Minimal Statistical Interpretation: How Does A Photon Pass Through a Filter Without Hidden Variables?

[Lynch101]

TL;DR Summary

How does a photon pass through a filter if there are no "pre-programmed" properties?

According to the minimal statistical interpretation (Ensemble interpretation?) if a photon doesn't have "pre-programmed" properties or hidden variables, which determine whether or not it will pass through a filter, how does any photon pass through a given filter, or why would it fail to pass through some filters, yet pass through others?

 

[PeterDonis]

According to the minimal statistical interpretation (Ensemble interpretation?) if a photon doesn't have "pre-programmed" properties or hidden variables, which determine whether or not it will pass through a filter, how does any photon pass through a given filter, or why would it fail to pass through some filters, yet pass through others?

The minimal statistical interpretation does not answer this question. It just predicts the probabilities and stops there.

 

[Lynch101]

The minimal statistical interpretation does not answer this question. It just predicts the probabilities and stops there.

Thanks PD.

Are there other interpretations which do the same?

I'm making the assumption that interpretations like Many Worlds (MW) and Bohmian Mechanics (BM) address a question like that, but there might be some nuance I'm missing.

Would the guiding wave in BM potentially answer that question? And does MW actually say there are such hidden variables, just that the probabilities imply a branching into many worlds?

 

[PeterDonis]

Are there other interpretations which do the same?

It depends on what you mean by "do the same".

I'm making the assumption that interpretations like Many Worlds (MW) and Bohmian Mechanics (BM) address a question like that, but there might be some nuance I'm missing.

The question isn't even well-defined in the MWI, since in the MWI all possible outcomes happen, so it's meaningless to ask why one happens instead of another.

The question isn't well-defined in Bohmian Mechanics either, since in BM there are hidden variables, they're just not local hidden variables (i.e., they don't meet Bell's locality condition).

 

[iste]

TL;DR Summary: How does a photon pass through a filter if there are no "pre-programmed" properties?

According to the minimal statistical interpretation (Ensemble interpretation?) if a photon doesn't have "pre-programmed" properties or hidden variables, which determine whether or not it will pass through a filter, how does any photon pass through a given filter, or why would it fail to pass through some filters, yet pass through others?

Surely if the quantum formalism were about ensembles, then it is the ensemble that doesn't have "pre-programmed properties", not the individual photons during an experiment?

 

[Morbert]

TL;DR Summary: How does a photon pass through a filter if there are no "pre-programmed" properties?

According to the minimal statistical interpretation (Ensemble interpretation?) if a photon doesn't have "pre-programmed" properties or hidden variables, which determine whether or not it will pass through a filter, how does any photon pass through a given filter, or why would it fail to pass through some filters, yet pass through others?

Your question pertains more an instrumentalist interpretation a la Peres or Kemble, where the normal notion of measurement as revealing properties of microscopic systems is discarded and replaced with the notion of testing a microscopic system and recording its response. Ensembles are still invoked, but in a more operational context.

In fact we have no satisfactory reason for ascribing objective existence to physical quantities as distinguished from the numbers obtained when we make the measurements which we correlate with them. As indicated in Sec. 19d, there is no real reason for supposing that a particle belonging to an assemblage described by a wave function has at every moment a definite, but unknown, position which may be revealed by a measurement of the right kind, or a definite momentum which can be revealed by a different measurement. On the contrary, we get into a maze of contradictions as soon as we inject into quantum mechanics such concepts carried over from the language and philosophy of our scientific, ancestors. As no scheme of operations can determine experimentally whether physical quantities such as position and momentum exist and have unique values when they are not at the moment under observation, nor whether the number obtained by a measurement describes some objective property of the thing measured, a strict adherence to the operational point of view requires that we eliminate such concepts from our theories. From the standpoint of classical physics such a rejection would perhaps be a bit of philosophical purism flying so unnecessarily in the face of common sense that few would care to adopt it. On the other hand this rejection is a demonstrable logical necessity for quantum mechanics.

