  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 the phase-space
geometry and dimensionality of the space-time continuum. It is suggested that
the problem of the normalization condition $U^* =c$ at $Q^2=0\, \rm{GeV}^2$ can
be solved naturally within the framework of ``Two-Time Physics'' developed by
I. Bars. 2T-physics is the theory with local symplectic $\mathrm{Sp(2,R)}$
gauge symmetry in phase-space and the space-time geometry of signature
$\mathrm{(1+1',d+1')}$ with one extra time-like and one extra space-like
dimensions.
