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«1 Quantum vacuum as the cause of the phenomena usually attributed to dark matter Dragan Slavkov Hajdukovic, Institute of Physics, Astrophysics and ...»


Quantum vacuum as the cause of the phenomena usually

attributed to dark matter

Dragan Slavkov Hajdukovic, Institute of Physics, Astrophysics and Cosmology

Cetinje, Montenegro


January 15, 2016


We show that if quantum vacuum fluctuations are virtual gravitational dipoles, then the phenomena usually attributed to hypothetical dark matter, may be considered as a consequence of the

gravitational polarization of the quantum vacuum by the immersed baryonic matter; apparently, at least mathematically, the galactic halo of dark matter can be replaced by the halo of the polarized quantum vacuum. The eventual gravitational effects of the quantum vacuum ”enriched” with virtual gravitational dipoles, can be revealed by the study of orbits of tiny satellites in trans-Neptunian binaries (for instance UX 25 and Eris-Dysnomia).

According to the Standard Model of Particles and Fields everything is made from quarks and leptons interacting through the exchange of gauge bosons. So far, the Standard Model is the most successful and the best tested theory of all time; together with General Relativity (our best theory of gravitation) it is one of the two cornerstones of our fundamental knowledge.

One of the greatest mysteries in contemporary physics is that in galaxies and clusters of galaxies, the gravitational field is much stronger than it should be according to our theory of gravitation and the existing amount of the Standard Model matter (note that astrophysicists use ”baryonic matter” as a synonym for the Standard Model matter). There are two schools of thinking related to this mystery.

According to the first school, our theory of gravitation is correct, but the content of the Universe proposed by the Standard Model is highly incomplete; additional sources of gravitational field are halos of hypothetical dark matter in which galaxies are immersed. For the second school the content of the Universe proposed by the Standard Model is correct but our theory of gravity must be modified.

In fact, both schools have in common the incorrect assumption that the matter of the Universe exists in the classical, non-quantum vacuum; hence, quantum vacuum [1] is neglected as the content of galaxies and clusters of galaxies (but also as the content of our Solar System). If quantum vacuum is the source of the gravitational field, any theory that neglects the existence of the quantum vacuum is blind to some crucial gravitational phenomena, and, as a compensation for the lost phenomena, must invoke some artificial mechanisms. The inevitable question is if dark matter and dark energy are such ”artificial stuff” which only mimics the phenomena which are in fact caused by the quantum vacuum.

We point out (and it may be the emergence of a third school of thinking) that, if we adopt the working hypothesis that, by their nature, quantum vacuum fluctuations are virtual gravitational dipoles, the phenomena usually attributed to hypothetical dark matter, may be considered as a consequence of the gravitational polarization of the quantum vacuum [2, 3, 4, 5, 6, 7] by the immersed baryonic matter within it. An analogous result for dark energy is presented in a separate paper in these proceedings.

Let us note that the simplest and the most elegant realization of this hypothesis is, if particles and antiparticles have the gravitational charge of the opposite sign; of course nature may surprise us with a different realization of the gravitational dipoles-like behavior of the quantum vacuum.

It is illuminating to remember that in quantum electrodynamics quantum vacuum behaves [1] as a fluid of virtual electric dipoles. For instance, quantum vacuum, as ”ocean” of virtual electric dipoles 28th Texas Symposium on Relativistic Astrophysics Geneva, Switzerland – December 13-18, 2015 has a tiny impact (but impact!) on the ”orbits” of electrons in atoms. It is known as the Lamb shift [1].

Another important example: An electron ”immersed” in the quantum vacuum produces around itself a halo of non-random oriented virtual electric dipoles, i.e. a halo of the polarized quantum vacuum. This halo screens the ”bare” charge of an electron; what we measure is the effective electric charge which decreases [1, 8] with distance! These phenomena well established within the quantum electrodynamics make more plausible the effects of the eventual existence of virtual gravitational dipoles.

