[bluepnume]

I take it you're a MWI fan then? Isn't the answer for why we "force wave-describing partial differential equations into a probabilistic model" because in our reality, when we look at an electron we observe something that looks like a particle and not a wave?

[timberfox]

I'm not a fan of the Many-Worlds Interpretation :-)

As for the electron, it is an oscillator described by a wave function, quantized, without locality. Here is an image of the wave function interpreted as a probability density:

https://en.wikipedia.org/wiki/Electron#/media/File:Hydrogen_...

The Quantum Mechanics interpretation is that the electron is a particle in an indeterminate location and the plot describes the probability of where the electron can be located. The Quantum Field Theory interpretation is that what we see is a field in an excited state, quantized. By looking at those plots, we can see a quantized field vibrating. If we send it through a double slit, it will behave like a wave. If instead we think about it as a single, indivisible particle, then we need to explain how it passes through two different slits at the same time. Thinking about it as a quantized oscillator disolves the paradox.

[bluepnume]

Makes sense -- but if you're saying "the electron travels through both slits at the same time because it is a wave", then why can't we detect that wave simultaneously at both slits?

At that point of measurement/detection we HAVE to start talking about probabilities, not just waves, right?

[rocqua]

What does it mean for a wave to quantize? That is not something I (as a mathematician) are familiar with. It feels like something that bears a lot of explanation. I would hazard a guess that the explanation makes it decently reasonable to call this process 'a particle'.

Certainly, to me it feels like saying 'it is just a wave' doesn't describe it because this quantization is a special thing.

[tome]

I guess it means that the governing equation has a solution space which is somehow discrete. I would like to know if there's a more precise definition than that!

[sterlind]

not a physicist, but afaik MWI doesn't work like that.

iirc, particles are actually excitations in a quantum field. the more particle-y an electron looks - the closer you bound its position - the more waves are needed to constructively/destructively interfere to make a peak there.

it's like a Fourier transform - if you want a perfect square wave you need infinite sine waves. in this analogy that's momentum space expanding out.

also, like, you're not really seeing individual electrons. you're seeing macroscopic phenomena, like your sensor or photomultiplier tube or whatever. you're seeing the interaction, not the particle. understanding that as your lab equipment, retina and brain entering the state space caused by resolving a wave to a spike makes more sense to me than some decoherence mechanism.