trajectories passing from the sources up to the point ⃗ q$_{1}$ . Along with the other virtual trajecto- ries generated by the other secondary sources, all together they create in the point ⃗ q$_{1}$ an averaged effect of contribution of these secondary sources. This averaged effect shows whether a real parti- cle passes by this route and what probability of this event can be. 

One can imagine, that all physical space is filled by such secondary sources of spherical waves. These sources are virtual in that sense, that they manifest themselves via zero-point os- cillations of vacuum. It means, that there are permanent creations and annihilations of virtual pairs ”particle-antiparticle”. Lifetime of such pairs are associated with their total energy by the Heisenberg uncertainty principle, i.e., the larger uncertainty of the total energy the smaller the lifetime of the pair. The same can be said about their scattering from each other: if the po- sition is known perfectly, then the momentum is completely unknown, and vice versa. 

Imagine now, let an area of scattering of such pairs be equal to about an effective width of the slit, σ , that is multiple of the wavelength. In that case, the momentum, p = h/σ , can be suffi- cient to force the particle to change a direction of scattering. Virtual spherical waves in the vicin- ity of the slit can effect to behavior of the particle 

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passing through the slit. Ensemble of such vir- tual waves, each attributed to its slit, creates a polarized effect similar to the domino effect. In other words, in a space, adjoining to the slit grat- ing, zero-point oscillations of vacuum are quite ordered. The slits in effect control the vacuum fluctuations. It is not analogous to ordered po- sitions of atoms in crystals. The ordering of vir- tual oscillations of vacuum, in the case of the slit grating, is expressed via organizing the wave function that describes transport of the particles through the grating. The wave function repre- sents itself the de Broglie pilot wave [30, 31] that guides a particle from a source to a detector. A path from the source to the detector, called the Bohmian trajectory, is resulted from solution of the guidance equation [19]. 

The author thanks V. Lozovskiy and A. I. Ioffe for a series of useful remarks. The author ex- presses his sincere thanks to Miss Pipa, the site administrator of Russian Quantum Portal, for developing and writing a program calculating the density distribution of the wave function at scattering particles on N -slit grating. The pro- gram draws also Bohmian trajectories outgoing from the slits. 

URL http://arxiv.org/abs/quant-ph/0702224 , (24 Feb 2007). 

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## Acknowledgments 

