Theoretical and CFD analysis of gravity and galaxy formation and rotation in a dilatant vacuum Marco Fedi, Mario R.L. Artigiani To cite this version: Marco Fedi, Mario R.L. Artigiani. Theoretical and CFD analysis of gravity and galaxy formation and rotation in a dilatant vacuum. 2019. hal-02343559v3 HAL Id: hal-02343559 https://hal.archives-ouvertes.fr/hal-02343559v3 Preprint submitted on 22 Dec 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Theoretical and CFD analysis of gravity and galaxy formation and rotation in a dilatant vacuum. Marco Fedi∗ Ministero dell’Istruzione, dell’Universita` e della Ricerca (MIUR), Rome, Italy Mario R. L. Artigiani† Engineering3D.it, Desenzano del Garda, Italy (Dated: 22 December 2019) Following some successful computations in which the vacuum has been treated as a non-Newtonian dilatant fluid to derive Einstein formula for the precession of perihelia and to obtain a better solution to the Pioneer anomaly, in this study we proceed by describing gravity, both at micro- and macro-level, as well as galaxy formation, shapes and rotation, still according to a shear-thickening vacuum, also by means of high-resolution computational fluid dynamics simulations. We show that the resulting gravitational model allow us to describe gravitational waves and to obtain various galaxy shapes, along with the flat profile of galaxy-rotation velocity. As the previous investigations, also this study reinforces the evidence that space is a dilatant fluid, probably an unexpected hydrodynamic feature of the viscous Higgs field. Keywords: dilatant vacuum, quantum gravity, spin, galaxy formation, flat profile, Higgs Introduction by describing fundamental fermions as toroidal vortices (Sect. I). In the second section we derive an equation for The vacuum as a superfluid has been studied in several quantum gravity, without the classical Newtonian constant. approaches [1–3], whose recent evolution is for instance the The quantum aspects of this formula are then discussed in logarithmic BEC vacuum theory [4, 5]. Nevertheless, the Sect. III. In the following section we simulate a quadrupole hydrodynamic characteristics of the vacuum seem to be much via computational fluid dynamics (CFD) and we show that different in various cases. The Nobel laureate R.B. Laughlin, gravitational waves can be described as negative pressure states: waves in a dilatant vacuum (Sect. IV). Further CFD simulations demonstrate that a binary black hole located in Studies with large particle accelerators have now the center of a galaxy and in a dilatant vacuum, can generate led us to understand that space is more like various galaxy shapes (Sect. V) a well as the flat profile of a piece of window glass than ideal Newtonian the rotation velocity (Sect. VI). Eventually, we describe an emptiness. It is filled with stuff that is normally unexpected effect obtained in the simulations: a breath of transparent but can be made visible by hitting it galaxies (Sect. VII). sufficiently hard to knock out a part. This behavior is typical of non-Newtonian shear-thickening I. Spin-generated Bernoulli force as the engine of gravity. fluids (dilatant fluids): they are fluid when low shear stress is applied and they progressively solidify as shear stress increases. The situation described by Laughlin, as regards Dilatant vacuum can be interpreted as a superfluid (dark large particle accelerators, has been in fact described as due energy [8]) doped with scattered dark-matter particles [9], to the existence of a dilatant vacuum [6], through which which together make up ∼ 95% of the mass-energy of charges accelerate. Not by case, by treating the vacuum as the universe: something like a cosmic oobleck [10]. The a shear-thickening fluid, the relativistic perihelion precession dilatant-vacuum model therefore goes in the direction of a of the planet Mercury has been solved by deriving Einstein unification of dark energy and dark matter into a single formula for the precession of perihelia in a simpler way dark fluid [11, 12]. At the same time, vacuum dilatancy and the Pioneer anomaly has been directly computed, with could be also interpreted as a hydrodynamic feature of the much greater accuracy, by using the Lorentz factor in Stokes’ viscous Higgs field. It has been proved that the apparent law, as a viscosity factor of the vacuum [7]. In this way viscosity of the vacuum obeys the Lorentz factor [7], thus, the curve expressed by the Lorentz factor turned out to be when shear