Minimal vs Instrumental vs Ensemble

[PeterDonis]

I wrote about the operational sense of the quantum state, and that's a preparation procedure on a single system.

Not according to Ballentine. You really should read his book before claiming that your interpretation is the same as his.

Indeed, see Chpt. 2 of Ballentine's book!

If you think Ballentine says that "the operational sense of the quantum state" is "a preparation procedure on a single system", then please provide an explicit quote from that chapter that does so. I can't find one.

We all know that in reality we deal with "statistical samples" and not infinite theoretical "ensembles".

Ballentine discusses this. If you want to claim that your interpretation is the same as his, you need to provide explicit quotes from his book that say so. I can't find any.

 

[Morbert]

@gentzen Again I will have to ask you for an example experiment, as your issue is unclear to me.

 

[Morbert]

Yes, or how else than just "collecting enough statistics" do you think the HEP physicists measure cross sections?

Statistical samples are a necessary part of many experiments. But these statistical samples might still be compatible with, say, an interpretation of quantum probabilities as propensities of individual systems, as opposed to relative frequencies of infinite ensembles.

 

[Morbert]

fwiw Asher Peres is the most "instrumentalist" physicist I know of and he heavily uses the notion of an ensemble.

Before we examine concrete examples, the notion of probability should be
clarified. It 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

Even if a formal distinction can be made between instrumentalist minimal, and minimal ensemble, there might not be any physicists advocating the former rather than the latter.

 

[gentzen]

@gentzen Again I will have to ask you for an example experiment, as your issue is unclear to me.

Is it unclear to you, whether my issue is really an issue, or unclear where I see a potential issue? It is not fully clear to me either, whether my issue is really fundamental, or just an apparent issue. I described my issue as:

The point is rather whether you have to wait until the experiment is over, before you can make conclusions from your classical measurement results, or whether you can update your conclusions (about the single system) on the fly, and maybe even adjust some control signals suitably (i.e. a time dependent reaction).

A good example for a time dependent reaction might be quantum teleportation. I described before why this seems to be problematic for Bohmian mechanics:

And Quantum State Teleportation where the measurement result dependent unitary transformations applied to particle 3 work fine for Copenhagen, but not for Bohmian mechanics (this is the paragraph just above section 6 Conclusion in the link above):

Simply by noting the actual position ($x_0$) of the measuring device, the observer, near particles 1 and 2, immediately knows which wavepacket $x_0$ has entered, and therefore which state is active for particle 3. The observer then sends this classical information to the observer at 3 who will then apply the appropriate unitary transformation $U_1\dots U_4$ so that the initial spin state of particle 1 can be recovered at particle 3.

To see that this is incompatible with Bohmian mechanics, note that what is described here would be a backaction of the trajectories on the wavefunction, which is not possible (or at least not included) in Bohmian mechanics.

I had written a description of quantum teleportation from a QBist perspective (which I see as instrumentalistic). I can paste it, if you want. But mostly it was just long. The point of that description was that there are time dependent quantum states, and actions dependent on those time dependent states. But the actions are based on subjective beliefs about quantum states, not on objective quantum states. At least that is the QBist perspective.

 

[Morbert]

A good example for a time dependent reaction might be quantum teleportation.

I had written a description of quantum teleportation from a QBist perspective (which I see as instrumentalistic). I can paste it, if you want. But mostly it was just long. The point of that description was that there are time dependent quantum states, and actions dependent on those time dependent states. But the actions are based on subjective beliefs about quantum states, not on objective quantum states. At least that is the QBist perspective.

Using this paper as a reference: An instrumentalist would say it describes a macroscopic protocol represented by the nonunitary transformation$$|\phi_1,\Psi^-_{23}\rangle\langle\phi_1,\Psi^-_{23}| \rightarrow \rho_{12}\otimes|\phi_3\rangle\langle\phi_3|$$The protocol involves Alice carrying out a test, and Bob carrying out an operation in his lab contingent on the outcome of Alice's test.

 

[gentzen]

Using this paper as a reference: An instrumentalist would say it describes a macroscopic protocol represented by the nonunitary transformation$$|\phi_1,\Psi^-_{23}\rangle\langle\phi_1,\Psi^-_{23}| \rightarrow \rho_{12}\otimes|\phi_3\rangle\langle\phi_3|$$The protocol involves Alice carrying out a test, and Bob carrying out an operation in his lab contingent on the outcome of Alice's test.

Wait, of course instrumentalist interpretations have no problem with time-dependent reactions. Like I said, they avail themselves of time parameters.
The issue was the other way round, i.e. how non-instrumentalist interpretation (like Bohmian mechanics or the minimal statistical interpretation) can deal with such situations.

