The Uncertainty Principle as normally stated is that (delta p) x (delta x) = a constant (where p is momentum, x is position and (delta p) is the uncertainty or error in the value of p etc.).<br /><br />Now momentum has units of mass times velocity. Mass has units of Energy divided by velocity squared (E=m.c.c), and velocity itself is distance divided by time. So:<br /><br />(delta p)(delta x) = (delta m)(delta v)(delta x) = (delta E/v.v)(delta v)(delta x) = ((delta E)/(delta v)(delta v))(delta v)(delta x) = (delta E)(delta x)/(delta v) = (delta E)(delta x)/((delta x)/(delta t)) = (delta E)(delta t).<br /><br />So the energy of a system can vary but only for a certain amount of a time. So for example, an electron and positron can both come into existence, but they can only remain in existence for a small amount of time. Such particles are called virtual particles.<br /><br />It should be noted though, that whilst they exist, such particles are just as real as any other electron or positron. So if there was a 'permanent' electron passing nearby when this pair came into existence, it would be influenced by their electric charges, and such interactions have to be taken into account when calculating paths and properties etc. Also, although an electron and positron must annihilate within the specified time, it doesn't have to be the <i>same</i> electron and positron. In our example, the positron could annihilate with the 'permanant' electron, thereby 'prmoting' the virtual electron to permanent.