I The thermal interpretation of quantum physics

[ftr]

I don't. Quantum mechanics in its standard formulation is just inconsistent. As I have said before, it's a "soft" inconsistency.

Why do you say that, in what sense it is soft.
Just saw your post thanks. Ignore.

 

[ftr]

There is no need for the Born rule to apply to all observables; it is enough to apply it to macroscopic observables.

Now I remember your other post that you elaborated on this point. But isn't still you need to explain the wavefunction since it is a pre-measurement entity. I think this problem is related to physics where usually we define variable as related to some physical character, but psi is an after thought ( maybe it is correct we are forced into it, maybe the model is simply awkward).

 

[stevendaryl]

Why do you say that, in what sense it is soft.

Let's suppose that we have a measuring device that starts off in some start state, $S_0$. It measures an electron's spin along the z-axis, and if it measures spin-up, it makes a transition to the state $S_{up}$, and if it measures spin-down, it makes a transition to the state $S_{down}$. Let $S_{other}$ be some third state of the measuring device.

Now, suppose we prepare the electron so that it's in a superposition of spin-up (with amplitude $\alpha$) and spin-down (with amplitude $\beta$). We want to compute the probability that the measuring device winds up in state $S_{other}$.

We can first compute amplitudes, and then square them to get probabilities. Let $\phi_{up, other}$ be the amplitude for the device to transition from state $S_{up}$ to state $S_{other}$. let $\phi_{down, other}$ be the amplitude to transition from $S_{down}$ to $S_{other}$. Then the amplitude for the device to end up in state $S_{other}$ is given by:

$\chi_{other} = \alpha \phi_{up, other} + \beta \phi_{\beta, other}$

The probability is the absolute square of the amplitude, so the probability of ending up in state $S_{other}$ is:

$|\chi_{other}|^2 = |\alpha|^2 |\phi_{up, other}|^2 + |\beta|^2 |\phi_{down, other}|^2 + \alpha^* \phi_{up, other}^* \beta \phi_{down, other} + \alpha \phi_{up, other} \beta^* \phi_{down, other}^*$

If we define $P_{other} = |\chi_{other}|^2$, $P_{up, other} = |\alpha|^2 |\phi_{up, other}|^2$, $P_{down, other} = |\beta|^2 |\phi_{down, other}|^2$ and $I = \alpha^* \phi_{up, other}^* \beta \phi_{down, other} + \alpha \phi_{up, other} \beta^* \phi_{down, other}^*$, then this becomes:

$P_{other} = P_{up, other} + P_{down, other} + I$

where $I$ is an interference term between the two intermediate possibilities.

This amounts to applying the Born rule only at the end. On the other hand, if we apply the Born rule at the point of measurement, then we get:

$P_{other} = P_{up, other} + P_{down, other}$

(without the $I$). So saying that the Born rule applies to every measurement gives a different answer for probabilities than if you only apply the Born rule at the end. That's a contradiction, it seems to me.

On the other hand, the difference between the two predictions is the interference term $I$. Interference terms between macroscopically distinct configurations are practically impossible to measure. It's impossible to calculate, in the first place, and is likely to be completely negligible.

So the contradiction is that there are two different ways to compute a probability, and they give different values. But it's a soft contradiction in the sense that those two different values are neglibly different.

 

[A. Neumaier]

The articles are very interesting. Nevertheless I do not like the style, especially of paper I.
It insinuates that there is only one universal "traditional" way of learning QM which follows the steps listed in 5.2.
Although it is more than 30 years now that I learned QM, this was certainly not the way I learned it.

Thanks for your critique. This section was kind of a caricature. Of course, not everyone is exposed to everything mentioned, also the order may be quite different. Nevertheless, one comes across all this stuff sooner or later when one is doing enough quantum mechanics.

I learned quantum mechanics not in a course but by self-teaching from books and later, articles. Certainly all these things puzzled me when I encountered them, and it took me a long time to figure out how to think of all this in a coherent way.

 

[vanhees71]

No, people have been living with this contradiction for nearly 100 years. It doesn't bother them any more.

Asking for an experiment in which a contradiction shows up doesn't make any sense. A contradiction is a property of a theory. The real world can't have any contradictions.

Ok, then tell me what you consider a contradiction. As far as I know there's no intrinsic contradiction in QT at all.

