Copenhagen: Restriction on knowledge or restriction on ontology?

[Demystifier]

The title of this thread is motivated by frequent arguments I had with other members here, especially @DarMM and @vanhees71 .

The so called "Copenhagen" interpretation of QM, known also as "standard" or "orthodox" interpretation, which is really a wide class of related but different interpretations, is often formulated as a statement that some things cannot be known. For instance, one cannot know both position and momentum of the particle at the same time. But on other hand, it is also not rare that one formulates such an interpretation as a statement that some things don't exist. For instance, position and momentum of the particle don't exist at the same time.

Which of those two formulations better describes the spirit of Copenhagen/standard/orthodox interpretations? To be sure, adherents of such interpretations often say that those restrictions refer to knowledge, without saying explicitly that those restrictions refer also to existence (ontology). Moreover, some of them say explicitly that things do exist even when we don't know it. But in my opinion, those who say so are often inconsistent with other things they say. In particular, they typically say that Nature is local despite the Bell theorem, which is inconsistent. It is inconsistent because the Bell theorem says that if something (ontology, reality, or whatever one calls it) exists, then this thing that exists obeys non-local laws. So one cannot avoid non-locality by saying that something is not known. Non-locality implied by the Bell theorem can only be avoided by assuming that something doesn't exist. Hence any version of Copenhagen/standard/orthodox interpretation that insists that Nature is local must insist that this interpretation puts a severe restriction on the existence of something, and not merely on the possibility to know something.

 

[Lord Jestocost]

To my mind, the spirit of the Copenhagen interpretation refers to the ontology. As Heisenberg puts it:

"However, all the opponents of the Copenhagen interpretation do agree on one point. It would, in their view, be desirable to return to the reality concept of classical physics or, to use a more general philosophic term, to the ontology of materialism. They would prefer to come back to the idea of an objective real world whose smallest parts exist objectively in the same sense as stones or trees exist, independently of whether or not we observe them."

In case one gives up the concept of 'physical realism' - a viewpoint according to which an external reality exists independent of observation – and doesn’t insist on thinking about quantum phenomena with classical ideas, quantum mechanics doesn’t unsettle anymore.

 

[DarMM]

Thanks for the thread. Always find these discussions useful to sharpen my understanding. Just to say I'm not going to defend these views in this thread only discuss what they say.
Okay so this is my understanding of these views.

EDIT: Here by Copenhagen I mean the non-representational views of Bohr, Heisenberg, Pauli, Haag, Peres, Healey, Bub and QBism. However my emphasis will be on later Neo-Copenhagen views like the final five as I understand them better.

I agree with you that (at least in most forms) Copenhagen doesn't just say you can't know the momentum and position of a particle, but that the position and momentum of a particle don't exist outside of measurement (to be detailed below). The same would apply to all Classical quantities. Only by placing a quantum system in a specific physical situation do we cause it to "take on" classical properties.

So for example Bub has the fact that quantum quantities form a non-Boolean algebra as basically meaning you can't talk about what's true or not of quantum quantities, i.e. it's not true or false that a particle has a given position. This is not to say he is going the quantum logic route. Rather the very structure of the algebra of propositions prohibits any kind of sensible logic. Only in certain situations when decoherence occurs do some quantities become Boolean and thus statements about them are true or false.

Similarly in Ensemble views in certain contexts, like measurements in our labs, for certain observables phases are washed away and the resulting density matrix can be interpreted as in Kolmogorov probability as pure ignorance. So after decoherence we know there is a momentum, we're just not sure which one. However before decoherence there is no momentum.

Similarly Healey views decoherence as granting certain statements meaningful content, i.e. it is true or false to say this atom has decayed.

The general idea as far as I can see is that Kolmogorov probability is for when propositions are true or false, but you don't know yet, however quantum probability is when you are dealing with quantities that don't exist independently of your examination.

There are many ways this is argued for. One is from the fact that proofs of the Bell's inequality can be shown to rely on the fact that the random variables are all functions over a single outcome space. Quantum Mechanics, by rejecting this, has multiple sample spaces. So the choice of variables to measure decides the sample space and the outcome is from that sample space. Other sample spaces and thus other quantities have no outcomes/values.

Also there are modifications to conditional probability where in quantum mechanics we have two separate notions of how probabilities for two random variables are related. If the random variables are $A$ and $B$ then their relation if I actually measure $A$ is:
$$P\left(B_j\right) = \sum_{i}P\left(B_j|A_i\right)P\left(A_i\right) $$
where $A_i$, $B_j$ are specific outcomes for these variables.
However if I don't measure $A$, then their relation is:
$$P(B_j) = \sum^{m}_{i} P(B_j|A_i)P(A_i) + \sum_{k<m} 2cos\left(\theta_k\right)\sqrt{P(A_k)P(B_j|A_k)P(A_m)P(B_j|A_m)}$$
So other variables have to be conditioned differently depending on whether $A$ gains a value.

