# The minimal statistical interpretation is neither minimal nor statistical

• A
• Demystifier
In summary, the Ballentine interpretation is neither minimal nor statistical because it insists that there is no wave function collapse, or state reduction.
vanhees71 said:
Why can one not have unitary evolution alone? If that were the case we'd need another dynamical law complementing it. I don't know of any such law nor of any necessity for it.

Standard textbooks don't have unitary evolution alone. So you do know of such a law.

The mistake you make is that you think the partial trace gives you what you need, but it doesn't. You still need the state preparation conditioned on the measurement outcome - which is also called state reduction. The state preparation conditioned on the measurement outcome cannot be derived from unitary evolution and the Born rule.

mattt
vanhees71 said:
Of course the QT state evolution is a deterministic law. That doesn't imply that the theory is deterministic.
I agree with both statements. But from them I infer 3 conclusions:

1. If the theory is not deterministic, while the evolution of the state is deterministic, then there is something in theory that is not uniquely defined by the state evolution. We don't know what this something is, but since it must exist (otherwise we have a logical inconsistency) let us give it the name ##\lambda##.

2. The only role of the Hamiltonian in the theory is to govern the state evolution. This state evolution is local because the Hamiltonian is local. But since ##\lambda## is not uniquely defined by the state evolution, it follows that the evolution of ##\lambda## is not uniquely determined by the Hamiltonian. So the fact that the Hamiltonian is local does not imply that the evolution of ##\lambda## must also be local. In other words, non-locality of ##\lambda## is not incompatible with the quantum theory.

3. Just by 2. we cannot decide whether the evolution of ##\lambda## is local or nonlocal, both options are open. But if some additional properties of ##\lambda## are assumed (determinism is not one of those assumptions), then Bell theorem proves that the evolution of ##\lambda## (deterministic or not) must be non-local.

PeterDonis and mattt
atyy said:
Standard textbooks don't have unitary evolution alone. So you do know of such a law.

The mistake you make is that you think the partial trace gives you what you need, but it doesn't. You still need the state preparation conditioned on the measurement outcome - which is also called state reduction. The state preparation conditioned on the measurement outcome cannot be derived from unitary evolution and the Born rule.
But the state preparation is in such a case through the interaction with the measurement device and maybe some other device dependent on the measurement result (like putting a blocking piece of matter in one partial beam of a Stern-Gerlach experiment) and these interactions follow the same dynamics as anything else. There's no other physical laws only because a physicist uses a piece of matter as measurement or preparation device for a quantum experiment.

The "collapse rule" in the textbooks is just a rule that works FAPP but it's not a description of what's really going on, namely the usual quantum-mechanical dynamics.

Demystifier said:
I agree with both statements. But from them I infer 3 conclusions:

1. If the theory is not deterministic, while the evolution of the state is deterministic, then there is something in theory that is not uniquely defined by the state evolution. We don't know what this something is, but since it must exist (otherwise we have a logical inconsistency) let us give it the name ##\lambda##.

2. The only role of the Hamiltonian in the theory is to govern the state evolution. This state evolution is local because the Hamiltonian is local. But since ##\lambda## is not uniquely defined by the state evolution, it follows that the evolution of ##\lambda## is not uniquely determined by the Hamiltonian. So the fact that the Hamiltonian is local does not imply that the evolution of ##\lambda## must also be local. In other words, non-locality of ##\lambda## is not incompatible with the quantum theory.

3. Just by 2. we cannot decide whether the evolution of ##\lambda## is local or nonlocal, both options are open. But if some additional properties of ##\lambda## are assumed (determinism is not one of those assumptions), then Bell theorem proves that the evolution of ##\lambda## (deterministic or not) must be non-local.

ad 1. The point is that the meaning of "state" in QT is a drastically different one than in classical physics. In classical physics the complete knowledge of the state implies that all observables take definite values, i.e., the values of the observables is determined at any time and also their time evolution. That's not the case in QT. There the complete knowledge of the state implies only that we have prepared the system in one possible pure state, but that doesn't determine the values of the observables but only the probabilities for the outcome of measurements for each possible observable.