 

[vanhees71]

I think it all boils down to what experiment proves that the position of a particle is an eigenvalue of the corresponding operator. can you name one?

Well, the spectrum of any position operator is $\mathbb{R}$. I don't think it makes sense to ask this very question in this case since by definition we measure positions with real numbers. It was not me who made the bold claim that there's a contradiction within QT! I don't think that there is one!

 

[stevendaryl]

Ok, then tell me what you consider a contradiction. As far as I know there's no intrinsic contradiction in QT at all.

I already told you the contradiction.

1. On the one hand, the minimal interpretation claims that a measurement of an observable produces a result that is one of the eigenvalues of that observable.
2. On the other hand, if the system being measured is in a superposition of eigenstates, and we treat the measuring device quantum-mechanically, then the device itself ends up in a superposition of different results.

That's a contradiction. According to 1, the device will end up in one of a number of possible macroscopic states, with probability given by the Born rule. According to 2, the device will definitely end up in a superposition state that is none of those possibilities.

 

[DarMM]

I already told you the contradiction.

1. On the one hand, the minimal interpretation claims that a measurement of an observable produces a result that is one of the eigenvalues of that observable.
2. On the other hand, if the system being measured is in a superposition of eigenstates, and we treat the measuring device quantum-mechanically, then the device itself ends up in a superposition of different results.

That's a contradiction. According to 1, the device will end up in one of a number of possible macroscopic states, with probability given by the Born rule. According to 2, the device will definitely end up in a superposition state that is none of those possibilities.

That's not a contradiction in my opinion, more a sign of possible incompleteness. So if we have the system:
$$\mathcal{H}_t = \mathcal{H}_{s}\otimes\mathcal{H}_{d}\otimes\mathcal{H}_{e}$$
where $s$ is the atomic system, $d$ is the device and $e$ is the entire rest of the lab environment.

A quantum mechanical model will say that the state of the whole system $|\psi\rangle \in \mathcal{H}_t$ is in a superposition after measurement and a superobserver will use such a superposed state.

However to date nobody has produced an actual proof that this is in contradiction with the subsystem $s + d$ being in a definite state. Frauchiger-Renner and Brukner's objectivity theorems are attempts at this, but the consensus by now is that they don't succeed.

 

[A. Neumaier]

would you say that because a system is in a state for which
$$P\left(S_z = \frac{1}{2}\right) = 1$$
that means the particle in fact already has the spin value of $S_z = \frac{1}{2}$ or does it only mean if you set up an $S_z$ measurement it's guaranteed to produce a specific result?

The answer to this would allow me to know if you're closer to Brukner-Zellinger or others like Haag.

Guaranteed? With probability zero (but still in finitely many of infinitely many cases) it could also have another value, form a purist point of view...

 

[DarMM]

Guaranteed? With probability zero (but still in finitely many of infinitely many cases) it could also have another value, form a purist point of view...

It is a discrete outcome space though.

 

[A. Neumaier]

Is a discrete outcome space though.

This doesn't help: $S_z$ could still be $-1/2$ in finitely many cases, without affecting the probability (which in statistics is a limiting concept only).

 

[stevendaryl]

However to date nobody has produced an actual proof that this is in contradiction with the subsystem $s + d$ being in a definite state. Frauchiger-Renner and Brukner's objectivity theorems are attempts at this, but the consensus by now is that they don't succeed.

Well, the FR paradox is easily resolved (in my mind) in a number of ways, but every one of those ways means a departure from the minimalist interpretation of quantum mechanics. If you assume that a measurement collapses the wave function, then there is no paradox, because you can't have a superposition of different measurement results. But assuming the collapse of the wave function means a violation of the minimalist interpretation. You can also resolve it by going to Many-Worlds, or by going to the Bohmian interpretation. But you can't resolve it using the minimal interpretation.

 

[DarMM]

This doesn't help: $S_z$ could still be $-1/2$ in finitely many cases, without affecting the probability (which in statistics is a limiting concept only).

Quite right.

 

[A. Neumaier]

A quantum mechanical model will say that the state of the whole system $|\psi\rangle \in \mathcal{H}_t$ is in a superposition [...]
However to date nobody has produced an actual proof that this is in contradiction with the subsystem $s + d$ being in a definite state.

