# Is Copenhagen interpretation a collapse theory?

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1. Nov 13, 2015

### SimmieKay

I have been learning about the different interpretations of QM, and I am trying to build a taxonomy of them in my mind (I find that trying to build taxonomies is a good way of learning about things). I have read about collapse theories and non-collapse theories. If I have got this right, the former accept the idea of the collapse of the wave function, even as they disagree about what exactly causes it; while the later argue that the concept of the wave function collapsing is better dispensed with. As I understand it, examples of collapse theories include subjective collapse theories, principally von Neumann-Wigner; and objective collapse theories, such as Ghirardi-Rimini-Weber theory and the Penrose interpretation; while examples of non-collapse theories include the various hidden variable theories, and many worlds. (Please correct me if I have got any of this wrong.)

My question then is whether Copenhagen interpretation should be classified as a collapse theory or a non-collapse theory, or is it some third type of interpretation which doesn't fit neatly into either classification? I would think that since it affirms that the wave function collapses, it is a collapse theory. But, if it is a collapse theory, is it an objective collapse theory, a subjective collapse theory, or some further type of collapse theory which does not fit under either the "objective" or "subjective" labels?

(PS: This is my first post, and I am not sure what the right value for "thread level" is. I picked high school because that is the highest level of physics I have formally studied, even though for me high school was over 15 years ago. I'd prefer accuracy in answers - even if they are challenging to understand - to simplification.)

2. Nov 13, 2015

### Simon Phoenix

My own personal perspective is that all of the various 'interpretations' are fascinating but there isn't really a satisfactory resolution to what might be termed the 'measurement problem' in QM. At least not in my mind. I think all the various interpretations do is to shift this basic problem around, so to speak, so that the head mangling occurs somewhere else in the chain of reasoning :-)

I think the first problem is really whether the state vector (or wavefunction, if you like) represents some 'real' description - or whether it's somehow a codification of 'knowledge', or what can be known. This gets dressed up in fancy language to make it all sound impressive - and I always promptly forget the correct technical terms, but words like ontology and epistemology get bandied about.

I'm not even sure there's universal agreement about what the Copenhagen interpretation actually is. But as far as I understand it I would say that Copenhagen is a collapse theory.

In the CI (again as I understand it, and I'm happy for others to correct me here) we solve for the state of our system of interest at some time t and then make a measurement. It's not really specified what a 'measurement' actually constitutes - but the result of this ad-hoc process is to select an eigenstate of the measurement operator with a certain probability - the eigenvalue becomes the measurement result. If we do the experiment again on another identically prepared system we might get another eigenstate and eigenvalue. The thing here is that this unspecified measurement process projects the system into a new state - which is what we mean by collapse.

If we view the state, or wavefunction, as having a physical reality then it's this physical reality that is collapsing. If we view the wavefunction merely as some abstract non-physical mathematical object that simply codifies our 'state of knowledge', then it's simply our state of knowledge that instantaneously changes or collapses. I've not properly understood this perspective because I've not yet understood how to make concepts like 'state of knowledge' absolutely precise. However, this knowledge-based view does have the attractive feature that collapse is nothing weird or wacky here - it's simply that when we make a measurement we get new information - and so our assessment of probabilities all changes instantaneously. Having said that, I struggle with the notion that an abstract mathematical entity (the wavefunction), which does not model reality in any meaningful sense, evolves in a way that has pretty deep connections with classical mechanics.

Ultimately I'm very much of the 'shut up and calculate' frame of mind - which is often misunderstood to mean that we just mechanically follow the rules - so what's really important is that we are able to get the right predictions for physical quantities we can measure. The nice thing about having all of these different interpretations of QM (which at the moment seem to all generate the same experimental predictions - apart from GRW type theories which are definitely not QM because they are non-linear) is that we can pick whichever interpretation we like that helps us solve a problem in the easiest way for us.

3. Nov 13, 2015

### Demystifier

For the sake of taxonomy, it is good to know that there are several substantially different variants of the so-called "Copenhagen" interpretation. Only one of them is a collapse interpretation.

4. Nov 13, 2015

### Staff: Mentor

Demystifier is correct - there are a number of variants.

