles.html)
The first problem that he [David Deutsch] must resolve is what he calls "the notorious difficulty of specifying the preferred instants t when a measurement is completed". These instants must be defined solely in terms of (1), the single evolving state of the universe, which evolves always via the Schroedinger equation, and (2), the law that governs this continuous unitary evolution.
The second problem is that at each of these distinct "instants of splitting" the unified actual universe must be decomposed in a specified way into two systems, the 'observed system' and 'observing system'. Hence the rule that defines how the unified universe is to be split at that instant into these two special parts must be specified in terms solely of the state vector itself and its law of evolution.
The third problem is to define for each instant a set of evolving basis vectors so that the state of the universe can at every instant be decomposed in a unique way into a sum of component vectors that can be associated with different worlds, or branches of reality, that possess definite values for the quantities "measured" at each instant of splitting.
I start with the State Vector of (universal) Substance. Substance has Attribute perceived by Intellect, where Attribute and Intellect are inherent in Substance. Substance is hence not physical, but is the world soul, or second hypostasis, of the Neoplatonists. Attribute is prima materia, the first hypostasis, and Intellect is nous, the third hypostasis. The relation of Intellect to Attribute is that of Operator to Eigenvector, so these are inherent in (universal) Substance.
Substance divides naturally into Subject and Object, where Object is the Thing-in-Itself, and Subject is the rather extraordinary Subject that can observe directly the Thing-in-Itself. This Subject is in a sense Everything else except the Thing-in-Itself under observation, but this Everything else is in a sense Nothing. It is basically the Etre Pour-Soi of Sartre, as juxtaposed to the Etre En-Soi. Now that we have a definition of the two subsystems in terms of their Being, we can recombine them, as does Sartre, on the phenomenal level. Etre Pour-Soi-En-Soi becomes Ens Causa Sui. This total system, decomposed naturally into observing and observed parts, would seem then to itself be observable, which means that the Operator and Eigenvector derived from Intellect and Attribute should be applicable to it.
The actual form of the Intellect Operator is derived from the present time considerations, having to do with "the preferred instants t when a measurement is completed". Hence the Intellect Operator is none other than the Present Time Operator, invoked recently by me in relation to Whiteheadian process theory. The basic idea here is that Subject and Object are essentially physical, and are hence described by Attribute (which is also physical) of (universal) Substance, while the Present Time Operator, as a meta-physical abstraction from the point and instant of physical reality, is anti-physical and hence identifiable with Intellect (or nous).
To understand how these considerations define representations for the State Vector of (universal) Substance, one must realize that ideas like Everything else and Nothing, which we used to define Subject as the observing subsystem, are essentially classical. Something and Nothing are the two subsystems of Object and Subject, but their oneness is Everything. Nothing is of course like the Vacuum and Everything is like the classical world that includes not only the Something and the Nothing, but all other Somethings, in an implicate sense, as well.
The point is that all of this defines a quantum object that can be projected onto nature and regarded as a ket vector in relation to the bra vector of the classical subject involving space and time. This yields the position representation for (universal) Substance. The momentum representation is defined by Whiteheadian process theory. The Present Time Operator is the Operator for the momentum representation, while the Place Operator, defining Motion as the Holomovement, is the Operator for the position representation. The combined system, Etre Pour-Soi-En-Soi as Ens Causa Sui, constitutes an Eigenvector for the Present Time Operator, while Das Man and Dasein constitute an Eigenvector for the Place Operator, as an expression of Sein, which is the quantum implicate order.