Why is the projection postulate needed?

[thaiqi]

TL;DR Summary

no summary

Why is the projection postulate needed? For the measurement result's repetition?

 

[anuttarasammyak]

Unitary transformation of states as described by Shroedinger equation does not explain why we always get one result in observation. We need additional theory to explain it.

 

[thaiqi]

Unitary transformation of states as described by Shroedinger equation does not explain why we always get one result in observation. We need additional theory to explain it.

Thanks.

 

[Demystifier]

Summary:: no summary

Why is the projection postulate needed? For the measurement result's repetition?

To make a prediction on a new measurement after the first measurement.

 

[martinbn]

This is a strange question. If you know what the postulate is, then it should be clear what it is for, if you don't, then no answer can help until you do.

 

[atyy]

Why is the projection postulate needed?

The answer is given by @Demystifier in post #4.

For the measurement result's repetition?

This is the reason that Dirac gives in his classic book. The reason given by @anuttarasammyak is related to the reason given by Dirac, and stated by Landau and Lifshitz in their classic text. However, nowadays, we usually think that the reason given by @Demystifier is the best, even though the others are important heuristics. This is because there is a rule that is in some sense a generalization of, and also in some sense a consequence of the projection postulate, in which a repetition of the same measurement need not give the same outcome. You can see this this in Matteo Paris's The modern tools of quantum mechanics. The projection postulate is given as part of Postulate 2 on p3 and Postulate 2.5 on p8, while its generalization is given as Postulate II.4 on p9.

For continuous variables, when a sequence of measurements is performed, due to mathematical difficulties, the projection postulate cannot be applied, and the more general rule is instead applied.

 

[thaiqi]

The answer is given by @Demystifier in post #4.
This is the reason that Dirac gives in his classic book. The reason given by @anuttarasammyak is related to the reason given by Dirac, and stated by Landau and Lifshitz in their classic text. However, nowadays, we usually think that the reason given by @Demystifier is the best, even though the others are important heuristics. This is because there is a rule that is in some sense a generalization of, and also in some sense a consequence of the projection postulate, in which a repetition of the same measurement need not give the same outcome. You can see this this in Matteo Paris's The modern tools of quantum mechanics. The projection postulate is given as part of Postulate 2 on p3 and Postulate 2.5 on p8, while its generalization is given as Postulate II.4 on p9.

For continuous variables, when a sequence of measurements is performed, due to mathematical difficulties, the projection postulate cannot be applied, and the more general rule is instead applied.

Thanks.

 

[akhmeteli]

Summary:: no summary

Why is the projection postulate needed? For the measurement result's repetition?

I would say the projection postulate is not needed as, strictly speaking, it contradicts unitary evolution, and there is no experimental evidence of violations of unitary evolution.

 

[akhmeteli]

Unitary transformation of states as described by Shroedinger equation does not explain why we always get one result in observation. We need additional theory to explain it.

Your statement seems to imply that unitary evolution does not hold during measurement. There is no experimental evidence for that. As for explanation of definite outcomes of measurements from unitary evolution, you may wish to look at https://arxiv.org/abs/1107.2138 (published in Phys. Rep., very long).

 

[PeterDonis]

there is no experimental evidence of violations of unitary evolution

Your statement seems to imply that unitary evolution does not hold during measurement. There is no experimental evidence for that.

These claims are interpretation dependent.

explanation of definite outcomes of measurements from unitary evolution, you may wish to look at https://arxiv.org/abs/1107.2138

This paper is using quantum statistical mechanics, which is not the same as "unitary evolution", so it does not support your claims.

 

[akhmeteli]

These claims are interpretation dependent.

Could you please explain that? In what interpretation is there experimental evidence of violations of unitary evolution?

This paper is using quantum statistical mechanics, which is not the same as "unitary evolution", so it does not support your claims.

I am not sure I understand that. The equation for evolution of the density matrix that they use does not seem to add anything essential compared to unitary evolution.

