On physical vacuum as an unobservable system

Modern astronomical observations in cosmology provide increasingly strong evidence that the expansion of the Universe is accelerating. Explanations of the cosmic acceleration within the framework of general relativity use the hypothesis about a dark energy field (physical vacuum) with unrealistic fine-tuned unnatural properties to the properties of the observable matter. The main difficulty of the speculative models is that the gravitational properties of the vacuum are unknown. In this work the geometric properties of the physical vacuum which are the consequence of its general property to be unobservable (vacuum does not affect the motions of any real bodies) are considered. It is shown that the effective homogeneous and isotropic space-time of the physical vacuum has four closed dimensions. The vacuum fluctuations create interactions of the real particles. It is shown if we assume the cause principle and there are not any arbitrary real particles births then the lengths of waves of vacuum fluctuations make the fractal manifold. In this case all real systems have the fractal properties.