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The title basically sums up the question. We know that if I shoot $N$ particles through a double slit then as $N$ gets large I see an interference pattern. Now if I take $N$ experiments and shoot one particle for each experiment and superimpose the outcome do I still see an interference pattern, or does the set up need to "warm-up" over some early particles?

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Theoretically, yes, the interference pattern should emerge if you shoot one particle in each of $N$ experiments and then merge the outcomes.

However, It is not practically feasible to conduct thousands, or millions of experiments using one particle each. So, this can not be experimentally verified.

But, what can be done for reasonable experimental proof is - conduct (say)100 experiments (with identical setups) with few hundred/thousand/million particles in each and then superimpose the outcomes.

QM community is convinced to an extent that is beyond any level of scrutiny, and it would not see any point in conducting such an experiment. So, this is not likely to happen.

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  • $\begingroup$ Right thankyou. I was speaking more at a thought experiment level. But that being said one could disturb the equipment somehow after each measurement so it is effectively a new experiment with one particle. $\endgroup$ – play Mar 28 '17 at 20:09
  • $\begingroup$ It has been experimentally verified. One electron at a time : en.wikipedia.org/wiki/… and one photon at a time sps.ch/en/articles/progresses/… . I have several answers here with these plots. $\endgroup$ – anna v Jun 1 '18 at 5:24
  • $\begingroup$ @annav: You are right. What I am referring to is - using a different equipment with each particle. That would require millions of equipment. $\endgroup$ – kpv Jun 1 '18 at 15:34
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The interference pattern emerges due to interference of the two wave fronts that emerge from two slits. Even if you shoot one particle at a time in a single setup, the interference pattern will emerge over time, since the single wave-particle interference with itself when passing through the slits.

Thus, if you have N experiments, where in each setup a single particle is shot, the aggregated interference pattern will be equivalent to the case where a single particle is shot at a time. So you will see the interference pattern.

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  • $\begingroup$ If the interference pattern is arising from the particle interfering with just itself then it should not matter how many particles have passed through the setup before say the $m^{th}$ one. So is it not identical to $N$ experiments with single particles, each one interfering with itself? $\endgroup$ – play Mar 28 '17 at 18:30
  • $\begingroup$ Actually you are right. N experiments, each with single self interfered particle will produce the interference pattern when aggregated. I will change my answer accordingly. $\endgroup$ – user3394040 Mar 28 '17 at 18:33
  • $\begingroup$ So it is established for certain that interference arises from the particle interfering with itself and not with some sort of accumulation of memory, somewhere, of past particles. $\endgroup$ – play Mar 28 '17 at 19:16
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    $\begingroup$ @play: the interference happens between the waves emerging from the two slits. This could for multiple wave-particles passing through at the same time, or could be single wave-particle that passes through. The current understanding is that the interference is merely due to interference and not due to accumulation of memory. That's why double slit experiment is the standard experiment to demonstrate the wave nature of particles. $\endgroup$ – user3394040 Mar 28 '17 at 19:45
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What exactly is meant by "seeing" an interference pattern?

Experimentally, it means this: You throw the particles at the two slit apparatus. You then set up a continuous array of detectors on the screen. The detectors give you a binary answer. They tell you if they collected the particle or not. Thats it. They certainly don't show you any pattern! enter image description here

You then plot the number of particles you collected against position after throwing many many particles. The plot you get when slit 2 is closed is plotted as $P_1$ and when slit 1 is closed is plotted as $P_2$ in figure(b).

If both were kept open the result is plotted in (c). This has a striking resemblance to our familiar interference pattern(And with good reason, it is the probability amplitudes that are interfering). This is often why it is referred to as interference.

The big lesson here is that this interference is inherently a statistical phenomenon. You simply can't obtain this pattern with one particle. It doesn't matter if you did the experiment with one set up or a different set up every time. Nature is inherently probabilistic, assigning in some manner the probabilities of going to a certain point. These are probabilities that you can "see" when you do sufficient re trials of the experiment with sufficient number of particles, using any number of identical apparatus in any order you like. The answer is the same. It certainly has nothing to do with memory, since we assume that in each particle reaches our detector independently of others.

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