kpmartin (08/09/82)
Can the speed of a particle temporarily exceed c? The uncertainty principle allows temporary violation of energy conservation, provided that the product of the 'borrowed' energy and the time for which it is 'borrowed' does not exceed h/(2*pi) (h is planck's constant). This constant has the dimensions of energy*time (or momentum*position). Unfortunately, as v approaches c, for any particle with a non-zero rest mass, the energy required becomes infinite. Since the energy deficit would be very large, the amount of time "allowed" would approach zero. (Note that the allowed time, even without relativistic corrections, is proportional to 1/(v*v), and the distance travelled is proportional to 1/v, so the faster you go, the less far you can go). So the particle can temporarily have a high velocity, but it won't have enough time to go anywhere. (Actually, the uncertainty principle states that the smallest energy deficit observable is proportional to how long you watch something, and the product of the observed deficit and the observation time cannot be less than h/(2*pi). Any "observed" deficit below this threshold is just noise from the observer. Thus the principle of conservation of energy can be violated, provided the time & energy deficit are small enough that no one can observe them.)