Time in special relativity and quantum mechanics The time is treated differently in special relativity and quantum mechanics. What is the exact difference and why relativistic quantum mechanics (Dirac equation etc.) works?
 A: Quantum mechanics can be reconciled with special relativity to make quantum field theory, but there are some awkward things going on in that marriage. SR treats time symmetrically with position, but in quantum mechanics, position is an operator and time isn't. Baez at UCR has a nice discussion of that here: http://math.ucr.edu/home/baez/uncertainty.html
A: Time is always time. It is special. Another thing is its involvement in transformations of measured data from one reference system to another. This involvement does not change its meaning. In a given reference frame the time is unique and the space coordinates are multiple - according to the number of particles to be observed.
Concerning Dirac equation, it took some efforts to make it work after its invention. It works because it was made work, if you like. Besides, it depends what exactly do you mean by "relativistic QM". QED, for example, is rather difficult to make work. Its sensible results only appear at page 500 or so, when the infrared catastrophe is resolved.