And their explanation of single outcomes of measurement in their model is that, while there can be no irreversibility with unitary evolution, the measurement system can persist in a "single outcome" state for a long time - Poincare reversal time. Eventually it evolves into a "different outcome" state. So the projection postulate is, strictly speaking, incompatible with unitary evolution.

 

[PeterDonis]

In what interpretation is there experimental evidence of violations of unitary evolution?

Any collapse interpretation.

the projection postulate is, strictly speaking, incompatible with unitary evolution.

Exactly. So in any interpretation where the projection postulate is taken to represent a real physical process, instead of just a mathematical rule for calculation, measurements having single outcomes is experimental evidence of violations of unitary evolution.

 

[PeterDonis]

their explanation of single outcomes of measurement in their model is that, while there can be no irreversibility with unitary evolution, the measurement system can persist in a "single outcome" state for a long time - Poincare reversal time.

How does this model explain measurements like Stern-Gerlach, where unitary evolution does not give a single outcome at all, but an entangled state that is a superposition of two outcomes?

 

[akhmeteli]

Any collapse interpretation.
Exactly. So in any interpretation where the projection postulate is taken to represent a real physical process, instead of just a mathematical rule for calculation, measurements having single outcomes is experimental evidence of violations of unitary evolution.

But there is no experimental evidence of single outcomes. I quoted the article by Schlosshauer several times: “(i) the universal validity of unitary dynamics and the superposition principle has been confirmed far into the mesoscopic and macroscopic realm in all experiments conducted thus far; (ii) all observed restrictions can be correctly and completely accounted for by taking into account environmental decoherence effects; (iii) no positive experimental evidence exists for physical state-vector collapse; (iv) the perception of single outcomes is likely to be explainable through decoherence effects in the neuronal apparatus.”(Annals of Physics, 321 (2006) 112-149). I doubt about his (iv), but I do believe all we have is "perception of single outcomes". Collapse interpretations per se are no experimental evidence, they are just interpretations. If you believe there has been a more recent evidence of violation of unitary evolution, please advise.

 

[PeterDonis]

there is no experimental evidence of single outcomes.

Not if you adopt an interpretation that explains away what most people think of as single outcomes. But, as I have already said, this is interpretation dependent.

Collapse interpretations per se are no experimental evidence, they are just interpretations.

The same is true for no collapse interpretations. But no collapse interpretations have an additional problem that collapse interpretations do not have: if you take what we observe in experiments at face value, they do have single outcomes. Collapse interpretations just accept that seemingly obvious fact as a fact. No collapse interpretations have to go to elaborate lengths to explain it away, as your own post illustrates.

Given that situation, it is simply wrong for you to make the claim that we have no experimental evidence of single outcomes as though it were just an innocuous truth and not an elaborately constructed interpretation that requires explaining away what look to most people like obvious facts. I understand that you have an interpretation which does this explaining away, but it's still explaining away: you can't just set that aside and pretend it isn't needed.

 

[akhmeteli]

How does this model explain measurements like Stern-Gerlach, where unitary evolution does not give a single outcome at all, but an entangled state that is a superposition of two outcomes?

Strictly speaking, it does not, as far as I can see. The model describes a specific instrument (a paramagnetic system) used to measure spin projection of the particle. However, their model suggests what we should expect to obtain through an analysis of the specific instrument used in Stern-Gerlach: the instrument will unitarily evolve into a state representing a different outcome (although this may take incredibly long time). There is practical irreversibility, but strict reversibility in principle.

 

[PeterDonis]

Strictly speaking, it does not, as far as I can see.

And yet you claim that we have no experimental evidence of single outcomes, as though it were just a simple innocuous truth?

I am beginning to wonder if you are trolling.

 

[PeterDonis]

The model describes a specific instrument (a paramagnetic system) used to measure spin projection of the particle.

Note that this is not a description of the standard Stern-Gerlach apparatus.

 

[akhmeteli]

Not if you adopt an interpretation that explains away what most people think of as single outcomes. But, as I have already said, this is interpretation dependent.