According to our hypothesis we consider a quantum vacuum fluctuation as a system of two gravitational charges of the opposite sign; consequently the total gravitational charge of a vacuum fluctuation

is zero but it has a non-zero gravitational dipole moment pg :

¯ h pg = mg d, |pg | (1) c Here, mg denotes the magnitude of the gravitational charge, while, by definition, the vector d is directed from the antiparticle to the particle, and has a magnitude d equal to the distance between them. The inequality in 1 follows from the fact that the size d of the virtual pair must be smaller than the reduced Compton wavelength. Consequently, the gravitational polarization density Pg, i.e.

the gravitational dipole moment per unit volume, may be attributed to the quantum vacuum. It is obvious that the magnitude of the gravitational polarization density |Pg | satisfies the inequality 0 ≤ |Pg | ≤ Pg max, where 0 corresponds to the random orientations of dipoles, while the maximal magnitude Pg max corresponds to the case of saturation (when all dipoles are aligned with the external field). The most plausible theoretical estimate [2, 3, 7] is Pg max = [0.06±0.02]kg/m3 ≈ 28.5MSun /pc2.

In addition, following the previous results [2, 3, 5, 7], in calculations concerning dipoles, we use the mass of a pion mπ (which is a typical mass in the physical vacuum of quantum chromodynamics).

In the limit of zero external gravitational field quantum vacuum may be considered as a fluid of randomly oriented gravitational dipoles 1; both the total gravitational charge and Pg are zero.

Random orientation of virtual dipoles may be broken by the immersed Standard Model matter.

Massive bodies (stars, black holes...) but also multi-body systems as galaxies are surrounded by an invisible halo of the gravitationally polarized quantum vacuum, i.e. a region of non-random orientation of virtual gravitational dipoles 2. This halo of the polarized quantum vacuum acts as an effective gravitational charge. Namely, the spatial variation of the gravitational polarization density Pg, generates a gravitational bound charge density [2, 3, 7] of the quantum vacuum

–  –  –

where a and µ are respectively the semi-major axis of the orbit and the total mass of the binary.

Transneptunian binaries (mini planets with miniscule satellites, as for instance UX25) are the best natural laboratory [4] to test the prediction 5 that quantum vacuum causes an anomalous perihelion precession (in fact a gravitational version of the Lamb shift!). Astronomers have already started [11] the preparation of the future tests.

Considering quantum vacuum as an ideal system of non-interacting gravitational dipoles in an external gravitational field (analogous to polarization of a dielectric in external electric field, or a paramagnetic in an external magnetic field) leads [6] to the following approximation Rsat Mqν (r) = 4πPg max r2 tanh (6) r valid also for the region r Rsat which is the most relevant for ”dark matter” phenomena.

It is encouraging that such a simplified model for a galaxy (spherical symmetry and ideal system of non-interacting gravitational dipoles) gives good results. Let us give a few examples. First, our theory of the gravitational effects of the quantum vacuum leads [2, 3, 7] to the Tully-Fisher relation which is one of the most robust empirical results, unexplained by ”dark matter”. Let us note that at this point (Tully-Fisher relation) MOND is more successful than ”dark matter” theory. The significant success of MOND is a sign that there is something special about their acceleration a0 ≈ 1.2 × 10−10 m/s2.

However, according to our model there is not any modification of the Newtons law, as proposed by MOND, for gravitational fields weaker than a0. In our model, a0 is rather a transition point, from saturation in stronger fields to non-saturated polarization in weaker fields. Second, according to observations [12] the median Milky Way mass within 260kpc is MM W (260kpc) = 1.6 × 1012 MSun with a 90% confidence interval of [1.0 − 2.4] × 1012 MSun, while our theoretical estimate [6, 7] is MM W (260kpc) ≈ 1.45 × 1012 MSun. Third, apparently the best estimate [13] for the local dark matter density (an average over a small volume, typically a few hundred parsecs around the Sun) is [0.0075 ± 0.0021]MSun /pc3 while our theoretical estimate is ≈ 0.0069MSun /pc3.

