Heisenberg’s Uncertainties and the Probabilistic Interpretation of Wave Mechanics: with Critical Notes of the Author

Asım Orhan Barut

Louis de Broglie

Philip L. Bowers

C.I. Christov

Michel Fliess

This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty principle, i.e., of the quantum fluctuations, which was brought to the forefront in some fractal approaches. It results, as in Nelson's stochastic mechanics, in stochastic differential equations which are deduced from infinitesimal random walks. An extended english abstract gives most of the details.

Venkat Venkatasubramanian

High Resolution Image Download MS PowerPoint Slide In July 1925, Werner Heisenberg submitted a paper to Zeitschrift für Physik entitled ‘On quantum-theoretical reinterpretation of kinematic and mechanical relationships’, thus giving birth to quantum mechanics. In the following year, building on de Broglie’s wave-particle duality, Erwin Schrödinger developed wave mechanics, and soon, Max Born provided a probabilistic interpretation of the wave function. The theory was further enriched by the exclusion principle of Wolfgang Pauli and the uncertainty principle of Heisenberg, which ultimately led to the development of relativistic quantum mechanics by Dirac. The Copenhagen Interpretation created a probabilistic framework for understanding the theory. Over the past century, quantum mechanics has paved the way for advances in quantum field theory, computing, and modern technologies. This historical narrative provides insights into the complex discovery process that led to the development of quantum mechanics, which can potentially guide novel breakthroughs amid challenging conceptual struggles, as seen in the field of artificial intelligence today.