The self-contradictory foundations of formalistic quantum measurement theories

Geoffrey L. Sewell

Gaisi Takeuti

As is well-known, Dirac [1 gave a very elegant foundation of quantum mechanics, which contained however some self-contradictory concepts from the mathematical point of view.J. von Neumann gave another foundation of the theory based upon his spectral theory of self-adjoint operators of Hilbert space.However the whole spec- tral theory is in fact not necessary and what Dirac actually needs 1 d is only that the self-adjoint operators t. and could be put in i dt diagonal forms.There is also another justification of "improper" iunctions introduced by Dirac to put these operators in the diagonal forms by means of the theory of distributions of L. Schwartz.But

Haṡok Chang

Jan Walleczek, Gerhard Grössing

What defines an emergent quantum mechanics (EmQM)? Can new insight be advanced into the nature of quantum nonlocality by seeking new links between quantum and emergent phenomena as described by self-organization, complexity, or emergence theory? Could the development of a future EmQM lead to a unified, relational image of the cosmos? One key motivation for adopting the concept of emergence in relation to quantum theory concerns the persistent failure in standard physics to unify the two pillars in the foundations of physics: quantum theory and general relativity theory (GRT). The total contradiction in the foundational, metaphysical assumptions that define orthodox quantum theory versus GRT might render inter -theoretic unification impossible. On the one hand, indeterminism and non -causality define orthodox quantum mechanics, and, on the other hand, GRT is governed by causality and determinism . How could these two metaphysically-contradictory theories ever be reconciled? The present work argues that metaphysical contradiction necessarily implies physical contradiction. The contradictions are essentially responsible also for the measurement problem in quantum mechanics. A common foundation may be needed for overcoming the contradictions between the two foundational theories. The concept of emergence, and the development of an EmQM, might help advance a common foundation - physical and metaphysical - as required for successfull inter-theory unification .

L. Foschini

The logic–linguistic structure of quantum physics is analysed. The role of formal systems and interpretations in the representation of nature is investigated. The problems of decidability, completeness, and consistency can affect quantum physics in different ways. Bohr’s complementarity is of great interest, because it is a contradictory proposition. We shall see that the flowing of time prevents the birth of contradictions in nature, because it makes a cut between two different, but complementary aspects of the reality. PACS 03.65.Bz: Foundations, theory of measurement, miscellaneous theories. PACS 02.10.By: Logic and foundations. 1 1

Leon N. Cooper, Deborah van Vechten