I Nature Physics on quantum foundations

[martinbn]

Of course. Let me remind you that we discuss examples that illustrate the difference between superluminal signalling and superluminal action. Standard QM is not a good example, which is why we discuss other examples.

No, we are discussing whether a statement was conraversial or not. If it is a consequence of QM it shouldn't be.

 

[Morbert]

So strictly speaking there are two stages of deduction required to get from the observed position of the flash on the detector to the "measured" value of spin.

I don't think you will ever be able to eliminate such deductions entirely, as we will always need to construct a logical implication between the macroscopic measurement outcome read by the experimenter, and the measured variable of the quantum system. I.e. There will always be an intermediate dynamical model of both the measured system and relevant degrees of freedom of the measurement apparatus that justifies any inferences we make from an experiment.

E.g. forget the SGE experiment and just consider a plate detector measuring the position of a photon that strikes it. Is the flash on this plate directly measuring the photon position, or is it indirectly measuring the photon position, since we might say it is really recording an electron cascade in one of its microchannels induced by the photon?

 

[PeterDonis]

we will always need to construct a logical implication between the macroscopic measurement outcome read by the experimenter, and the measured variable of the quantum system.

Yes, this is obvious since by hypothesis the measuring device and the measured system are different degrees of freedom. But one can still look at how many stages of deduction are required to get from the measuring device to the observable of the measured system that we are interested in.

 

[Demystifier]

Maybe it's nomenclature

Yes, and I'd say this nomenclature is somewhat outdated.

 

[Demystifier]

How can there be a non-local action at a distance and no faster than light signaling at the same time?

Let me remind you that we discuss examples that illustrate the difference between superluminal signalling and superluminal action.

No, we are discussing whether a statement was conraversial or not.

Do I miss something? Did you perhaps got a satisfying answer to your question above and then switched to another topic? Discussions with you would be much easier if you could occasionally say something like: "OK, now I understand this, thank you for explaining it to me, now I have another question.". Or if that would be too much, a simple "like" would be enough to signal that I answered your question at least partially satisfying. Or if a "like" would be too much as well, you could still indicate somehow that you are no longer interested in the initial question. Otherwise, I have an impression that all your later questions are motivated by the initial one.

So, what's your question, exactly?

 

[CoolMint]

I see this claim more often on PF, but why exactly? To me, the duality states that quantum objects show both particle and wave behaviour, which is captured in a new ontological category for the quantum object we call "quantum particle". This is how I've understood this concept for a long time. What's outdated about that? I'd say the concept has evolved, not that it's outdated.

Didn't read all the replies, sorry if this has been asked before.

Because the classical scale of everyday objects is just too imposing.
The world is best described with the use of the 4 fundamental forces of nature - the Gravitational force, the Weak Nuclear force, the Electromagnetic force and the Strong Nuclear force.
We get 'particles'("matter") when these forces interact and produce observable and measurable effects. The wavefunction is almost certainly a mathematical abstract and nothing else and what it describes is the unobservable lower layer that underlies the observations.
The Wave/particle duality is an inferior concept to the new notion of how the world works:

Quantum fields(mathematical entities describing the underlying reality/mechanisms of nature) -- The four fundamental forces(which produce measurable outcomes upon a measurement context) -- Measurement results(observable macro reality of tables and chairs)

The wave/particle notion seems to suggest that there are two entities at play(waves and particles). The new notion explicitly states that the field is fundamental and the 'particles' are emergent momentary excitations.

 

[vanhees71]

"Not predetermined" random outcomes at spacelike separated (spacetime) points/events which are not independent.

In other words that's what I call "far-distant correlations".

The "not predetermined" is the important part of that notion, and also the part where some vagueness enters. Just because the outcome was not yet "fully" predetermined at any point in the intersection of the past lightcones of the points/events doesn't mean that it got determined exactly at the moment where the random outcomes became known and recorded.

That's true for "von Neumann filter measurements". Usually in experiments with photons the photons get absorbed by the detector. Then there are no photons with any properties prepared. In such a case we simply get a measurement result with probabilities according to the quantum state (prediction), which we can test with these experiments on an ensemble of equally prepared systems.

But in the simplest form of the notion, one could imagine it indeed as if the random outcomes only got determined at the moment where they got recorded. The notion is unproblematic even in this "simple but unrealistic" form.

That's my point! It's "unproblematic", but particularly this is what's denied by all those who think that there's a "measurement problem", because it's very hard to accept that completely undetermined properties can be strongly correlated, even if the measured properties are measured at parts of the system at very far distant places. This inseparability feature of entangled state was what Einstein really bothered (according to his Dialectica article of 1948 which is much clearer than the (in)famous EPR article).

 

[Demystifier]

That's true for "von Neumann filter measurements".