Whether or not this is a "complete" description of not depends on, whether the values of observables are in fact determined in nature (as Einstein, Schrödinger et al believed and thus considered QT incomplete) or whether there is objective randomness in Nature. Since nobody has found any "hidden variables" so far, explaining the randomness described by the probabilistic meaning of the quantum state as being just by ignorance of the observer as in classical statistical physics, I consider the status of QT complete at the moment. If something like HV are discovered, of course, we have to adapt our theories to something deterministic. Then QT would be found incomplete.

ad 2+3. I still do not know, what this enigmatic ##\lambda## really is. Is there a mathematical description of it or is it some vague philosophical construct?

vanhees71 said:
But the state preparation is in such a case through the interaction with the measurement device and maybe some other device dependent on the measurement result (like putting a blocking piece of matter in one partial beam of a Stern-Gerlach experiment) and these interactions follow the same dynamics as anything else. There's no other physical laws only because a physicist uses a piece of matter as measurement or preparation device for a quantum experiment.

If you work this out, you will find it is not possible. This is because in a selective measurement, subensembles are assigned conditional quantum states. If you only have unitary evolution, there are no subensembles defined (and of course the non-existent subensembles are not assigned any conditional quantum states).

vanhees71 said:
The "collapse rule" in the textbooks is just a rule that works FAPP but it's not a description of what's really going on, namely the usual quantum-mechanical dynamics.

From the textbook point of view, the quantum state and the observables are all FAPP. Only measurement outcomes and their probabilities are real.

vanhees71 said:
ad 2+3. I still do not know, what this enigmatic ##\lambda## really is. Is there a mathematical description of it or is it some vague philosophical construct?
It is like asking what is the enigmatic notion of group in abstract algebra. Is there a mathematical description of it or is it some vague philosophical construct?

Even if you don't specify what group are you talking about (e.g. group of real numbers or group SO(3)), you can formulate general mathematical axioms of group theory and prove some general theorems. The same is with ##\lambda##. Furthermore, you can find concrete examples of a group (e.g. SO(3) is such an example), and similarly you can find concrete examples of ##\lambda## (e.g. Bohmian particle positions).

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vanhees71 said:
The "collapse rule" in the textbooks is just a rule that works FAPP but it's not a description of what's really going on, namely the usual quantum-mechanical dynamics.
What do you mean by "really going on"? Do you mean ontologically happening even when it is not measured? I thought your opinion was that it's philosophy, not physics.

But I'm glad that you finally admit that collapse rule works FAPP.

vanhees71 said:
The "collapse rule" in the textbooks is just a rule that works FAPP but it's not a description of what's really going on, namely the usual quantum-mechanical dynamics.
From the inside view, I see it the opposite way :)

From the "agents/observers" perspective the "information update" is excatly what IS going on.

In between the measurements, the systems is closed and a black box, we don't know what is going on then.
The unitary evolution, I see as an EXPECTATION only of what is "possibly going in" - in between the events.

(The only specualtive quest is: how can the inside agent, infer, store and react upon its understanding of the environment? This is where QM comes in, the hamiltoninan etc. All this is put in by hand. I exepct a revised theory to have this emerge in the agents inference process.)

/Fredrik

Demystifier and atyy
Demystifier said:
It is like asking what is the enigmatic notion of group in abstract algebra. Is there a mathematical description of it or is it some vague philosophical construct?

Even if you don't specify what group are you talking about (e.g. group of real numbers or group SO(3)), you can formulate general mathematical axioms of group theory and prove some general theorems. The same is with ##\lambda##. Furthermore, you can find concrete examples of a group (e.g. SO(3) is such an example), and similarly you can find concrete examples of ##\lambda## (e.g. Bohmian particle positions).
But what kind of a mathematical thing is ##\lambda##? Is it a group, a function, a triangle, ...? There is a difference between saying "a group" and I don't know what that is so it is my problem, and saying "lambda" and you make no effort to clarify. Giving a name is not the same as showing existence.
1. If the theory is not deterministic, while the evolution of the state is deterministic, then there is something in theory that is not uniquely defined by the state evolution. We don't know what this something is, but since it must exist (otherwise we have a logical inconsistency) let us give it the name ##\lambda##.
What is the logical inconsistency?

atyy said:
From the textbook point of view, the quantum state and the observables are all FAPP. Only measurement outcomes and their probabilities are real.
Why then don't you simply accept this and insist on some spooky mechanism called collapse, which is not necessary and contradicting the very foundation of the theory (at least for local relativistic QFTs)?

Demystifier said:
What do you mean by "really going on"? Do you mean ontologically happening even when it is not measured? I thought your opinion was that it's philosophy, not physics.

But I'm glad that you finally admit that collapse rule works FAPP.
I don't care for "ologies". The collapse rule works FAPP when it works (depending on how you prepare your state) but it's not telling you what's going on within the theory. The theory is clearly formulated in terms of the math describing the dynamics of what's observable, namely the probabilities for the outcome of measurements.