https://archive.org/details/in.ernet.dli.2015.474838

A quantum system is a useful abstraction, which frequently appears in the literature, but does not really exist in nature. In general, a quantum system is defined by an equivalence class of preparations. (Recall that “preparations” and “tests” are the primitive notions of quantum theory. Their meaning is the set of instructions to be followed by an experimenter.) For example, there are many equivalent macroscopic procedures for producing what we call a photon, or a free hydrogen atom, etc. The equivalence of different preparation procedures should be verifiable by suitable tests.
[...]
A [quantum] state is characterized by the probabilities of the various outcomes of every conceivable test
[...]
[Probability] means the following. We imagine that the test is performed an infinite number of times, on an infinite number of replicas of our quantum system, all identically prepared. This infinite set of experiments is called a statistical ensemble.

https://ds.amu.edu.et/xmlui/bitstream/handle/123456789/1982/20268.pdf?sequence=1&isAllowed=y

 

[DrChinese]

Surely if the quantum formalism were about ensembles, then it is the ensemble that doesn't have "pre-programmed properties", not the individual photons during an experiment?

The GHZ theorem tells us that even an individual photon cannot have “pre-programmed properties” of the type discussed here. No ensemble required. :)

With GHZ entanglement, there are perfect correlations. I.e. the outcome of a measurement on a single individual photon can be predicted with 100% certainty. However, the quantum mechanical prediction is exactly opposite what would be expected if the measured attribute was pre-existing.

https://www.drchinese.com/David/Bell-MultiPhotonGHZ.pdf

I would conclude that there is no advantage to an interpretation that is dependent in any way on an ensemble of measurements to explain the quantum expectation.

 

[PeterDonis]

The GHZ theorem tells us that even an individual photon cannot have “pre-programmed properties” of the type discussed here. No ensemble required. :)

To be clear, no ensemble is required to rule out local realistic models, at least if we are confident enough in our measuring equipment to trust a single result that contradicts the predictions of those models.

But ensemble interpretations are based on the idea that doing enough runs to do statistical analysis is necessary to test the predictions of QM. That is still true even if the prediction of QM is that 100% of the results of a particular experiment should be the same. You still have to do statistical tests to see if that is actually the case; just one result that matches the QM prediction isn't enough.

 

[DrChinese]

But ensemble interpretations are based on the idea that doing enough runs to do statistical analysis is necessary to test the predictions of QM. That is still true even if the prediction of QM is that 100% of the results of a particular experiment should be the same. You still have to do statistical tests to see if that is actually the case; just one result that matches the QM prediction isn't enough.

I of course agree that actual experiments require sufficient runs to support the QM prediction within some range. But that is a little different usage of the term “statistical”.

Ensemble interpretations distinguish between ascribing the wave function to the group of similarly prepared group of particles (as opposed to an individual particle). I don’t see how to make that view consistent with GHZ, which applies to each and every run (in principle, since actual experiments are imperfect).

From demystifier in the Statistical Ensemble thread:

The main source of confusion is whether SEI talks about individual systems, or only about large ensembles of systems. In particular, within SEI, does it make sense to say that we have one particle in the state $|\psi\rangle$?

 

[martinbn]

I of course agree that actual experiments require sufficient runs to support the QM prediction within some range. But that is a little different usage of the term “statistical”.

Ensemble interpretations distinguish between ascribing the wave function to the group of similarly prepared group of particles (as opposed to an individual particle). I don’t see how to make that view consistent with GHZ, which applies to each and every run (in principle, since actual experiments are imperfect).

In what sense does GHZ apply to every individual run?

 

[PeterDonis]

Ensemble interpretations distinguish between ascribing the wave function to the group of similarly prepared group of particles (as opposed to an individual particle). I don’t see how to make that view consistent with GHZ, which applies to each and every run (in principle, since actual experiments are imperfect).

