Where, in Minkowski space, is phase velocity?

In special relativity, the product of group velocity v_g with phase velocity v_p , in a free massive particle, is the square of the speed of light c². At low momentum, the group velocity is Newtonian, KE=¹/₂ mv_g² ; at high energy v_g -> c. In Minkowski space [1] v_g <c lies within the light cones; while v_p lies outside them. Is the phase interactive? The free particle wave function implies that the trajectories of the two velocities separate in Minkowski space. However, they have significant joint amplitude only where they overlap near the center of mass of the wave particle phi=Aexp(X²/2sigma² + X’) where X=i(omega.t-kx) and the prime indicates mean values (at the Gaussian maximum) The uncertainty is the FWHM of the wave function. The phase interferes where the amplitude is ‘uncertain’ around the median group trajectory. [1] A.J.Bourdillon, Journal of Modern Physics, (2024) 15 [10] doi:https://doi.org/10.4236/jmp.2024.1510065