I would like to stress that all POVM measurements, not only projective measurements, are described by a collapse postulate in standard QM. The QM postulates are summarized nicely in the following excerpt from the book "Quantum Computations and Quantum Information" by Nielsen and Chuang. Eq. (2.160) is the collapse postulate for general (not necessarily projective) measurements.

 

[Lord Jestocost]

This inseparability feature of entangled state was what Einstein really bothered ...

To my mind, Einstein’s illusion was that the experiential reality could be represented by a physical theory that could be based on the assumption that the entities and their characters the theory is about might exist objectively in an ontological sense and thus literally experiencer-independently (“scientific realism”).

 

[gentzen]

I don't want to be the translator from @vanhees71 to English, but I think that non-local randomness is something he would agree is part of QFT.

[...]

In other words that's what I call "far-distant correlations".

Wow, martinbn was indeed right!

That's my point! It's "unproblematic", but particularly this is what's denied by all those who think that there's a "measurement problem", because it's very hard to accept that completely undetermined properties can be strongly correlated, even if the measured properties are measured at parts of the system at very far distant places.

I had a conversation with Ruth E. Kastner (a long time ago) on Mateus Araújo's blog, where she agreed that

Of course there is nothing wrong with instrumentalism as a ‘shut up and calculate’ tactic for evading the conceptual and physical puzzles presented by QM. What is wrong is elevating that evasion to a dogmatic prescription about how to ‘interpret’ QM–which is what we see from many instrumentalists. That’s the only thing I’ve been contesting.

Except for using ‘shut up and calculate’ as a bad name for instrumentalism (I implicitly proposed 'let me calculate and explain' instead in that exchange), I had no problems (and still don't have) with that reaction. At about the same time also Steven Weinberg's attack on quantum interpretations and specifically instrumentalism appeared, which I found totally unacceptable back then. At some later point I read something which temporarily made me understand his attack (it had something to do with being able to explain such stuff in a textbook in a satisfying way), but I forgot it again in the meantime.

That's true for "von Neumann filter measurements".

I would like to stress that all POVM measurements, not only projective measurements, are described by a collapse postulate in standard QM. The QM postulates are summarized nicely in the following excerpt from the book "Quantum Computations and Quantum Information" by Nielsen and Chuang. Eq. (2.160) is the collapse postulate for general (not necessarily projective) measurements.

Eq. (2.160) (which first appeared as Eq. 2.92) does not describe a POVM measurement. Section 8.2.4 explains something about the interpretational background of that formulation, but (from my POV) this doesn't change that vanhees71 is "not wrong" here.
I learned this later and also that this equation is related to Kraus operators

The axioms are the same as defining Kraus operators, or quantum channels/maps/operations, as N&C do in 8.2.4, and they're even on wikipedia

N&C never mention Kraus operators, but refer to [Kra83] (K. Kraus. States, Effects, and Operations: Fundamental Notions of Quantum Theory. Lecture Notes in Physics, Vol. 190. Springer-Verlag, Berlin, 1983) via "The theory of generalized measurements which we have employed was developed between the 1940s and 1970s. Much of the history can be distilled from the book of Kraus [Kra83]." and "We mention just a few key references, primarily the book by Kraus [Kra83] , which contains references to much earlier work on the subject."

 

[vanhees71]

[...]

Wow, martinbn was indeed right!I had a conversation with Ruth E. Kastner (a long time ago) on Mateus Araújo's blog, where she agreed that

Except for using ‘shut up and calculate’ as a bad name for instrumentalism (I implicitly proposed 'let me calculate and explain' instead in that exchange), I had no problems (and still don't have) with that reaction. At about the same time also Steven Weinberg's attack on quantum interpretations and specifically instrumentalism appeared, which I found totally unacceptable back then. At some later point I read something which temporarily made me understand his attack (it had something to do with being able to explain such stuff in a textbook in a satisfying way), but I forgot it again in the meantime.

The point is, of course, that you are free to "want more" from science than it "promises" to do, i.e., to deliver a way to find "laws of nature" that describe, how nature behaves (or more precisely how we observe it to behave). That's why there are so many "interpretations" of the QT formalism. In principle it indeed describes what we observe (except that there's this fundamental problem of "quantum gravitation", i.e., the incompatibility between GR and QT) when just accepting the probabilistic interpretation of the "quantum state", using Born's rule, as well as the quantum-mechanical time evolution. That's in a way a "shut up and calculate" paradigm, because we restrict ourselves of the purely scientific meaning of the theory and don't expect to find some "deeper truth" in it. What I never understood is the fact that such a demand nobody ever had in view of classical physics ;-)).