A more accurate/modern view is that these quantities don't exist outside of the right decoherent environment. A particle doesn't possesses momentum unless decoherence occurs in the momentum basis. Four hydrogen atoms in the Sun have not fused or remained unfused unless decoherence has occurred in the "helium basis" due to interaction with the core's plasma.

So all our physical quantities are not really possessed by quantum systems. So what are quantum systems actually like and what is achieving entanglement. I'll deal with that next.

 

[DarMM]

So these views say that quantities from Classical physics like Energy, Momentum, Angular Momentum, are not properties of quantum systems.

So quantum systems must have some other set of properties which we will model with a set of variables $\lambda$. So now we must characterize $\lambda$.

the Bell theorem says that if something (ontology, reality, or whatever one calls it) exists, then this thing that exists obeys non-local laws

So this I don't agree with. What Bell's theorem says in full is that $\lambda$ must involve one or more of:

1. Non-local laws
2. Highly nontrivial spacetime (i.e. ubiquity of wormholes)
3. Retrocausal laws
4. Acausal laws
5. Multiple Worlds
6. Superdeterminism

1 and 2 are related in that they are ultimately a form of nonlocality, it's just that in option 2 the laws are local but the topology means that there can exist shortcuts to spatially distant systems.

The Copenhagen response to each is:

1. Relativity seems true, it is hard to countenance that it is an illusion brought on by some kind of equilibrium conditions etc
2. Same
3. Require either a fine-tuning or at least a hitherto unknown symmetry in order to not be visible
4. I have not heard any response to this.
5. Takes the wavefunction to be physically real when its mathematical properties are most similar to those of a probability distribution. Also failure of the Born derivations.
6. Says quantum mechanics is actually wrong, we just keep coincidentally measuring the wrong results and thinking it is true. Requires a vast conspiracy

So putting aside the novelty of option 4 this leads them to reject $\lambda$, that is a mathematical description of the real properties. As Matt Leifer phrases it:

Quantum systems have properties but they are ineffable: it is literally impossible to talk about them. The moon is there when nobody is looking, but it is fundamentally impossible to describe its properties in language, pictures, mathematics, computer code, or anything else.

So in short:

1. Classical properties do not exist outside of a measurement or more accurately a decoherence inducing environment. As @Demystifier said it's not that you don't know them, they don't exist until measurement (taken in the more general decoherence sense not literal lab equipment)
2. There are real properties, i.e. something does exist outside of measurement.
3. However the true properties are not amenable to mathematical description

As Omnès (Intepretation of Quantum Mechanics, p.507) says:

This impossibility could mean that quantum mechanics has reached an ultimate limit in the agreement between a mathematical theory and physical reality

Or Rüdiger Schack (final sentence refers to QM understood as generalized Bayesianism):

QBist reading: There are indeed no laws.God has done it thoroughly. There are no laws of nature, not even stochastic ones. The world does not evolve according to a mechanism. What God has provided, on the other hand, is tools for agents to navigate the world, to survive in the world

Bohr tended to go for "utterly incomprehensible", QBists more go for "not completely amenable to mathematical description".

 

[A. Neumaier]

1. Non-local laws
2. Highly nontrivial spacetime (i.e. ubiquity of wormholes)
3. Retrocausal laws
4. Acausal laws [°°°] I have not heard any response to this.

4. Is the old Copenhagen view, quite explicitly in older work.

 

[DarMM]

4. Is the old Coüebhagen view, quite explicitly in older work.

Old Copenhagen had acausal laws?! As in the set of events is selected by a 4D constraint. Do you have a reference?

 

[A. Neumaier]

Old Copenhagen had acausal laws?! As in the set of events is selected by a 4D constraint. Do you have a reference?

Will have to find some. Need more time for this.

The details are subtle [some are now provided in post #21] and apparently not well studied. People find it easier to create their own versions of Copenhagen rather than to study the originals.

 

[N88]

To my mind, the spirit of the Copenhagen interpretation refers to the ontology. As Heisenberg puts it:

"However, all the opponents of the Copenhagen interpretation do agree on one point. It would, in their view, be desirable to return to the reality concept of classical physics or, to use a more general philosophic term, to the ontology of materialism. They would prefer to come back to the idea of an objective real world whose smallest parts exist objectively in the same sense as stones or trees exist, independently of whether or not we observe them."

In case one gives up the concept of 'physical realism' - a viewpoint according to which an external reality exists independent of observation – and doesn’t insist on thinking about quantum phenomena with classical ideas, quantum mechanics doesn’t unsettle anymore.

