What does it take to solve the measurement problem? (new paper published)

[bhobba]

The experts in the field don't agree with you. Have you read Schlosshauer's book on decoherence?

Excellent book. He does delve deeply into the issue.

Thanks
Bill

 

[Fra]

There is no such thing as the measurement problem. This is the creation of some very dated and wrong ideas, picked up by science writers to create some drama in their profession.

In fact observer A can take a measurement of a particle and the particle wave function would not "collapse"!

Imagine we have two observers A and B. A is coherent w.r.t. the environment E and the observer B, and observer B is embedded in E (entangled with E).

A particle arrives in a superposition of states for both A and B. A measures the particle and it "collapses" (an unfortunate word) for A. But the particle has NOT collapsed for B.

The state of the particle depends on who is asking or measuring. There is no such thing as an absolute wave function. A wave function is always between two (or more) parties. Just like velocity. You can't have V(a) the absolute velocity of object a. You can only have V(a, b).

This is the Relational Interpretation of Carlo Rovelli (1994).

One of Rovelli's sound points is that there are no absolute observations, he even goes on to acqknowledge that there are no absolute relations between observations, it should take a third observer to assess it. But onfortunately at some point he claims that communication between observers follows the rules of QM. So he ends up explaining nothing IMO. I think the reasons is that while he at the same time wants to make a nice interpretation, he does not wish to CHANGE the theory, so his solution is conservative. And I think that is a mistake.

Even if the collapse is relative, and I agree there, that is not the real problem. The problem is to consider what happens if one if observers is participating in the interaction, and is makde both a quantum system from the perspective of one observer, and at the same time connecting to the firm classical background (where the commuting information is encoded) relative to another observer. This creates strange things, that requires that we need to EXPLAIN the hamiltonian in terms of infromation updates, and vice versa. This is for me the heart of the measurement problem, that is not yet solved, and i think it's rooted deeply. Decoherence solves nothing of this.

/Fredrik

 

[PeterDonis]

One of Rovelli's sound points is that there are no absolute observations

I'm not sure this is a sound point. Taken as it is stated, it denies the possibility of irreversible observer-independent experimental results, and without those, we have nothing on which to build a theory.

Another way of putting this point is that, when we start considering scenarios in which observers are supposed to be modeled using QM, we have a serious problem: any such QM model will have to include the possibility of reversing any observation (because time evolution in QM is unitary and any unitary operation can be reversed). But that amounts to allowing the possibility of reversing decoherence, and again, once you allow that, you have no irreversible observer-independent experimental results, and thus nothing on which to build a theory.

In short, it seems to me that this kind of "relational" viewpoint undermines the possibility of doing physics at all.

 

[bhobba]

It fits in nicely with the QFT view of things IMHO, as it should.

Rodney Brooks wrote an article describing this in more detail. I dont always agree with Rodney - eg his idea physicists have ignored QFT or even Schwingers great contributions (I really like Schwingers EM textbook personally) were ignored - they certainly were not. Be that as it may he does make a resonable effort describing what I was getting at::
https://www.quantum-field-theory.net/quantum-field-theory-a-solution-to-the-measurement-problem/

Problems still remain, but objects not having properties until measured is understood better. Everything is a field. Properties emerge when fields interact, otherwise they are a field of operators.

Thanks
Bill

 

[Fra]

I'm not sure this is a sound point. Taken as it is stated, it denies the possibility of irreversible observer-independent experimental results, and without those, we have nothing on which to build a theory.

Another way of putting this point is that, when we start considering scenarios in which observers are supposed to be modeled using QM, we have a serious problem: any such QM model will have to include the possibility of reversing any observation (because time evolution in QM is unitary and any unitary operation can be reversed). But that amounts to allowing the possibility of reversing decoherence, and again, once you allow that, you have no irreversible observer-independent experimental results, and thus nothing on which to build a theory.

In short, it seems to me that this kind of "relational" viewpoint undermines the possibility of doing physics at all.

I get why it can seem this way. And it certainly complicates things. But the same can be said qbout science. How can we do science if we are never sure about anything? Here the answer is corroboration.

