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Nonlinearity

Three quantum obsessions

Michael Berry

Published Jan 21, 2008• 20 citations
Publisher

Abstract

Is there a connection between the Riemann zeros and the quantum physics of classical chaos? Can the relation between spin and statistics be understood within elementary quantum mechanics? How are the phase singularities in classical optics smoothed by quantum effects?
DOI
10.1088/0951-7715/21/2/t02

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Quantum mechanics is the most precisely confirmed theory in physics, yet its central equation is an unexplained postulate, and its description of matter has never been connected to the dark components that dominate the universe. Independently, mathematics has long hinted that the zeros of the Riemann zeta function form the spectrum of an unidentified physical operator. Here we show that a standing-wave first principle—every elementary physical entity is a globally coherent standing-wave mode on a compact cosmic manifold—combined with the established empirical relations E=ℏω and p=ℏk and the standard non-relativistic energy balance, reconstructs the core structure of quantum kinematics, including the Schrödinger equation, the discreteness of quantum spectra, and the stability of quantum states; the reconstruction thus rests on these empirical inputs together with the standing-wave postulate, not on a single principle alone. A further, explicitly conjectural clause identifying the admissible spectrum with the Riemann zeros suggests interpreting ordinary matter, dark matter, and dark energy as three tiers of one spectral ladder, pending the construction of a dynamical coupling mechanism. The energy fractions of the three tiers, evaluated with the standard regulator schemes of quantum field theory, agree with cosmological measurements to within 0.2 percentage points at a fitted regulator scale—a threshold- and scheme-dependent consistency check rather than a parameter-free prediction. The framework makes four falsifiable predictions, from the statistics of vacuum noise to coherence signatures of dark matter in gravitational lensing. These results suggest a conjectural connection between number theory, quantum foundations, and cosmology, converting long-standing conceptual problems into concrete questions about the spectrum of a single operator.
In quantum mechanics, the theory of quantum transitions is grounded on the convergence of a series of time-dependent perturbation theory. In nuclear and atomic physics, this series converges because the dynamics of quantum transitions (quantum jumps) are absent by definition. In molecular and chemical physics, on the contrary, the dynamics of "quantum" transitions, being determined by the joint motion of a light electron (or electrons) and very heavy nuclei, are present by definition, and the series of time-dependent perturbation theory becomes singular. An exception is the dynamic problem for stationary states in the Born-Oppenheimer adiabatic approximation, when the electronic subsystem turns out to be "off" from the general dynamic process and therefore is not dynamically full-fledged: it only forms an electric potential in which the nuclei oscillate. Removing the aforementioned singularity can be accomplished in two ways. The first method was consisted of introducing an additional postulate in the form of the Franck-Condon principle into molecular quantum mechanics, in which the adiabatic approximation is used. The second method was proposed by the author and consisted of damping the singular dynamics of the joint motion of an electron and nuclei in the intermediate (transient) state of molecular "quantum" transitions by introducing chaos. This chaos arises only during molecular quantum transitions and is called dozy chaos. Formally, the damping is carried out by replacing an infinitely small imaginary addition in the spectral representation of the complete Green's function of the system with its finite quantity. The damping chaos (dozy chaos) leads to the continuity of the energy spectrum in the molecular transient state, which is a sign of classical mechanics. Meanwhile, the initial and final states of the molecule obey quantum mechanics in the adiabatic approximation. Molecular quantum mechanics, which takes into account the chaotic dynamics of the transient state of molecular "quantum" transitions, can be called quantum-classical (dozy-chaos) mechanics. The efficacy of the damping for the aforementioned singularity was previously shown by dozy-chaos mechanics of elementary electron transfers in condensed matter, which is the simplest case of dozy-chaos mechanics, and its applications to a whole number of problems, especially to the optical spectra in polymethine dyes and their aggregates. This paper provides a regular exposition of this dozy-chaos (quantum-classical) mechanics of the elementary electron transfers. The main results of its applications presented in the introduction are also described.