For what it's worth:

1. I do not give up on physical realism -- a mind-and-theory independent viewpoint according to which an external reality exists, independent of observation -- allowing (of course) that observation and other interactions may perturb that reality [since Planck's constant is not zero].

2. I insist on thinking about quantum phenomena with classical ideas* like mass, physical realism, locality, separability, particles, fields, waves, hidden-variables, energy, momentum, angular momentum, Planck's constant, dynamic-interactions, advanced probability theory (based on Fourier analysis that leads to Born's rule).**

3. Quantum mechanics does not unsettle me.

4. I cannot oppose the Copenhagen interpetation until I'm given the details of which one is meant.

* Influenced by Einstein -- see Bell (2004), "Speakable and Unspeakable in Quantum Mechanics" (p.86) -- I believe that EPR correlations are "made intelligible" by completing the quantum mechanical account in a classical way.

** For example, see Fröhner (1988): Z. Naturforsch. 53a, 637-654.
http://zfn.mpdl.mpg.de/data/Reihe_A/53/ZNA-1998-53a-0637.pdfFröhner (1988): Z. Naturforsch. 53a, 637-654.

 

[DarMM]

Will have to find some. Need more time for this.

The details are subtle and apparently not well studied. People find it easier to create their own versions of Copenhagen rather than to study the originals.

Fascinating, no rush I appreciate the effort.

 

[A. Neumaier]

Fascinating, no rush I appreciate the effort.

The problem is that there is no consensus Copenhagen interpretation, and any attempt to present one distorts the actual views on record, thereby destroying subtle issues through the necessary reconciliation effort. To get the full picture, one must resist unification.

In some (appropriate but not completely serious) sense, the Copenhagen interpretation is a superposition of complementary views.

The history of the Copenhagen interpretation constitutes the first experimental realization of a truly macroscopic superposition of eigenstates (of the Copenhagen interpretation). It shows how each attempt to observe it in the form of a permanent record collapsed the superposition into a different result.

The many known repetitions of the experiment amply demonstrated this, though so far nobody has been able to determine the correct probability distribution.

The latter is an important open research problem because it could lead to a test of Born's rule in the truly macroscopic domain - testing not just a single degree of freedom of a microsystem but a large set of simultaneously observable quantities.

 

[Demystifier]

@DarMM your analysis can be summarized by saying that there are two kinds of stuff:
a) Classical properties that can be described mathematically, but exist only when measured.
b) Real ontological stuff that exists even without measurement, but cannot be described mathematically.

Now I am interested in two questions.

1) The question of locality

What does the claim "The Nature is local" refer to? I think it cannot refer to b) because something that cannot be described mathematically cannot be said to be local or non-local. So locality can only refer to a). But as long as it refers to a), I think that, within Copenhagen, it is provably wrong. Namely, the classical measurement outcomes do obey non-local correlations, that's an experimental fact. Now you are right that such correlations can in principle be explained by certain local mechanisms (2., 3., 5., and 6. in your post #4 above), but those mechanisms are not Copenhagenish in spirit. I don't know any version of Copenhagen-like interpretation that invokes local mechanisms such as 2., 3., 5., and 6. On the other hand, many Copenhagen-like interpretations do accept non-locality. For instance, Asher Peres at page 173 of his book concludes
"In summary, there is no escape from nonlocality. The experimental violation of Bell’s inequality leaves only two logical possibilities: either some simple physical systems (such as correlated photon pairs) are essentially nonlocal, or it is forbidden to consider simultaneously the possible outcomes of mutually exclusive experiments, even though anyone of these experiments is actually realizable. The second alternative effectively rules out the introduction of exophysical automatons with a random behavior—let alone observers endowed with free will. If you are willing to accept that option, then it is the entire universe which is an indivisible, nonlocal entity."

What about your option 4. acausal laws? That option is indeed quite Copenhagenish in spirit. But can this option save locality? No. An acausal law either does or does not have a mathematical form. If it doesn't, then it is neither local nor non-local. If it does have a mathematical form (an example is a stochastic law), then the Bell theorem (or at least some versions of it) proves that such a law must be nonlocal.

To conclude, the claim "The Nature is local" cannot refer to b). And when it refers to a) then, within Copenhagen-like interpretations, it is provably wrong.

2) The question of evidence for b)

What evidence do we have for the claim that the real stuff cannot be described mathematically? Is there a theorem that, perhaps under certain additional assumptions, suggests or attempts to prove something like that? I am not aware of anything like that. So what is the argument for the claim that real stuff cannot be described mathematically?

 

[zonde]

So this I don't agree with. What Bell's theorem says in full is that $\lambda$ must involve one or more of:

1. Non-local laws
2. Highly nontrivial spacetime (i.e. ubiquity of wormholes)
3. Retrocausal laws
4. Acausal laws
5. Multiple Worlds
6. Superdeterminism

Retrocausal laws, Acausal laws and Superdeterminism are similar. They say there exists correlation between initial conditions of experiment and independent parameters (measurement angles). Based on this it can be argued that they all are unscientific in the same way.

