 In this approach the physical vacuum is viewed as the quantum superfluid which is essentially non-relativistic whereas the Lorentz symmetry is not an exact symmetry of nature but rather the approximate description valid only for the small fluctuations of the superfluid background.Within the framework of the approach a theory was proposed in which the physical vacuum is conjectured to be the quantum Bose liquid whose ground-state wavefunction is described by the logarithmic Schrödinger equation.It was shown that the relativistic gravitational interaction arises as the small-amplitude collective excitation mode whereas relativistic elementary particles can be described by the particle-like modes in the limit of low momenta.