Let us end with three important notes-clarifications. First, it is obvious that gravitational field can align only quantum vacuum fluctuations which are gravitational dipoles but not electric dipoles.

Second, only a weak interaction such as gravity can polarize large volumes of quantum vacuum and create large galactic halos! Namely, the gravitational acceleration produced by a pion (roughly a typical mass in the physical vacuum of quantum chromodynamics) at the distance of its Compton wavelength is ≈ 2.1 × 10−10 m/s2. The mean distance between two dipoles which are first neighbours is one Compton wavelength; hence, the small value of this acceleration indicates that the gravitational polarization can be caused by a very weak gravitational field. Third, and the most important, there is a maximum size of the halo for each massive body, galaxy or cluster of galaxies; simply, after a characteristic size the random orientation of dipoles dominates again. A halo of the maximum size can be formed only if other bodies are sufficiently far; hence galactic halos, and consequently the effective gravitational charge of the Universe, increase with the expansion of the Universe asymptotically

–  –  –

reaching a maximum size. The ratio of the effective gravitational charge and the baryonic mass of the Universe is not a constant, contrary to the ratio of the quantity of hypothetical dark matter and baryonic matter.

References [1] Aitchison, I. J. R. (1985). Nothing’s plenty the vacuum in modern quantum field theory. Contemporary Physics, 26(4), 333-391.

[2] Hajdukovic, D. S. (2011). Is dark matter an illusion created by the gravitational polarization of the quantum vacuum? Astrophysics and Space Science, 334(2), 215-218.

[3] Hajdukovic, D. S. (2012). Quantum vacuum and dark matter. Astrophysics and Space Science, 337(1), 9-14.

[4] Hajdukovic, D. S. (2013). Can observations inside the Solar System reveal the gravitational properties of the quantum vacuum? Astrophysics and Space Science, 343(2), 505-509. Hajdukovic, D. (2014). Testing the gravitational properties of the quantum vacuum within the Solar System.

[5] Hajdukovic, D. S. (2013). The signatures of new physics, astrophysics and cosmology? Modern Physics Letters A, 28(29), 1350124.

[6] Hajdukovic, D. S. (2014). A new model of dark matter distribution in galaxies. Astrophysics and Space Science, 349(1), 1-4.

[7] Hajdukovic, D. S. (2014). Virtual gravitational dipoles: The key for the understanding of the Universe? Physics of the Dark Universe, 3, 34-40. Hajdukovic, D. S. (2014). The basis for a new model of the universe. Preprint hal-01078947v2.

[8] Acciarri, M., Achard, P., Adriani, O., Aguilar-Benitez, M., Alcaraz, J., Alemanni, G., Allaby, J., Aloisio, A., Alviggi, M.G., Ambrosi, G. & Anderhub, H. (2000). Measurement of the running of the fine-structure constant. Physics Letters B, 476(1), 40-48.

[9] Kormendy, J., & Freeman, K. C. (2004). Scaling laws for dark matter halos in late-type and dwarf spheroidal galaxies. arXiv preprint astro-ph/0407321.

[10] Donato, F., Gentile, G., Salucci, P., Martins, C. F., Wilkinson, M. I., Gilmore, G., Grebel, E. K., Koch, A. & Wyse, R. (2009). A constant dark matter halo surface density in galaxies. Monthly Notices of the Royal Astronomical Society, 397(3), 1169-1176.

[11] Gai, M., & Vecchiato, A. (2014). Astrometric detection feasibility of gravitational effects of quantum vacuum. arXiv preprint arXiv:1406.3611.

[12] Boylan-Kolchin, M., Bullock, J. S., Sohn, S. T., Besla, G., & van der Marel, R. P. (2013). The space motion of Leo I: the mass of the Milky Way’s dark matter halo. The Astrophysical Journal, 768(2), 140.

[13] Zhang, L., Rix, H. W., van de Ven, G., Bovy, J., Liu, C., & Zhao, G. (2013). The gravitational potential near the sun from SEGUE K-dwarf kinematics. The Astrophysical Journal, 772(2), 108.

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