How could it be theoretically possible that system S plus environment E is in a superposition but system S is in a definite state for some of its observables A? This is surely impossible in a nonsubjective setting, where not subjective knowledge but only objective facts of preparation and measurement count.

 

[DarMM]

This doesn't help: $S_z$ could still be $-1/2$ in finitely many cases, without affecting the probability (which in statistics is a limiting concept only).

This (embarrassingly obvious to forget!) fact means a view like @vanhees71 would have to view the values as being generated on the spot as opposed to being prepossessed even in the $P(a) = 1$ case for discrete events $a$. I think at least.

 

[DarMM]

How could it be theoretically possible that system S plus environment E is in a superposition but system S is in a definite state for some of its observables A? This is surely impossible in a nonsubjective setting, where not subjective knowledge but only objective facts of preparation and measurement count.

Spekkens toy model provides a nice example in a local classical theory that still has superposition. However in general people have been trying to show there is a contradiction and constantly failing.

It's avoided by the quantum state being epistemic.

I can give some references for the discussion if you wish.

 

[A. Neumaier]

It's avoided by the quantum state being epistemic.

I can give some references for the discussion if you wish.

Not needed. I am not interested in epistemic views. For me physics is about objective facts only. The subjective views are compromises that attempt to cope with insufficient understanding.

 

[DarMM]

Not needed. I am not interested in epistemic views. For me physics is about objective facts only.

I don't think they're mutually exclusive though. The macrostate in statistical mechanics can be seen as epistemic without the results of statistical mechanics not being objective facts.

The use of epistemic quantities like probability distributions doesn't preclude objective facts, unless I'm missing something.

 

[A. Neumaier]

The use of epistemic quantities like probability distributions doesn't preclude objective facts, unless I'm missing something.

You are missing the point mentioned in #373. It means that probability distributions strictly speaking predict nothing at all for any finite number of experiments. This is one of the reasons why one can never get beyond FAPP arguments when starting with irreducible quantum probability.

 

[DarMM]

Well, the FR paradox is easily resolved (in my mind) in a number of ways, but every one of those ways means a departure from the minimalist interpretation of quantum mechanics. If you assume that a measurement collapses the wave function, then there is no paradox, because you can't have a superposition of different measurement results. But assuming the collapse of the wave function means a violation of the minimalist interpretation. You can also resolve it by going to Many-Worlds, or by going to the Bohmian interpretation. But you can't resolve it using the minimal interpretation.

Perhaps it does require a modification of the minimalist view, I've never been clear on what that really is.

What I mean is that a superposition of the total system is not in contradiction with definite outcomes for subsystems even in Copenhagen or similar views like Healey and Bub, but these probably add things beyond the minimal view such a intervention sensitivity mentioned in Healey's paper.

 

[A. Neumaier]

a superposition of the total system is not in contradiction with definite outcomes for subsystems even in Copenhagen

Standard Copenhagen (Heisenberg, Bohr) always considers the state of a single quantum system only, never that of a system and a subsystem (except in the separable case before interaction), where this has a clear interpretation. See post #284.

 

[A. Neumaier]

the minimalist view, I've never been clear on what that really is.

There is no written account of it. The postulates of @vanhees71 in his various lecture notes (partly in German) are only an approximation to his actual (somewhat sloppy) views as revealed in discussions - he doesn't value the precision of mathematical physicists.

The book by Peres is perhaps the most consequent exposition of the minimalist view. But even he wavers when considering applications to large systems (p.424f):

This would cause no conceptual difficulty with quantum theory if the Moon, the planets, the interstellar atoms, etc., had a well defined state $\rho$. However, I have insisted throughout this book that $\rho$ is not a property of an individual system, but represents the procedure for preparing an ensemble of such systems. How shall we describe situations that have no preparer? [...] Thus, a macroscopic object effectively [...] mimics, with a good approximation, a statistical ensemble. [...] You must have noted the difference between the present pragmatic approach and the dogmas held in the early chapters of this book.

The mimicking is of course only FAPP (pragmatic), not in any logically convincing sense. But at least he acknowledges it while @vanhees71 insists on the absence of all problems in his version of the minimal interpretation.

The thermal interpretation has no such problems and still is minimalist in a similar (but content-wise diametrically opposed) way.

 

[DarMM]

You are missing the point mentioned in #373. It means that probability distributions strictly speaking predict nothing at all for any finite number of experiments.

