The minimal statistical interpretation is neither minimal nor statistical

[vanhees71]

But if you have only unitary evolution, you have no measurements, no measurement outcomes, and no physics?

Why? A measurement device shows values for the measured quantity. Quantum mechanically the system is entangled with the measurement device such that the "macroscopic pointer state" of the measurement device is in one-to-one correlation with the value of the measured observable. It's clear that the state of the measured system (provided it can be separated from the measurement device after the measurement at all, which is, e.g., usually not the case for a photon which is absorbed due to the measurement by a photodetector) is given by tracing out the measurement device. Due to the entanglement necessary to have a precise measurment of the measured observable this state is necessarily a proper mixed state. You can call this "collapse", but it's not the naive collapse given handwavingly in a few words in textbooks but one that is completely consistent with the local nature of interactions and the "unitary" quantum dynamics of the composite system.

 

[Fra]

Yes, but the wave function evolves only unitarily.

But only for closed proper systems.

Not sure what the pure bohmist take is on that, but does bohmians think of the hidden variables as closed or if they allow for secret storage of info?

/Fredrik

 

[vanhees71]

I think the Bohmians claim that particles move in the trajectories they calculate. The trouble I have with this ontic interpretation of the Bohmian trajectories is that they cannot be observed. At least I'm not aware of any experiment which unambigously demonstrates Bohmian trajectories (leaving out the problem with BM in the relativistic context; I think it's in principle a sound and solid framework for non-relativistic QM but that's not convincingly the case in application to relativistic QFT).

 

[atyy]

Why? A measurement device shows values for the measured quantity. Quantum mechanically the system is entangled with the measurement device such that the "macroscopic pointer state" of the measurement device is in one-to-one correlation with the value of the measured observable. It's clear that the state of the measured system (provided it can be separated from the measurement device after the measurement at all, which is, e.g., usually not the case for a photon which is absorbed due to the measurement by a photodetector) is given by tracing out the measurement device. Due to the entanglement necessary to have a precise measurment of the measured observable this state is necessarily a proper mixed state. You can call this "collapse", but it's not the naive collapse given handwavingly in a few words in textbooks but one that is completely consistent with the local nature of interactions and the "unitary" quantum dynamics of the composite system.

But in this formalism, sequential measurements are not possible. For a sequence of measurements, you substitute one simultaneous measurement of everything after all the measurement devices have interacted with the system being measured. If you never have sequential measurements, you don't need state reduction.

 

[Lord Jestocost]

All I'm saying is that there's no cut nor a collapse of the state. Measurement devices behave classically because at the level of precision I need to describe them it's sufficient to describe macroscopic coarse-grained observables (e.g., the pointer position of a galvanometer).

What are you actually trying to tell the forum readers? Whether you think that measurement devices behave classically is completely irrelevant. Do you seriously think that your "measurement devices“ (when entangled with the quantum entity which is measured on) break physically the linear nature of quantum theory (a superpostion cannot be replaced by the logical alternative 'either … or').
Maybe, you don’t really understand what the ‘macro-objectification problem’ means in the framework of quantum theory. I therefore deeply recommend to read Giancarlo Ghirardi’s entry “Collapse Theories“ on the “Stanford Encyclopedia of Philosophy”. https://plato.stanford.edu/entries/qm-collapse/

 

[vanhees71]

If I can isolate the measured system again after the measurement, I have a new state given by the partial trace. Why shouldn't I be able to describe another measurement when the measured system is known to be prepared in this state?

 

[atyy]

If I can isolate the measured system again after the measurement, I have a new state given by the partial trace. Why shouldn't I be able to describe another measurement when the measured system is known to be prepared in this state?

If you only have a unitarily evolving wave function, the only rule you have is the Born rule, which gives the probabilities of outcomes at one times. So let's say you measure observable A with possible outcomes {ai} at t1, and observable B with possoble outcomes {bi} at t2. You do not have any rule to give you the joint probability P(ai, bj). So you are not able to predict all the probabilities for sequential measurement.

