Additional Dimensions of Space and Time in the Region of Deep Inelastic Processes

We prove that the well-known Heisenberg uncertainty relations and Landau–Peierls uncertainty relations implicitly contain ‘‘hidden’’ angular variables, which belong to new uncertainty relations. Based on the obtained relations, we derive a formula for estimating the speed $$U^{*}$$ of a virtual particle in indirect measurements. We applied the theory of indirect measurements and the derived formula to estimate the module of the group velocity of virtual photons from the DIS HERA data. The HERA data indicate that the speed of virtual photons exceeds the speed of light $$c$$ in free space, $$U^{*}>c$$ . The properties of virtual photons and a hypothetical tachyon particle are almost identical. It is found that in the realm of particle interaction, the new angular parameters are closely related to the type of geometry and dimension of the space-time continuum. The superluminal speed of virtual photons finds its natural interpretation within the framework of ‘‘two-time physics’’ developed by I. Bars. 2T-physics is the theory with local gauge symmetry Sp(2,R) and the space-time geometry of signature (1+1’,d+1’) with one extra time-like and one extra space-like dimensions.