So the intention behind your question for "an example experiment" was that you either can see my problem, or else show me your solution so that I should understand why there really was no problem? Makes sense. Only problem is that somewhere on the way a mixup happened regarding which interpretations were meant when I said: "It is not fully clear to me either, whether my issue is really fundamental, or just an apparent issue."

 

[PeterDonis]

how non-instrumentalist interpretation (like Bohmian mechanics or the minimal statistical interpretation) can deal with such situations.

I'm not sure I understand. Bohmian mechanics would say the time dependence of the quantum potential and the particle positions accounts for any time dependence in the situation. The minimal statistical interpretation would wonder why you are talking about this "time dependence" at all, since it has nothing to do with the statistical properties of measurement results.

 

[gentzen]

I'm not sure I understand. Bohmian mechanics would say the time dependence of the quantum potential and the particle positions accounts for any time dependence in the situation.

The "trick" to understand me might be to interpret my statements not as absolute statements of facts, but as statements about where things are currently unclear for me: Because it was unclear to me how one would model quantum teleportation in Bohmian mechanics (BM), I tried to find existing accounts of how it is done. The only one I found was the link I gave above (Quantum State Teleportation understood through the Bohm Interpretation) from which I took the quote:

Simply by noting the actual position ($x_0$) of the measuring device, the observer, near particles 1 and 2, immediately knows which wavepacket $x_0$ has entered, and therefore which state is active for particle 3. The observer then sends this classical information to the observer at 3 who will then apply the appropriate unitary transformation $U_1\dots U_4$ so that the initial spin state of particle 1 can be recovered at particle 3.

The first step to understand why things are unclear to me, is to understand why the quoted part is not valid in BM, based on my current understanding. The devil is in the details for me. If the goal would just be to model the actually performed entanglement swap experiments in BM, then it is perfectly fine for me to do postselection based on particle trajectories. But for the general case, where different unitary transformations are applied to the "receiving qubit" of the pair of entangled qubits based on measurement results, some modeling needs to be found that makes it sufficiently clear what actually happens in BM. Otherwise, one should not claim to have shown that BM is indeed able to account for this type of experiment.

The minimal statistical interpretation would wonder why you are talking about this "time dependence" at all, since it has nothing to do with the statistical properties of measurement results.

For the minimal statistical interpretation, my uncertainty arises from the involved limit processes during verification:

If you look at SEI from an operational verification perspective, then yes, you must associate a single system with a state before you know the results of the non-preparation measurements. This allows it to take part in some verification. Of course, no statistical verification can ever fully reject your state assignments, at most it can tell you that winning the jackpot of a lottery would have been more probable than your obtained measurement results given your previous state assignments.

The issue arises, because the statistical verification requires a limit process of accumulating measurement statistics. But this limit process requires that the equivalence classes of preparation procedures are kept fixed during the verification. And what I intent to measure on the system can impact those equivalence classes.

Now I admit that "good taste" allows to relax those "rules" significantly in practice. But the idealized description should still be the one explained above. It is simply too easy to fool oneself with statistics, not least because our human intuition is not very good in that domain.

 

[kered rettop]

To quibble over "infinite ensembles" versus "finite empirical sample" (or whatever was the correct name) feels like a fight over words to me, probably vanhees71 would call it "philosophy".

I doubt whether a philosopher would agree, though. I suspect they would chuck it in the bin labelled "Semantics - Nothing to see here".

As Humphrey Denham noted, arguments often proceed by the method of dichotomy, not to be confused with trichotomy, which is hair-splitting.

 

[vanhees71]

fwiw Asher Peres is the most "instrumentalist" physicist I know of and he heavily uses the notion of an ensemble.Even if a formal distinction can be made between instrumentalist minimal, and minimal ensemble, there might not be any physicists advocating the former rather than the latter.

I'd not make the issue more complicated than it is. I call an ensemble ensemble also when it's in fact a statistical sample of a real-world experiment in the lab. Anybody knows what's meant. One must be pedantic with the language at other places, where there's really a lot of confusion caused by sloppy language. In this forum you can observe this: the words getting almost unusable since there's no clear use of them in the foundation community are not "ensemble" but rather "local" and "nonlocal" ;-)).

 

[PeterDonis]

for the general case, where different unitary transformations are applied to the "receiving qubit" of the pair of entangled qubits based on measurement results, some modeling needs to be found that makes it sufficiently clear what actually happens in BM

The unitary transformations affect the quantum potential. The quantum potential affects the qubit that has not yet been measured.

Remember, all QM interpretations make the same predictions for all experimental results, because they all use the same (or equivalent) math. If you find yourself concluding that some interpretation doesn't predict what you know QM predicts, you have made a mistake in applying the interpretation.

