Harmony in many-particle quantum problem

Philip L. Bowers

Константин Владимирович Чукбар

Abstract The model quantum problem of a harmonically trapped cloud of identical nonrelativistic particles interacting via a harmonic oscillator potential has an exact solution that can be used to assess the efficiency of approximate methods standardly used in more realistic many-particle calculations.

Partha Ghose

The main purpose of this paper is to review the progress that has taken place so far in the search for a single unifying principle that harmonizes (i) the wave and particle natures of matter and radiation, both at the quantum and the classical levels, on the one hand and (ii) the classical and quantum theories of matter and radiation on the other hand. The famous paradoxes of quantum theory, the mysterious nature of measurements in quantum theory and the principal no-go theorems for hidden variables are first briefly reviewed. The Koopman-von Neumann Hilbert space theory based on complex wave functions underlying particle trajectories in classical phase space, is an important step forward in that direction. It provides a clear and beautiful harmony of classical waves and particles. Sudarshan has given an alternative but equivalent formulation that shows that classical mechanics can be regarded as a quantum theory with essentially hidden non-commuting variables. An extension of KvNS theory to classical electrodynamics provides a sound Hilbert space foundation to it and satisfactorily accounts for entanglement and Bell-CHSH-like violations already observed in classical polarization optics. An important new insight that has been obtained through these developments is that entanglement and Bell-like inequality violations are neither unique signatures of quantumness nor of non-locality---they are rather signatures of non-separability. Finally, Sudarshan's proposed solution to the measurement problem using KvNS theory for the measuring apparatus is sketched to show to what extent wave and particles can be harmonized in quantum theory.

Heine Olsson Aabø

Leo Van Hove, Nicolaas Marinus Hugenholtz, L. P. Howland

Donatello Dolce B

Life and quantum mechanics can be seen as expressions of universal harmony. From the heart beat to the DNA vibrations and neurons spikes, living systems unfold through cycles; physics, too, is built on matter waves, resonances and quantized spectra. Schrödinger envisioned life’s stability in molecular vibrational modes. Here we extend that idea: information, perception, cognition as much as the whole quantum mechanics can be described as temporal cycles. Elementary Cycles Theory, validated in many peer-reviewed publications, elevates de Broglie’s idea of particles as intrinsic clocks to the principle from which quantum mechanics can be fully derived. Entanglement is not “spooky action” but harmony: synchronized clocks, like two lovers whose hearts beat in unison even across distance. Life is quantum because it is woven from the same laws of harmony that underlie the universe itself.