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Hydrodynamics of the Dark Superfluid: II. Photon-Phonon Analogy Marco Fedi

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Hydrodynamics of the Dark Superfluid: II. Photon-Phonon Analogy Marco Fedi Hydrodynamics of the dark superfluid: II. photon-phonon analogy Marco Fedi To cite this version: Marco Fedi. Hydrodynamics of the dark superfluid: II. photon-phonon analogy. 2017. hal- 01532718v2 HAL Id: hal-01532718 https://hal.archives-ouvertes.fr/hal-01532718v2 Preprint submitted on 28 Jun 2017 (v2), last revised 19 Jul 2017 (v3) 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: II. photon-phonon analogy. Marco Fedi Received: date / Accepted: date Abstract In “Hydrodynamic of the dark superfluid: I. gen- have already discussed the possibility that quantum vacu- esis of fundamental particles” we have presented dark en- um be a hydrodynamic manifestation of the dark superflu- ergy as an ubiquitous superfluid which fills the universe. id (DS), [1] which may correspond to mainly dark energy Here we analyze light propagation through this “dark su- with superfluid properties, as a cosmic Bose-Einstein con- perfluid” (which also dark matter would be a hydrodynamic densate [2–8,14]. Dark energy would confer on space the manifestation of) by considering a photon-phonon analogy, features of a superfluid quantum space. Taking into accoun- where photon is a quasi-particle which acoustically propa- t light propagation through the DS, a photon could be ei- gates through this dark superfluid as a transverse wave. The ther a real particle behaving as a wave or a quasi-particle discussion is structured in four parts: (a) shared features and possessing wave-particle duality as a phonon. We opt for behavior photon-phonon according to current knowledge; the second case and we discuss photon propagation through (b) phonons in fluids and their role in expressing energy, the DS via a transverse phonon-like dynamics (arguing that along with the transient solid-like (quasi-lattice) structure light is the sound of the DS) and we support this hypoth- arising in fluids and superfluids during relaxation time; (c) esis in four steps. We reflect (Sect. 1) on an interestingly Gremaud’s analogy of Maxwell’s equations in a lattice ap- wide set of currently known analogies, also valid for flu- plied to the quasi-lattice environment of a superfluid; (d) ids and superfluids, between phonons and photons and in Lorentz factor as the rheogram of dark energy and a pos- Sect. 2, referring to Bolmatov [15], we discuss transversal sible basis for a quantum interpretation of special relativity. wave propagation and heat transmission in fluids on acous- tic basis (phonons), in analogy with thermal photons. From Keywords Nature of light · Light propagation · Dark Gremaud (Sect. 3) [26] we resort to a complete analogy be- energy · Dark superfluid · Maxwell’s equations · Special tween Maxwell’s equations for electromagnetism and non- relativity divergent deformations of an isotropic lattice in Euler’s co- PACS 42.25.Bs · 95.36.+x · 12.20.-m · 03.30.+p ordinates, translated in our case into the quasi-lattice struc- ture of fluids which manifests within their relaxation time, a structural property which has been discussed also for super- fluid 4He [39]. Finally (Sect. 4), arguing a possible dilatant Introduction behavior of some superfluids under shear stress in a rela- tivistic regime, we present Lorentz factor as the rheogram We know that light propagates through a quantum vacuum of dark energy, opening a perspective onto the explanation but also through dark energy, since according to recent mea- of special relativity on a quantum basis and reinforcing the surings it constitutes 69.1% of the universe mass-energy, concept of transverse propagation of phonons in the DS. As which along with dark matter reaches 95%. The remain- a consequence, we understand that the main component of ing 5% baryon matter is in any case >99% vacuum. We the DS, dark energy, would be undetectable only as long as it remains unperturbed, being light its most evident manifes- M.Fedi Ministero dell’Istruzione, Dell’Universita` e della Ricerca (MIUR), tation, along with its famous repulsive action which avoids Rome, Italy the gravitational collapse of the universe, probably due to its E-mail: [email protected] 2 Marco Fedi 3 internal pressure as a superfluid. Its energy density (J=m ) is on the contrary accepted, and we equate e0m0 = bdrd, corresponds in fact to pressure. where rd is the density of the DS and bd its isentropic com- pressibility (expressed in Pa−1), we may state that the speed of light is given as [5,10] 1 Current photon-phonon analogies. 