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Photon-Phonon Analogy in a Superfluid Vacuum. Marco Fedi

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Photon-Phonon Analogy in a Superfluid Vacuum. Marco Fedi Photon-phonon analogy in a superfluid vacuum. Marco Fedi To cite this version: Marco Fedi. Photon-phonon analogy in a superfluid vacuum. 2017. hal-01532718v1 HAL Id: hal-01532718 https://hal.archives-ouvertes.fr/hal-01532718v1 Preprint submitted on 2 Jun 2017 (v1), 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 Photon-phonon analogy in a superuid vacuum. Marco Fedi* Ministero dell'Istruzione, dell'Università e della Ricerca (MIUR), Rome, Italy June 2, 2017 Abstract for uids and superuids, between phonons and photons and (3) referring to Bolmatov [14], we discuss transver- We discuss clues to consider quantum vacuum as a su- sal wave propagation and heat transmission in uids on peruid, probably superuid dark energy, in which we acoustic basis (phonons). From Gremaud (4) [25] we re- analyze a photon-phonon analogy. The discussion is sort to a complete analogy between Maxwell's equations structured in four parts: (a) shared features and behav- for electromagnetism and non-divergent deformations of ior photon-phonon; (b) phonons in uids and their role an isotropic lattice in Euler's coordinates, translated in in expressing energy, along with the transient solid-like our case into the quasi-lattice structure of uids which (quasi-lattice) structure arising in uids and superuids manifests within their relaxation time, a structural prop- during Frenkel relaxation time; (c) Gremaud's analogy erty which has been discussed also for superuid 4He [38]. of Maxwell's equations in a lattice; (d) Lorentz factor as Finally (5), arguing a possible dilatant behavior of some the rheogram of dark energy and a possible basis for a superuids under shear stress in a relativistic regime, we quantum interpretation of special relativity. present Lorentz factor as the rheogram of dark energy, opening a perspective onto the explanation of special rel- PACS numbers: 42.25.Bs, 95.36.+x, 47.35.Rs, 12.20.-m, ativity on a quantum hydrodynamic basis and reinforcing 95.35.+d, 03.30.+p transverse propagation of phonons in superuid dark en- ergy due its dilatancy within a relativistic regime. As a consequence, we understand that dark energy would be undetectable only as long as it remains unperturbed, be- Introduction ing light its most evident manifestation, along with its (at the moment more known) repulsive action which avoids We know that light propagates through a quantum vac- the gravitational collapse of the universe, probably due uum but also through dark energy, since according to to its internal pressure as a superuid. recent measurings it constitutes 69.1% of the universe mass-energy, which, along with dark matter, comes to 95%. We show that quantum vacuum uctuations pos- 1 Light propagates through a sess a hydrodynamic nature appearing as quantized vor- tices, so we can interpret quantum vacuum as the sponta- quantum vacuum, correspond- neous hydrodynamic perturbation of an ubiquitous cos- ing to superuid dark energy. mic superuid, which may correspond to dark energy with superuid characteristics, as a cosmic Bose-Einstein The existence of a false vacuum with non-zero energy con- condensate [1, 2, 3, 4, 5, 6, 7, 13]. Thus, dark energy tent is denitively accepted and proven in a lot of phys- would confer on space the features of a superuid quan- ical phenomena: the Lamb shift, the Casimir eect, the tum space (SQS). According to our considerations, here a Unruh eect, the anomalous magnetic moment, vacuum photon might propagate as a transverse phonon (arguing birefringence [12]etc. From the point of view of quantum that light is the sound of dark energy) and we support physics, light travels through such a quantum vacuum. this thesis in four steps. We reect (2) on an interest- This environment is known for the continuous appearance ingly wide set of currently known analogies, also valid and annihilation of virtual particle-antiparticle pairs, as *[email protected] initially formulated by Dirac. The relationship for these 1 uctuations is with the structure of a vortex web arising in a familiar h 4E4t ≥ = : (1) superuid such as 4He. In this analogy all the space 2π ~ among the laments is occupied by liquid helium in (a) The Bohr-Sommerfeld quantization condition, expressing and by superuid dark energy (SDE) in (b). mass circulation in a quantized vortex p · dx = nh (2) ˛C for n = 1 tells us that the quantum of