This discusses the main variant:
https://en.m.wikipedia.org/wiki/Copenhagen_interpretation

'A widely propagated myth is that the Copenhagen interpretation is all about the "collapse". However, if you look at the six principles above, there is not even a glimpse of a comment about a "collapse" because it's not needed. The notion of an objective collapse was introduced by John von Neumann in 1932 and he was clearly not a part of the Copenhagen school of thought anymore. Comments that Heisenberg later switched to an "objective wave function" or an "objective collapse" are untrue, and even if these legends were true, these new opinions wouldn't be a part of the Copenhagen interpretation and, more importantly, they wouldn't be valid.'

Most versions of Copenhagen has the state as subjective, like probability in the Bayesian view of probability. In fact a lot of interpretations of QM is simply an argument about what probability is:
http://math.ucr.edu/home/baez/bayes.html

Thanks
Bill

Last edited by a moderator: Nov 15, 2015
5. Nov 13, 2015

### Simon Phoenix

Bill,

I've never really delved too deeply into the original version of Copenhagen - so I guess when I do QM I'm following my own weird and wonderful flavour based on von Neumann - I always thought I was following the CI. I blame my original QM lecturers lol!

I always adopt the working methodology of thinking about states and projections - which I guess would give Lubos another of his characteristic fits of apoplexy :-)
This methodology does, if I do the sums right, give the right answers at least.

I see from the link that the first statement of the CI, according to Lubos, is
"A system is completely described by a wave function ψ, representing an observer's subjective knowledge of the system. (Heisenberg)"

Is there a precise formulation of what is meant by 'subjective knowledge' here? This is the bit that I've always found a bit unclear - and even in the consistent histories formulation, which is claimed to be most wondrously clear, I find things to be somewhat vague on this point - maybe I've read the wrong things (and what the heck is a 'pre-probability' anyway?)

I think the CI is still all about collapse - OK it's not a collapse of a real physical entity if we take the CI as outlined in the link - but a 'collapse' of this ephemeral 'state of knowledge' upon measurement - perhaps change is a better word than collapse anyway even if we want to think of the wavefunction as having some real physical character. The point being that measurement is not a passive process in QM whereas it is (ideally) in the classical view. In fact one of the things that is obscured (for me) in this subjective knowledge approach is the distinction between QM and classical - after all our 'state of knowledge' changes upon measurement whether we are classical or quantum - so it really comes down to why this mathematical entity describes a state of knowledge in QM and why it evolves in the way it does. This is not at all intuitively clear to me. Why does something that represents our subjective knowledge follow a dynamical evolution that has a strong connection (via the Poisson bracket/commutator) with classical evolution? If you have any thoughts on that they'd be most welcome. I would certainly like to understand the 'subjective knowledge' and consistent histories view much better than I currently do. I've always been quite happy with the state/projection approach when working stuff out :-)

Perhaps I need to invest in a copy of Ballentine - although I still rather like Dirac.

6. Nov 13, 2015

### Staff: Mentor

See post 137:

In the subjectivist view the state is simply an aid in calculating probabilities implied by the basic axiom in the above.

Ballentine wont help you with subjectivism. He takes, like I do, a frequentest view. Its the age old debate on what probability is.

However it will help you in understanding the why of Schroedinger's equation etc - its symmetry - but you need to see for yourself.

Thanks
Bill

7. Nov 13, 2015

### Simon Phoenix

Thanks Bill,

it will take me some time to work through your post in that thread. I'm familiar with POVMs and their use in quantum optics and quantum information theory, but I've never seen QM being built up from these axioms/concepts before - so maybe it would be worthwhile to invest in a copy of Ballentine.

For me I think the essential point is that we have some state ψ and QM says that when we make a measurement it changes to some other state φ - with probabilities given by the Born rule. That seems to me to be true whether we conceive the state to be merely a state of knowledge (or possible knowledge) or whether we consider it to be some real physical entity with some aspect of objective 'existence'.

So if we restrict the word collapse to only refer to the change of this state when we assume some objective character to this state then I would agree that under this definition there is no collapse in the CI as outlined on Lubos' blog. There is still, however, a change of state even with the subjective knowledge view of the state (we just don't call it 'collapse' in this instance). Would you say that's a fair summary of the position regarding collapse in the CI?

8. Nov 13, 2015

### Staff: Mentor

Its a matter of how you view it. If you view a state as the equivalence class of preparation procedures then what's going on is rather trivial.

In that view all an observation is, is you have subjected the system to a different preparation procedure so of course you get a different state.