I see, you would like to see the removal of epistemic quantities from physics since they strictly speaking don't predict anything.

It's an "extreme" (not meant pejoratively) view that I haven't seen before, so I didn't consider it.

Standard Copenhagen (Heisenberg, Bohr) always considers the state of a single quantum system only, never that of a system and a subsystem (except in the separable case before interaction), where this has a clear interpretation. See post #284.

I'm referring to a very nebulous "Copenhagen" since the phrase simply cannot refer to something specific and yet is a standard term for these views. Matt Leifer has a good summary of the kind of view I mean in his lecture notes here:
http://mattleifer.info/wordpress/wp-content/uploads/2018/05/Lecture26.pdfWhat he calls Copenhagenish.

I find it hard to know exactly what Old Copenhagen is sometimes as I find it very hard to understand the subtleties of what Heisenberg and Bohr's disagreements over the cut were about. Though I think I might get it, but there are still the points where they disagreed with Pauli etc.

 

[DarMM]

There is no written account of it. The postulates of @vanhees71 in his various lecture notes (partly in German) are only an approximation to his actual (somewhat sloppy) views as revealed in discussions. The book by Peres is perhaps the most consequent exposition of the minimalist view. But even he wavers when considering applications to large systems (p.424f):

I in fact just read Peres yesterday! I see he has statements like "There are no super-observers". Maybe @vanhees71 thinks the same.

 

[A. Neumaier]

I find it hard to know exactly what Old Copenhagen is sometimes as I find it very hard to understand the subtleties

The strength of Old Copenhagen is precisely their lack of precision about details that would be needed to get definite statements that can be refuted. This allowed (almost) everyone to accept it with small reservations only, which was enough for the first 40 years. Those who try to make it precise (all in their own way) only create problematic variants of it!

 

[A. Neumaier]

you would like to see the removal of epistemic quantities from physics since they strictly speaking don't predict anything.

Not from physics; only from the foundations! If the foundations have no logical force then any argument built on them will have the same problem. I don't have reservations about introducing probability as an approximate concept as in tossing classical dice!

 

[A. Neumaier]

I'm referring to a very nebulous "Copenhagen" since the phrase simply cannot refer to something specific and yet is a standard term for these views. Matt Leifer has a good summary of the kind of view I mean in his lecture notes here:
http://mattleifer.info/wordpress/wp-content/uploads/2018/05/Lecture26.pdfWhat he calls Copenhagenish.

• Objective: There is an objective fact of the matter about what an observer observes.
• Perspectival: What is true depends on where you are sitting.

I don't see how these are disjoint. Classical relativity is deemed objective although what is true depends on where the observer sits. Does he mean with perspectival ''What is true depends on a not further investigated state of mind of the observer?'' When he distinguishes ''facts of the matter'' (or ''objective facts'') and ''facts for you'', doesn't he turn subjective opinions into some sort of facts?

I doubt very much that this gives clearer notions than the original Copenhagen spirit.

 

[DarMM]

It's like Rovelli's relational interpretation. A system only has a property $P$ relative to me, i.e. all propeties of an object $A$ can have a separate value depending on the observer $B$, so they'd be indexed as $P_{A,B}$ roughly. There's no "universal" value for a property. Schrodinger had similar thoughts if I remember correctly (though he wasn't committed to them).

In the Objective case he mentions this is not the case.

 

[A. Neumaier]

all properties of an object $A$ can have a separate value depending on the observer $B$, so they'd be indexed as $P_{A,B}$ roughly. There's no "universal" value for a property.

But this is the same as with the length of an object $A$ in special relativity (or even Euclidean geometry at a distance). Every observer $B$ sees a different length and measures it objectively as this length. It is just a convention to define the ''true'' length as the eigenlength that would be measured in the rest frame located at the center of mass of $A$ to give the appearance of being non-relational.

Maybe one needs eigenproperties in the quantum domain?

 

[DarMM]

But this is the same as with the length of an object $A$ in special relativity (or even Euclidean geometry at a distance). Every observer $B$ sees a different length and measures it objectively as this length. It is just a convention to define the ''true'' length as the eigenlength that would be measured in the rest frame located at the center of mass of $A$ to give the appearance of being non-relational.

Maybe one needs eigenproperties in the quantum domain?

