Talk:Wave function collapse

Distinguishing the two topics

Wave function collapse has two meanings: 1) a synonym for the mathematical procedure of state-reduction or projection used to calculate predicted observations from wave functions 2) a description of the fate of an ontological wave in some interpretations of quantum mechanics. The top half of this article reflects the first meaning and the bottom half seems to be about the second one.

I think the article would be much clearer if these two meanings where discussed explicitly. Johnjbarton (talk) 17:27, 24 March 2024 (UTC)

I re-orged the article creating a section "Physical approaches to collapse" which I will next edit based on the Stamatescu encyclopedic article. Johnjbarton (talk) 01:37, 29 March 2024 (UTC)

Something about quantum non-demolition

The article has this cryptic sentence:

• Mathematically it can be shown that collapse is equivalent to interaction with a classical system modeled within quantum theory as systems with Boolean algebras of observables and equivalent to a conditional expectation value.

The sentence has two refs. This one is interesting:

• Belavkin, V. P. (May 1994). "Nondemolition Principle of Quantum Measurement Theory". Foundations of Physics. 24 (5): 685–714

This one is essentially a math review, there are tons of quantum probability theories beyond what they discuss.

• Redei, Miklos; Summers, Stephen J. (2006-08-07). "Quantum Probability Theory"

Neither ref says anything like the sentence. Both primary refs have a reasonable number of refs but no obvious review or summary needed to evaluate them.

I think it may be worth discussing quantum non-demolition, but maybe in the context of zeno rather than just a random paragraph. Johnjbarton (talk) 01:09, 31 March 2024 (UTC)

Something about C* algebra

Another cryptic paragraph includes:

• the collapse of the wave function corresponds to a non-unitary quantum operation.

I guess that this obvious claim is not intended as the main import. Two refs are cited, an interesting but non-notable book

• Primas, Hans (2017). Atmanspacher, Harald (ed.). Knowledge and Time. Springer International Publishing. ISBN 978-3-319-47369-7.

and another quantum probability review article by the excellent J. Fröhlich:

• Fröhlich, J.; Schubnel, B. (2013-10-05). "Quantum Probability Theory and the Foundations of Quantum Mechanics". arXiv:1310.1484 [quant-ph].

(The article here does not ref the one in the previous topic or vice versa).

Again we have a complex topic in one paragraph with no secondary overview to verify how this is related to collapse. Johnjbarton (talk) 01:29, 31 March 2024 (UTC)

Mathematical description

@Johnjbarton Could you please stop removing all mathematics from this article (and subsequently renaming the subsection from "mathematical description" to "description)? The simple fact that it is not of interest to you, doesn't mean it's irrelevant.

The reason I made the edit today, was because what you wrote down was demonstrably false. The way you rephrased the beginning of the subsection would imply that the eigenstate of the Position operator; the dirac delta, is a wave function for example. Roffaduft (talk) 15:44, 31 March 2024 (UTC)

Hi @Roffaduft. Thanks for your review.

In my view, a long mathematical buildup obscures this topic rather than clarifies it. If you look at Griffiths text you will see he agrees. He is already talking about collapse on page 18.

I don't follow what you consider "demonstrably false".

I do think we could try to do a better job on explaining the expansion. This mathematical aspect seems obvious but I think for an untrained reader (our audience), the idea that an arbitrary wavefunction can be written in terms of a complete set of measurement outcomes is not obvious. Simply stating it as a fact may be the best we can do. But I don't think we need to add a lot of other math facts that don't directly bear upon the "collapse' topic. If we do, then these topics should come later in the article. We're not "proving" collapse we are describing it. Johnjbarton (talk) 16:00, 31 March 2024 (UTC)

Griffiths is not the best textbook if you're looking for a mathematical description. In fact, he implicitly says so in the preface of his book. Some physicists have a tendency to start hand-waving when it comes to mathematics ;).

The problem is that it's very easy to think that the wave function and the eigenstate of an observable are interchangeable concepts, while in fact they are not. It really depends, among other things, on how the quantum state space is defined, on normalizability and the continuous/discrete spectrum etc.

I do understand that it's a bad idea to discuss all those topics, that would be overkill. However, a clear distinction between the (eigen)state and the wave function is critical in understanding why the collapse of the wave function is completely valid from a mathematical point of view. Roffaduft (talk) 16:12, 31 March 2024 (UTC)

Sorry I think we completely disagree here.

I used Griffith because I'm not looking for a mathematical description. This is a page about physics. The entire topic is hand waving.

The collapse is not at all valid from any mathematical point of view. We wrote an expression with some greek letters with an arrow that is equivalent to "something strange happened to completely changed the problem we have to solve". I think more math layered on top just obscures this base reality.

I do agree my previous versions glossed over difference between wavefunction and state vector. So how can we express the key concepts without getting into an entire lecture on QM?

My proposal is to change to "quantum state" and "eigenstate" and "state reduction" and connect to 'wave-function collapse' and "wavefunction" just after collapse is defined. What do you think? Johnjbarton (talk) 00:13, 1 April 2024 (UTC)

I'm not going to argue about the mathematical validity, let's just agree to disagree for now. I do agree that from a physics point of view it makes little sense though.

I'm fine with your proposal. As long as it's clear that the eigenstate and wave function are different concepts (in line with the Quantum_state#Pure_states_of_wave_functions and observable) then that's more than sufficient.

If you're looking for books with a more mathematical approach toward quantum mechanics, i can recommend:

• Hall, Brian C. (2013). Quantum theory for mathematicians
• Teschl, Gerald (2009). Mathematical Methods in Quantum Mechanics
• Pretty much anything by Barry Simon

Roffaduft (talk) 04:41, 1 April 2024 (UTC)

ps. the reason I undid this revision was because in footnote 16 on page 107 of Griffith (2005) it was emphasized that $|c_{i}|^{2}$ is not the probability that a particle is in state $\phi _{i}$. Also, the linear expansion was already mentionned above, though I figure that's merely a consequence of the subsection being a work-in-progress at this point.

I'm fine with just referring to Griffith 2018 page 133, though I'd like to add $c_{i}=\langle \phi _{i}|\psi \rangle$ (function (3.43) from p133) as it makes it clear why $c_{i}$ is a probability amplitude and $\phi _{i}$ an eigenstate without having to elaborate on it being an orthonormal eigenbasis. Roffaduft (talk) 07:14, 1 April 2024 (UTC)

My text that you reverted did not say anything about a particle or a particle in a state $\phi _{i}$. Here is what I said:

• According to the Born’s statistical interpretation, the square modulus is the probability that a measurement yields result corresponding the eigenstate $\phi _{i}$.

Johnjbarton (talk) 15:30, 1 April 2024 (UTC)

That's the point, it didn't say anything about it. Roffaduft (talk) 04:15, 2 April 2024 (UTC)

? Which 'it'? Which specific words did I use that are "demonstrably false"? Johnjbarton (talk) 15:31, 2 April 2024 (UTC)

In my first reaction I already gave an example why your original phrasing in the subsection “mathematical description” was wrong.

The “it” refers to your reply on 15:30 1 April.

I’ve agreed with your proposal and I see that you also included my proposed addition. To me the issue has been resolved. Roffaduft (talk) 16:11, 2 April 2024 (UTC)