Conceptually in anyalogy in the relational view, "corroboration" in the lack of perfect objectivity is replaced by negotiation among fellow observers. A middle path is formed from negotiating everbodies collective observations. And the most extreme outliers are destabilized. (Analogous to falsified). Meaning beeing so fatally wrong that it cant be adjusted by revising the state. The whole statespace needs to change.

/Fredrik

 

[PeterDonis]

How can we do science if we are never sure about anything?

We don't have to be "sure" to make predictions and decide whether or not to act on them. You can do that based on probabilities--how likely is it that this number we just calculated from our scientific theory is correct? And it doesn't have to be exactly correct; it just has to be close enough for whatever purpose we are using it for.

Here the answer is corroboration.

Of course this helps in collecting data on how accurate a scientific theory's predictions are; it's a lot easier to get a large amount of data to work with if you have multiple people doing it.

However, I'm not sure I would describe this as "negotiation".

 

[Fra]

However, I'm not sure I would describe this as "negotiation".

Fair enough. That choice is word isnt meant to play down science and suggets it's just politics. I meant it a also deeper way where reality is emerget.

But I agree this is concetpually strange and strips even more away from "realism" that already is done, and its not without problems. It's not a route for those, that already have problems with the lack of realism in standard QM. This is making all this worse - but with other pros IMO.

(It's related to what I labelled "observer democracy", as opposed to "observer equivalence". In theory building, the things that in the latter view as used as a constraint, are supposedly emergent in the former view)

/Fredrik

 

[physika]

isn't Hossenfelder on the verge of crackpot soon?

The main sources which are to be discussed in this thread is an arxiv manuscript and a blogpost. I thought only peer-review published work were allowed on this forum? I am just trying to understand

https://iopscience.iop.org/article/10.1088/2399-6528/ac96cf#jpcoac96cfs5-4

 

[Morbert]

Just to re-emphasise an issue I have. From the paper:

It is sometimes questioned whether the Collapse Postulate is actually necessary (e.g. in [6]). Without it, quantum mechanics would still correctly predict average values for large numbers of repetitions of the same experiment. This is the statistical interpretation suggested by Ballentine [7].

However, we do not merely observe averages of many experiments: we also observe the outcomes of individual experiments. And we know from observations that the outcome of an experiment is never a superposition of detector eigenstates, nor is it ever a mixed state (whatever that would look like)—a detector either detects a particle or it doesn't, but not both. As Maudlin put it [2], 'it is a plain physical fact that some individual cats are alive and some dead' (emphasis original). Without the Collapse Postulate, the mathematical machinery of quantum mechanics just does not describe this aspect of physical reality correctly.

The bit in bold could be interpreted two ways:
i) Without the Collapse Postulate, the mathematical machinery of quantum mechanics does not describe this aspect of physical reality.

ii) Without the Collapse Postulate, the mathematical machinery of quantum mechanics incorrectly describes this aspect of physical reality.

The latter would mean the measurement problem really is a problem, in the sense that it is a point of incorrectness.

The former is a better reading of interpretations like those presented by Ballentine: QM is correct everywhere in its domain, and it is not a problem that QM returns probabilities for possibilities rather than a definite actuality.

 

[vanhees71]

Just to re-emphasise an issue I have. From the paper:The bit in bold could be interpreted two ways:
i) Without the Collapse Postulate, the mathematical machinery of quantum mechanics does not describe this aspect of physical reality.

There cannot be a generally valid collapse postulate, because it depends on your experimental setup, what happens to the measured object. E.g., if you detect a photon with a photo detector you use the photoelectric effect, i.e., the photon is absorbed by the detector and for sure not in an eigenstate of the measured quantity (e.g., the polarization in a given direction). Of course there are (approximations of) ideal von Neumann "filter measurements", e.g., using a polarization filter, which lets through only photons with linear polarization in a given direction. Then the projection postulate holds, and you have a kind of "collapse of the state".

ii) Without the Collapse Postulate, the mathematical machinery of quantum mechanics incorrectly describes this aspect of physical reality.

The latter would mean the measurement problem really is a problem, in the sense that it is a point of incorrectness.

The former is a better reading of interpretations like those presented by Ballentine: QM is correct everywhere in its domain, and it is not a problem that QM returns probabilities for possibilities rather than a definite actuality.

