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The Western Ontario series in philosophy of science

Is There a Relation Between the Breakdown of the Superposition Principle and an Indeterminacy in the Structure of the Einsteinian Space-Time?

Andor Frenkel

Published Jan 1, 2009• 0 citations
Publisher
DOI
10.1007/978-1-4020-9107-0_15

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I explain in what sense the structure of space and time is probably vague or indefinite, a notion I define. This leads to the mathematical representation of location in space and time by a vague interval. From this, a principle of complementary inaccuracy between spatial location and velocity is derived, and its relation to the Uncertainty Principle discussed. In addition, even if the laws of nature are deterministic, the behaviour of systems will be random to some degree. These and other considerations draw classical physics closer to Quantum Mechanics. An arrow of entropy is also derived, given an arrow of time. Lastly, chaos is given an additional, objective meaning.
Abstract Traditional philosophy has long enshrined "determinacy" as the essential attribute of Being, while relegating "indeterminacy" to the status of a temporary defect of human cognition, a vague state awaiting elimination. The revolutionary development of quantum mechanics has thoroughly shattered this millennia-old cognitive presupposition: the superposition state of microscopic particles is not an "undetermined intermediate state," but an intrinsic property of Being itself; wave-particle duality is not a random mutation of particles, but the determinate manifestation of the same indeterminate ontological substance, emerging within different observational relations. This paper proposes a fundamentally new ontological principle: determinacy is the skeleton of Being that emerges from and is anchored by indeterminacy; indeterminacy, in turn, is the primordial matrix from which determinacy is generated, described, and manifested. These two dimensions do not exist in a relation of sequential dependence or hierarchical subordination, but constitute a reciprocal generative structure in which they define each other in opposition and emerge simultaneously in dynamic interaction. Taking quantum mechanical superposition and wave-particle duality as its core empirical evidence, this paper demonstrates the universal penetrative power of this ontological principle, and points out that eliminating indeterminacy is not the core task of philosophy; rather, modern philosophy must urgently break free from the shackles of traditional paradigms and return to the dynamic, authentic state of Being itself in order to reconstruct cognition. Keywords: Determinacy; Indeterminacy; Reciprocal Emergence in Opposition; Emergence; Manifestation; Desire/Contradiction; Ontology