The argument goes like this. We can agree that superluminal communication device would falsify local model. So any model that can explain superluminal communication device as obeying locality should be considered unscientific. But allowing correlation between initial conditions of experiment and independent parameters allows exactly that. We simply consider message to be transmitted as independent parameter and production moment of superluminal communication device as initial conditions. Obviously if at the moment of production the message to be transmitted is known, two parts of device can be made so as to reproduce at the other end the message received at first end.

 

[DarMM]

Retrocausal laws, Acausal laws and Superdeterminism are similar.

I don't think so, but I'll discuss it on another thread. I only want to discuss the non-Representational/Copenhagenish views here.

 

[DarMM]

The problem is that there is no consensus Copenhagen interpretation

That's true. For the purpose of this thread I mean the non-representational views of Bohr, Heisenberg, Pauli, Haag, Peres, Healey, Bub and QBism.

 

[A. Neumaier]

1. I do not give up on physical realism -- a mind-and-theory independent viewpoint according to which an external reality exists, independent of observation.

2. I insist on thinking about quantum phenomena with classical ideas

The the thermal interpretation is for you!

 

[A. Neumaier]

What about your option 4. acausal laws? That option is indeed quite Copenhagenish in spirit. But can this option save locality? No. An acausal law either does or does not have a mathematical form. If it doesn't, then it is neither local nor non-local.

It may also have a partially mathematical form...

 

[Demystifier]

It may also have a partially mathematical form...

Such as?

 

[stevendaryl]

The Copenhagen interpretation is said to treat measuring devices and observers as classical, while treating microscopic objects quantum-mechanically. But what does it mean to treat something as classical?

Typically, people tend to split the world into three parts for the purposes of applying quantum-mechanics: (1) the system of interest, (2) the measuring device, (3) the rest of the universe. Sometimes the observer is lumped into (2) or (3), and sometimes it's treated separately. But I think the empirical content of Copenhagen can be formulated without such a split (but with a different split):

let $A_j$ be an enumeration of a complete set of "macroscopic observables" for the world. I'll leave it imprecise exactly what they are, but they include coarse-grained averages of quantum fields, coarse-grained particle densities etc. It should be the case that anything you would consider a persistent measurement result, such as a spot on a photographic plate, the position of a pointer, a light bulb turning on or off, etc., is a function of the macroscopic observables. It should also be the case that they approximately commute. You may not be able to know the position and momentum of a microscopic particle at the same time, but you can certainly know the approximate position and approximate momentum of a basketball at the same time.

I'm assuming that the macroscopic observables are expressible as averages and sums of microscopic variables. Then the Schrodinger equation will allow us to compute, from some assumed initial state, what the probability amplitude is that $A_j = a$ is at any time $t$ (where $a$ is one of the. You square that amplitude, and you get a probability that the macroscopic observable has value $a$ at time $t$.

So one way to think about Copenhagen is that it is a stochastic theory of macroscopic observables. In this view, microscopic observables can just be thought of as mathematical fictions that are an aid to computing the probabilities for macroscopic observables. Some people would say that microsopic observables don't have values until they observed, but it's equally correct to say that they don't have values ever. The only thing that exists (according to this way of looking at it) is the macroscopic world.

I think it's a little silly, because obviously macroscopic observables are made up out of microscopic variables, so I don't see how the former can be real if the latter are not, but it more or less works as an empirical theory.

 

[Lord Jestocost]

As Hilary Putnam puts it in “Philosophical Papers: Volume 1, Mathematics, Matter and Method”:

“The full CI [Copenhagen Interpretation], to put it another way, is the minimal statistical interpretation plus the statement that hidden variables do not exist and that the wave representation gives a complete description of the physical system.” [italics in the original]

 

[DarMM]

The only thing that exists (according to this way of looking at it) is the macroscopic world.

I think it would be more accurate to say "the only thing that is mathematically described is the macroscopic world". At least that's what comes through in the writings of proponents of these views. Most of them are fairly explicit that something microscopic exists, just that QM doesn't give you access to it.

 

[A. Neumaier]

The problem is that there is no consensus Copenhagen interpretation

That's true. For the purpose of this thread I mean the non-representational views of Bohr, Heisenberg, Pauli, Haag, Peres, Healey, Bub and QBism.

So these are taken from a whole spectrum of Copenhagen-like interpretations.

Old Copenhagen had acausal laws?! [...] Do you have a reference?

Will have to find some. Need more time for this.

The details are subtle and apparently not well studied.

