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"In Mathematical Language": On Mathematical Foundations of Quantum Foundations
1Literature, Theory, and Cultural Studies, and Philosophy and Literature Program, Purdue University, West Lafayette, IN 47907, USA.
Entropy (Basel, Switzerland)
|November 27, 2024
Summary
Modern physics advances through new mathematical structures. Quantum theory uniquely uses mathematical postulates for probabilistic predictions, redefining scientific realism without explaining physical phenomena.
Area of Science:
- Physics
- Philosophy of Science
Background:
- Modern physics, particularly since the 16th century, has advanced through the development of novel mathematical structures.
- The nature of scientific advancement in physics is intrinsically linked to the invention of new mathematical frameworks.
Purpose of the Study:
- To argue that the advancement of modern physics is defined by the invention of new mathematical structures.
- To explore how quantum theory, specifically quantum mechanics and quantum field theory, imbues this thesis with new meaning through unique physical and mathematical features.
- To introduce the mathematical complexity principle and offer a new perspective on continuity and discontinuity in quantum physics.
Main Methods:
- Analysis of the historical development of mathematical structures in physics.
- Examination of the foundational principles of quantum mechanics and quantum field theory.
- Exploration of "reality without realism" (RWR) interpretations of quantum theory.
- Introduction and application of the mathematical complexity principle.
Main Results:
- Quantum theory distinguishes itself by defining phenomena through purely physical features and employing purely mathematical postulates.
- Quantum mechanics and quantum field theory connect to phenomena via probabilities, without representing their physical causation, aligning with RWR interpretations.
- A new perspective on the continuity-discontinuity problem in quantum physics is offered, focusing on probabilistic predictions and the exclusion of representational accounts.
Conclusions:
- The advancement of physics is fundamentally tied to mathematical innovation.
- Quantum theory represents a paradigm shift, utilizing mathematical structures to predict phenomena probabilistically without recourse to mechanistic explanations.
- The mathematical complexity principle offers a novel framework for understanding quantum phenomena and their relationship to mathematical formalisms.
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