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III. Superfluid Quantum Gravity Marco Fedi Hydrodynamics of the dark superfluid: III. Superfluid Quantum Gravity Marco Fedi To cite this version: Marco Fedi. Hydrodynamics of the dark superfluid: III. Superfluid Quantum Gravity. 2016. hal- 01423134v6 HAL Id: hal-01423134 https://hal.archives-ouvertes.fr/hal-01423134v6 Preprint submitted on 19 Jul 2017 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. Distributed under a Creative Commons Attribution| 4.0 International License manuscript No. (will be inserted by the editor) Hydrodynamics of the dark superfluid: III. Superfluid Quantum Gravity. Marco Fedi Received: date / Accepted: date Abstract Having described in previous articles dark ener- dark matter as a dark superfluid (DS) whose quantum hydro- gy, dark matter and quantum vacuum as different aspects dynamics produces both what we call quantum vacuum (as of a dark superfluid which permeates the universe and hav- hydrodynamic fluctuations in the DS) and the massive parti- ing analyzed the fundamental massive particles as toroidal cles of the Standard Model, as torus-shaped superfluid quan- vortices in this superfluid, we reflect here on the Bernoulli tum vortices, where the ratio of the toroidal angular velocity pressure observed in quantum vortices, to propose it as the to the poloidal one may hydrodynamically describe the spin. mechanism of quantum gravity. In this view, the dark su- Furthermore, in [2] we have analyzed the theoretical pos- perfluid surrounding a particle would be attracted toward it: sibilities that a photon be a transverse phonon propagating a pressure gradient along with a velocity field would man- through the DS, concluding that there are good hints to con- ifest around the particle and would be currently interpreted sider light as “the sound of the dark superfluid”, as all prop- as the gravitational field. We call this hypothesis Superfluid erties and behaviors of light can be observed within a quan- Quantum Gravity. Here the hydrodynamics of the dark su- tum hydrodynamic approach. In this third paper, we return to perfluid would replace the curved spacetime of general rela- fundamental particles as quantum vortices and we focus on tivity, still respecting its observed predictions. Here the pic- the Bernoulli effect experimentally observed in superfluid ture of gravity is that of an apparent force driven by spin. vortices [25,26,28], suggesting that it can be the core mech- When this model is applied to a quadrupole dynamics, grav- anism of quantum gravity, which in turn is driven by spin [1] itational waves arise as negative pressure waves through the as a particle’s internal, vorticous motion. In this model we dark superfluid. Here the geometry of spacetime is indeed do not resort to gravitons, since the quantum aspect of grav- replaced by the hydrodynamics of the dark superfluid. A test ity is found in the quantized nature of the dark superfluid is eventually suggested to confirm the gravitational field as and in the attraction of its quanta into vortex-particles. Here an inflow of DS. Einstein’s curved spacetime is replaced by the hydrodynam- ics of the dark superfluid and time itself arises from the dy- Keywords Quantum gravity · general relativity · dark namical aspect of this superfluid. All known phenomena at- energy · gravitational waves · analog gravity tributed in general relativity to the Riemannian geometry of PACS 04.60.-m · 95.36.+x · 47.37.+q · 04.62.+v · 04.30.w spacetime possess an equivalent explanation resorting to the hydrodynamics of the DS, from Lense-Thirring precession and gravitational lensing up to gravitational waves. Introduction 1 Superfluid quantum gravity (SQG): Bernoulli In the first article on the hydrodynamics of the dark superflu- pressure in the DS as the mechanism of quantum id [1] we have provided reasons to interpret dark energy and gravity M.Fedi Ministero dell’Istruzione, Dell’Universita` e della Ricerca (MIUR), We refer here to the description of massive fundamental par- Rome, Italy ticles as torus-shaped quantum vortices in the DS [1], for E-mail: [email protected] which an hydrodynamic analogy with the fundamental en- 2 Marco Fedi tities introduced in Loop Quantum Gravity [9,10], where space is similarly granular and quantized, shall be reported for some aspects. From that, we focus on the Bernoulli force observed [25,26,29,28] when vortices form in superfluids. The formula reads [29] Z Fb = K(r)n(r)dS (1) S where K(r) = rv2=2 expresses the density of kinetic energy (which dominates on the vortex surface, while the density of the superfluid drops to zero within the so-called healing Fig. 1 Metallic