This would require a thread of its own, but the rough idea would be imagine if there were only the relative quantities. An analogy would be relativity with only frame dependent quantities, but no rules indicating they were the coordinate "reflections" of coordinate independent Tensors. Of course relativity is not like this.

Relativity would still ascribe an objective state to me that has different forms in different coordinates, but they are coordinate expressions of one thing. In the relational view a piece of matter genuinely has several different states, not different expressions of the same state, one for each other piece of matter.

QBism is perspectival in a different sense that would take us too far afield, but just to mention.

 

[A. Neumaier]

In the relational view a piece of matter genuinely has several different states

So each observer $B$ has for each bounded part $A$ of the universe (disjoint from $B$?) a different $\psi_{A,B}$ and nothing at all defines how these are related?

No surprise that weird stuff comes out...

 

[DarMM]

It's not an interpretation I have much confidence in, in case that might affect my description.

More so it would be saying that there are ontic states $\mathcal{O}_{AB}$, which aren't wavefunctions, but since each observer doesn't know what their state for $A$ is like until they look at it, they use $\psi$ to manage their expectations.

So imagine you and I are in a laboratory, you could have a particle with DarMM-spin $\frac{1}{2}$ and Neumaier-spin $-\frac{1}{2}$. And these are separate properties. However we'd both use the same $\psi$ when we haven't observed it yet.

It would make for a strange world.

 

[A. Neumaier]

It's not an interpretation I have much confidence in, in case that might affect my description.

More so it would be saying that there are ontic states $\mathcal{O}_{AB}$, which aren't wavefunctions, but since each observer doesn't know what their state for $A$ is like until they look at it, they use $\psi$ to manage their expectations.

So imagine you and I are in a laboratory, you could have a particle with DarMM-spin $\frac{1}{2}$ and Neumaier-spin $-\frac{1}{2}$. And these are separate properties. However we'd both use the same $\psi$ when we haven't observed it yet.

It would make for a strange world.

It would also make QM very incomplete, as the universe now consists of objects, observers (a vaguely defined class of objects) and is described by QM states $\psi$ and, in addition, mostly unknown (unless watched) ontic states $\mathcal{O}_{AB}$, with very little connection between these. Not a good start for doing physics...

 

[DarMM]

In it any object can be an observer. So there is Neumaier-spin, but also X-spin, where X can be a helium atom in the air or a photon.

So just remove the observers part and the rest of what you say is true, especially the enormous set of mostly unknown ontic states.

 

[A. Neumaier]

In it any object can be an observer. So there is Neumaier-spin, but also X-spin, where X can be a helium atom in the air or a photon.

So just remove the observers part and the rest of what you say is true, especially the enormous set of mostly unknown ontic states.

In particular, all ontic states $\mathcal{O}_{AX}$ would remain for ever unknowable and irrelevant, since a helium atom in the air or a photon cannot look at $A$. Very heavy overparameterization, an ideal opportunity for applying Ockham's razor.

 

[vanhees71]

I already told you the contradiction.

1. On the one hand, the minimal interpretation claims that a measurement of an observable produces a result that is one of the eigenvalues of that observable.
2. On the other hand, if the system being measured is in a superposition of eigenstates, and we treat the measuring device quantum-mechanically, then the device itself ends up in a superposition of different results.

That's a contradiction. According to 1, the device will end up in one of a number of possible macroscopic states, with probability given by the Born rule. According to 2, the device will definitely end up in a superposition state that is none of those possibilities.

I agree with 1, but not with 2. If this were so, then you'd simple have a bad measurement device. A measurement device gives a unique result, when measuring an observable (within its accuracy of course).

 

[A. Neumaier]

A measurement device gives a unique result, when measuring an observable (within its accuracy of course).

But @stevendaryl claims that this contradicts the linearity of the Schrödinger equation when applied to system+device and the three system states up, down, and superposed.

 

[DarMM]

In particular, all ontic states $\mathcal{O}_{AX}$ would remain for ever unknowable and irrelevant, since a helium atom in the air or a photon cannot look at $A$. Very heavy overparameterization, an ideal opportunity for applying Ockham's razor.

It would say it could "look" at it in terms of scattering or interacting. So for one photon it will encounter the electron with one spin, another photon will meet another value for spin. Similar for momenta, etc. Every other particle will encounter its own private set of classical values for quantities when it interacts with the electron.