GHZ "applies to each and every run" in the sense that (again assuming we trust our measuring apparatus enough) a single run whose result is impossible according to a local realistic model is enough to rule out the local realistic model.

But that does not mean GHZ "applies to each and every run" in terms of QM interpretation. One can still adopt an ensemble interpretation when analyzing GHZ experiments in order to test the predictions of QM. In an ensemble interpretation, the GHZ prediction that a particular measurement should give the same result 100% of the time is still a statistical prediction.

 

[lodbrok]

TL;DR Summary: How does a photon pass through a filter if there are no "pre-programmed" properties?

According to the minimal statistical interpretation (Ensemble interpretation?) if a photon doesn't have "pre-programmed" properties or hidden variables, which determine whether or not it will pass through a filter, how does any photon pass through a given filter, or why would it fail to pass through some filters, yet pass through others?

The photon has a "state" right? And the "state" is responsible for the measurement outcome right? And the state is "prepared" before the measurement right?

 

[PeterDonis]

The photon has a "state" right?

Not according to the interpretation under discussion here. On that interpretation the quantum state describes the probabilities for different possible measurement outcomes. It does not describe individual systems.

And the "state" is responsible for the measurement outcome right?

Not according to the interpretation under discussion here. On that interpretation the quantum state describes the probabilities of different possible measurement outcomes, but it is not "responsible" for any particular outcome.

And the state is "prepared" before the measurement right?

On some versions of the statistical/ensemble interpretation (such as Ballentine's), the state can be interpreted as describing the preparation procedure that corresponds to a given set of probabilities of different possible measurement outcomes. But that still does not mean individual systems are prepared in that state, as the state on this type of interpretation does not describe individual systems.

 

[lodbrok]

Not according to the interpretation under discussion here. On that interpretation the quantum state describes the probabilities for different possible measurement outcomes. It does not describe individual systems.

Does the ensemble have a "state" in the interpretation under discussion here? Would such a "state" of the ensemble (if it exists) be said to exist prior to measurement and be responsible for the measurement outcomes? Otherwise, what's the purpose of "preparation"?

 

[PeterDonis]

Does the ensemble have a "state" in the interpretation under discussion here?

On some versions of this type of interpretation (such as Ballentine's), yes, the state can be taken to describe the abstract ensemble of all possible systems that could be prepared by the preparation procedure.

Would such a "state" of the ensemble (if it exists) be said to exist prior to measurement

On this interpretation states aren't things that "exist". They are part of our model, not part of "reality".

and be responsible for the measurement outcomes?

No. See above.

Otherwise, what's the purpose of "preparation"?

To prepare systems in a particular way so we can make measurements on them and test QM's predictions for the probabilities of different possible measurement outcomes. None of this requires the state to be "real" or to be a property of individual systems or to be "responsible" for measurement outcomes.

 

[DrChinese]

To prepare systems in a particular way so we can make measurements on them and test QM's predictions for the probabilities of different possible measurement outcomes. None of this requires the state to be "real" or to be a property of individual systems or to be "responsible" for measurement outcomes.

(Also addressing @lodbrok ‘s comment.)

I don’t agree that GHZ is just another statistical prediction, similar to Bell and others. From the reference I provided above:

“In the case of Bell’s inequalities for two photons the conflict between local realism and quantum physics arises for statistical predictions of the theory; but for three entangled particles the conflict arises even for the definite predictions. Statistics now only results from the inevitable experimental limitations occurring in any and every experiment, even in classical physics.”

In other words: The Statistical Ensemble Interpretation hopes to explain Bell test results using some sort of mechanism that might exist within the ensemble, where there is only a small difference between the local realistic boundary and the quantum expectation value. On the other hand, that same interpretation might be successful at explaining EPR perfect correlations. But GHZ demonstrates that those perfect correlations cannot always be explained by such an interpretation. There are no ensembles to consider, unless you call one an ensemble.