The lack of causality is explicitly stated on p.566 of

• N. Bohr, The recent quantum postulate and the recent development of atomic theory, pp.565--588. Proc. Int. Conf. Physicists, Como 1927.

the quantum postulate, which to any atomic process attributes an essential discontinuity or rather individuality, completely foreign to the classical theories and symbolized by Planck's quantum of action.
This postulate implies a renunciation as regards the causal space-time co-ordinates of atomic processes.

To understand Bohr's reasoning in the paper, it is important to realize that Bohr's notion of state was different from von Neumann's - for him a state was always a stationary state of a system without external interactions. (One finds the same in all papers by Born before 1930.)
This state had the character of a beable (definite energy, momentum, conserved internal quantum numbers), whereas the other quantities were only statistical measurables. (See also Subsection 3.1 of my Part I.) The wave function provided probabilities for quantum jumps between stationary states and uncertainties for statistical measurables.

• p.567: if in order to make observation possible we permit certain interactions [...] an unambiguous definition of its state is naturally no longer possible
• p.579: [Born], who in connexion with his important investigation of collision problems has suggested a simple statistical interpretation of Schrödinger's wave functions.
• p.581: while the definition of energy and momentum of individuals is attached to the idea of a harmonic elementary wave, every space-time feature of the description of phenomena is, as we have seen, based on a consideration of the interferences taking place inside a group of such elementary waves.
• p.582: the probability of the presence of a free electron is measured in a similar way by the electric density associated with the wave field as the probability of the presence of a light quantum by the energy density of radiation.
• p.582: In the conception of stationary states we are, as mentioned, concerned with a characteristic application of the quantum postulate. By its very nature this conception means a complete renunciation as regards a time description. From the point of view taken here just this renunciation forms the necessary condition for an unambiguous definition of the energy of the atom.
• p.582: stability of the stationary states, according to which the atom, before as well as after an external influence, always will be found in a stationary state.
• p.587: Summarising, it might be said that the concepts of stationary states and individual transition processes within their proper field of application possesses just as much or as little 'reality' as the very idea of individual particles.

Heisenberg's 1927 paper is also very clear about causality. On p.179, he writes: ''Now, since the statistical character of quantum theory is so closely connected with the uncertainty of all perception, one could be lured into the conjecture that behind the perceived statistical world another 'true' world is hidden in which the causal law is valid. But such speculations seem to us, as we explicitly emphasize, unproductive and meaningless. Physics shall formally describe only the connectivity of the perceptions. Rather one may characterize the true state of affairs much better as follows: Since all experiments are subject to the laws of quantum mechanics and hence to equation (1) [the uncertainty relation for position and momentum], quantum mechanics definitely establishes the invalidity of the causal law.''

Da nun der statistische Charakter der Quantentheorie so eng an die Ungenauigkeit aller Wahrnehmung geknüpft ist, könnte man zu der Vermutung verleitet werden, daß sich hinter der wahrgenommenen statistischen Welt noch eine 'wirkliche' Welt verberge, in der das Kausalgesetz gilt. Aber solche Spekulationen scheinen uns, das betonen wir ausdrücklich, unfruchtbar und sinnlos. Die Physik soll nur den Zusammenhang der Wahrnehmungen formal beschreiben. Vielmehr kann man den wahren Sachverhalt viel besser so charakterisieren: Weil alle Experimente den Gesetzen der Quantenmechanik und damit der Gleichung (1) unterworfen sind, so wird durch die Quantenmechanik die Ungültigkeit des Kausalgesetzes definitiv festgestellt.

On p.181f, Heisenberg mentions an ontology resembling the thermal interpretation in that ''associated with every quantum-theoretical quantity or matrix is a number which gives its 'value' within a certain definite probable error. The statistical error depends on the coordinate system. For every quantum-theoretical quantity there exists a coordinate system in which the statistical error for this quantity is zero. Therefore a definite experiment can never give exact information on all
quantum-theoretical quantities.''

Jeder quantentheoretischen Größe oder Matrix läßt sich eine Zahl, die ihren 'Wert' angibt, mit einem bestimmten wahrscheinlichen Fehler zuordnen; der wahrscheinliche Fehler hängt vom Koordinatensystem ab; für jede quantentheoretische Größe gibt es je ein Koordinatensystem, in dem der wahrscheinliche Fehler für diese Größe verschwindet. Ein bestimmtes Experiment kann also niemals für alle quantentheoretischen Größen genaue Auskunft geben

Thus only exact values are denied to exist; approximate values of every quantity are accepted as objectively real properties, with definite probable error. An exception are conserved quantities:
On p.178, Heisenberg writes ''Finally those experiments must be pointed out that permit to measure the energy or the values of the action variable $J$ [discrete angular momentum]; such experiments are especially important, since only with their help we can define what we mean when we talk about the discontinuous change of energy and the $J$.''