Reading Ballintine will help a lot especially if your exposure is Dirac and Von-Neumann. They are the books I learned QM from and wish I didn't. I became absorbed with that damnable Dirac delta function Von Neumann panned - correctly. It sent me on a sojourn into dark arcane areas of functional analysis. Fortunately my undergraduate training included that - but it still was time consuming. I came out the other end understanding what was happening, but put on hold my actual understanding of QM.

Ballentine corrected that. He carefully examines foundational issues.

If you are interested in Consistent Histories then you will find the following helpful:
http://quantum.phys.cmu.edu/CQT/index.html

It not my favourite view of that interpretation which also goes under the name of decoherent histories. In that view there is no observation - QM is the stochastic theory about histories.

Interestingly my favourite book on that is Wallaces book on Many Worlds:
http://users.ox.ac.uk/~mert0130/books-emergent.shtml

It contains much more mathematical detail of the approach because decoherent histories is basically many worlds without the actual many worlds - nifty hey.

Why don't I hold to it - for me it looks a lot like defining your way out of problems rather than face them head on.

I hold to the ignorance Ensemble interpretation:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

If that approach appeals THE book to get is:
https://www.amazon.com/Decoherence-Classical-Transition-Frontiers-Collection/dp/3540357734

Thanks
Bill

Last edited by a moderator: May 7, 2017
9. Nov 13, 2015

### SimmieKay

Thanks for pointing me to that thread, Demystifier, it is very interesting. Since the thread is now locked and I can't reply to it, let me share some comments on it here: As other replies argued, I don't think "Shut up and calculate" is a interpretation of QM as such. In my mind, interpretations of QM propose answers to questions like "Is the wave function a real physical thing which exists in the universe, or just an abstract construct used to calculate probabilities?". Since "Shut up and calculate" doesn't want to debate that question, it doesn't constitute an interpretation of QM, rather the absence of one.

If we define CI as "what Bohr and Heisenberg believed", then I don't think "Shut up and calculate" is CI, since neither man was opposed to discussing the philosophical implications of QM.

What Bohr's philosophy was is an interesting topic. From what I've read in the Stanford Encyclopedia of Philosophy's article on CI, Bohr was not a pure positivist/instrumentalist. He was an instrumentalist about the wave function, but he was a realist about classical physics, including the atom. Part of his argument seems to be, that the wave function cannot be "real" because it is complex-valued, but classical physics is "real" because it deals with non-imaginary quantities:
Also, "Bohr thought of the atom as real. Atoms are neither heuristic nor logical constructions". (BTW, these are not quotes from Bohr, they are Jan Faye's summary of Bohr's essays collected in The Philosophical Writings of Niels Bohr, which I have not read.) I'm not sure how much sense that sort of hybrid instrumentalist/realist position makes. Would many people who describe themselves as CI today agree with that position?

10. Nov 13, 2015

### Staff: Mentor

Indeed it is. His debates with Einstein are justifiably famous.

But do understand things have moved on since then - its now known they were basically both wrong:
http://www.fisica.ufmg.br/~dsoares/cosmos/10/weinberg-einsteinsmistakes.pdf

IMHO it's best to study the modern understanding from a book like Ballentine before venturing into the writings of the early pioneers.

Thanks
Bill

11. Nov 14, 2015

### Simon Phoenix

Forgive me, because I think I may have missed the point you are making, but isn't this just rather playing with semantics? Haven't you just replaced 'measurement' with the words 'preparation procedure'? I'm not really seeing the benefit here. I can't see how this actually helps us understand better what a measurement in QM is.

Fundamentally the issue, I feel, is the disconnect between the unitary evolution between measurements (or preparations) and the non-unitary process of measurement (or preparation). Apart from the decoherence approach I haven't really seen anything that comes close to 'explaining' this in any satisfactory way.

But I don't really think the decoherence approach properly resolves this measurement issue either - although as a way of treating open quantum systems I do very much like the decoherence approach. I also like the way in which with the consistent histories approach ends up with just classical probabilities - but this seems to me to rely very much on decoherence arguments for its consistency (as far as I have been able to understand it).

So to come back to the original question of whether the CI is a 'collapse theory' then I guess it depends what is meant by 'collapse'. It would seem that if by 'collapse' we mean the instantaneous change of some real objective entity then CI is not a collapse theory. But I still think the fundamental issue is that of change - there is a before measurement and after measurement and something changes, irreversibly. When some real classical information (real bits) are recorded somewhere - be that in our brains or in some inanimate object - then a measurement, or preparation, has occurred.

