Hydrodynamics of the Physical Vacuum: I. Scalar Quantum Sector

Abstract

Physical vacuum is a special superfluid medium. Its motion is described by the Navier-Stokes equation having two slightly modified terms that relate to internal forces. They are the pressure gradient and the dissipation force because of viscosity. The modifications are as follows: (a) the pressure gradient contains an added term describing the pressure multiplied by the entropy gradient; (b) time-averaged viscosity is zero, but its variance is not zero. Owing to these modifications, the Navier-Stokes equation can be reduced to the Schrödinger equation describing behavior of a particle into the vacuum, which looks like a superfluid medium populated by enormous amount of virtual particle-antiparticle pairs.

Superfluid Quantum Space and Evolution of the Universe

“…The Navier-Stokes equation is written above in the modified form [34]. The modification is due to (a) presence of the quantum potentials Q ¼ P Q =ρ and…”

“…The first term follows from Eq. (10) that is ϕ ¼ P G =ρ m ¼ Q ϕ =M and the second term is the intrinsic quantum potential of SQS [5,34] divided by mass. The integer multiplier N D is equal to the sum of all the quantum potentials, which arise from the contribution of all dark energy and dark matter in SQS.…”

“…(45), n ¼ 1, 2, ⋯,N. Let us substitute the expression (45) into the integral (34). After computing it, we get the following view of the denominator Σðν,t,σÞ:…”

Quantum consciousness in warm, wet and noisy brain

“…Suppose that the vorticity ω is not compensated by the magnetic field. Then, this equation can also give vortex solutions [57,74]. One can imagine a helicoidal vortex ring rising over the head that resembles the torus.…”

“…Let it be subjected to the following modification [38]. It will be important for us when we begin to derive the Schrödinger equation.…”