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Modern Physics Letters B

QUANTUM FLUID MECHANICS AND QUANTUM ELECTRODYNAMICS

A. Widom, Yogendra Narain Srivastava

Published Jan 10, 1990• 1 citation
Publisher

Abstract

The commutation relations of Landau quantum fluid mechanics are compared with those of quantum electrodynamics. In both cases, the operator representation of the commutators require a macroscopic phase, and a wavefunction periodic in that phase. A physical discussion is given for analogous effects in superfluids and superconductors, with regard to quantum coherence on a macroscopic scale. Other applications are then briefly described.

DOI
10.1142/s0217984990000027

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The commutation relations of Landau quantum fluid mechanics are compared with those of quantum electrodynamics. In both cases, the operator representation of the commutators require a macroscopic phase, and a wavefunction periodic in that phase. A physical discussion is given for analogous effects in superfluids and superconductors, with regard to quantum coherence on a macroscopic scale. Other applications are then briefly described.
It is known from quantum mechanics that particles are associated with wave functions, and that the probability of observing a particle at some future location is proportional to the squared modulus of the amplitude of its wave function. Although this statistical relationship is well quantified, the interpretations have remained controversial, with many split between the classical Copenhagen interpretation and some variation of the de Broglie-Bohm pilot wave models. Recent experiments with Hydrodynamic Quantum Analogs (HQAs) have demonstrated that droplets of real fluid may achieve stable dynamical states, where interaction of the droplets with their own ripples results in motion analogous to the motion of particles subject to the guiding equation under the pilot wave models. Indeed, many effects previously thought to be exclusively quantum have now been observed as emergent phenomena in these macroscopic HQAs. This has motivated us to explore the possibility that quantum mechanics may actually be the result of fluid dynamics on some real quantum scale fluid. In this paper, we show that if there is a real quantum scale fluid having dynamics analogous to the fluid in HQAs, then this fluid must be a superfluid, and the dynamics of that fluid must take place on the surface of a 4-dimensional hypersphere. Under the influence of cosmological inflation, we further show that these bouncing droplets would have the illusion of a property analogous to rest mass, and that the principles of inertia, momentum, mass-energy equivalence, general relativity, the uncertainty principle and the appearance of a time-like dimension can all be derived for droplets as purely emergent phenomena from the fluid dynamics of this system. As such, we believe that this model merits consideration as a potential foundation for a new unifying theory of physics at all scales.
The concept of pressure in quantum fluids has traditionally been treated as a static scalar quantity derived from macroscopic equations of state. In this work we introduce a dynamic, frequency-resolved pressure field P(ω) that captures the intrinsic oscillatory stresses within a quantum liquid. This Quantum Liquid Pressure Spectrum (QLPS) framework derives from the fundamental commutation relations of the field operators and the continuity equation for mass and momentum. We present a systematic derivation of P(ω), illustrate its dependence on the excitation spectrum, and discuss its implications for superfluid helium, ultracold Fermi gases, and potential applications in quantum sensing and precision metrology. The QLPS concept reveals a previously inaccessible quantum variable that may provide a new handle on the collective excitations and phase transitions in strongly correlated quantum fluids, offering a pathway toward novel quantum technologies and a deeper understanding of quantum many-body physics.
The concept of pressure in quantum fluids has traditionally been treated as a static scalar quantity derived from macroscopic equations of state. In this work we introduce a dynamic, frequency-resolved pressure field P(ω) that captures the intrinsic oscillatory stresses within a quantum liquid. This Quantum Liquid Pressure Spectrum (QLPS) framework derives from the fundamental commutation relations of the field operators and the continuity equation for mass and momentum. We present a systematic derivation of P(ω), illustrate its dependence on the excitation spectrum, and discuss its implications for superfluid helium, ultracold Fermi gases, and potential applications in quantum sensing and precision metrology. The QLPS concept reveals a previously inaccessible quantum variable that may provide a new handle on the collective excitations and phase transitions in strongly correlated quantum fluids, offering a pathway toward novel quantum technologies and a deeper understanding of quantum many-body physics.