stress is low, the vacuum is in a superfluid-like the rheogram of the vacuum. Vacuum dilatancy arises both regime. Just like classical mechanics is placed at the with particles and with macroscopic bodies (probes, planets) beginning of the curve expressed by the Lorentz factor. The traveling through a vacuum. temperature of the superfluid vacuum at 2:72K, i.e. that of In this study, the analysis of the vacuum as a dilatant fluid the cosmic microwave background (CMB), would match that is continued as regards gravity and galaxy formation and of laboratory superfluids. In superfluids, quantized vortices rotation. We start from the vacuum in superfluid regime, spontaneously arise and since a vortex tube must extend to a boundary or close in a loop (an interesting connection with loop quantum gravity [13] can be seen in this fact), obeying Helmholtz’s second principle, vortex rings (vortex ∗ E-mail: [email protected] tori) can form in a superfluid vacuum (Fig 1) [2, 3, 14]. † E-mail: [email protected] However, what is also important is the fact that only vortices 2 analogue of the Euler equation ¶r /0 + ∇ · (r v ) = 0 (2) ¶t /0 S 2 2p ¶r/0 h¯ ∇ r/0 m + vS · ∇ vS = ∇ m0 − gr + p (3) ¶t 2m r/0 h¯ where vS = m ∇j is the superfluid velocity and 2 2p h¯ ∇ r/0 p (4) 2m r/0 the quantum potential. The condensate must be a continuous function in space, so its phase is continuous modulo 2p. We define the quantized circulation (G) with the line integral I 2ph¯ dx · vS = n ≡ G (n = 0;±1;±2;:::) (5) C m where C is a close loop in space, encircling a vortex line, y = 0, and the superfluid’s density vanishes. The problem of ultraviolet divergence and of the radius of the fundamental particles is solved in this approach by considering toroidal vortices of vacuum’s quanta instead of point-like particles, whose radius is r = 2x, with x defined as the healing length, FIG. 1. A vortex line with healing length x, actually a vortex tube, closes r in a circle, becoming a vortex torus. Below: the Mobius-strip¨ trajectory of V x ≡ ; (6) a hypothetical vacuum’s quantum in the vortex torus: the quantum returns 8paN to any initial position after a rotation of 720° of the torus, so the ratio rotations/revolutions represents spin ½ (fermion). Below, on the right-hand where V is the volume in which the vortex arises, a the side, we see the paths of 12 quanta. scattering length and N a normalized number of vacuum’s quanta in the volume. A hydrodynamic reformulation of the Barut-Zanghi theory [17], which includes spin, was proposed in a doped superfluid show correct attraction-repulsion by Salesi and Recami, who suggested [18], similarly to us, interactions among them [15] (mathematically corresponding that quantum potential to gravity or electromagnetic interactions). Thus, to describe 1 ~2 1 a fundamental fermion as a toroidal vortex in a superfluid Q = − mv S − ∇ ·~vS (7) vacuum, it is necessary to specify that this superfluid has to 2 2 be doped. The dilatant-vacuum picture is therefore fit for (in natural units, h¯ = 1) totally arises from the internal motion the purpose, since a dilatant is made up of a (super)fluid and of a particle~vS ×~s, where scattered dopant particles. For example scattered dark matter in a sea of superfluid dark energy. 1 1 ∇R2 ~v = r−1∇r = ; (8) Let us analyze the fundamental equations of what above S 2m 2m R2 described. Considering the physical vacuum as a doped Bose-Einstein condensate (BEC), we start from the being ~s the direction of spin. The link to the concept of Gross-Pitaevskii equation (GPE) to analyze its hydrodynamic vortex-particle is, in this way, quite immediate. If, to complete behavior [16] a turn in the poloidal direction, a quantum in the vortex needs the same time the vortex needs to complete two turns in the ¶y h2 toroidal direction, then the vortex has spin ½ (fermion), i.e. ih¯ = − ∇2y + gy jyj2 − ym (1) ¶t 2m 0 the system returns to the same state after a rotation of 720° and after each quantum in the vortex has traveled along a where y is the condensate wave function, m the mass of a Mobius-strip¨ path (Fig. 1). By defining w1; w2 as the angular velocities (toroidal and poloidal), the spin angular momentum quantum of the fluid vacuum, m0 the chemical potential and g = 4pah¯ 2=m a low-energy parameter, where a represents (S) is determined by the ratio w1=w2 = (np=dt)=(2p=dt) and the scattering length between vacuum’s quanta. In the phase after the cancellations p representation y = r eij , r = jyj2 is vacuum’s density.