# HUP: Particles <=> ?

Dmitry67
Well, I will try to explain it.

So, HUP and non-conjugate variables. If we know the position precisely, we don't know the momentum. On the contrary, if we know the momentum, we don't know the position. Sorry for repeating the obvious.

Interpret HUP as a spectrum: on one side we know the position, on another we know the momentum. There is a symmery of the both sides, right?

On one side of a spectrum there is a particle, on another... well, there is no name for such entity. It is like a vector everywhere, so I can call it a flow, but there is no name for such thing.

Now my question: if there is a symmery between both side of the spectrum, why one side attracts much more attention thjen the other?
* Why we have particles, but don't have even the name for a 'flow'?
* Why Bohr was talking about particle-wave duality, not mentioning flows?
* Why in the pilot wave theories we talk about a 'particle', definitely preferring one side of the spectrum?
* Why in CI wavefunction 'collapses' to something particle-like? But we can measure the momentum as well...

Staff Emeritus
Position and momentum are operators, and Heisenberg tells us the relation between them. "Particle" is not.

camboy
* Why we have particles, but don't have even the name for a 'flow'?

It's called the probability current. Which, when you divide by psi squared, becomes the particle velocity field.

* Why Bohr was talking about particle-wave duality, not mentioning flows?

Because diffracted 'matter waves' passing through slits are detected as particles, but repeated detections are grouped in an interference pattern, like waves. He didn't talk about flow because he was a positivist, and didn't want to talk about flows or trajectories of things that couldn't be seen directly.

(Despite the fact that the mathematics implies it directly if one simply says that probability means the probability that a particle is at x, rather than the probability of being found at x in a suitable measurement. Then psi squared is the probability density of particles, and if the probability density changes with time, the particles must `flow'.).

* Why in the pilot wave theories we talk about a 'particle', definitely preferring one side of the spectrum?

Because in pilot wave theory, particles have both positions and velocities. Thus, they exist and they flow.

* Why in CI wavefunction 'collapses' to something particle-like? But we can measure the momentum as well...

Who knows? The definition of momentum according to Heisenberg is based on classical physics, and does not correspond to the actual momentum of the thing that is flowing. If you analyze it more closely, Heisenberg's momentum uncertainity can be identified with a component of the total stress tensor of the psi-field. And who cares about that?

Believing that a 'momentum measurement' measures the momentum of something derives from the viewpoint commonly called 'naive realism about operators'.