I don't know, what you mean here. There is no problem with filter measurements nor with other kinds of experiments. The "proof" is simple: QT works with great success whereever it is applied!

 

[A. Neumaier]

There cannot be a generally valid collapse postulate, because it depends on your experimental setup, what happens to the measured object.

There can be, and in fact there is:

The dependence of the collapse on the setup is correctly accounted for by the notion of a quantum instrument (or quantum operation, or quantum channel), which generalizes the Heisenberg collapse in the same way as the POVM concept generalizes the Born rule.

The quantum instrument formalism is routinely taught in quantum information theory. For example, the well-known textbook

• M.A. Nielsen and I.L, Chuang, Quantum computation and quantum information: 10th Anniversary Edition, Cambridge Univ. Press, Cambridge 2011.

introduces them (in Section 2.2.3 on quantum measurement, without introducing a name for the concept) even before defining the traditional projective measurements.

I also discuss them in Section 6.6 of my paper

• Quantum tomography explains quantum mechanics.

 

[gentzen]

(in Section 2.2.3 on quantum measurement, without introducing a name for the concept)

See also section 8.2.4 (because it "explains something about the interpretational background" of that concept) ...

 

[Morbert]

There cannot be a generally valid collapse postulate, because it depends on your experimental setup, what happens to the measured object. E.g., if you detect a photon with a photo detector you use the photoelectric effect, i.e., the photon is absorbed by the detector and for sure not in an eigenstate of the measured quantity (e.g., the polarization in a given direction). Of course there are (approximations of) ideal von Neumann "filter measurements", e.g., using a polarization filter, which lets through only photons with linear polarization in a given direction. Then the projection postulate holds, and you have a kind of "collapse of the state".

Adding to the point made by A. Neumaier above, we can also recover a collapse postulate if we generalise our description of the experiment to possible histories $\{C_\alpha\}$ of the joint system (measured system + instrument). Collapse is the change $\rho \rightarrow \frac{C_\alpha \rho C^\dagger_\alpha}{\mathrm{tr}C_\alpha \rho C^\dagger_\alpha}$

https://arxiv.org/abs/gr-qc/9210010

I don't know, what you mean here. There is no problem with filter measurements nor with other kinds of experiments. The "proof" is simple: QT works with great success whereever it is applied!

What Hossenfelder is arguing (unsuccessfully imo) is that, without a collapse postulate, QM's inability to account for the realisation of one possibility over others is a point of incorrectness of the theory.

 

[vanhees71]

What is meant by "QM's inability to account for the realization of one possibility over others"? QT describes, in accordance with all observations, the probabilities for the outcome of any possible measurement, given the state of the system. Which outcome is realized in each individual measurement is inherently random. That's an observed elementary fact about how Nature behaves, and this inherent randomness in Nature was a big problem for physicists used to the classical, deterministic picture of classical physics, and the quest for finding some deterministic description of the random behavior was in vain until today. So far nobody could find any deterministic description of this random behavior. Of course, you cannot exclude the possibility that we simple haven't been clever enough to find such a description, but according to today's knowledge there's not the slightest hint that there exists one.

 

[Morbert]

Actually, to her credit, she clarifies in the very next sentence, the ambiguity I raised. I should have been more patient.

"This means quantum mechanics without the Collapse Postulate is not wrong, but it describes less of what we observe. The Collapse Postulate is hence useful, and part of the axioms because it increases the explanatory power of the theory. It cannot simply be discarded."

 

[vanhees71]

What is it that's observed, which needs a collapse to describe it? These pseudophilosophical texts are all too enigmatic to make sense.

 

[PeterDonis]

What is it that's observed, which needs a collapse to describe it?

The fact that we only observe single outcomes. For example, we observe Schrödinger's cat to be either alive or dead, but without the collapse postulate, unitary QM predicts that it ends up in a superposition of alive and dead.

