Yet Another Double-Slit Question I'm not a physics graduate, I studied the subject to high school level but don't 'know the math'. But I'm interested in philosophy of science, and have read a number of popular books on the topic (e.g. Manjit Kumar, Brian Greene, David Lindley etc.)
The question is this. I have learned that with the double-slit experiment, you can considerably vary the rate at which particles are fired without effecting the resulting interference pattern. That is, roughly speaking, 24 hours at 1 particle fired per second would give the same pattern as 86,400 particles fired in 1 second (all else being equal). 
I know this is one of the strange things about the experiment, and as I understand it, this is the origin of the idea that the particles fired one-at-a-time 'interfere with themselves', which I think seems a very lame idea (but as I said, I'm not a physicist).
However the point which struck me is that if the inteference pattern is not rate-dependent, then it means that time is not a factor in the generation of the interference pattern i.e. if the same pattern can be generated in 1 second as in 24 hours, then 'time' is not a variable. And that struck me as being at least philosophically significant. //edit// - what are other examples of wave functions in physics, where 'time' is not a variable? //end edit//
Is this a point of discussion about the double-slit experiment?
 A: The independence of an interference pattern produced by a given number of photons from the time required for those photons to be registered is simply further confirmation of the assertion that each "interferes with itself". Each transmission seems to be independent of how the others play out. 
This famous, not always correct, statement (due to Dirac) makes more sense once you lose the misconception that "photons" are particles in the same sense that billiard balls are. As far as physics understands, there is one one entity to do with the electromagentic part of your experiment and that is the electromagnetic quantum field. "Photons" and "numbers of photons" are simply labels we use to describe different states of the same electromagnetic field. We believe that various "modes" of this field can take on only discrete states and the field is a collection of these modes. We describe the field's state by saying which discrete "notch" each of its modes are in. It's a little like the financial state of a business: there are various accounts and one describes the business's financial state  by naming how many dollars and cents there are in each.  And the values the accounts can take are of course quantized.
So, back to our experiment, it's the electromagnetic quantum field in a one photon state that inteferes with itself.
You should read the answers to the question Which is more fundamental, Fields or Particles?, especially Daniel Sank's answer, where he gives further description of what we mean by a quantum field.
I also said that Dirac's aphorism is not always correct. There can arise situations (although they are very unusual) where there are correlations between the successive single photonic transmission events. But Dirac's statement is a good one to describe the slit experiments. 
A: 
if the same pattern can be generated in 1 second as in 24 hours, then 'time' is not a variable. 

At the quantum mechanical level of the experiment, there is a time independent solution of "particle scattering off double slit". This solution defines  the probability of finding the particle at an (x,y,z) at time t, where time is irrelevant in this case. This is because the boundary values of the specific problem are time independent. If the size of the slit changed with time, or the screen moved in the z direction in time, then the solution would have a time dependence.
The rate of incoming particles is irrelevant if the boundary conditions are time independent, so it is not a matter for discussion.
The interference is at the probability level for the measurement, it is not the mass or the charge or .... that interferes, the individual particle comes through whole, the accumulation measures the probability distribution.
See these electrons building up the interference pattern in their probability distribution


electron build up over time.