nano-particles adhere onto vortex-filaments in super- length [1]) and n(r) is a unit vector normal to the cylindrical fluid 4He making them visible, thanks to Bernoulli pressure [25,26]. surface S over which the integral is calculated. A schemati- The attraction of the surrounding quanta in the DS exerted by vortex- cal description of this force as superposition of the vortices’ particles is by us indicated as the quantum mechanism of gravity. velocity fields obeying a 1=r function, which pressure fields are associated to, has been made in [29]. Due to Bernoulli pressure we see in Fig. 1 that particles of various sizes ad- here onto the vortices, making them visible as filaments. The amazing analogy with the observed cosmic web of dark mat- ter filaments showed in [1] is significant and tells us how the DS hydrodynamics may express both the cosmos of galax- ies and the microcosm of particle physics. Also interesting is the appearance of attractive or repulsive (depending on the chirality) Bernoulli pressure between quantum vortices only in two-component superfluids [29], where we have a Fig. 2 Since macroscopic bodies consist of fundamental particles, they small amount of a “doping substance” (e.g. metallic atoms) also produce a pressure gradient which becomes strong and evident scattered in a superfluid, such as superfluid 4He. The analo- around large celestial bodies and determines attraction. This is what we gy with a two-component DS in which a smaller amount of call “gravitational field”. This hypothesis is nothing more than Gauss’s real dark matter (∼ 25%) is immersed in a vast ocean of superflu- law for gravity, however considering here a flux of DS. id dark energy (∼ 70%) [1] is relevant. Thus, if macroscopic bodies were made up of vortex-particles in a two-component created by the action of spin, once this quantum number DS [1], they would show as well a pressure gradient around has been defined as the circulation of quanta in a superflu- them and would exert (and be subject to) Bernoulli force. id vortex taking shape in the DS (see [1] Sect. 3). So the This pressure gradient is called “gravitational field”. Fig. 2 core mechanism of quantum gravity would be actually spin, represents the gravitational field as inflow of dark superfluid described as vorticity of quanta in the DS. which consequently causes attraction between two or more bodies floating in it [16], while in Fig. 3 the pressure gradi- ent causing attraction is shown through a set of CFD sim- 2 From classical to quantum gravity without gravitons ulations. Here we can verify that the consequent attractive force mathematically equals Gauss’s law for gravity We know that a pressure gradient generates a force, for which I the acceleration is expressed as Fg = g · n(r)dS = −4pGM; (2) S P a = −∇ ; (3) for which we consider a “real” incoming flow (in our case r of DS), and is compatible with the Schwarzschild solution. Similarity with (1) is also evident. A similar hypothesis of being P and r respectively pressure and density. In our case, hydrodynamic gravity was proposed by Cahill [17] and Kirk- (3) has to correspond to the gravitational acceleration caused wood [18] previously thought of the gravitational field as an by the attraction of dark superfluid quanta (DSQ) due to the ether inflow, moving from the interpretation of the equiv- Bernoulli effect (Fig. 1, 2), then we write alence principle (also see Sect. 7) and analyzing this issue Pd in terms of particle and light motion in a gravitational field. g = −∇ ; (4) rd Also other efforts in the context of analog gravity, as those by Visser, Barcel, Consoli, have to be mentioned [19–21]. where the subscript d refers to DS. By using (4) in Newton’s Finally, it is important to notice that Bernoulli pressure is second law, we can write a formula for universal gravitation, Hydrodynamics of the dark superfluid: III. Superfluid Quantum Gravity. 3 a scale and conversion factor and this is indeed the role as- sumed by G. It is also interesting to note that the units in (6) correspond to Gray (Gy), i.e. to the unit used for ener- gy absorption (J/kg). In this case, absorption of DS (of dark energy), as hypothesized for SQG. The Newtonian gravitational constant now would read r Pd r G = −jh = = const: (7) M rd M So, its value and utility remain but it would now reveal the physical quantities and the relationships among them which produce that constant output on a quantum hydrodynamic basis. Furthermore, we see that the same hydrodynamic ex- pression (6) is used for the equation of state of cosmology: w = P=r, that we already considered as the equation of state of the DS [1,8].
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