1 c = p : (1) Let us start with listing all current analogies between pho- bdrd tons and phonons (which can also manifest in superfluids Indeed, starting from the equation which defines the speed [17,27]). Both are bosons [18], since identical excitations of sound in a fluid, a = pK=r, where K is the bulk modulus, can be created by repeatedly applying the creation opera- and putting b = 1 as isentropic compressibility (in the spe- tor, b†; both possess wave-particle duality [19,20], indeed S K cific case of the DS we say b ), we obtain (1). This acoustic in a lattice, or quasi-lattice we expect that waves appear d analogy of the speed of light is also confirmed possible in that behave like particles; they obey the doppler effect, z = [26], as discussed in Sect. 3. ( f − f )= f ; are symmetric under exchange, ja;bi = emit obs obs Amendola and Tsujikawa [14], by introducing the speed jb;ai; possess a momentum, where that of a phonon1 is of sound through a cosmological ultra-light scalar field f, p ≡ hk¯ = h=l; with k = 2p=l (hence the parallelism: ra- ph possibly coinciding with dark energy, state that it is the key diation pressure , sound pressure); are involved in photo- parameter to understand the (background) dynamics of such electric effect and Compton scattering thanks to their mo- a field. Starting from the ratio pressure/density, they define mentum; they can spin [21,22]. As far as spin is concerned, the speed of sound through this cosmic fluid as it would be realistic in our opinion that the higher degree of freedom of a phonon in the quasi-lattice of a fluid medium, s s dP H2(f 0j0 − f 02Y) −V j may allow it to possess spin 1. For this reason we consid- f ;f cs;f = = 2 0 0 02 : (2) er the photon as a special spin-1 phonon. Rotating phonons drf H (f j − f Y) +V;f j have been described also as regards the physics of nanotubes where we see that, when the potential of the field becomes [23]). Moreover, we actually know that photon spin can have flat, V ! 0, we may have the speed of sound through the three different values (-1, 0, 1), so, at most, magnitude 1. ;f field coinciding with that of light (natural units are used by Photon and phonon can form squeezed coherent states [24] the authors, where the speed of light is c = 1). and can interact via parametric down conversion [25]. For both, h¯w=2 is vacuum’s (we say dark energy’s) contribu- tion, since the harmonic oscillator eigenvalues for the mode 2 Thermal photons and phonons-driven energy w (k is the wave number) are E = (n + 1=2)h¯w with k n k propagation in fluids and superfluids. n = 1;2;3;::: and (to confirm the presence of a “false vacu- um”) also for n = 0 the energy is not zero. This means that We discuss now the possibility that photons-driven energy what we think to be the vacuum actually contains energy radiation be phonons-driven energy propagation when it oc- and according to E = mc2, a certain density (r in the cos- 0 curs in the DS. We have remarked that phonons, which are mological constant l = kr ), where c2 = (b r )−1 would 0 d d typically associated to a solid state, also manifest in fluids be precisely linked to dark energy’s intrinsic parameters, as and superfluids [15–17]. Particularly relevant for our case is from Eq. (1). There is a medium throughout the universe the paper of Bolmatov, Brazhkin and Trachenko [15], about owning density r 6= 0 which light propagates through and a phonon theory of heat diffusion in classical and quantum which can be described as a dark superfluid. fluids where longitudinal and transversal phonons are de- scribed considering Frenkel [16], who first noticed that the density of liquids is much different from that of gases but 1.1 The formula for the speed of light. only slightly different from the density of solids and who also defined the existence of transversal waves in liquid- It is worth recalling the fact that Maxwell derived the di- s, as previously observed in solids, for frequencies larger electric constant (e ) and the magnetic permeability (m ) of 0 p 0 than 1=t, where t is the relaxation time of the fluid, i.e. the “vacuum”, from which the formula c = 1= e m follows, 0 0 time during which the structure of the liquid remains unal- in terms of density and transverse elasticity of the ether (see tered, similar to a solid lattice.
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