Abstract
The Paradigms introduced in philosophy of science one century ago are shown to be quite more satisfactory of that introduced by Galileo. This is particularly evident in the physics based on Hilbert Spaces and related mathematical structures that we apply in this paper to Quantum Mechanics and to Theory of Images. An exhaustive discussion, that include the algebraic analysis of the operators acting on them, exhibits that the Hilbert Spaces-that have fixed dimension-must be generalized to the Rigged Hilbert Spaces that contain spaces with continuous and discrete dimensions. This is the property of Rigged Hilbert Spaces that allows a consistent formal description of the physics we are considering. Theory of Quantum Mechanics and of Images are similar and the fundamental difference between them comes from the definition of measure that is outside the theory of the spaces: while in Quantum Mechanics the measure is a probabilistic action, in Images it is a classical functional.
Highlights
IntroductionParadigm in philosophy of science is the Gestalt, the general frame, that define the fundamental attitudes of scientists active in similar fields
Paradigm in philosophy of science is the Gestalt, the general frame, that define the fundamental attitudes of scientists active in similar fields.The first general paradigm in science has been stated by Galileo: it could be summarized in the statement that experience is necessary and sufficient to find the ”Truth”
The role of the general paradigm is relevant in physics, where we have at least three conflicted sectorial paradigms that, at the moment, we have not been able to reduce to a single one
Summary
Paradigm in philosophy of science is the Gestalt, the general frame, that define the fundamental attitudes of scientists active in similar fields. The author point of view can be summed up in the Wittgenstein statement: ”The procedure of induction consists in accepting as true the simplest law that can be reconciled with our experience” [1] This means that a law is considered a recipe that worked -up to now- every time has been taken into account and, between the working recipes, is the ”simplest” one. The role of the general paradigm is relevant in physics, where we have at least three conflicted sectorial paradigms that, at the moment, we have not been able to reduce to a single one They are General Relativity, Classical Physics and theories related to Hilbert Spaces with their operators. A fundamental difference between QM and TI exists but it is not at the level of the spaces but at the level of something added to the scheme from outside RHS: it is the definition of the measure that is probabilistic in QM and described by deterministic functionals in TI
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