Eq. (2.160) (which first appeared as Eq. 2.92) does not describe a POVM measurement. Section 8.2.4 explains something about the interpretational background of that formulation, but (from my POV) this doesn't change that vanhees71 is "not wrong" here.
I learned this later and also that this equation is related to Kraus operators

I don't think that the measurement problem, whatever you think it might be, is solved by generalizing the very idealized idea of von Neumann filter measurements (POV) with POVMs, which is simply taking into account the possibility for "incomplete measurements", which is almost always what we are able to do in the lab. The probabilistic nature of the quantum state persists also in this more general formulation. I don't see that POVMs is something that goes much beyond standard QT, although of course you can take POVMs as the measurement postulate as in the book quoted above (this seems to be a very concise formulation of the postulates, which is much more careful than the standard formulations in the introductory textbooks).

N&C never mention Kraus operators, but refer to [Kra83] (K. Kraus. States, Effects, and Operations: Fundamental Notions of Quantum Theory. Lecture Notes in Physics, Vol. 190. Springer-Verlag, Berlin, 1983) via "The theory of generalized measurements which we have employed was developed between the 1940s and 1970s. Much of the history can be distilled from the book of Kraus [Kra83]." and "We mention just a few key references, primarily the book by Kraus [Kra83] , which contains references to much earlier work on the subject."

Sounds interesting. My source for this direction of more recent research is A. Peres, Quantum Theory, Concepts and Methods.

 

[Demystifier]

Eq. (2.160) (which first appeared as Eq. 2.92) does not describe a POVM measurement.

Then what does Eq. (2.160) describe? Perhaps it doesn't describe the POVM measurement itself, but it certainly describes the update of information after the POVM measurement.

Of course there is nothing wrong with instrumentalism as a ‘shut up and calculate’ tactic for evading the conceptual and physical puzzles presented by QM. What is wrong is elevating that evasion to a dogmatic prescription about how to ‘interpret’ QM–which is what we see from many instrumentalists. That’s the only thing I’ve been contesting.

With that, I absolutely agree.

 

[Demystifier]

I don't see that POVMs is something that goes much beyond standard QT, although of course you can take POVMs as the measurement postulate as in the book quoted above

Indeed, today POVM is considered to be a part of standard QT. In fact, POVM measurement of a measured system can be described as a projective measurement of a larger system, which includes not only the measured system but also a part of its "ancilla" environment. From this bigger point of view, all measurement are projective.

 

[gentzen]

Eq. (2.160) (which first appeared as Eq. 2.92) does not describe a POVM measurement.

Then what does Eq. (2.160) describe?

The provided wikipedia link succinctly explains this:

A measurement upon a quantum system will generally bring about a change of the quantum state of that system. Writing a POVM does not provide the complete information necessary to describe this state-change process.  To remedy this, further information is specified by decomposing each POVM element into a product: ...

In my own words: A POVM doesn't include a collapse postulate (a change of the quantum state), but Eq. (2.160) does include one.

 

[Demystifier]

In my own words: A POVM doesn't include a collapse postulate (a change of the quantum state), but Eq. (2.160) does include one.

With that I agree. But my point was to deny a frequent misconception that "a collapse is something that is associated only with projective measurements, not with POVM measurements".

 

[gentzen]

With that I agree. But my point was to deny a frequent misconception that "a collapse is something that is associated only with projective measurements, not with POVM measurements".

Interesting. What exactly is the misconception that you have in mind? You agree that a collapse postulate (a change of the quantum state) is not included in a POVM measurement. I guess you also agree that a typical description of a projective measurement includes a collapse postulate.

Is the "misconception" the believe that there would be some deeper reason (beyond mere historical accident and convention) why descriptions of projective measurements typically include a collapse postulate, and POVM do not?

 

[vanhees71]

Indeed, today POVM is considered to be a part of standard QT. In fact, POVM measurement of a measured system can be described as a projective measurement of a larger system, which includes not only the measured system but also a part of its "ancilla" environment. From this bigger point of view, all measurement are projective.

Sure, that's why I don't think that it changes any of the "fundamental quibbles" some people have, and I'd also take only the part giving the probabilities for the "POVM measurement" result but not the "collapse postulate" since as in the case of the more restricted POV measurements it depends on the specific apparatus used to realize the POVM measurement. So whether or not the measured system is described after the POVM measurement by the assumed "collapsed state", cannot be generally stated either but maybe for some specific POVM measurement it's possible to realize such a specific "state preparation by measurement".

 

[Demystifier]

Interesting. What exactly is the misconception that you have in mind? You agree that a collapse postulate (a change of the quantum state) is not included in a POVM measurement. I guess you also agree a typical description of a projective measurement include a collapse postulate.

It's a misconception to say that one of those includes a collapse postulate and the other doesn't. In a consistent joint treatment of projective and POVM measurements, either both include a collapse postulate or neither does. Unfortunately, some "typical" presentations of projective and POVM measurements look as you described above, which is a misconception.

Is the "misconception" the believe that there would be some deeper reason (beyond mere historical accident and convention) why descriptions of projective measurements typically include a collapse postulate, and POVM do not?

