  We have suggested, that the size of extra spatial dimensions (if they exist)
should be related to the quantum vacuum fluctuations; an extra dimension must
be sufficiently large to allow appearance of virtual quark-antiquark pairs,
which are an inherent part of the physical vacuum in quantum chromodynamics. We
argue that the conjecture of extra dimensions with the universal size equal to
the reduced Compton wavelength of a pion is a serious alternative to the
postulated universal mass in the theory of large extra dimensions (LED). Our
conjecture leads to the conclusion that the production of artificial mini black
holes at LHC at CERN is unlikely. It is shown that the recent lower limit on
the mass of a microscopic black hole (established by CMS collaboration at CERN)
may be interpreted as the upper limit (equal to six) for the number of extra
dimensions. Additionally, we challenge the current wisdom that mini black holes
disintegrate through the Hawking radiation. We point that it might be wrong, if
there is a hypothetical repulsion between matter and antimatter; resulting in
the creation of particle-antiparticle pairs from the quantum vacuum and
matter-antimatter asymmetry in the spectrum of radiation.
