Talk:Wave function collapse

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)

Source for claim that Bohr espoused "Copenhagen" model.

The article says:

• The "Copenhagen" model espoused by Heisenberg and Bohr separated the quantum system from the classical measurement apparatus.

I removed "Copenhagen" is inaccurate and unclear and completely unnecessary. I have not seen any evidence that Bohr ever adopted or supported the so-called Copenhagen model. Bohr had his own well known and extensively published views. As far as I know he never called them the "Copenhagen model". The sentence is correct and can be sourced without the mysteriously quoted word.

I challenge this claim and it is not sourced. @Tercer put it back without a source. I want to remove it. Johnjbarton (talk) 15:38, 29 October 2024 (UTC)

Plenty of sources at Copenhagen interpretation. I find it rather incredible that you would question that. Bohr's views are the Copenhagen interpretation, as far as it's possible to define the Copenhagen interpretation at all. Tercer (talk) 15:50, 29 October 2024 (UTC)

Exactly as you say "as far as it's possible to define the Copenhagen interpretation at all": the term is unclear and I contend any source for the definition will not include Bohr's name. On the other hand, if Bohr's views are Copenhagen, the we can simply say what Bohr's views are without the confusing, unclear, and unsourced label.

As I am checking myself here I think we should go further. The sentence just before says:

• Niels Bohr also repeatedly cautioned that we must give up a "pictorial representation", and perhaps also interpreted collapse as a formal, not physical, process.

"perhaps also"? So we are giving weight to a comment by a historian. The same historian notes that Bohr, despite a huge number of published works on quantum mechanics, never publish any discussion on collapse. That cannot be an accident. To now claim that Copenhagen is Bohr and collapse is part of Copenhagen is not correct.

If there are plenty of sources that Bohr espoused "Copenhagen" then you can easily provide one. Otherwise we can simply let Bohr speak on his own behalf. Johnjbarton (talk) 16:15, 29 October 2024 (UTC)

You are doing a huge disservice to our readers by removing the connection between Bohr's views and the Copenhagen interpretation. You want to remove the word "Copenhagen" from The "Copenhagen" model espoused by Heisenberg and Bohr separated the quantum system from the classical measurement apparatus.. What on Earth is this "model" espoused by Bohr and Heisenberg then? And do you seriously dispute anything from this sentence? Quantum-classical dualism is the most fundamental aspect of Copenhagen. Tercer (talk) 16:54, 29 October 2024 (UTC)

Bohr never "espoused" the Copenhagen model and his views do not align with some aspects of it. We could say that proponents of the Copenhagen model adopted many of Bohr's view. That is the opposite attribution that we have now.

Yes, I want to remove the quoted word "Copenhagen" from that sentence. It is unnecessary, incorrect, and unsourced. As for "model" we don't need to have that word either. Yes, I dispute the sentence, that is why I changed it.

We can also just delete the sentence and start the paragraph with

• In 1932 von Neumann developed an "ideal" measurement scheme that postulated...

I think the connection between the disputed sentence and the rest of the material would only be clear to someone already familiar with the topic. For most readers I assume the sentence actually makes no sense at all-- what is the quantum system? what means "classical" here?-- and how does this split related to the two dense postulates that follow? There is not enough said and much implied.

This is a section on History. Historically Bohr never espoused Copenhagen. Historically, Copenhagen, as a collection of things, was a name Heisenberg used off-hand and later writers ran with: they adopted some of Bohr's ideas not the other way around. Johnjbarton (talk) 17:56, 29 October 2024 (UTC)

"Copenhagen" is the name everyone uses to describe Bohr's ideas. Whether Bohr himself used this name is irrelevant. Tercer (talk) 18:51, 29 October 2024 (UTC)

No, "Copenhagen" is the name given to set of ideas; many of these ideas were Bohr's. Even our article on the Copenhagen interpretation makes this clear. Many sources discuss the non-equivalence of Copenhagen and Bohr's ideas. I am yet to find one that says they are equivalent. The main sources on the the Principles part of that article discuss this issue and clearly do not equate Bohr and Copenhagen. For example,

• In fact Bohr and Heisenberg never totally agreed on how to understand the mathematical formalism of quantum mechanics, and neither of them ever used the term “the Copenhagen interpretation” as a joint name for their ideas. In fact, Bohr once distanced himself from what he considered to be Heisenberg’s more subjective interpretation (APHK, p. 51). The term is rather a label introduced by people opposing Bohr’s idea of complementarity, to identify what they saw as the common features behind the Bohr-Heisenberg interpretation as it emerged in the late 1920s. Today the Copenhagen interpretation is mostly regarded as synonymous with indeterminism, Bohr’s correspondence principle, Born’s statistical interpretation of the wave function, and Bohr’s complementarity interpretation of certain atomic phenomena. [1]

To my reading this passage makes the sentence under discussion incorrect.

