Consequences of Wavelet Analysis for the Philosophy of Quantum Mechanics: from generalized uncertainty relations to the Planck scale

• Grant number: 25/07651-4
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: October 01, 2025
• End date: September 30, 2027
• Field of knowledge: Humanities - Philosophy - Epistemology
• Principal Investigator: Osvaldo Frota Pessoa Junior
• Grantee: Filipe Pamplona Nascimento Gonçalves
• Host Institution: Faculdade de Filosofia, Letras e Ciências Humanas (FFLCH). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 24/03736-2 - Towards a global understanding of how accreting white dwarfs form and evolve, AP.JP

Abstract

This project explores the intersection of the philosophy of quantum mechanics, the philosophy of physical space, and the history and foundations of wavelet analysis. Wavelet analysis is a mathematical method that allows us to describe various functions through the superposition of "local waves" (known as wavelet functions). This method differs from the "non-local" harmonic Fourier analysis used in orthodox quantum mechanics. By applying wavelets to the foundations of quantum theory, it becomes possible to revise and reformulate the "quantum uncertainty principle". For instance, José Croca has proposed generalized uncertainty relations within the framework of his nonlinear causal quantum theory. In this generalization, Heisenberg's relations emerge as a particular limiting case. Our primary goal is to examine the status of the "uncertainty principle" following the advent of wavelet analysis. We will conduct a comparative study between two methods adopted in physics: local analysis using wavelets and non-local Fourier analysis. Since the Planck length can be correlated with both the Schwarzschild radius and Heisenberg's uncertainty relation, this lead us into the philosophy of space to question: through the generalized uncertainty relations, would it be possible to construct spatial scales more elementary than the Planck scale? - This corresponds to a significant open question, and one of the expected outcomes of this project: to demonstrate that the spatial quantum does not necessarily have to be based on the Planck length. We suggest that it is possible to develop even smaller spatial scales, which could further support the hypothesis of a spatial continuum. The results of this research could have significant philosophical and scientific implications, if we verify that Heisenberg's uncertainty relations do not set an insurmountable "limit" in nature.