2015/02/21 by Réal Tremblay, Real Tremblay, Tremblay, Real +5
Computer Science · Engineering · Physics and Astronomy · #Black-body radiation #Constant (computer programming) #Electromagnetic field #Electron #FOS: Physical sciences #Fine-structure constant #Optics (physics.optics) #Photon #Photonic and Optical Devices #Physics #Planck #Planck constant #Planck length #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum electrodynamics #Quantum gravity #Quantum mechanics #Radiation #Theoretical physics #physics.optics
paper · pdf · doi:10.48550/arxiv.1502.06141
published in arXiv (Cornell University) (Cornell University) · 26 pages, 4 figures 1 table
openalex publication_date 2015/02/21 · arxiv created 2015/05/01 · arxiv updated 2015/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Planck constant (ℏ) plays a pivotal role in quantum physics. Historically, it has been proposed as postulate, part of a genius empirical relationship E=ℏ ω in order to explain the intensity spectrum of the blackbody radiation for which classical electrodynamic theory led to an unacceptable prediction: The ultraviolet catastrophe. While the usefulness of the Planck constant in various fields of physics is undisputed, its derivation (or lack of) remains unsatisfactory from a fundamental point of view. In this paper, the analysis of the blackbody problem is performed with a series expansion of the electromagnetic field in terms of TE, TM modes in a metallic cavity with small losses, that leads to developing the electromagnetic fields in a complete set of orthonormal functions. This expansion, based on coupled power theory, maintains both space and time together enabling modeling of the blackbody's evolution toward equilibrium. Reaching equilibrium with a multimodal waveguide analysis brings into consideration the coupling between modes in addition to absorption and emission of radiation. The properties of the modes, such as spectral broadening, losses and lifetime, then progressively become independent of frequency and explains how equilibrium is allowed in good conductor metallic cavities. Based on the free electron relaxation time in gold, a value of ℏ = 1.02 × 10-34 J⋅s for the reduced Planck constant is found and the uncertainty principle is also emerging from this a priori classical study. The Planck constant is then obtained no longer as an ad hoc addition but as a natural consequence of the analysis taking boundary conditions into account as into optical resonators. That analysis based on finite-spacetime paradigm, also shine new light on the notion of decoherence in classical optics and electrodynamics.