 

[vanhees71]

Not according to Ballentine. You really should read his book before claiming that your interpretation is the same as his.

I read his book, and I also checked it again. He clearly says that concerning a single system the state represents a preparation procdedure. The whole formalism wouldn't make sense if you couldn't assign a state somehow to a real-world physical system (e.g., an electron).

If you think Ballentine says that "the operational sense of the quantum state" is "a preparation

See the attached page from his book.

procedure on a single system", then please provide an explicit quote from that chapter that does so. I can't find one.Ballentine discusses this. If you want to claim that your interpretation is the same as his, you need to provide explicit quotes from his book that say so. I can't find any.

Or look at his paper, where the formalism is put in more compact form.

L. E. Ballentine, The Statistical Interpretation of Quantum
Mechanics, Rev. Mod. Phys. 42, 358 (1970),
https://doi.org/10.1103/RevModPhys.42.358

 

[PeterDonis]

you must associate a single system with a state

In the minimal statistical interpretation, no, you don't do this. States do not describe single systems in this interpretation. They either describe abstract ensembles, or they describe preparation procedures.

 

[PeterDonis]

He clearly says that concerning a single system the state represents a preparation procdedure.

No, he clearly says that "the state represents a preparation procedure" is one possible interpretation of the state. But he does not say this "concerning a single system". In fact he explicitly denies this when he explains why we cannot say that it is "the particle" that is being prepared (except in a "obvious and trivial sense" that is not useful). It's right there in the middle of the page you attached.

 

[gentzen]

The unitary transformations affect the quantum potential. The quantum potential affects the qubit that has not yet been measured.

Yes, so it could be possible in principle, given a suitable modeling of the measurement process and its impact on the subsequently applied unitary transformation. But for BM, this modeling has to be done explicitly. One does not need to worry about it for an instrumentalist interpretation like Copenhagen.

Remember, all QM interpretations make the same predictions for all experimental results, because they all use the same (or equivalent) math.

BM and Copenhagen don't use the same math, but the math has been proven equivalent for a very general type of scenario. You could use post-selection to apply this proof to the quantum teleportation scenario, but that still misses an element which seems to be present in the Copenhagen model of it. One could call this "reliable" or "efficient" quantum teleportation, namely that you don't have to throw away 3 out of 4 results.

You would have to prove that BM can model this "measurement result controls Hamiltonian" behavior, which is allowed by Copenhagen. Maybe it has already been done, and I am just not aware of the corresponding paper or book chapter.

If you find yourself concluding that some interpretation doesn't predict what you know QM predicts, you have made a mistake in applying the interpretation.

I concluded that I don't know whether (or how) BM allows to model a specific experiment that Copenhagen can easily model. I don't conclude that it is impossible, just that the proofs known to me (which show that BM and Copenhagen make the same predictions) are not sufficient to conclude this.

 

[PeterDonis]

it could be possible in principle, given a suitable modeling of the measurement process and its impact on the subsequently applied unitary transformation. But for BM, this modeling has to be done explicitly.

If you've done the QM math, the "explicit" modeling is already done. All interpretations use the same (or equivalent) math.

One does not need to worry about it for an instrumentalist interpretation like Copenhagen.

Why not? You have to do the same math either way.

BM and Copenhagen don't use the same math, but the math has been proven equivalent for a very general type of scenario.

That's why I explicitly included the qualifier "or equivalent" with reference to the math.

You could use post-selection to apply this proof to the quantum teleportation scenario

Why do you need to use "post-selection" for Bohmian but not for Copenhagen? You need to do it to do the math properly. That means you need to do it for every interpretation.

I concluded that I don't know whether (or how) BM allows to model a specific experiment that Copenhagen can easily model.

The "model" is the math. The math is equivalent for both. So I simply don't see what problem you are referring to. The difference between interpretations is not a difference in being able to account for experimental results; all interpretations make the same predictions for experimental results. It's just a difference in what story you tell in ordinary language.

 

[gentzen]

Why do you need to use "post-selection" for Bohmian but not for Copenhagen? You need to do it to do the math properly. That means you need to do it for every interpretation.

Yes, you are right. Even for Copenhagen, it makes sense to prove that one can model this "measurement result controls Hamiltonian" behavior. And having that proof will make it much simpler to find a corresponding proof for BM, because one can probably easily "adapt" that proof.

 

[vanhees71]

No, he clearly says that "the state represents a preparation procedure" is one possible interpretation of the state. But he does not say this "concerning a single system". In fact he explicitly denies this when he explains why we cannot say that it is "the particle" that is being prepared (except in a "obvious and trivial sense" that is not useful). It's right there in the middle of the page you attached.