 

[vanhees71]

What has this to do with the collapse? The collapse occurs when the measurement result is obtained, simply as a postulate, i.e., if the state before the measurement is $\hat{\rho}$ and you measure the observable $A$ with the outcome $a$ (an eigenvalue of the corresponding self-adjoint operator $\hat{A}$), and the eigenspace is spanned by the CONS $|a,\alpha \rangle$, then it's assumed that after the measurement the state has to be descibed by
$$\hat{\rho}'=\frac{1}{\mathrm{Tr} (\hat{P}_a \hat{\rho} \hat{P}_a)} \hat{P}_a \hat{\rho} \hat{P}_a) \quad \text{with} \quad \hat{P}_a =\sum_{\alpha} |a, \alpha \rangle \langle a,\alpha|.$$
This doesn't explain, why there is "a single outcome".

For me this holds true for very specific kinds of measurements, which can only quite rarely realized for very simple systems. One example are single photons run through a polarization filter. Then FAPP there is a collapse in the above described sense, i.e., if a specific photon goes through the filter it's in a linear-polarization state given by this projection, but in no way can this description explain, whether and why a given specific photon goes through the filter or not. All I can say, given the state before the photon hits the filter is the probability that it will go through.

For me all this refers to the fundamental postulates of the quantum formalism, which cannot be explained by simpler assumptions of some more comprehensive theory (yet). The fundamental postulates have been figured out by a lot of intertwined observation-model-building processes, and they cannot be mathematically proven or otherwise be inferred. It's as with Newtonian mechanics, where you also have Newton's postulates, which cannot be explained by anything but by the fact that they work (within their realm of applicability).

 

[PeterDonis]

What has this to do with the collapse?

You can't get single outcomes without it. With just unitary evolution you don't get single outcomes.

This doesn't explain, why there is "a single outcome".

Whether it "explains" it depends on what you consider to be an "explanation". But mathematically, the state after applying the collapse postulate describes a single outcome having happened. The state before applying the collapse postulate does not.

I suppose one could say all this is interpretation dependent, since on an ensemble interpretation states don't apply to individual runs of experiments anyway.

 

[vanhees71]

My question is simply, what has to be explaned?

For me the alleged interpretation of the collapse postulate doesn't make sense. It doesn't explain the single outcome but the preparation procedure by filtering, and whether this is realized in a specific experiment depends on the measurement procedure/manipulation of the object under investigation and cannot be stated as a generally valid postulate.

E.g., you can also prepare a linearly polarized photon by using a polarizing beam splitter (like a birefringent) crystal. This entangles the polarization (H or V wrt. the chosen orientation of the crystal) with the momentum of the photon. Also here you cannot predict, which momentum and thus polarization any given photon will take (except if it's prepared already as being H or V polarized before), and this is not described by a projection but by a unitary operator (for an ideal PBS).

 

[PeterDonis]

My question is simply, what has to be explaned?

That's going to depend on what you think needs to be explained.

It doesn't explain the single outcome but the preparation procedure by filtering

A measurement with a single outcome is a preparation procedure by filtering. If I pass a photon through a horizontal polarizer and it is transmitted (instead of absorbed), I can either say I've measured its polarization and the result (single outcome) is "horizontal", or I can say I've filtered it so that only horizontally polarized photons get through. It's the same thing either way.

And either way I need the collapse postulate to get to the final state where I just have a horizontally polarized photon in the output beam of the polarizer. If I just use unitary evolution, I get a superposition of "horizontally polarized photon in the output beam of the polarizer" and "vertically polarized photon absorbed by the polarizer".

 

[vanhees71]

No, it doesn't need to be a preparation procedure. E.g., a photon usually a photon is detected via the photoelectric effect and then is gone and not prepared in another state. Of course, when doing a filter measurement, it's described FAPP by the projection/collapse postulate. This is of course not described by a unitary evolution, since it's described within the "open-quantum-system formalism", i.e., you "trace out" the equipment the photon is interacting with to be measured and, maybe, prepared in a new state.

 

[PeterDonis]

Of course, when doing a filter measurement, it's described FAPP by the projection/collapse postulate.

This is also the case for a photon measured (and destroyed) by a detector. Otherwise you wouldn't be able to explain why just one detector fires in any experiment with multiple detectors (for example, a beam splitter with a detector in each output arm). Unitary evolution predicts a superposition of "detector A fires" and "detector B fires" for a case like that.