 

[vanhees71]

Indeed, I think Peres's book is among the best if it comes to interpretation (perhaps only Weinberg's chapter on the issue is better than that).

My lecture notes are about theoretical and not mathematical physics. I'm not knowledgeable enough to teach mathematical physics. Usually, however, I think mathematical physics doesn't deal much with these interpretational issues, because these are about the physics and not the mathematics of theories.

The equation for the measurement device's macroscopic pointer readings alone is not according to linear quantum-time evolution, as is the case for any open system. A measurement device necessarily has some dissipation to lead to an irreversible storage of the measured result.

In our Stern-Gerlach example this device is the screen, where you fix the Ag atoms after running through the magnet to be able to carefully and classically measure their positions.

 

[A. Neumaier]

The equation for the measurement device's macroscopic pointer readings alone is not according to linear quantum-time evolution, as is the case for any open system. A measurement device necessarily has some dissipation to lead to an irreversible storage of the measured result.

Ah, so you change the fundamental law of quantum mechanics and say that it applies never. For the only truly closed system we have access to is the whole universe, and you mentioned repeatedly that to apply quantum mechanics to it is nonsense.

So where does the dissipative description of the measurement device that you invoke come from, from a fundamental perspective?

 

[stevendaryl]

I agree with 1, but not with 2. If this were so, then you'd simple have a bad measurement device. A measurement device gives a unique result, when measuring an observable (within its accuracy of course).

Well, that contradicts the linearity of quantum evolution, it seems to me.

 

[stevendaryl]

The equation for the measurement device's macroscopic pointer readings alone is not according to linear quantum-time evolution, as is the case for any open system. A measurement device necessarily has some dissipation to lead to an irreversible storage of the measured result.

There can't be something magical happening in open systems. The point of an open system is that you have the system of interest interacting with another system whose details we either do not know completely, or choose to abstract away from.

What you're doing by saying "Oh, we don't have to obey linear evolution because it's an open system" is that your pushing the contradiction out into the part of the composite system that you're ignoring (the environment). That's bogus.

 

[DarMM]

I agree with 1, but not with 2. If this were so, then you'd simple have a bad measurement device. A measurement device gives a unique result, when measuring an observable (within its accuracy of course).

Well if you model the atomic object, the device and the lab environment, then the total system as modeled by an external observer outside the lab will be a superposition. That's a fact.

So either you're saying that QM cuts off at some scale, or you're just saying the device subsystem enters a specific (but unknown for the outside observer) state. You can't say the whole lab state evolves into a single eigenstate.

 

[kith]

The only slighly mysterious thing is why Alice can predict Bob's measurement. Here I don't have a full explanation, but only arguments that show that nothing goes wrong with relativistic causality.

Like others, I don't think that this is only "slightly mysterious" but the central mystery. But I agree with you that some tangible calculations are missing.

My recollection of studying the dynamics of open quantum systems a while back is the following: The Lindblad equation, which encompasses transitions from pure system states to mixed system states, can be derived from unitary dynamics of the system together with the environment in general as well as in specific settings, if one makes certain assumptions (mainly the Born-Markov approximation). What I didn't find in the literature back then, was a model of an entangled system consisting of two subsystems with only one of them interacting with an environment. Depending on the level of detail, seeing decoherence in such an entangled system arise dynamically from a local interaction between a single subsystem and an environment might shed some light on the machinery of non-local correlations.

 

[N88]

The only slighly mysterious thing is why Alice can predict Bob's measurement. Here I don't have a full explanation, but only arguments that show that nothing goes wrong with relativistic causality.

Note also that the prediction comes out correct only when the entangled state is undisturbed and the detector is not switched off at the time the photon hits - things that Alice cannot check until having compared notes with Bob. Thus her prediction is not a certainty but a conditional prediction only.

Like others, I don't think that this is only "slightly mysterious" but the central mystery. But I agree with you that some tangible calculations are missing.

A question: Why is there anything mysterious when Alice can predict Bob's measurement with certainty?

Under idealised EPRB and relativistic-causality there are no tricks, so the mechanics appear to be straight-forward: Let Alice observe the result A = +1, and let her predict that Bob will observe B = -1. Then, via Bell (1964; eqns (1) & (13)), we have the following mechanics:

$$A = +1 = A(a,\lambda). \;\;B= B(a,\lambda)= -A(a,\lambda) = -1.$$
QED? For a theory that disagrees or that sees mystery here would, it seems to me, be suspicious.

