I recently heard an argument to the effect that there is no problem in the universe coming from nothing because current cosmological evidence points to a flat universe; in such a universe positive energy is completely cancelled by negative gravitational energy and therefore the universe could have come from nothing. (I suppose a similar point could be made about cancelling electric charges)
Now, I think this mathematical jiggery-pokery was all rather tongue in cheek and not meant to be taken seriously. So with my tongue also firmly in my cheek let me engage in a little mathematical sleight of hand.
Let me define a quantity that I call the quadratic field operator. This operator takes a differentiated field of energy and sums up the squares of the energy components. If we start with absolutely nothing at all then clearly the quadratic field operator returns zero (=nothing). No problem. But as soon as there is any differentiation of energy into a field of cancelling negative and positive energy components the quadratic field operator quietly slips past the outer parentheses into the field of energy and hey presto you end up with a finite quantity (=something) Thus, if absolutely nothing suddenly resolves itself into a field of canceling energy terms the quadratic field operator reveals that something has come from nothing. Tough luck! We are back to square one! (or should that be square zero?)
Of course, all this by passes some rather abstruse philosophical questions: Do the “laws of physics” have any real meaning unless they are reified on an existing material ontology? What comes first; the laws of physics or the stuff whose patterns of behavior those laws describe? Does the description of an ontology proceed the ontology it describes? Do ethereal immaterial laws actually bring something into existence? Can existence be treated as a mere property that may be attributed or unattributed to an entity, or is it a fundamentally different category all together? I seem to remember that Anselm’s ontological argument foundered on this latter question!