Sigh. Do I really have to copy the parts from the texts I quoted. One should also note that physics is not so much about "text exegesis", but about formulating clear concepts. QT wouldn't be applicable to the real world if the state had no operational meaning for single systems, because you couldn't tell, which ensemble is described by these states in the real world, and indeed Ballentine gives the very operational definition of the state that I quoted. In the quoted paper the statement couldn't be more clear (p. 361):

 

[martinbn]

Sigh. Do I really have to copy the parts from the texts I quoted. One should also note that physics is not so much about "text exegesis", but about formulating clear concepts. QT wouldn't be applicable to the real world if the state had no operational meaning for single systems, because you couldn't tell, which ensemble is described by these states in the real world, and indeed Ballentine gives the very operational definition of the state that I quoted. In the quoted paper the statement couldn't be more clear (p. 361):

View attachment 339125

He says that the state represents an ensemble of similarly prepared systems.

You said

He clearly says that concerning a single system the state represents a preparation procdedure.

Do you not see the difference?

 

[vanhees71]

I see the difference, and that difference is crucial. For the single system the state (statistical operator) represents a preparation procedure. Concerning the properties, i.e., the values of observables, of this state it only describes the statistics for the outcome of measurements for an ensemble of equally and independently prepared systems.

 

[martinbn]

... For the single system the state (statistical operator) represents a preparation procedure. ...

Not in his preferred interpretation. Or can you quote him saying exactly this?

 

[kered rettop]

One should also note that physics is not so much about "text exegesis", but about formulating clear concepts.

That's a very appealing statement, thanks. Of course it will get you into trouble.

 

[vanhees71]

Not in his preferred interpretation. Or can you quote him saying exactly this?

I quoted him above in #49. The scan is from Ballentine's famous RMP paper where he explains the minimal statistical interpretation in detail:

L. E. Ballentine, The Statistical Interpretation of Quantum
Mechanics, Rev. Mod. Phys. 42, 358 (1970),
https://doi.org/10.1103/RevModPhys.42.358

 

[martinbn]

I quoted him above in #49. The scan is from Ballentine's famous RMP paper where he explains the minimal statistical interpretation in detail:

L. E. Ballentine, The Statistical Interpretation of Quantum
Mechanics, Rev. Mod. Phys. 42, 358 (1970),
https://doi.org/10.1103/RevModPhys.42.358

Yes, and he clearly says that the state represents an ensemble not an individual system!!!!!!!!!!!

 

[vanhees71]

Yes, but he says both! Please read the quoted text above carefully again. The first sentence says:

"We see a quantum state is a mathematical representation of the result of a certain preparation procedure."

 

[martinbn]

Yes, but he says both! Please read the quoted text above carefully again. The first sentence says:

"We see a quantum state is a mathematical representation of the result of a certain preparation procedure."

But this doesn't say that the state is of an individual system. The preparation procedure produces many systems. And the state describes the ensemble, not the individuals. I think you need to read it carefully.

 

[Morbert]

Yes, but he says both! Please read the quoted text above carefully again. The first sentence says:

"We see a quantum state is a mathematical representation of the result of a certain preparation procedure."

You're going to hate this: What do you make of the distinction between a preparation procedure, and the result of a preparation procedure?

Consider this logic:
- The state represents the result of a preparation procedure
- A single system, a statistical sample, and an infinite ensemble are all hypothetical results of a preparation procedure
- Quantum theory only makes direct statements about infinite ensembles
- Therefore: The state represents an infinite ensemble, the result of a prepartion procedure

 

[Morbert]

I'd not make the issue more complicated than it is. I call an ensemble ensemble also when it's in fact a statistical sample of a real-world experiment in the lab. Anybody knows what's meant. One must be pedantic with the language at other places, where there's really a lot of confusion caused by sloppy language. In this forum you can observe this: the words getting almost unusable since there's no clear use of them in the foundation community are not "ensemble" but rather "local" and "nonlocal" ;-)).

I don't object to the use of a phrase like "finite ensemble", but my understanding is the "ensemble" in ensemble interpretations is necessarily infinite. Ensemble interpretations attempt to overcome apparent ambiguities when discussing individual systems, and a statistical sample is still, in a sense, an individual system (e.g. see this post of mine). Any statistical sample/finite ensemble falls back into the trappings of quantum theories of individual systems.

 

[gentzen]

Any statistical sample/finite ensemble falls back into the trappings of quantum theories of individual systems.

But maybe the trappings of ... individual systems are not so bad overall, as long one is sufficiently careful to apply "good taste":

Now I admit that "good taste" allows to relax those "rules" significantly in practice. But the idealized description should still be the one explained above. It is simply too easy to fool oneself with statistics, not least because our human intuition is not very good in that domain.