 

[kith]

Then, via Bell (1964; eqns (1) & (13)), we have the following mechanics:

$$A = +1 = A(a,\lambda). \;\;B= B(a,\lambda)= -A(a,\lambda) = -1.$$

That's not the mechanics, that's the thing which needs to be explained. It's like balancing energies: you know that you have the correct result (actually, I haven't checked, if what you write is correct) because your initial and your final value are in agreement with experiment but you don't know how the system gets from the initial to the final state.

In order to understand, I want to know how the fundamental entities of the theory evolve in time. In classical mechanics, Newton's laws accomplish this and in QM, the Schrödinger equation should do it. But alas, a) we have the measurement problem and b) I can't picture how dynamical decoherence works in entangled systems, so I'm not satisfied.

Of course, there's the possibility, that these problems can't be solved and that this is the lesson, QM is trying to teach us. But then, the answer is still not "we know the mechanics" but "the mechanics can't be known".

 

[stevendaryl]

A question: Why is there anything mysterious when Alice can predict Bob's measurement with certainty?

Well, let's assume that Bob and Alice agreed ahead of time to measure spin along the z-axis. For definiteness, let's assume that in Alice's rest frame, she measures her particle's spin before Bob measures his. Then let's consider the statement "Bob will measure spin-down".

1. Immediately before Alice's measurement, she doesn't know what value Bob will get. So she doesn't know whether the statement is true or false.
2. Immediately afterward, when she gets spin-up, she knows that Bob will get spin-down. So she knows the statement is true.

Between 1 & 2, what happened? Did the truth value of the statement change because of her measurement? Or did she just learn its truth value? In other words, did the statement become true when Alice performed her measurement, or was it true beforehand, and Alice just didn't know it?

The first possibility, that it only became true when Alice performed her measurement, would seem to suggest that Alice's actions affected Bob's situation. That is, it suggests action-at-a-distance. The second possibility, that it was true before her measurement, and her measurement just informed her of this fact, seems to suggest a hidden-variable (the value of a variable before it's measured). But Bell's theorem shows that there can't be a hidden-variables explanation of the EPR experiment without nonlocality (or superdeterminism, there is that loophole in the argument).

 

[DarMM]

Of course, there's the possibility, that these problems can't be solved and that this is the lesson, QM is trying to teach us. But then, the answer is still not "we know the mechanics" but "the mechanics can't be known".

That's essentially the view of all Copenhagen flavors (Bohr, Heisenberg, Haag, Bub, Healey, Peres, Brukner, Zeilinger, Wheeler), Consistent Histories (Gell-Mann, Griffiths, Omnès) and QBism (Fuchs, Schack)

QM is a break from the previous representational theories of physics, it doesn't fundamentally tell you what is going on.

 

[stevendaryl]

In order to understand, I want to know how the fundamental entities of the theory evolve in time.

Right. Some people, though, would say that physics isn't about how the world evolves with time, but how our knowledge of the world evolves. I don't agree with that. "Knowledge" doesn't mean anything (to me) if there is isn't a truth that you can know. And making observations and measurements into the basic entities of physics seems perverse to me. Observations and measurements are physical acts performed by physical systems (if very complicated ones). It doesn't make sense to me to make them fundamental.

 

[DarMM]

Right. Some people, though, would say that physics isn't about how the world evolves with time, but how our knowledge of the world evolves. I don't agree with that. "Knowledge" doesn't mean anything (to me) if there is isn't a truth that you can know. And making observations and measurements into the basic entities of physics seems perverse to me. Observations and measurements are physical acts performed by physical systems (if very complicated ones). It doesn't make sense to me to make them fundamental.

The common explanation of this in the views I described above is that although Observations and Measurements aren't actually fundamental physically (i.e. out in the world) that QM represents a point where you can't do any better than a generalized probability theory and by being a probability theory it just has observations as a primitive notion in the theory (though not assumed to be so in reality).

In the QBism papers and the works of Gell-Mann, Griffiths and Omnès you can read that they think that "under" QM nature becomes non-mathematical or not fully susceptible to mathematization.