Furthermore: we again have an experiment (GHZ) in which a quantum system’s state is changed by a remote operation. A decision by an experimenter to perform (or not) a specific measurement on 2 of 3 indistinguishable GHZ entangled photons will cast a distant 3rd photon into an eigenstate with a value that can be predicted with certainty each and every time (within experimental bounds). If the experimenter instead makes the 2 photons distinguishable, the 3rd photon arrives in a maximally random state - regardless of distance. (Of course, despite evidencing quantum nonlocality, signal locality is respected.)

“Thus, in every one of the three yyx, yxy and xyy experiments, any individual measurement result – both for circular polarization and for linear H′/V ′ polarization – can be predicted with cer- tainty for every photon given the corresponding measurement results of the other two.

“We now analyze the implications of these predictions from the point of view of local realism. First, note that the predictions are independent of the spatial separation of the photons and independent of the relative time order of the measurements. Let us thus consider the experiment to be performed such that the three measurements are performed simultaneously in a given reference frame, say, for conceptual simplicity, in the reference frame of the source. Thus we can employ the notion of Einstein locality, which implies that no information can travel faster than the speed of light. Hence the specific measurement result obtained for any photon must not depend on which specific measurement is performed simultaneously on the other two or on the outcome of these measurements. The only way then to explain from a local realistic point of view the perfect correlations discussed above is to assume that each photon carries elements of reality for both x and y measurements considered and that these elements of reality determine the specific individual measurement result [7, 8, 12].”

There is no refuge in an interpretation dependent on an ensemble.

 

[PeterDonis]

I don’t agree that GHZ is just another statistical prediction

The predictions of QM, even in cases where the prediction is for a particular result to occur 100% of the time--for example, when measuring the z spin of a qubit prepared in the z spin up state--are still statistical predictions; you still need to do a sufficiently large number of runs of the experiment to verify them. A single run with the predicted result is not enough

The Statistical Ensemble Interpretation hopes to explain Bell test results using some sort of mechanism that might exist within the ensemble, where there is only a small difference between the local realistic boundary and the quantum expectation value.

Do you have any references from physicists who use the statistical ensemble interpretation (e.g., Ballentine) that make this claim? My understanding from reading sources like Ballentine is that they make no claim whatever about any "underlying mechanisms". They simply state that the predictions of QM, since they are predictions of probabilities of measurement results, require statistical methods to verify them. As above, this is true even in cases where the prediction is for a particular result to occur 100% of the time; that is just an edge case of predicting probabilities, not a qualitatively different case.

 

[PeterDonis]

There is no refuge in an interpretation dependent on an ensemble.

No, there is no refuge in a local realistic hidden variable interpretation--which could be viewed as one proposal for an "underlying mechanism" beneath an ensemble, but is not so viewed, as far as I can tell, by any proponents of an ensemble interpretation.

 

[vanhees71]

To be clear, no ensemble is required to rule out local realistic models, at least if we are confident enough in our measuring equipment to trust a single result that contradicts the predictions of those models.

But ensemble interpretations are based on the idea that doing enough runs to do statistical analysis is necessary to test the predictions of QM. That is still true even if the prediction of QM is that 100% of the results of a particular experiment should be the same. You still have to do statistical tests to see if that is actually the case; just one result that matches the QM prediction isn't enough.

Anybody, who went through the introductory physics lab in the early semesters when studying physics knows that you need "statistical samples" even when measuring entirely classical systems. One measurement is not enough to do even the minimal requirements of measurement-error analysis!

 

[DrChinese]

Anybody, who went through the introductory physics lab in the early semesters when studying physics knows that you need "statistical samples" even when measuring entirely classical systems. One measurement is not enough to do even the minimal requirements of measurement-error analysis!

