The principle is
Which means, if the uncertainty of distance is small , the uncertainty of momentum is large.
For matching dimension, we have energy and angular momentum:
The meaning of the energy-time uncertainty is that, if the uncertainty of time is small, the energy variation can be large.
Say, if we had reached the limit of the principle, i.e. The inequality becomes equality. We divided the equation an get.
Which is the velocity of the particle is given by the ratio of energy and momentum.
In relativistic, energy is related with momentum
The derivative is:
Thus the principle consistence with relativity in limit case.
However, when the time-energy relation is an equality but the distance-momentum is not. The velocity can be larger then speed of light. Nevertheless, this hyper velocity cannot be measured.