Schließlich sei noch auf die Experimente hingewiesen, welche gestatten, die Energie oder die Werte der Wirkungsvariablen $J$ zu messen; solche Experimente sind besonders wichtig, da wir nur mit ihrer Hilfe definieren können, was wir meinen, wenn wir von der diskontinuierlichen Änderung der Energie und der $J$ sprechen.

And on p.185, Heisenberg writes ''In order that the determination of the position shall be not much too uncertain, the Compton recoil will cause that after the collision, the atom is in some particular state between, say, the 950th and the 1050th; at the same time, the momentum of the electron can be deduced from the Doppler effect with an accuracy determined by (1).''

Wenn die Bestimmung des Ortes nicht allzu ungenau sein soll, so wird der Comptonrückstoß zur Folge haben, daß das Atom sich nach dem Stoß in irgend einem Zustand zwischen, sagen wir, dem 950. und 1050. befindet; gleichzeitig kann der Impuls des Elektrons mit einer aus (1) bestimmbaren Genauigkeit aus dem Dopplereffekt geschlossen werden.

Thus Heisenberg, too, considers conserved quantities as beables that change discontinuously during interactions. As concrete calculations in various papers show, these interactions were, at the time, always considered as being of finite, very short duration, so that the scattering problem was well-defined without an asymptotic analysis as in modern treatments involving the S-matrix (which is a much later concept).

With the above background as Ariadne thread it should be much easier to navigate within the lectures given at the Solvay conference 1927 by Born and Heisenberg, and by Bohr. The proceedings contain printed lectures in French; but Bohr's printed lecture there is a translation of a German translation of the Como lectures. An English translation of the Born/Heisenberg lecture is in Part III of the book:

• Bacciagaluppi, G., & Valentini, A. (2009). Quantum theory at the crossroads: reconsidering the 1927 Solvay conference. Cambridge University Press.

This conference (which also featured the dispute with Einstein) is generally regarded as the final consensus about the interpretation issues for nearly half a century (with only Einstein, Schrödinger, and de Broglie dissenting, and with minor variants introduced by Dirac and von Neumann). These two lectures and the two papers from which I quoted above constitute in my view the definition of the original Copenhagen interpretation.

The book mentioned gives a lot of other background information on the Solvay conference, including (p.24) the following quote from Heisenberg:

In relating the development of the quantum theory, one must in particular not forget the discussions at the Solvay conference in Brussels in 1927, chaired by Lorentz. Through the possibility of exchange [Aussprache] between the representatives of different lines of research, this conference has contributed extraordinarily to the clarification of the physical foundations of the quantum theory; it forms so to speak the outward completion of the quantum theory ... .

 

[DarMM]

So these are taken from a whole spectrum of Copenhagen-like interpretations.

Yes I've amended the initial post to indicate this. Also indicated there I'm going to stick more to Neo-Copenhagen views (Bub, Healey) or Qbism (Fuchs, Schack) because it's quite subtle what Bohr and Heisenberg actually meant and I don't fully understand their disagreements on the cut for example (the whole functional/structural vs epistemological/ontological distinction).
I find the later views easier to parse, more explicit and they take modern findings (e.g. POVMs) into account so it's possible to talk about decoherence and superobservers more easily for example.

 

[A. Neumaier]

Such as?

a statistical connection; see here.

As Hilary Putnam puts it in “Philosophical Papers: Volume 1, Mathematics, Matter and Method”:

“The full CI [Copenhagen Interpretation], to put it another way, is the minimal statistical interpretation plus the statement that hidden variables do not exist and that the wave representation gives a complete description of the physical system.” [italics in the original]

But he forgets the collapse, which is not part of the minimal statistical interpretation (at least not in Ballentine's version). A statistical interpretation with collapse is therefore no longer minimal.

 

[DarMM]

@DarMM your analysis can be summarized by saying that there are two kinds of stuff:
a) Classical properties that can be described mathematically, but exist only when measured.
b) Real ontological stuff that exists even without measurement, but cannot be described mathematically.

Yes I would say that is correct. That would be my reading of Neo-Copenhagenists and QBism. Then with decoherence you can tell when (b) gives rise to (a).

What does the claim "The Nature is local" refer to? I think it cannot refer to b) because something that cannot be described mathematically cannot be said to be local or non-local. So locality can only refer to a). But as long as it refers to a), I think that, within Copenhagen, it is provably wrong. Namely, the classical measurement outcomes do obey non-local correlations, that's an experimental fact. Now you are right that such correlations can in principle be explained by certain local mechanisms (2., 3., 5., and 6. in your post #4 above), but those mechanisms are not Copenhagenish in spirit.

