Why does it take lots of quanta to show the interference pattern in the double-slit experiment?

Question

Why does the interference pattern in the double-slit experiment take lots of single particles (quanta of energy) to build? Why does sending just one not result in the pattern, even it interferes with itself?

Answer 1

Quantum Mechanics describes probabilities. Probabilities reveal themselves through multiple event probings, an estimator. So, one coin toss cannot reveal the heads/tails probability of a coin face emergence.

It is the associated probability amplitudes in the two slit experiment which interfere with themselves, individually, not the finally observed quanta themselves.

So, one electron, a point particle of zero size, will produce a dot on the screen; but you need many similar such to probe/assay their identical probability distribution, revealing the probability wave, as ,e.g., in the pedagogical Hitach experiment of 35 years ago...

Answer 2

Imagine you're throwing an unfair coin (say, it's more likely to result in heads than in tails), and you don't know in advance that it is unfair - the "pattern" of unfairness is embedded in the structure/material of the coin (e.g. maybe one side weighs more), but you have to perform many throws before you can see that the odds are not 50:50, because each time you only get a single, definite result. I.e., without repeating the throwing experiment over and over, you wouldn't even know that it's an unfair coin.

Similarly, the interference pattern is present in the wavefunction of a single particle (the "structure" that is in in some sense underlying the physics of a single particle) as it spreads out away from the two slits - it's kind of like two overlapping ripples in the underlying quantum field. The resulting amplitude of the wave crests and troughs throughout these interfering ripples determines how likely it is for a particle to be detected at any particular point, but what you detect appears as a single, localized particle (this rippling sort of ends up "manifesting" itself as a point particle to the detector) - and while this phenomenon is described variously as the collapse of the wavefunction due to a measurement, or perhaps as a consequence of something called decoherence, nobody really knows with certainty exactly how or why this happens.

So, the problem is that these ripples cannot be observed directly; in each individual experiment you only get a point-like blip in the detector, so you need many repeated experiments to even know that these ripples are there in the first place - like how you needed many throws to determine what kind of a coin you had.

But maybe you're looking at it a bit backwards.

Before quantum physics, we didn't even know these ripples were a thing. We used to think particles were like these tiny spheres or points whizzing around like little bullets. When you send a bullet through a slit, it might go straight through, or maybe bounce off of the wall and change direction to some extent, but at the target, you get a single bullet hole - that's what you'd expect, and so it was not surprising that you'd see a similar kind of thing with particles (you detect them at a single point). In a double slit experiment with many bullets, what you get is two overlapping bunches of bullet holes, but no interference pattern.

What was surprising is that this is not the case for particles. With particles, the interference pattern builds up even if you wait a long time before you send each particle, in order to make sure that the pattern is not due to some interaction between the particles themselves when you send out a bunch of them at once. So, if there's no interaction between the particles, then how does each particle "know" where to show up in relation to the pattern built up so far, without messing it up?

As similar interference patterns were known from other areas of physics to be wave-related phenomena, this (and other experiments) suggested that there was a previously unrecognized wave-like aspect to particles, and that the "tiny bullets" picture we had before was not quite correct. Since more or less the same pattern of overlapping ripples happens independently every time you send a particle through the slits, the cumulative interference-revealing pattern at the detector is preserved even when you send one particle at a time, with long pauses in between.