The thermal interpretation of quantum physics

[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. Schrödinger 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?