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Physical Vacuum Is a Special Superfluid Medium

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Physical Vacuum Is a Special Superfluid Medium Physical vacuum is a special superfluid medium Valeriy I. Sbitnev∗ St. Petersburg B. P. Konstantinov Nuclear Physics Institute, NRC Kurchatov Institute, Gatchina, Leningrad district, 188350, Russia; Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, CA 94720, USA (Dated: August 9, 2016) The Navier-Stokes equation contains two terms which have been subjected to slight modification: (a) the viscosity term depends of time (the viscosity in average on time is zero, but its variance is non-zero); (b) the pressure gradient contains an added term describing the quantum entropy gradient multiplied by the pressure. Owing to these modifications, the Navier-Stokes equation can be reduced to the Schr¨odingerequation describing behavior of a particle into the vacuum being as a superfluid medium. Vortex structures arising in this medium show infinitely long life owing to zeroth average viscosity. The non-zero variance describes exchange of the vortex energy with zero-point energy of the vacuum. Radius of the vortex trembles around some average value. This observation sheds the light to the Zitterbewegung phenomenon. The long-lived vortex has a non-zero core where the vortex velocity vanishes. Keywords: Navier-Stokes; Schr¨odinger; zero-point fluctuations; superfluid vacuum; vortex; Bohmian trajectory; interference I. INTRODUCTION registered. Instead, the wave function represents it existence within an experimental scene [13]. A dramatic situation in physical understand- Another interpretation was proposed by Louis ing of the nature emerged in the late of 19th cen- de Broglie [18], which permits to explain such an tury. Observed phenomena on micro scales came experiment. In de Broglie's wave mechanics and into contradiction with the general positions of the double solution theory there are two waves. classical physics. It was a time of the origina- There is the wave function that is a mathemat- tion of new physical ideas explaining these phe- ical construct. It does not physically exist and nomena. Actually, in a very short period, pos- is used to determine the probabilistic results of tulates of the new science, quantum mechanics experiments. There is also a physical wave guid- were formulated. The Copenhagen interpreta- ing the particle from its creation to detection. tion was first who proposed an ontological ba- As the particle moves from a source to a detec- sis of quantum mechanics [32]. These positions tor, the particle perturbs the wave field and gets can be stated in the following points: (a) the a reverse effect from it. As a result, the physi- description of nature is essentially probabilistic; cal wave guides the particle along some optimal (b) a quantum system is completely described by trajectory, Bohmian trajectory [9, 10], up to its arXiv:1501.06763v4 [quant-ph] 8 Aug 2016 a wave function; (c) the system manifests wave{ detection. particle duality; (d) it is not possible to measure A question arises, what is the de Broglie phys- all variables of the system at the same time; (e) ical wave? Recently, Couder and Fort [15] has each measurement of the quantum system entails executed the experiment with the classical oil the collapse of the wave function. droplets bouncing on the oil surface. A re- markable observation is that an ensemble of the Can one imagine a passage of a quantum parti- droplets passing through the barrier having two cle (the heavy fullerene molecule [35], for exam- gates shows the interference fringes typical for ple) through all slits, in once, at the interference the two slit experiment. Their explanation is experiment? Following the Copenhagen inter- that the droplet while moving on the surface in- pretation, the particle does not exists until it is duces on this surface the weak Faraday waves. The latter provide the guidance conditions for the droplets. In this perspective, we can draw ∗Electronic address: [email protected] conclusion that the de Broglie physical wave 2 can be represented by perturbations of the ether velocity; (b) the second law states: the net force when the particle moves through it. In order applied to a body with a mass M is equal to to describe behavior of such an unusual medium the rate of change of its linear momentum in an we shall use the Navier-Stokes equation with inertial reference frame slightly modified some terms. As the final re- d~v sult we shall get the Schr¨odinger equation. In F~ = M~a = M ; (1) d t physical science of the New time the assumption for the existence of the ether medium was origi- (c) the third law states: for every action there is nally used to explain