Yes I would say all the methods given above are not in line with Neo-Copenhagen and QBism as they explicitly reject additional $\lambda$ variables.

So how can the world be local? I admit to having struggled with this myself while reading Healey, Bub and the QBists. The basic answer is tied to Tsirelson and Landau's papers as well as Contextuality. Basically it is nothing more than an extended test of local incompatibility.

As you know ultimately the CHSH inequality comes from the statistics of four observables, two for Alice and Bob:
$$A_1, A_2, B_1, B_2$$

Let us form a composite operator out of this:
$$C = \frac{1}{2}\left[A_1\left(B_1 + B_2\right) + A_2\left(B_1 - B_2\right)\right]$$

If $A_1, A_2, B_1, B_2$ are any set of observables it can be proved that they will have statistics satisfying the Bell inequality if:
$$C^{2} \leq \mathbb{I}$$

Now if we actually work out $C^{2}$ we have:
$$C^{2} = 1 + \frac{1}{4}\left[A_1,A_2\right]\left[B_1,B_2\right]$$

Thus the conditions for non-classical statistics are entirely local. The local measurements of Alice have to be incompatible and so do those of Bob. For example if Alice and Bob are spacelike seperated, but Alice only measures compatible observables, even if Bob measures incompatible ones, there will be no CHSH inequality violations.

It is simply a spatially extended test of complimentarity.

I have more to say, but I would prefer to see what you think of this before proceeding.

 

[A. Neumaier]

With the above background as Ariadne thread it should be much easier to navigate within the lectures given at the Solvay conference 1927 by Born and Heisenberg, and by Bohr. The proceedings contain printed lectures in French; but Bohr's printed lecture there is a translation of a German translation of the Como lectures. An English translation of the Born/Heisenberg lecture is in Part III of the book:

• Bacciagaluppi, G., & Valentini, A. (2009). Quantum theory at the crossroads: reconsidering the 1927 Solvay conference. Cambridge University Press.

This conference (which also featured the dispute with Einstein) is generally regarded as the final consensus about the interpretation issues for nearly half a century (with only Einstein, Schrödinger, and de Broglie dissenting, and with minor variants introduced by Dirac and von Neumann). These two lectures and the two papers from which I quoted above constitute in my view the definition of the original Copenhagen interpretation.

The book mentioned gives a lot of other background information on the Solvay conference, including (p.24) the following quote from Heisenberg:

In relating the development of the quantum theory, one must in particular not forget the discussions at the Solvay conference in Brussels in 1927, chaired by Lorentz. Through the possibility of exchange [Aussprache] between the representatives of different lines of research, this conference has contributed extraordinarily to the clarification of the physical foundations of the quantum theory; it forms so to speak the outward completion of the quantum theory ... .

I updated my original posting #21 to give these details.

 

[Demystifier]

I have more to say, but I would prefer to see what you think of this before proceeding.

I must admit that I didn't get your point. What explicit or implicit assumptions of the Bell theorem are violated in local Copenhagen-like interpretations?

 

[DarMM]

I must admit that I didn't get your point. What explicit or implicit assumptions of the Bell theorem are violated in local Copenhagen-like interpretations?

The ability of all four measurements to be placed in a single sample space, i.e. Contextuality/Complementarity. CHSH experiments are just extended tests of this property in non-Representational views.

 

[Demystifier]

The ability of all four measurements to be placed in a single sample space, i.e. Contextuality/Complementarity. CHSH experiments are just extended tests of this property in non-Representational views.

Let me try to understand it better. As an example of two complementary observables, consider spin of the same particle in two different directions $d1$ and $d2$. This corresponds to a macroscopic "classical" Stern-Gerlach apparatus oriented in directions $d1$ and $d2$. So does Copenhagen interpretation claim that two orientations of the macroscopic SG apparatus cannot be placed in a single sample space? If it claims so, then it doesn't make sense to me. If it doesn't claim so, then what does it claim in terms of macroscopic SG apparatuses?

 

[DarMM]

[This is not a response to what you just posted, more a clarification of your my last post]

On reflection that is a bit opaque and I found it difficult to understand as well. So let me try again.

Basically as we've already discussed Classical quantities emerge from the fundamental non-mathematical "stuff" in decoherence inducing environments. The most common such case being our measurements. However only the classical quantities we choose to measure are "summoned" into being. You can't talk about counterfactuals.

Thus the correlations on distantly measured quantities are not as constrained as they would be if all classical quantities existed, i.e. $A_1$ and $B_2$ say can have broader range of correlations since they aren't constrained to occupy the same outcome space as $A_2, B_1$. If you analyse the correlations they simply break conditions on four variables on a single sample space have like the CHSH inequalities. No surprise though as there is no common outcome for all four variables.