action, h; actu- ally refers to a complete turn along a circular path of a quantum whose momentum is p. In (1) 2π also refers to a 360° turn and we can therefore interpret vacuum uc- tuations as quantized vortices. The sign≥ states that we consider n ≥ 1 complete rotations of the vortex during a time 4t as the vacuum uctuation. Quantum vortices are known to manifest in superu- ids, as in 4He [8, 37]. We also observe vortex-antivortex pairs, which form and annihilate [39, 8, 37], exactly as particles-antiparticles pairs in quantum vacuum. In our opinion, these are therefore clues for considering quantum vacuum as a superuid. The analogy particles-quantized vortices is reinforced by the fact that fermions spin-½ may be described in hydrodynamic terms as the circulation of quanta in a torus vortex (see [4], 3.1). Thus, if vacuum Figure 1: Left [10]: (a) Metal atoms trapped in superuid he- lium vortices highlight a structure of vortex laments; (b) galactic uctuations are superuid vortices, what is the underly- laments of dark matter which galaxies aggregate on [11]. Here ing superuid in which they arise? the relationship between dark energy and dark matter is the same The possible answers are the Higgs eld or dark energy, existing between superuid helium and the vortex laments which manifest in it, i.e. dark matter is a hydrodynamic manifestation of both observed as dark scalar elds. Being the Higgs dark energy [1]. boson the fundamental excitation of the Higgs eld and very massive, it is probably a vortex itself, so we opt for dark energy, as a cosmic fundamental superuid. After The internal pressure of SDE would be responsible [9] all, we know it constitutes of the mass-energy of ∼ 69% for the repulsive force traditionally attributed to dark the universe, also expressed in the cosmological constant, energy in cosmology. Moreover, the equation of state , where ( 00 as regards the stress-energy Λ = kρ0 ρ0 T ; of cosmology for a single-uid model can be referred to tensor) indicates the density of dark energy. Along with SDE, where P and ρ are respectively the pressure and dark matter, which can be interpreted as condensed dark d d the density of dark energy [13] energy [1, 2, 3, 4] and whose existence is for instance evident in the dark halos of spiral galaxies which the at P w = d (3) proles of orbital velocities are believed to be due to, we ρd arrive at . ∼ 95% As far as the propagation of light through this ubiquitous As for any form of energy, also dark energy has to superuid is concerned, we can still believe that photon be quantized. We speak of dark energy quanta (DEQ). is a real particle whose energy is not aected by any min- The hydrodynamical perturbation of these quanta would imal friction while traveling through this superuid or we produce the known picture of quantum vacuum as well can analyze, as below, the possibility that a photon is ac- as the Higgs boson itself. tually a transverse phonon (a quasi-particle) propagating The temperature of the cosmic microwaves background in superuid dark energy. According to this view, dark radiation (CMB), ∼ 2:72 K, would be in agreement with energy does not interact with baryon matter unless it is the temperature of other superuids such as 4He. Fig. 1 hydrodynamically perturbed and the most evident pertur- shows dark matter distribution in the universe in analogy bation might coincide with light itself. 2 2 Current photon-phonon analo- of light is given as [4, 9] gies. 1 c = p : (4) βdρd Let us start with listing all current analogies be- Indeed, starting from the equation which denes the tween photons and phonons (which can also manifest speed of sound in a uid, a = pK/ρ, where K is the in superuids [16, 26]). Both are bosons [17]; have bulk modulus, and putting β = 1 as isentropic com- wave-particle duality [18, 19]; obey the doppler eect, S K pressibility (in the specic case of SDE we say βd), we z = (f − f ) =f ; are symmetric under exchange, emit obs obs obtain (4). This acoustic analogy of the speed of light is jα; βi = jβ; αi; can be created by repeatedly applying the also conrmed possible in [25], as discussed in 4. creation operator, ay; possess a momentum, where that Amendola and Tsujikawa [13], by introducing the of a phonon1 is with (hence pph ≡ ~k = h/λ, k = 2π/λ speed of sound through a ultra-light scalar eld φ, state the parallelism: radiation pressure , sound pressure); that it is the key parameter to understand the (back- are involved in photoelectric eect and Compton scat- ground) dynamics of such a eld.
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