 

[vanhees71]

We always detect one photon only once (as also with massive particles). That's why Born introduced the probability interpretation of the quantum state in contradiction with Schrödinger's original interpretation as a classical-field description of particles. Born's rule, in my opinion, is also simply one of the other independent postulates of QT, and it has nothing to do with the collapse postulate.

 

[PeterDonis]

We always detect one photon only once

Of course, I'm not saying we don't. I'm saying that if we only use unitary evolution and do not use the collapse postulate, QM does not predict this. It predicts a superposition of detection by different detetors, not a single detection by just one detector.

 

[PeterDonis]

That's why Born introduced the probability interpretation of the quantum state

Yes, but that "interpretation" still doesn't narrow down very much. Advocates of all of the known QM interpretations say that they are consistent with Born's probability interpretation of the state and the Born rule.

Born's rule, in my opinion, is also simply one of the other independent postulates of QT, and it has nothing to do with the collapse postulate.

Yes, that's how we view them in our 7 Basic Rules.

 

[vanhees71]

It's of course again a matter of interpretation. For me the meaning of the state is strictly probabilistic, i.e., a single-photon state tells me the probability to find the photon with a detector at a given position (note, it's not the position of the photon, because a photon has no position observable in the usual sense) and, if I bother to measure it, a given polarization. It's not to be interpreted in a classical-field sense. This was the original interpretation by Schrödinger of his wave function for a (nonrelativistic massive) particle, i.e., Schrödinger thought he could describe the electron as a classical field rather than as a classical point particle, but of course pretty soon it turned out that this is incompatible with what's observed, i.e., an electron is detected always as a point but not as a continuously smeared charge distribution as is predicted by the Schrödinger equation, when interpreting the wave function as a classical field with $-e|\psi(t,\vec{x})|^2$ as a continuous charge distribution. That's why Schrödinger introduced the probabilistic interpretation, and it's the only consistent interpretation of the quantum state until today. As with any fundamental law you can only explain how the physicists historically came to this theory, including its interpretation (in the sense of how the mathematical description has to be applied to the description of real-world observations and measurements), but you cannot explain "why it must be so", except you find some new, more comprehensive theory, for which QT follows in some approximate sense. So far we neither have such a more comprehensive theory nor do we have any idea, whether there's any need for it.

The one big issue, of course, is the question of quantum gravity (or in your preferred geometric interpretation of gravity a quantum theory of spacetime), but I don't think that this has anything to do with the measurement (pseudo-)problem of the philosophers. It's simply lack of empirical guidance that pushes some theorists into the right ansatz for the resolution of this quibble.

 

[Demystifier]

Of course there are (approximations of) ideal von Neumann "filter measurements", e.g., using a polarization filter, which lets through only photons with linear polarization in a given direction. Then the projection postulate holds, and you have a kind of "collapse of the state".

What about the Stern-Gerlach apparatus that measures spin of a massive particle? Would you say that the projection postulate holds in this case?

 

[Demystifier]

This doesn't explain, why there is "a single outcome".

The minimal statistical interpretation also does not explain why there is a single outcome.

 

[Fra]

My question is simply, what has to be explaned?

From my perspective, the collapse just declares in a simplified way that the agents expectation is changed after an information update. It is just a "reset" required before again applying unitary evolution. What needs to be explained is the detailed HOW the interaction/observation by the agent is processed and revise the expectation of the agent.

As the unitary evolution only defines the agents expectations - in between - information updates, what happens AT the "information updates" is like some boundary process, that is left unexplained in QM.

I view this missing thing as an internal process of the agent. And the process of how the agents state is "changed" by post-processing new input, seems to me to be like a "repreparation". But without ensembles. The preparation refers then not to an ensemble, but to the single agents state. That view can still view the agents "state" as isomorphic to the "information about an ensemble" in some cases, but the state of a single agent makes sense always, even when the ensemble realization does not.

Also, if one like I do, think that agents are simply matter systems interacting, what is missing in QM is ultimately to understand how the hamiltonian emerges as two agents interact. The postulated hamiltonian evolution in between measurements, must then be in principle sequence of "collapses".

As long as we don't understand this better, the collapse postulate seems required, but it does itself not really "explain" anything. It's just required to "reset" the evolution after measurements. But the physics of this reset is not understood. This is also the sense is which I see this as connected to the unification quest.

/Fredrik