I don't quite understand what you're saying. So is there experimental evidence of single outcomes, in your opinion? If you believe there is such an evidence, it means you believe there is experimental evidence of violation of unitary evolution. Maybe you should have another look at the Nobel lecture by Haroche (https://www.nobelprize.org/uploads/2018/06/haroche-lecture.pdf), who mentions Schrödinger's cat dozens of times describing his experiments.

The same is true for no collapse interpretations. But no collapse interpretations have an additional problem that collapse interpretations do not have: if you take what we observe in experiments at face value, they do have single outcomes. Collapse interpretations just accept that seemingly obvious fact as a fact. No collapse interpretations have to go to elaborate lengths to explain it away, as your own post illustrates.

Given that situation, it is simply wrong for you to make the claim that we have no experimental evidence of single outcomes as though it were just an innocuous truth and not an elaborately constructed interpretation that requires explaining away what look to most people like obvious facts. I understand that you have an interpretation which does this explaining away, but it's still explaining away: you can't just set that aside and pretend it isn't needed.

So all interpretations have their problems. How is this my problem? Experimental evidence of violation of unitary evolution either exists or not. Schlosshauer does not believe it exists. Haroche shows validity of unitary evolution for more and more complex quantum systems. If there is a perception of single outcomes, it does not mean there are single outcomes. There is obvious perception of irreversibility in our world, but there is no irreversibility in principle. Why do I need to explain a perception? Allahverdyan et al. explained it (the perception) in a specific model using just unitary evolution, as far as I can judge. Am I supposed to write 300-page-long papers for every measurement instrument? If collapse interpretations take the perception for granted, it does not mean there is experimental evidence.

 

[akhmeteli]

And yet you claim that we have no experimental evidence of single outcomes, as though it were just a simple innocuous truth?

Again, Allahverdyan et al. showed how unitary evolution can create perception of single outcome for a specific measurement instrument. I am not able to perform a similar 300-page-long analysis for Stern-Gerlach. That does not mean it cannot be done.

I am beginning to wonder if you are trolling.

I can assure you I am not trolling. I just believe that unitary evolution has extensive experimental evidence, so I just am not ready to believe without proof that there is experimental evidence of its violation.

 

[akhmeteli]

Note that this is not a description of the standard Stern-Gerlach apparatus.

I agree. That's what I said. But again, I don't feel I need to repeat Allahverdyan's analysis for every measurement instrument in existence.

 

[PeterDonis]

is there experimental evidence of single outcomes, in your opinion?

I've already answered this question, multiple times: what you think the evidence shows depends on your interpretation of QM. On a collapse interpretation, the fact that experiments seem to have single outcomes is evidence that they do have single outcomes. On a no collapse interpretation, it isn't.

Experimental evidence of violation of unitary evolution either exists or not.

Wrong. If how the evidence is interpreted depends on your interpretation of QM, then whether or not there is evidence of violation of unitary evolution is not a simple yes/no question. It is an interpretation dependent question.

I can assure you I am not trolling. I just believe that unitary evolution has extensive experimental evidence

There is extensive experimental evidence for unitary evolution in the absence of measurement. All QM interpretations agree on that. But that is not what we are talking about here.

You are claiming that there is extensive experimental evidence of unitary evolution in a measurement. That claim is interpretation dependent, as I have already said multiple times.

 

[PeterDonis]

Allahverdyan et al. showed how unitary evolution can create perception of single outcome for a specific measurement instrument.

Everett already described this in the general case in his original paper on the MWI. That is not the issue.

The issue is that saying that unitary evolution can create "perception of a single outcome" (by entangling the observer with the measured system, as the MWI describes) is not the same as saying that unitary evolution actually does create "perception of a single outcome", when actually there isn't. The latter statement would amount to an experimental proof that the MWI is the only possible correct interpretation of quantum mechanics. Nobody has such a proof; certainly you don't. And the claims you are making cannot be made without qualification if you do not have such a proof.