Yes, exactly!

 

[Demystifier]

Sure, that's why I don't think that it changes any of the "fundamental quibbles" some people have

Exactly!

 

[gentzen]

In a consistent joint treatment of projective and POVM measurements, either both include a collapse postulate or neither does.

The only problem is that the definition of POVM explicitly doesn't include a collapse postulate. The general case presented by N&C seems to be called "quantum measurement" by them. Wikipedia claims that also the name quantum instrument would be in use, but the reference section of that article does not convince me. More convincing is Wikipedia's claim that the mathematical formalism is actually called quantum operation, and used to describe the effects of measurement and transient interactions with an environment. The reference section seems to support that claim, and it is also plausible: Why on Earth would anybody want to call every manipulation or preparation of a quantum system a measurement?

 

[Morbert]

As an aside, there is an interesting ambiguity in N&C's account of measurement, since a sequence of projective measurement results can be expressed as a sequence of projectors $E_{m_1}(t_1)E_{m_2}(t_2)\dots E_{m_N}(t_N)$ which can be considered an operator $M_m$ i.e. a single POVM result, since $\sum_m M_m = I$. So by describing the measurement process with a series of projectors or just one operator, we can decide if collapse happens many times or just once.

 

[Demystifier]

The only problem is that the definition of POVM explicitly doesn't include a collapse postulate.

Nor does PVM (projector valued measure).

 

[Demystifier]

As an aside, there is an interesting ambiguity in N&C's account of measurement, since a sequence of projective measurement results can be expressed as a sequence of projectors $E_{m_1}(t_1)E_{m_2}(t_2)\dots E_{m_N}(t_N)$ which can be considered an operator $M_m$ i.e. a single POVM result, since $\sum_m M_m = I$. So by describing the measurement process with a series of projectors or just one operator, we can decide if collapse happens many times or just once.

If you interpret it as one collapse, then you cannot say at what time this collapse happens. Hence, if you postulate that collapse must happen at a definite time, then the one-collapse interpretation is ruled out, so the ambiguity is removed.

Conversely, if you don't make such a postulate, then the collapse may be a process taking a long time, in which case I see no conceptual problem with thinking of a series of collapses as one collapse. It has a classical analog. If you travel by car from New York to Los Angeles, you will have many intermediate stops. You can think of it either as one travel or a series of many travels, there is no any problem with that "ambiguity".

 

[A. Neumaier]

POVM measurement of a measured system can be described as a projective measurement of a larger system, which includes not only the measured system but also a part of its "ancilla" environment. From this bigger point of view, all measurement are projective.

...except that this ancilla is a purely mathematical construct in a nonphysical Hilbert space, hence something without any physical content.

 

[Demystifier]

...except that this ancilla is a purely mathematical construct in a nonphysical Hilbert space, hence something without any physical content.

... except that there are many explicit counterexamples to your claim.

 

[A. Neumaier]

... except that there are many explicit counterexamples to your claim.

Please point to one of them.

 

[Demystifier]

Please point to one of them.

Take e.g. the book A. Peres, Quantum Theory: Concepts and Methods, Sec. 9-6.
In the very first sentence he writes "It will now be shown that there always exists a physical mechanism (that is, a realizable experimental procedure) generating any desired POVM represented by given matrices Aμ" (his italics). The preparation procedure is then explained at page 288.

 

[A. Neumaier]

Take e.g. the book A. Peres, Quantum Theory: Concepts and Methods, Sec. 9-6.
In the very first sentence he writes "It will now be shown that there always exists a physical mechanism (that is, a realizable experimental procedure) generating any desired POVM represented by given matrices Aμ" (his italics). The preparation procedure is then explained at page 288.

This id a counterclaim but not a counterexmple.
Never take words for a valid argument if the details don't support them!

On p.288 Peres assumes already the existence of the ancilla! But the Hilbert space in which the ancilla is constructed - through Neumark's (or Naimark's) theorem as mentioned on p.285 - is non-physical, constructed in a purely mathematical way. The projection matrices defined on p.288 are only formal, not physical, since they are realized not in the physical Hilbert space in which the experimental POVM to be replicated, but only in a mathematical Hilbert space!

Thus the claim about the physicality of the mechanism is unsupported by the details Peres provides.

 

[Demystifier]

Never take words for a valid argument if the details don't support them!

Do you have a reference (not your own) that supports the claim that ancilla is unphysical?

 

[A. Neumaier]

Do you have a reference (not your own) that supports the claim that ancilla is unphysical?

The ancilla is clearly a purely mathematical construct. Thus my claim follows from common sense and needs no reference.

On the other hand, claiming that a purely mathematical construction of a Hilbert space and objects in it is physical is a nontrivial assertion that would require a justification with a reference.