Agreed, which pretty well matches the words of Zeilinger and Pan:

“Statistics now only results from the inevitable experimental limitations occurring in any and every experiment, even in classical physics.”

This is NOT what is meant by the word “statistical” in the Statistical interpretation. Essentially, I say the GHZ theorem+experimental confirmation implies that each and every run represents the prepared state, and there is nothing to be found differently in any ensemble. As always in the orthodox (minimal) view, outcomes are indeterministic, QT is “complete”, and the theory is contextual.

 

[vanhees71]

I fully agree with this, and I think that's the only consistent "interpretation" of QT, given all the experimental and theoretical work done since the theory has been completely formulated in 1926.

 

[martinbn]

Agreed, which pretty well matches the words of Zeilinger and Pan:

“Statistics now only results from the inevitable experimental limitations occurring in any and every experiment, even in classical physics.”

This is NOT what is meant by the word “statistical” in the Statistical interpretation. Essentially, I say the GHZ theorem+experimental confirmation implies that each and every run represents the prepared state, and there is nothing to be found differently in any ensemble. As always in the orthodox (minimal) view, outcomes are indeterministic, QT is “complete”, and the theory is contextual.

I am probably misreading you, but at times it seems that you are saying that the theory and experiment around GHZ disprove the ensemble interpretation. Are you claiming that?

 

[vanhees71]

The point of GHZ is that in a very idealized sense one observation on a single system can decide whether "local realistic HV theories" in Bell's sense or Q(F)T is correct. Of course in a real experiments you always need a proper statistical analysis. Here's one of the early realizations of a GHZ experiment using three-photon entangled states:

https://www.nature.com/articles/35000514

 

[PeterDonis]

This is NOT what is meant by the word “statistical” in the Statistical interpretation.

Ballentine does not agree with you in his discussion of the ensemble interpretation (Ch. 2 of his book).

Essentially, I say the GHZ theorem+experimental confirmation implies that each and every run represents the prepared state

Ballentine does not agree with you on this either. He discusses the GHZ experiment in Section 20.6 of his book.

More generally, as is noted in the guidelines for this subforum, you cannot prove any QM interpretation wrong by experiment because they all make the same predictions for the outcomes of all experiments. You can express your opinion (which might be the same as the opinion of physicists as expressed in the literature) that a particular interpretation is wrong, but that is just an opinion, with which others (including other physicists in the literature) may disagree.

 

[iste]

The GHZ theorem tells us that even an individual photon cannot have “pre-programmed properties” of the type discussed here. No ensemble required. :)

With GHZ entanglement, there are perfect correlations. I.e. the outcome of a measurement on a single individual photon can be predicted with 100% certainty. However, the quantum mechanical prediction is exactly opposite what would be expected if the measured attribute was pre-existing.

https://www.drchinese.com/David/Bell-MultiPhotonGHZ.pdf

I would conclude that there is no advantage to an interpretation that is dependent in any way on an ensemble of measurements to explain the quantum expectation.

But these results would still just about probabilities, not individual outcomes. The Bell violation could still be instantiated by many outcomes of the individual particles. You might even have different context-dependent distributions that depend on measurement settings.

 

[DrChinese]

But these results would still just about probabilities, not individual outcomes. The Bell violation could still be instantiated by many outcomes of the individual particles. You might even have different context-dependent distributions that depend on measurement settings.

In GHZ, each and every outcome of an XXX measurement is the opposite of the local realistic prediction (in the ideal case of course). In principle, a single run is proof. See figure 16.6 of the reference.

Yes, there can be 4 different outcomes. But all 4 violate local realism and all 4 individually demonstrate quantum nonlocality. "On the basis of measurements on three-photon entanglement, we have realized the first experimental test of quantum non-locality following from the GHZ argument."

 

[iste]

In GHZ, each and every outcome of an XXX measurement is the opposite of the local realistic prediction (in the ideal case of course). In principle, a single run is proof. See figure 16.6 of the reference.