 

[physika]

Summary:: no summary

Why is the projection postulate needed? For the measurement result's repetition?

.

https://royalsocietypublishing.org/doi/10.1098/rsta.2011.0490#FN3— The Measurement Algorithm. Observable quantities are represented by self-adjoint operators; the possible outcomes of a measurement of some observable are the eigenvalues of the associated operator; the probability of a given measurement outcome obtaining is given by the usual (Born) probability rule.

— The Projection Postulate. While in the absence of measurement, a system evolves unitarily and deterministically, according to the Schrödinger equation, when a measurement is made the system evolves stochastically, with its state vector being projected onto the eigensubspace corresponding to the actual measurement outcome. As such, the dynamics of quantum theory have a dual nature, with one evolution rule for non-measurement situations and one for measurement situations.

"Often (including by Dirac), the second is derived from the first by consideration of repeat measurements: presumably (so goes the reasoning), two measurements in succession had better give the same result, and this can only be guaranteed if the Projection Postulate holds. "

"We can see this pretty straightforwardly in the case of the Projection Postulate. The postulate tells us how a quantum system evolves during measurement, and this tells us immediately that it can only play a role in applications of quantum physics in situations where we want to analyse repeated measurements. If all we care about is the outcome of single measurements, the Measurement Algorithm tells us all we need to know."

"But if the point of the Projection Postulate is to analyse repeated measurements, there is an embarrassing problem: the Postulate tells us successive measurements of the same quantity always give the same result, and this is straightforwardly false in many—perhaps most—experimental contexts. (We can see this particularly dramatically in quantum optics: when we make a measurement of a photon, the photon is typically gone at the end of the measurement.)".

 

[PeterDonis]

if the point of the Projection Postulate is to analyse repeated measurements, there is an embarrassing problem: the Postulate tells us successive measurements of the same quantity always give the same result

I think Wallace is misstating the postulate. The point of the postulate is to analyze repeated measurements on the same quantum system, and it says that successive measurements of the same quantity on the same quantum system always give the same result. Obviously if your first measurement destroys the quantum system, as is usually the case in quantum optics, you can't even make repeated measurements on the same quantum system, so the projection postulate doesn't even apply.

(There is also another qualifier to the postulate, which is that the successive measurements on the same quantum system cannot have any other interactions in between them. Or, to put it another way, the state of the quantum system that results from the first measurement must be an eigenstate of whatever observable is being measured in both measurements, as well as of the Hamiltonian of the system in between the measurements. Otherwise unitary evolution alone can change the value of the observable between the measurements.)

 

[PeterDonis]

I think Wallace is misstating the postulate.

I also don't understand why Wallace gives a Geiger counter as an example of a "continuous measurement". From the standpoint of QM, each click of a Geiger counter is a measurement: it records the irreversible interaction of a particle with the detector. Keeping a running total of how many clicks there have been, which is the only way I can make sense of the term "continuous measurement" in this context, is only a "measurement" in the classical sense and does not raise any issues at all related to QM.

 

[Morbert]

I also don't understand why Wallace gives a Geiger counter as an example of a "continuous measurement". From the standpoint of QM, each click of a Geiger counter is a measurement: it records the irreversible interaction of a particle with the detector. Keeping a running total of how many clicks there have been, which is the only way I can make sense of the term "continuous measurement" in this context, is only a "measurement" in the classical sense and does not raise any issues at all related to QM.

I'd have to work through the example but maybe he is presenting the "no click" moments as measurement outcomes correlated with no decay.

[edit] - Do you have a reference to Wallace's example? (e.g. book or article?)

 

[PeterDonis]

Do you have a reference to Wallace's example? (e.g. book or article?)

It's in the article linked to in post #24.

 

[Morbert]

I've now read the article and a few of the references and this is indeed he is referring to.

It only seems to be a problem if the projection postulate is understood as a dynamic process. I have checked the limiting behaviour of this "continuous measurement scenario" using the consistent histories formalism and it behaves just fine.