 

[DarMM]

Let me try to understand it better. As an example of two complementary observables, consider spin of the same particle in two different directions $d1$ and $d2$. This corresponds to a macroscopic "classical" Stern-Gerlach apparatus oriented in directions $d1$ and $d2$. So does Copenhagen interpretation claim that two orientations of the macroscopic SG apparatus cannot be placed in a single sample space? If it claims so, then it doesn't make sense to me. If it doesn't claim so, then what does it claim in terms of macroscopic SG apparatuses?

Not the orientations of the device, but the outcomes of spin measurements cannot be placed in a single sample space. The results of spin measurements. The outcomes you get from the device oriented one way don't share a common sample space with the outcomes when it is placed another way.

This is just a bare mathematical fact of the formalism. In a hidden variable program can be seen as connecting the outcomes into one sample space via an additional set of variables $\lambda$.

 

[Demystifier]

Not the orientations of the device, but the outcomes of spin measurements cannot be placed in a single sample space. The results of spin measurements. The outcomes you get from the device oriented one way don't share a common sample space with the outcomes when it is placed another way.

This is just a bare mathematical fact of the formalism. In a hidden variable program can be seen as connecting the outcomes into one sample space via an additional set of variables $\lambda$.

But I refuse to think of it as formalism, with or without $\lambda$. I insist on thinking about it as possible events in the laboratory, which is quite Copenhagenish in spirit. In the case of spin measurement by SG apparatus, the possible outcomes are macroscopic dark spots on the screen at 4 possible positions (corresponding to 2 possible spins in direction $d1$ plus 2 possible spins in direction $d2$). Those 4 possible positions of macroscopic dark spots on the screen can certainly be placed in a single sample space.

 

[DarMM]

But I refuse to think of it as formalism, with or without $\lambda$. I insist on thinking about it as possible events in the laboratory, which is quite Copenhagenish in spirit. In the case of spin measurement by SG apparatus, the possible outcomes are macroscopic dark spots on the screen at 4 possible positions (corresponding to 2 possible spins in direction $d1$ plus 2 possible spins in direction $d2$). Those 4 possible positions of macroscopic dark spots on the screen can certainly be placed in a single sample space.

Well in the case of a single spin measurement on one spin-1/2 system they can, because that has a locally real model. For more general quantum systems you don't have a single sample space, that's why quantum probability is different from Kolmogorov probability theory.

EDIT: Although of course these non-Representational views then work backward from the general case and reject such a local model for the single spin-1/2 case as being what is going on in that case.

 

[DarMM]

Perhaps this will work better. Say Alice and Bob perform billions of experiments on observables $A_1, A_2, B_1, B_2$. Each time they perform one of four pair measurements:

1. $A_1, B_1$
2. $A_2, B_1$
3. $A_1, B_2$
4. $A_2, B_2$

The point is that afterwards when they look at the statistics they are incompatible with the notion that the results are drawn from a distribution $p\left(a_1,a_2,b_1,b_2\right)$ over a common sample space. They can only be drawn from individual distributions like $p\left(a_1,b_1\right)$.

Thus the approach these views take is that is because in a $A_1, B_1$ test only those two variables gain values the sample space is just the space of pairs $\left(a_1,b_1\right)$. Since the other variables have no value in a $A_1, B_1$ test, not unmeasured values but none, the distribution $p\left(a_1,b_1\right)$ has more freedom because it is not a marginal of some $p\left(a_1,a_2,b_1,b_2\right)$.

In short the measurements Alice and Bob perform need not be consistent with another they could have performed.

The only way around this is to introduce an additional $\lambda$ that allows them to be drawn from $p\left(a_1,a_2,b_1,b_2,\lambda\right)$

 

[A. Neumaier]

Well in the case of a single spin measurement on one spin-1/2 system they can, because that has a locally real model. For more general quantum systems you don't have a single sample space, that's why quantum probability is different from Kolmogorov probability theory.

But since spin 1 particles don't have a local realist model, your argument wouldn't account for Demystifier's setting in post #31 when measuring single spins of spin 1 particles, giving 9 spots that are simultaneously measurable.

 

[zonde]

Perhaps this will work better. Say Alice and Bob perform billions of experiments on observables $A_1, A_2, B_1, B_2$. Each time they perform one of four pair measurements:

1. $A_1, B_1$
2. $A_2, B_1$
3. $A_1, B_2$
4. $A_2, B_2$

The point is that afterwards when they look at the statistics they are incompatible with the notion that the results are drawn from a distribution $p\left(a_1,a_2,b_1,b_2\right)$ over a common sample space. They can only be drawn from individual distributions like $p\left(a_1,b_1\right)$.

But is the sample space $p\left(b_1\right)$ from the first experiment ($A_1, B_1$) the same as sample space $p\left(b_1\right)$ from the second experiment ($A_2, B_1$)?