Update:
So, yes, the “Adding Probabilities” method is wrong. As it turns out, the reason I was getting
such bad distributions when using Mathematica to produce graphs for the (correct)
“Adding Fields” method is that I had not properly adjusted the phase for each
field point source within each of the slits.
When I do that, it produces distributions in the near- and far-fields
that, I think, are consistent with what would be observed in actual
experiments.
But this essay is important to me for several reasons. First, it underscores one of the problematic
assumptions I’d been making, namely the assumption that there is some reality
about where, in each slit, a particle is located. Identifying that as incorrect helped me come
to what I believe is a better understanding/interpretation of QM, which I
describe here, in which a superposition is indicative of a lack of a fact. Second, writing it helped me to understand
the relationship between single-slit Fraunhofer distributions and double-slit
interference distributions. Third, it
makes some good points about problems in QM, and is mostly correct if you’ll
ignore any nonphysical wackiness in the “Adding Fields” graphs.
I have made huge progress in understanding physics over
the past couple years and wouldn’t be where I am today without the experiences
of yesterday.