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Conference on the Foundations of Quantum Mechanics: Historical Analysis and Open Questions

HERMANN WEYL'S PHENOMENOLOGICAL CONTRIBUTION TO QUANTUM PHYSICS

Giorgio Jules Mastrobisi

Published May 1, 2000• 0 citations
Publisher
DOI
10.1142/9789812793560_0022

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Grete Hermann’s essay “Die naturphilosophischen Grundlagen der Quantenmechanik” (1935) has received much deserved scholarly attention in recent years. In this paper, I follow the lead of Elise Crull (2017) who sees in Hermann’s work the general outlines of a neo-Kantian interpretation of quantum theory. In full support of this view, I focus on Hermann’s central claim that limited spatio-temporal, and even analogically causal, representations of events exist within an overall relational structure of entangled quantum mechanical states that defy any unified spatio-temporal description. In my view, Hermann also advances an important transcendental argument that perspectival spatio-temporal representations of nature have their foundations in general relational networks that are not spatio-temporal. The key point is that the adoption of a perspectival system within the general network induces the representation but only for that context. These ideas are consistent with a perspectival subject–object principle in Kant and also with Weyl’s work on Lie groups and their representations.

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The new theoretical and experimental developments in neurosciences project an idea of consciouness deeply bound to the physical nature. Nevertheless, consciousness does enigmatically keep without scientific explanation. The phenomenum per se is commonly known, but its definition and position in the modern scientific frames are not well determined. Consequently, there are plenty different interpretations full of speculation and imagination. On the opposite side, the scientific consciousness research is not frequent and it is exclusively done by a reduced group of researchers that works on the psycho-physical connection between physical matter and its psychical emergent activity from the neuroscientific experimental data. In this paper we widely explain a fundamental contextualized synthesis of two scientific geniuses in the mind-matter relationship problem. Although they belong to a near past, Erwin Schrödinger and Hermann Weyl are both paradigmatic personalities because of their methodical rigor and widespread investigations, which characterize the strong scientific spirit. Their styles are stout, their works inspire future researches and their conclusions connect well with the last frontiers results in neurosciences and quantum physics.

•Feb 1, 2015•0 citations
Grete Hermann’s essay “Die naturphilosophischen Grundlagen der Quantenmechanik” (1935) has received much deserved scholarly attention in recent years. In this paper, I follow the lead of Elise Crull (2017) who sees in Hermann’s work the general outlines of a neo-Kantian interpretation of quantum theory. In full support of this view, I focus on Hermann’s central claim that limited spatio-temporal, and even analogically causal, representations of events exist within an overall relational structure of entangled quantum mechanical states that defy any unified spatio-temporal description. In my view, Hermann also advances an important transcendental argument that perspectival spatio-temporal representations of nature have their foundations in general relational networks that are not spatio-temporal. The key point is that the adoption of a perspectival system within the general network induces the representation but only for that context. These ideas are consistent with a perspectival subject–object principle in Kant and also with Weyl’s work on Lie groups and their representations.
The kinematics of quantum systems, as is well known, are generally governed by the Heisenberg commutation rules. It was Hermann Weyl who suggested the consideration of the global versions of these rules which define a projective unitary representation of the additive group of the classical phase space. This prompted Weyl to formulate his principle that quantum kinematics is always governed by a projective unitary representation of some abelian group. The ideas of Weyl, and their natural development by his successors, notably Stone, Von Neumann, Mackey, Segal, Shale, Weil, and many others have had and still continue to have a great impact on many areas of mathematics and physics. This paper is an exposition of some of the themes that flow from these ideas.
The new theoretical and experimental developments in neurosciences project an idea of consciouness deeply bound to the physical nature. Nevertheless, consciousness does enigmatically keep without scientific explanation. The phenomenum per se is commonly known, but its definition and position in the modern scientific frames are not well determined. Consequently, there are plenty different interpretations full of speculation and imagination. On the opposite side, the scientific consciousness research is not frequent and it is exclusively done by a reduced group of researchers that works on the psycho-physical connection between physical matter and its psychical emergent activity from the neuroscientific experimental data. In this paper we widely explain a fundamental contextualized synthesis of two scientific geniuses in the mind-matter relationship problem. Although they belong to a near past, Erwin Schrödinger and Hermann Weyl are both paradigmatic personalities because of their methodical rigor and widespread investigations, which characterize the strong scientific spirit. Their styles are stout, their works inspire future researches and their conclusions connect well with the last frontiers results in neurosciences and quantum physics.