Many a happy hour can be spent ruminating on these issues of meaning in QM, and at some point we need to 'get our grubby little classical hands dirty' and actually calculate something - which is a way I have heard it expressed. I think this is the meaning of the humorous phrase 'shut up and calculate' - it's really telling us that we could spend the rest of our lives trying to figure out what it all means - and meanwhile that complicated system of beamsplitters and parametric downconverters we were supposed to analyse is waiting in our notebooks :-)

12. Nov 14, 2015

### Simon Phoenix

13. Nov 14, 2015

### Staff: Mentor

Hi Simon

You are correct the preparation idea doesn't help with explaining what an observation is - all you have done is replaced observation with preparation. What it does however is go to the heart of collapse. The state doesn't instantaneously change from an observation - its just like any other preparation - it is what results from a preparation.

I could say more - but I would rather not. Much better if you read some of the stuff I suggested and make up your own mind.

Thanks
Bill

14. Nov 14, 2015

### Simon Phoenix

:-)

Thanks Bill - the links are very much appreciated. I've been doing QM calculations from the von Neumann projection point of view for 3 decades now - and this way of thinking about QM now seems 'natural' to me. I may be a bit long in the tooth to find an alternative approach to be more 'natural' - but I'll give it a go :-)

15. Nov 14, 2015

### Mentz114

To me, 'instantaneous collapse' is unbelievable.
The transition cannot be instantaneous. 'Instantaneous' is not feasible if only because $d/dt$ diverges and equations are useless. It must be a process that evolves the system, which seems to lead to something like decoherence.

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I bought Ballentine just a few weeks ago so I'll wait a while.

Last edited by a moderator: May 7, 2017
16. Nov 14, 2015

### Staff: Mentor

This changes nothing of the formalism.

Ballentines advantage is its careful axiomatic approach.

Thanks
Bill

17. Nov 14, 2015

### atyy

Copenhagen is a collapse theory in some sense, if by collapse one simply means "state reduction" as a procedure used to make predictions about experimental outcomes.

However, GRW is not a collapse theory in the same sense. GRW produces derviations from quantum mechanics, and is not a "pure" interpretation of quantum mechanics.

The more useful comparison of GRW is with Bohmian Mechanics, which is also not a "pure" interpretation of quantum mechanics, as it produces deviations from quantum mechanics.

GRW and BM are solutions to the measurement problem for some domain of quantum mechanics.

Copenhagen is simply pure quantum mechanics, and it has the measurement problem.

The only pure interpretation of quantum mechanics that does not have collapse is Many-Worlds. However, it is not clear if Many-Worlds actually works.

Ballentine's quantum mechanics is essentially rubbish (because of his nonsensical chapter 9).

So the overall classification is pure and impure interpretations.

1. Pure, collapse or state reduction as a formal step in the calculation with uncertain physical meaning: Copenhagen.

2. Pure, no collapse: MWI

3. Impure, physical collapse: GRW

4. Impure, no collapse: BM

18. Nov 14, 2015

### Simon Phoenix

Quite :-)

Much of the difficulty I think is really in this disconnect between evolution and measurement. QM doesn't really say anything about 'reality' in between experiments or preparations. In an operational sense it's just a rule book for connecting initial preparations and measurements.

If we try to imbue the in-between bit with some meaning then we end up performing all sorts of mental contortions - and it's easy to get our knickers in a twist - especially with some notion of collapse. Issues with the instantaneous collapse of some objective physical quantity are neatly sidestepped by adopting a subjective knowledge view in which the wavefunction is just some mathematical device, codifying our subjective knowledge, that allows us to connect the preparation and measurement processes - but I confess I have no real idea what this means in any physical sense. Nor do I understand why something so abstract as this assumed codification of subjective knowledge should follow an evolution specified by the Schrodinger equation.

As Bill has said there are other approaches which might help shed light on this - but, as a physicist, I'm much more comfortable with the notion that there is some aspect of physical reality to the wavefunction, whatever the logical and mathematical shortcomings of this approach. At least then we have some hope of connecting things to physical processes rather than mathematical abstractions.

I like the book by the late Asher Peres "Quantum Theory : Concepts and Methods" which follows a nice logical exposition from experimental properties. I haven't read Ballentine but it also seems like a worthwhile book from the comments on here.