"Wave-particle duality" and double-slit experiment

[gentzen]

I'm so sorry, but I couldn't understand this distinction (which, as you say, is subtle). Could you please explain it better?

If you assume that particles have definite positions, then you get the de Broglie-Bohm interpretation. To avoid this, you just talk about measurement results, instead of making statements about supposedly real positions of particles.

 

[PeterDonis]

HUP places no limits on the precision with which we can measure the position or momentum of a particle.

For single measurements of either position or momentum, no.

More simply, we cannot confine the electron in a very small space and control its momentum in a very small range.

This is not a "more simply" version of your previous statement. It is a different statement, which relates to trying to control both position and momentum at the same time. The HUP places a limit on the product of the uncertainties of the two.

It is possible to know both velocity and position simultaneously with some precision, but only up to a certain point. We cannot know both with arbitrary precision.

Not at the same time, no.

Another way of putting it is that the HUP is giving a limitation on the possible states of the quantum system: for any given state, the product of the position and momentum uncertainties must satisfy the HUP inequality.

 

[PeroK]

I'm so sorry, but I couldn't understand this distinction (which, as you say, is subtle). Could you please explain it better?

Ultimately this is what all the fuss was about, especially regarding quantum entanglement, which culminated in the EPR paper and Bell's Theorem. If the electron has a definite position, then that is a so-called local hidden-variables theory. Bell proved that QM can do better in terms of the correlation of spin/polarization measurements on entangled particles than is possible using local hidden variables. And, when the tests where carried out, they corroborated QM. This means that an electron cannot have a fully-determined spin in all directions. Hence, dynamic quantities such as position, momentum, angular momentum and spin, simply do not have well-defined values until they are measured.

This implies that QM is not locally realistic (that phrase has a precise meaning). In other words, you shouldn't think of the electron having a definite position before measurement. It's only after a measurement of position that talking about the position of an electron makes any sense.

Again, this is non-classical thinking. QM is not classical mechanics with a bit of probability and uncertainty thrown in. It's a completely different theory of nature, where abstract states are the fundamental building blocks, rather than well-defined dynamic quantities.

 

[PeterDonis]

If the electron has a definite position, then that is a so-called local hidden-variables theory.

Not necessarily; as @gentzen pointed out earlier, particle positions are definite in the Bohmian interpretation--but that is a nonlocal hidden variable model. You are correct that local hidden variable models are ruled out.

 

[sillyputty]

I'm so sorry, but I couldn't understand this distinction (which, as you say, is subtle). Could you please explain it better?

He means this: The probability distribution is for where the particle will be when measurement happens, and is NOT for where the particle is before measurement happens. He is trying to make you understand that the particle does not have position before measuring it.

 

[HighPhy]

Not at the same time, no.

Sorry, your answer refers to the fact that both momentum and position cannot be known at the same time with arbitrary precision, right?
Or are you referring to the fact that both momentum and position cannot be known at the same time in any way?

Just to be sure.

 

[PeterDonis]

your answer refers to the fact that both momentum and position cannot be known at the same time with arbitrary precision, right?

Yes.