propagation of light and the an equal and opposite reaction. long-range interactions. As for the propagation Leonard Euler had generalized Newton's laws of light, the wave ideas of Huygens and Fresnel of motion on deformable bodies that are assumed require the existence of a continuous intermedi- as a continuum [25]. We rewrite the second New- ate environment between a source and a receiver ton's law for the case of deformed medium. Let of the light - the light-bearing ether. It is instruc- us imagine that a volume ∆V contains a fluid tive to compare here the two opposite doctrines medium of the mass M. We divide Eq. (1) by ∆V about the nature of light belonging to Sir Isaac and determine the time-dependent mass density ~ Newton and Christian Huygens. Newton main- ρM = M=∆V [58]. In this case F is understood tained the theory that the light was made up of as the force per volume. Then the second law in tiny particles, corpuscles. They spread through this case takes a form: an empty space in accordance with the law of the dρ ~v d~v dρ classical mechanics. Christian Huygens (a con- F~ = M = ρ + ~v M : (2) d t M d t d t temporary of Newton), believed that the light was made up of waves vibrating up and down The total derivatives in the right side can be perpendicularly to the direction of its propa- written down through partial derivatives: gation, as waves on a water surface. One can dρM @ρM imagine all space populated everywhere densely = + (~v r)ρM ; (3) by Huygens's vibrators. All vibrators are silent d t @ t d~v @~v until a wave reaches them. As soon as a wave = + (~v r)~v: (4) front reaches them, the vibrators begin to radi- d t @ t ate waves on the frequency of the incident wave. Eq. (3) equated to zero is seen to be the conti- So, the infinitesimal volume δV is populated by nuity equation. As for Eq. (4) we may rewrite infinite amount of the vibrators with frequen- the rightmost term in detail cies of visible light. These vibrators populate the v 2 ether facilitating propagation of the light waves (~v r)~v = r − [~v × [r × ~v]]: (5) through the space. 2 In order to come to idea about existence of As follows from this formula the first term, mul- the intermediate medium (ether) that penetrates tiplied by the mass, is gradient of the kinetic overall material world, we begin from the funda- energy. It is a force applied to the fluid element mental laws of classical physics. Three Newton's for its shifting on the unit of length, δs. The laws first published in Mathematical Principles second term is acceleration of the fluid element of Natural Philosophy in 1687 [3] we recognize as directed perpendicularly to the velocity. Let the basic laws of physics. Namely: (a) the first law fluid element move along some curve in 3D space. postulates existence of inertial reference frames: Tangent to the curve in each point refers to ori- an object that is at rest will stay at rest unless entation of the body motion. In turn, the vector an external force acts upon it; an object that ~! = [r × ~v] is orientated perpendicularly to the is in motion will not change its velocity unless plane, where an arbitrarily small segment of the an external force acts upon it. The inertia is a curve lies. This vector characterizes a quantita- property of the bodies to resist to changing their tive measure of the vortex motion and it is called 3 vorticity. Vector product [~v ×~!] is perpendicular particles form, in any moment of the time, a to the both vectors ~v and ~!. It represents the vortex line, then the same particles support the Coriolis acceleration of the body under rotating vortex line both in the past and in the future; it around the vector ~!. (ii) ensemble of the vortex lines traced through The term (5) entering in the Navier-Stokes a closed contour forms a vortex tube. Intensity equation [38, 39] is responsible for emergence of the vortex tube is constant along its length of vortex structures. The Navier-Stokes equa- and does not change in time. The vortex tube tion stems from Eq. (2) if we omit the rightmost (a) either goes to infinity by both endings; (b) or term, representing the continuity equation, and these endings lean on walls of bath containing specify forces in this equation in detail [57]: the fluid; (c) or these endings are locked to each on other forming a vortex ring. @~v ! Assuming that the fluid is a physical vacuum, ρM + (~v · r)~v @ t which meets the requirements specified earlier, F~ P ! we must say that the viscosity vanishes. In that = + µ(t) r 2~v − ρ r : (6) ∆V M ρ case, the vorticity ~! is concentrated in the cen- M ter of the vortex, i.e., in the point. Mathemati- This equation contains two modifications repre- cal representation of the vorticity is δ-function.
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