[lisper]

The key to understanding entanglement for me was to understand that the wave function does not live in physical 3-D space, it lives in configuration space. A wave function that lives in physical 3-D space is a special case that applies only to a system that consists of a single unentangled particle. In that case, physical 3-D space and configuration space are the same. But in general, a wave function for N particles will live in a 3N-dimensional configuration space.

[mlmonge]

It seems to me that the configuration space of which you speak essentially explains the wave/particle duality. My B.S. Physics education from years ago never explained it as such as far as I can recall. I'm far from any expertise understanding, but this makes much sense. Any further pedagogical commentary would be most appreciated!

[lisper]

> configuration space ... explains the wave/particle duality

I don't think so. You can have a wave function in physical 3-D space as a (very common) special case and you still have the wave-particle dichotomy.

Why do you think configuration space explains WPD?

[elcritch]

Really WPD more fundamentally arrives from the “conversion” of the probability wave (living in configuration space as you put it) into properties in 3D physical space. Measuring the QM system is analogous to a Fourier transformation and has the same mathematical limitations arising from a Fourier transform from wave to discrete space. Depending on the question you ask (tied to the convolution function) you get either discrete particle answers or wavelike answers. The probability wave does live in 3D space AFAICT, but the QM properties like spin, charge, momentum etc are tied into that 3D space and form a combined configuration space.

The really odd part to me is that at macro scales the probability waves collapse neatly into classic physics in 3D space, but still react in quantum fashion at small local atomic scales. As in the configuration spaces generally can only be determined for small subsystems but not a whole macro system without the “conversion” step.

[mlmonge]

The “conversion” of the probability wave--now that's much more specific with regards to the "configuration" space and well put. When I had first learned about WPD it really didn't strike me as odd or mysterious as historically described. In effect, I thought, both realities must be there simultaneously--that sounds like normal QM nature. The collapse of the duality simply depends on the "conversion" function. On this note, are there any fascinating presentations on WPD that take the "mystery" out of it?

[btilly]

Configuration space leads to the Everett interpretation, which leads to us being a superposition of observers, all of whom observed something that looked like a particle.