Thanks, Doug! Yes, I definitely remember you... Looking forward to your seminar at SJSU!
I'll let you know if I spark any dynamics-mutinies for my physics students... But my quantum students still seem to manage to learn how to do QM despite my occasional claim that none of this is what's really going on, so I think I should be safe on that count... :-)
On your first comment, I'm not claiming that time and space are identical in all regards, but I'm still not quite sure about your argument here. The sentence "from t=0 one can only access t>0" has the word "access", which is already time- and causality-ladened, and doesn't have a good physics translation. If you mean "have worldlines that extend to" by "access", then this isn't true.
I guess one can complain that the past "isn't accessible", but if by "access" you mean experience-forward-in-time, then this is simply a tautology. If I defined the word "flerb" to mean a translation in the +x direction, then starting from x=0 one can only flerb to x>0. (As for why our experience has an arrow, that's a second-law-related issue, partially addressed in some of my replies to Ian Durham above.)
On your technical question, the key is to break the symmetry, or else all the probabilities are always equal. (Both of those examples you gave would lead to 50% probabilities for both diagrams, it turns out. Squaring 1:1 is still 1:1.) But you could do it with 4 colors, so long as (say) 3 colors were matched with H-H and T-T, or any other uneven setup.
As for whether one should even "expect" photons to adhere to Maxwell's equations, well, perhaps I'm coming at this from a 1905-perspective right now (see the piece just posted at arxiv.org/abs/1307.7744 to see what I'm talking about here). But I'm far more happy with the guts of QED than I am QM itself; I think it's the path-integral version of the former that has the best chance for a realistic interpretation (at least if one permits some modification).
I'm glad you found the essay thought-provoking! I know a bit about your work concerning the path integral, and I hope that you keep playing around with it, perhaps with some of these ideas in mind. From my perspective, the path integral is the ridiculously-neglected stepchild of quantum foundations, and certainly deserves more attention in general.
Best,
Ken