Comment by T-A

> These waves are not particles. But they differ from the classical waves because they can only be scaled down to a certain length.

No, the limitation is not length; it's amplitude.

In Dirac's formalism, there is a vector which describes the state of the world, and there are operators which act on that vector. Those operators can create and destroy integer quantities of things. So you can have zero things, or one thing, or two things, or a million things... but not half a thing, or some other fraction. That is the "indivisible" part. The things can be smeared out over macroscopic distances, as in the case of the double slit experiment, but their number is an integer.

But if the story ended there, you still wouldn't have a quantum theory. You would just have a (partially) discrete, classical theory. You could write down a set of differential equations (indeed, wave equations) involving your operators and use them to study how a given vector will evolve over time. The whole thing would be completely deterministic, just like classical mechanics. And yes, it would describe a world made of "wavicles".

Strassler seems to be thinking of that world. But there is one last step you need to take in order to have a quantum field theory.

I like the way Wikipedia tells the story of how it was discovered [1]. Snipping wildly:

Following up on de Broglie's ideas, physicist Peter Debye made an offhand comment that if particles behaved as waves, they should satisfy some sort of wave equation. Inspired by Debye's remark, Schrödinger decided to find a proper 3-dimensional wave equation for the electron. [...] The Schrödinger equation details the behavior of Ψ but says nothing of its nature. Schrödinger tried to interpret the real part of Ψ ∂Ψ / ∂t as a charge density, and then revised this proposal, saying in his next paper that the modulus squared of Ψ is a charge density. This approach was, however, unsuccessful. In 1926, just a few days after this paper was published, Max Born successfully interpreted Ψ as the probability amplitude, whose modulus squared is equal to probability density.

That is what sets quantum theories apart from classical ones. The math is deceptively similar, but once you're done evolving your wav(icl)es, you need to take that last step: compute their amplitude squared to get a probability density.

If you are trying to predict a position, like the position of an electron in the double slit experiment, you won't get a set of coordinates; you will get a probability density covering the entire photographic plate. That probability density will look like a wave interference pattern, because that's exactly what it is: it's a pattern of interfering waves of probability.

So the "wavicles" are not particles; they encode the probability of detecting a particle. When you do the experiment, each particle shows up as a dot, and you can do other experiments to convince yourself that electrons really are point-like, at least up to the resolution achievable with the largest accelerators built to date.

Pondering what that all means - what quantum theory is telling us about the nature of reality - will lead you to a swamp known as "interpretations of quantum mechanics" [2].

[1] https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation#Hist...

[2] https://en.wikipedia.org/wiki/Interpretations_of_quantum_mec...