Instead, what you must do in this formalism, to avoid sequential measurement is to have all the measuring devices interact in sequence, then separate out and maintain their pointer states. After the sequence of unitary interactions, you make a simultaneous measurement of all measuring devices. The probabilities will be the same as what you get with sequential measurement and state reduction, but here one does not acknowledge the reality of sequential measurement outcomes.

 

[vanhees71]

I don't have only unitary time evolution but also the partial tracing. The time evolution of the statistical operator for a part of a closed system (which by definition is an open system) is not unitary.

Of course, if you can the entire sequence exactly then you don't need anything else than unitary time evolution and Born's rule, but I don't know any macroscopic system, where this is feasible.

 

[Morbert]

If you only have a unitarily evolving wave function, the only rule you have is the Born rule, which gives the probabilities of outcomes at one times. So let's say you measure observable A with possible outcomes {ai} at t1, and observable B with possoble outcomes {bi} at t2. You do not have any rule to give you the joint probability P(ai, bj). So you are not able to predict all the probabilities for sequential measurement.

You could just extend the state space to include both times: $\mathcal{H} = \mathcal{H}_{t_1} \otimes \mathcal{H}_{t_2}$

We could then define suitable projector $\Pi_{a_i\land b_j} =\Pi_{b_j}^{t_2} \Pi_{a_i}^{t_1}$

Applying the Born rule then tells us the probability of the outcome $a_i \land b_j$ is given by $\mathrm{tr}(\Pi_{a_i\land b_j}\rho)$

 

[atyy]

I don't have only unitary time evolution but also the partial tracing. The time evolution of the statistical operator for a part of a closed system (which by definition is an open system) is not unitary.

But the partial trace will not allow you do derive P(ai,bj). The partial trace derives the state reduction for non-selective measurements (where the results of the first measurement are discarded), but it does not derive the state reduction for selective measurements, which is needed for P(ai,bj).

 

[vanhees71]

But those local interactions are deterministic, and yet quantum events are random. So if you believe in fundamental randomness (which you do), then consistency requires the existence of something which is not described by those local interactions. So if you cared about consistency (which you don't, because for you consistency is just an aspect of philosophy), you would conclude that it cannot be true that all is working with those local interactions.

QFT is not relativistic. So I don't understand your first sentence. What do you think does not work with local interactions? Do you have a falsification of local relativistic QFTs?

 

[Demystifier]

QFT is not relativistic. So I don't understand your first sentence. What do you think does not work with local interactions? Do you have a falsification of local relativistic QFTs?

I'm afraid I don't understand your first sentence.

Anyway, interactions are deterministic because if you know the state at one time, then Hamiltonian evolution determines the state at any other time.

 

[vanhees71]

Argh. I meant of course "QFT is not deterministic".

Of course the QT state evolution is a deterministic law. That doesn't imply that the theory is deterministic. This is really what we are discussing about the whole time.

 

[atyy]

You could just extend the state space to include both times: $\mathcal{H} = \mathcal{H}_{t_1} \otimes \mathcal{H}_{t_2}$

We could then define suitable projector $\Pi_{a_i\land b_j} =\Pi_{b_j}^{t_2} \Pi_{a_i}^{t_1}$

Applying the Born rule then tells us the probability of the outcome $a_i \land b_j$ is given by $\mathrm{tr}(\Pi_{a_i\land b_j}\rho)$

Yes, but when we write this in the Schroedinger picture, we will find non-unitary evolution. The point is that state reduction is part of the standard operational view of QM, and one cannot have unitary evolution alone (without many worlds or Bohmian mechanics).

 

[vanhees71]

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.

 

[atyy]

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.

 

[Demystifier]

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.

 

[vanhees71]

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.

 

[vanhees71]

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?

 

[atyy]

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).

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.

 

[Demystifier]

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).

 

[Demystifier]

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.

 

[Fra]

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

 

[martinbn]

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?

 

[vanhees71]

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)?

 

[vanhees71]

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.

 

[vanhees71]

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).

 

[vanhees71]

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.

 

[atyy]

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.

 

[vanhees71]

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.