Yes, there can be 4 different outcomes. But all 4 violate local realism and all 4 individually demonstrate quantum nonlocality. "On the basis of measurements on three-photon entanglement, we have realized the first experimental test of quantum non-locality following from the GHZ argument."

I am not trying to imply that "local realism" isn't violated. Just that if you don't commit to the wave function being a real physical entity, and only being about the probabilistic predictions, there isn't anything logically stopping you from giving particles definite states in some way. Probably closest thing to what I am thinking about is the particle trajectories in Bohmian mechanics which, as far as I know, is also contextual and nonlocal.

 

[DrChinese]

I am not trying to imply that "local realism" isn't violated. Just that if you don't commit to the wave function being a real physical entity, and only being about the probabilistic predictions, there isn't anything logically stopping you from giving particles definite states in some way. Probably closest thing to what I am thinking about is the particle trajectories in Bohmian mechanics which, as far as I know, is also contextual and nonlocal.

I am not a Bohmian, but I consider the wave function (actually the state of quantum systems) to be be "real" or ontic in the sense of PBR. So in a strange way I agree with you, in the limited sense that those that believe the quantum state is epistemic might believe "particles [have] definite states in some way."

I just don't see how one holds on to the assertion that "particles have definite values for observables independent of the act of observation" and say that is part of the minimal statistical interpretation. Minimal would mean dropping that assertion as being extra baggage.

 

[martinbn]

I just don't see how one holds on to the assertion that "particles have definite values for observables independent of the act of observation" and say that is part of the minimal statistical interpretation. Minimal would mean dropping that assertion as being extra baggage.

Who and where says that?

 

[DrChinese]

Who and where says that?

I was referring to iste's comment, and generalizing it to anyone who might claim to adhere to the interpretation we are discussing in this thread and its close variants. You mentioned the ensemble interpretation in post #22. Yes, I would assert that ensemble interpretations are ruled out by GHZ.

Now, PeterDonis said in #23: "you cannot prove any QM interpretation wrong by experiment because they all make the same predictions for the outcomes of all experiments." Well, let's just say they all CLAIM to give the same predictions - I agree to that extent. But it has become more and more obvious in the past 40 years that the claimed mechanisms or assumptions of many interpretations cannot withstand critical review - there are many experiments that cannot be properly reconciled with their key tenets.

[Moderator's note: Last paragraph moved to new thread; see moderator post below.]

 

[PeterDonis]

they all CLAIM to give the same predictions

It's not just a matter of "claiming". All QM interpretations are interpretations of the same math (or equivalent math). Same math = same predictions.

Some models in the literature, such as the GRW stochastic collapse model, are not QM interpretations, although they might sometimes be informally thought of as such: they are different theories from QM, because they use different math (for example, GRW's stochastic collapse is different math), and thus make different predictions. Those models are in principle distinguishable from standard QM by experiment. But those aren't what is referred to in the forum guidelines by the term "QM interpretation".

 

[PeterDonis]

Moderator's note: Discussion of whether the MWI is local has been moved to a separate thread:

https://www.physicsforums.com/threads/is-the-mwi-local.1057817/

 

[martinbn]

I was referring to iste's comment, and generalizing it to anyone who might claim to adhere to the interpretation we are discussing in this thread and its close variants. You mentioned the ensemble interpretation in post #22. Yes, I would assert that ensemble interpretations are ruled out by GHZ.

This is very strong! How is it ruled out by GHZ? All interpretations say the same thing about the GHZ state and measurements on it. It is just core QM, the interpretations don't really play a role here.

 

[PeterDonis]

I would assert that ensemble interpretations are ruled out by GHZ.

We already had this discussion earlier in the thread. See in particular my post #24.

 

[PeterDonis]

All interpretations say the same thing about the GHZ state and measurements on it. It is just core QM, the interpretations don't really play a role here.

Yes, this is what I pointed out at the end of my post #24.