English: The free-particle dispersion-relation (K vs. p) at anyspeed: Plots of kinetic energy K = mass m × (γ-1)c² where Lorentz-factor γ ≡ dt/dτ versus momentum p = h/λ = mass m × proper-velocity w ≡ dx/dτ, for an almost comprehensive range of everyday values along both axes^[1].

Here τ is proper-time elapsed between two events on the world-line of our traveling object, x is the map-distance and t the map-time separating those events, h stands for Planck's constant, and as usual c stands for the space-time conversion-constant also known as lightspeed.

Lines of constant coordinate-velocity v ≡ dx/dt on this log-log plot have a slope of 1, while lines of constant rest-mass m well below the lightspeed curtain on this plot have a slope of 2.