We are unlikely to agree on this point, so I suggest we just delete the sentence as not helpful to the article and move on. Johnjbarton (talk) 21:39, 29 October 2024 (UTC)

And so we won't have a single mention of Copenhagen in the History section, and hardly any in the entire article. Just some mysterious mentions about an interpretation defended by Bohr and Heisenberg.

Perhaps some reader would come to this article wanting to know what the most famous interpretation of quantum mechanics says about wavefunction collapse. Too bad, they're not going to learn it. Tercer (talk) 22:09, 29 October 2024 (UTC)

"Perhaps some reader would come to this article wanting to know what the most famous interpretation of quantum mechanics says about wavefunction collapse."

Here we completely agree. Let's add content about wavefunction collapse associated with the Copenhagen interpretation. It just can't come from Bohr because he said nothing on the subject. Johnjbarton (talk) 01:31, 30 October 2024 (UTC)

I agree with Tercer and support using the sentence in question. Whatever Bohr thought, sources certainly associate the Copenhagen interpretation with him, and I think the article should too:

• "Quantum mechanics had hardly been discovered when worries about interpretation began to appear. Bohr, Heisenberg, and Pauli recognised its main difficulties and proposed a first essential answer. They often met in Copenhagen, where Bohr had his laboratory, whence the name Copenhagen Interpretation." Omnes 1999 Understanding quantum mechanics, p.41
• "What will matter for us is the legacy which Bohr and his followers have left, by whatever route, and whatever they themselves have originally thought, to quantum mechanics. ... The name of that legacy is the Copenhagen Interpretation of quantum mechanics David Albert, 2007, Quantum Mechanics and Experience, p.17
• "The Copenhagen interpretation was the first general attempt to understand the world of atoms as this is represented by quantum mechanics. The founding father was mainly the Danish physicist Niels Bohr, but also Werner Heisenberg, Max Born and other physicists made important contributions..." Copenhagen interpretation of quantum mechanics, Stanford Encyclopedia of Philosophy
• "...This view (the so-called Copenhagen Interpretation) is associated with Bohr and his followers." David Griffiths, Darrell Schroter, 2019, Introduction to Quantum Mechanics, p.5

--Chetvorno^TALK 01:03, 30 October 2024 (UTC)

Gee guys you are making a mountain out of a mole hill.

None of these quotes support the claim that Bohr "adopted or supported" the Copenhagen model. That is all I am complaining about. Of course it was named after his lab. Sure the model is part of his legacy. As I said earlier he made the key contributions. And of course it is associated with Bohr! But all of this is reverse of what the sentence says.

Here are some more alternatives that would work if this curious and out of place sentence just has to remain:

1. The Copenhagen model separates the quantum system from the classical measurement apparatus.
2. The Copenhagen model, derived from the work of Heisenberg and Bohr, separated the quantum system from the classical measurement apparatus.
3. Heisenberg and Bohr described the quantum system as separate from the classical measurement apparatus and this concept was adopted by Copenhagen model.

and so on. Are you really going to claim that the exact words currently used are the only possible ones? Johnjbarton (talk) 02:54, 30 October 2024 (UTC)

An undergraduate textbook like Griffiths and Schroter is not going to be a good source for any details about the history and philosophy of physics. That's not what those books are there to teach; instead, they pass on what Feynman called the "physicist's history of physics". The Stanford Encyclopedia of Philosophy source was already provided by Johnjbarton above. It goes on to give the In fact Bohr and Heisenberg never totally agreed... quote. And later: many physicists and philosophers see the reduction of the wave function as an important part of the Copenhagen interpretation. This may be true for people like Heisenberg. But Bohr never talked about the collapse of the wave packet. So, no, we can't equate "Bohr" and "Copenhagen". We can say what "the Copenhagen interpretation", as conventionally understood, says about collapse. In fact, one fix would be to just change the sentence in question to, e.g., The Copenhagen interpretation separates the quantum system from the classical measurement apparatus. The names are a distraction, in addition to being 50% ahistorical, and the term "model" is nonstandard and confusing in this context.

I'm unhappy with that sentence for another reason, however. It segues from Bohr and Heisenberg to von Neumann, in a way that implies a contrast that doesn't really exist. Von Neumann also separated the measured system from the measuring apparatus. See chapter 5 of Mathematical Foundations of Quantum Mechanics: we are obliged always to divide the world into two parts, the one being the observed system, the other the observer. he thought of the distinction in a different way, but he had the distinction in mind, so the contrast as written doesn't work. XOR'easter (talk) 03:43, 30 October 2024 (UTC)