if a beam of identical particles at random distances from each other (or exactly 1/2 lambda between each other) travelling with the same v towards a double sllit do not interfere with each others wave function, so that the wave function of each particle upon reaching the double slit is always lambda / p, thus producing a predictable interference pattern,
how come the wave function of the region BETWEEN the slits DOES interact with the wavefunction of each particle so as to 'block' (or greatly reduce) it so that each particle's wave function can interfere with ITSELF via the two slits?
conversely, since the wavefunction of one particle (the inter-slit 'substance') can and seemingly does affect the wavefunction of another 'particle' (that of the approaching particle), why don't the particles in a beam interfere with each other so as to randomoly destroy any assignable wavelength to them?
if the inter-slit region had no affect on the wavefunctions of the approaching particles, the diffraction grating / double slit apparatus would be entirely transparent to the beam and there would be no interference at all.
The probability function is an entirely mathematical construct, and yet how it evolves over space must be dependent on whether there is any 'matter' in the region through which it passes. Is there something like a "damping factor" of freespace, for the probability function, like electrical permitivity of freespace?