Generalized Differential and Integral Calculus and Heisenberg Uncertainty Principle

TL;DR

This paper introduces a generalized calculus framework that extends traditional derivatives and integrals, allowing precise measurement of time and frequency in signals, challenging the Heisenberg Uncertainty Principle.

Contribution

It proposes a novel generalized calculus with derivatives and integrals for various functions, enabling exact time-frequency analysis and questioning established quantum uncertainty limits.

Findings

Generalized derivatives and integrals are defined for polynomial, exponential, and trigonometric functions.

The approach allows precise determination of time and frequency in signals.

It provides a mathematical basis to challenge the Heisenberg Uncertainty Principle.

Abstract

This paper presents a generalization for Differential and Integral Calculus. Just as the derivative is the instantaneous angular coefficient of the tangent line to a function, the generalized derivative is the instantaneous parameter value of a reference function (derivator function) tangent to the function. The generalized integral reverses the generalized derivative, and its calculation is presented without antiderivatives. Generalized derivatives and integrals are presented for polynomial, exponential and trigonometric derivators and integrators functions. As an example of the application of Generalized Calculus, the concept of instantaneous value provided by the derivative is used to precisely determine time and frequency (or position and momentum) in a function (signal or wave function), opposing Heisenberg's Uncertainty Principle.