The Fundamental Approach to Math and Physics [Peter Mutnick] Henry Stapp has rewritten the paper on David Deutsch's approach that I posted earlier. Below is the rewritten abstract, with my comments. You can see the whole rewritten paper of Stapp at: http://www-physics.lbl.gov/~stapp/stappfiles.html [Henry Stapp] September 25, 2001........LBNL-48917 The Basis Problem in Many-Worlds Theories {This work is supported in part by the Director, Office of Science, Office of High Energy and Nuclear Physics, Division of High Energy Physics, of the U.S. Department of Energy under Contract DE-AC03-76SF00098} Henry P. Stapp Lawrence Berkeley National Laboratory University of California Berkeley, California 94720 {abstract} It is argued that a many-worlds interpretation of quantum theory exists only to the extent that the associated basis problem is solved. The core basis problem is that the robust enduring states specified by environmental decoherence effects are essentially Gaussian wave packets that form continua of non-orthogonal states. Hence they are not a discrete set of orthogonal basis states to which finite probabilities can be assigned by the usual rules. The natural way to get an orthogonal basis without going outside the Schroedinger dynamics is to use the eigenstates of the reduced density matrix, and this idea is the basis of some recent attempts by many-worlds proponents to solve the basis problem. But these eigenstates do not enjoy the locality and quasi-classicality properties of the states defined by environmental decoherence effects, and hence are not satisfactory preferred basis states. This core problem is obscured by approaches that treat the universe as a quantum computer, but it needs to be addressed and resolved before a many-worlds-type interpretation can be said to exist. [Peter Mutnick] The Density Matrix is naturally imbedded in an Einstein-like GR where, however, the Stress-Energy-Tensor is taken as fundamental, rather than the spacetime geometry. The second order tensors are the Metric Tensor, the Curvature Tensor, and the Torsion Tensor. The degrees of freedom of the Density Matrix of QM are related to torsion, which is zero in Einstein's original GR. The reason the Stress-Energy-Tensor is primary in a fundamental approach is that it relates to SET theory as the foundation of all mathematical structures. This word game really works because sets of things are always related to logical predicates, which are idea-like. Hence, any SET possesses pure ideational energy, which finds expression in the fundamental Stress-Energy-Tensor. Differential geometry is indeed one of the mathematical structures that can be derived from SET theory. The Hilbert space formalism of QM is another mathematical structure that can be derived from SET theory. I just saw Hal Puthoff on the TV program "Psychic Espionage". He seems like an intelligent and open-minded fellow. So, in his honor, I might add that the fundamental Stress-Energy-Tensor is indeed an expression of the Zero-Point Energy, which is in turn an expression of Stapp's Body-World Schema. Hence my motivation is laid bare in saying that the Stress-Energy-Tensor is embedded in GR extended to include torsion. I am trying to account for the fact that, in Stapp's view, we can know what the degrees of freedom of the Density Matrix or reduced Density Matrix are prior to knowing what its eigenstates are. My program of deriving GR from the Body-World Schema and embedding the Density Matrix in the formalism of GR would allow for Stapp's prerequisite in a meaningful way, which otherwise would not be the case. Stapp intends that the degrees of freedom of the Density Matrix are to be established from experimental considerations, but this must be suitably formalized in a fundamental approach that aims at getting beyond the need for actual observers. The Density Matrix is quantal in the extended sense (the psycho-physical sense), but not in the physical or purely noumenal sense. Hence, one need not assume that it obeys the Schrodinger Equation. This gives one the freedom one needs to discover the proper law for the time-development of the Density Matrix that enables its Eigenvectors to also be Eigenvectors of an observable Operator and hence to be candidates for "satisfactory preferred basis states". The shared Eigenvectors will ensure classicality, and the locality requirement is obtained by making sure that we are talking about the Event-Particles of Whitehead rather than the Point-Particles of Bohm. It is paradoxical that the literal locality of the Bohm-Point in configuration space is what spoils its locality in real space. In fact we must always deal with the Point-Instant and not just the Point. By introducing the nonlocality of the Instant at the fundamental level, we ensure the locality of the relativistic Point-Instant at the level of phenomenal Events. The only thing that made Bohm's theory objectionable to the founders of QM is corrected by making the Bohm theory relativistic in the way specified by Whitehead. Eigenvectors of Event-Particles are abstractions, as are Point-Instants. The real things (res verae) are the Present Subjects of Present Moments that become Actual Entities and eventually Subject-Superjects or Concrescences. These becomings do not occur in a unique temporal sequence, and what Whitehead is really getting at by stating this is more than the relativity of time - it is the relativity of being - that every being is a potential for becoming. The conclusion is that process does not occur in a temporal sequence at all, but rather in parallel. Everything happens at once, and limited processors introduce temporal sequence as a convenience. This character of parallel processing is how and why this approach is inherently a MWI, in the sense of David Deutsch. This is something like the block universe of Einstein, except that it is not static at all, but rather like an infinite process - everything happens at once. There is some reason to believe that this is in fact how Einstein understood his so-called "block universe". To wit, he endorsed the God of Spinoza, which is defined as "substance consisting of infinite attributes, each one of which expresses eternal and infinite essence". The latter phrase indicates that this is not static quantum mechanics, exclusive of the "selection" process, but a complete quantum mechanics, fully inclusive of the "selection" process. Moreover, it clearly has a MWI flavor. In fact, it is unabashedly a crystal clear statement of MWI. It also provides the approach to a theory that that is fully noumenal or physical and hence quantal in the most literal sense. Such a theory must be based on the State Vector of (universal) Substance and its *inherent* representations, which are defined by the Present Time Operator of Whitehead and the Place Operator of Bohm. |