Are quantum mechanics and relativity incompatible?
The visitor pointed out the apparent difficulty in certain infinities that appear in the solution of some problems in relativistic quantum mechanics, and asked why physicists haven’t been able to deal with these infinities. This question has a two-part answer. First, quantum mechanics and special relativity have in fact been brought together very nicely in the field we call quantum electrodynamics, sometimes also called “The Standard Model.” This field of investigation is incredibly successful, In fact, The Casual Observer recalls with fondness (?!) the calculation of the Lamb shift he made in his advanced quantum mechanics class in graduate school. The inclusion of the first order of perturbation theory (using the Feynmann diagram approach) gives an incredibly accurate answer for the (small!) value of the Lamb shift. The small difference in energy levels in the hydrogen atom comes from the (relativistic!) interaction of the electron with virtual particles in the vacuum. The successful
