Using a naive view of Einstein's Energy Mass Equivalence $E=mc^2$ (where m is mass and c is the speed of light), it seems tempting to interpret this as a quantum mechanical version of the inherent kinetic energy for a collection of relativistic particles.
If we assume that all quantum particles travel with constant velocity c through 4-dimensional spacetime, this means that if a particle has attained geometrical lightspeed, it's velocity in the time dimension must be zero. If we try to freeze a particle at some location, it will still move randomly in spacetime with velocity c, and consequently it becomes increasingly blurred, as we try to fix it's position by cooling it down.
In this naive view, quantum uncertainty is related to the inherent kinetic energy of quantum particles. The expectation would then be that the kinetic energy equivalence of mass would be $\frac{1}{2} m c^2$.
Is there any actual relation between the equations for mass-energy and kinetic energy, and if so what happens with the $\frac{1}{2}$ factor?