AlexCaledin
Fra said:
From the inside view, I see it the opposite way :)

From the "agents/observers" perspective the "information update" is excatly what IS going on.

In between the measurements, the systems is closed and a black box, we don't know what is going on then.
The unitary evolution, I see as an EXPECTATION only of what is "possibly going in" - in between the events.

(The only specualtive quest is: how can the inside agent, infer, store and react upon its understanding of the environment? This is where QM comes in, the hamiltoninan etc. All this is put in by hand. I exepct a revised theory to have this emerge in the agents inference process.)

/Fredrik
If you interpret what the collapse proponents call "collapse" just as the "information update" of an observer, there's no problem, because this doesn't claim that there is some undefined dynamics going on besides the quantum dynamical description. I'd even claim that this is just the minimal interpretation using different words. It's a tautology: If I've measured an observable and look at the pointer reading of the measurement device I know the value. Whether or not then the system is prepared in the corresponding state, is of course not necessarily clear but has to be analyzed by looking at the specific setup of the experiment.

I don't know, what you mean with your last sentence in parenthesis. I don't see any necessity for some theory beyond QT. This is all explained by standard quantum theory of open systems, decoherence, and all that, including the explanation for the "emergence of a classical world" (concerning macroscopic systems).

Demystifier said:
It is like asking what is the enigmatic notion of group in abstract algebra. Is there a mathematical description of it or is it some vague philosophical construct?

Even if you don't specify what group are you talking about (e.g. group of real numbers or group SO(3)), you can formulate general mathematical axioms of group theory and prove some general theorems. The same is with ##\lambda##. Furthermore, you can find concrete examples of a group (e.g. SO(3) is such an example), and similarly you can find concrete examples of ##\lambda## (e.g. Bohmian particle positions).
Group theory is of course a clear mathematical not a vague philosophical construct. This doesn't answer my question, what ##\lambda## is. Bohmian mechanics (concerning non-relativistic single-particle QT) doesn't make any other predictions than standard QT. The Bohmian trajectories are not observable. At least I don't have seen any measurement of the "Bohmian streamlines" behind a double slit for single electrons.

vanhees71 said:
Why then don't you simply accept this and insist on some spooky mechanism called collapse, which is not necessary and contradicting the very foundation of the theory (at least for local relativistic QFTs)?

That is my preferred interpretation. I have used the term "state reduction" to be clear, since you insist "collapse" is physical.

You are the one who is always bringing collapse as a spooky mechanism. For most of us, even the term "collapse" is simply a tool for calculation, since to us the quantum state is not necessarily real.

You also use wrong reasons for rejecting collapse, which is why we have such long discussions. Your two major errors are
1) Insisting on unitary evolution alone (without state reduction or hidden variables or many worlds)
2) Insisting that a physical collapse contradicts the locality of relativistic QFT

And you also misunderstand the FAPP nature of the Heisenberg cut, so you wrongly reject it.

I always thought "state reduction" and "collapse" are just synonyms, but I don't think that this discussion is very fruitful, and I'd like to stop it here. We'll never reach an agreement, because it's about opinions not science, and I think concerning the science it's not very important anyway, because all physicists get the same results concerning the physics from quantum mechanics, be their interpretations of the formalism different or not ;-)).

In the formalism there's no collapse, no state reduction and no Heisenberg cut but a consistent formalism describing the dynamics of the observable quantities.

atyy
vanhees71 said:
This doesn't answer my question, what ##\lambda## is.
It's an abstract mathematical object satisfying axioms need to prove a Bell-like theorem. This also answers a question by @martinbn.

mattt
vanhees71 said:
In the formalism there's no collapse
In most QM textbook there is.

vanhees71 said:
The Bohmian trajectories are not observable. At least I don't have seen any measurement of the "Bohmian streamlines" behind a double slit for single electrons.
The same can be said for the wave function.

martinbn said:
What is the logical inconsistency?
Read again the text you quoted. The first sentence shows that it must exist, while the second one considers the possibility that it doesn't exist. That's logical inconsistency, or more precisely a contradiction.

Just found this 50 year old H. Stapp paper. Stapp had read so many contradictory accounts of the Copenhagen interpretation that he became compelled to delineate it precisely.
- it's based on his correspondence with Heisenberg.

atyy and mattt
Could you give the source. Already the first paragraph of the above picture says it all! I guess the author had to clarify his mind after correspondence with Heisenberg, leading to such a clear and no-nonsense statement. SCNR.

