[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!