AlexCaledin

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AlexCaledin said:
- sorry - forgot to attach it! It's also in Mind, Matter and Quantum Mechanics
Already the abstract of the forwarded pdf makes no sense. Quantum theory does NOT say that its completeness were incompatible with the objective existence of classical spacetime. To the contrary the standard quantum theory builds on classical spacetime descriptions (Newtonian or special relativistic, depending on whether you do non-relativistic quantum mechanics or relativistic quantum (field) theory). The Rules of Quantum Mechanics, defined by the realization of the observable algebras are based on the spacetime structure as defined by classical physics. E.g., the commutation relations between the position and momentum operators and thus the entire construction of non-relativistic quantum theory, formulated in one of its standard representations like Schrödinger wave mechanics, follows from the Galilei symmetry of Newton-Galilei spacetime. The same holds for relativistic QFT and the Standard Model of elementary particle physics, which looks as it looks because of the Poincare symmetry of Minkowski spacetime.

The main difficulty to also quantize the gravitational interaction, as far as I understand it, seems to be the more complicated spacetime model of GR (or its extension to Einstein-Cartan theory which one needs already to formulate QFT for particles with spin in a given classical spacetime-manifold, i.e., without quantizing also the gravitational interaction). In GR the spacetime itself becomes part of the dynamics (that's why Wheeler dubbed the nice name "geometrodynamics" for it) and thus in a complete QT of gravitation spacetime itself must in some way be quantized.

- but the actual variant of spacetime, as well as everything we observe, is the outcome of the quantum dice throwing, right? That's why the pragmatic theory is working.

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vanhees71
All we can say is that what we observe is consistent with our theoretical models, with a "classical" spacetime model and quantum theory for matter and all interactions except gravity. Quantum theory works well within and is based on the classical spacetime models, in not too complicated spacetimes of GR even in that case. What we don't know is how to quantize the gravitational interaction and thus, because in GR the gravitational interaction is reinterpreted as a dynamical spacetime geometry, spacetime itself. From the experimental point of view, it's of course also difficult to find hints for how to build a quantum theory of gravitation, because so far all observations where gravity plays a significant role are involving macroscopic (usually even astronomical) objects, which are well-described within classical (continuum) mechanics, and there are not quantum effects of the gravitational interaction seen. What's known to work right is the quantum theory of particles in the gravitational field of macroscopic objects (like the experiment with cold neutrons in the gravitational field on Earth, for which the energy-eigenvalue problem is a standard exercise in the QM 1 lecture).

bhobba and AlexCaledin
vanhees71 said:
What we don't know is how to quantize the ... spacetime itself.
Perhaps it's quite enough to know that a sort of Branching Spacetime interpretation is quite possible? or Hartle's Spacetime Alternatives? - anyway, the actual coarse grained reality is somehow chosen - with the spacetime - and it seems not very scientific to speculate how exactly the choice occurs - it makes the QM working, that's all...

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I would describe it as typical Einstein, who, of course, Ballentine got it from. Einstein was not the only one to believe in it, nor its originator. Einstein was what I call an opportunistic realist. He believed in realism but was agnostic to the various nuanced versions. He picked the version that suited his purposes the best. It may not really be statistical or minimal, but that was of no worry to him. It is those that followed in his footsteps that debate such concerns. For example, is probability real? The wave function can be looked at as a tool to calculate probabilities, so it is just as real or not real as probabilities. If not real, how can it collapse? We can debate that one for ages, but one must ask - to what end? I would classify myself as a Model Dependant Realist (a version of realism advocated by Hawking):
https://en.wikipedia.org/wiki/Model-dependent_realism

I do not worry about its various versions - yes, with realism, we have various versions. Those versions also have various versions - no wonder philosophers make slow progress - some would say no progress at all. Feynman, from my reading, was even worse - he didn't care what philosophy he used to make progress, was openly contemptuous of it, and just tried various ideas whether it involved a particular philosophy or not.

Thanks
Bill

Demystifier
Morbert said:
I always thought the minimal interpretation was the "shut up and calculate" interpretation: If you set up an ensemble of identically prepared systems and specify a measurement procedure that generates data, QM will report the frequencies and correlations that will be present in the data.
I would describe a couple of interpretations as minimal, e.g. I also think the Bayesian interpretation is minimal. In fact, I prefer it to Copenhagen, which has always seemed to come in various versions.

I would call Ballentine's interpretation minimal in the sense he takes the most common probability interpretation (frequentist) and applies it to the wave function (or state) but goes no further.

Thanks
Bill

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