I Nature Physics on quantum foundations

[vanhees71]

Like $\{M_{px} \mid p\in P, x\in X\}$, where $M_{px}= \frac{1}{2}(|p\rangle\langle p| + |x\rangle\langle x|)$. (Or rather some more physical expression such as an integral over nearby coherent states - I doubt that your expression can be realized.)

The measurement picks one $M_{px}$, from which you can read off both $p$ and $x$.

If this is your POVM for a joint measurement of $x$ and $p$, so how is this concretely realized in an experiment? Maybe it's easier to give the POVM (math) first, and then give a measurement device?

 

[Morbert]

As an aside: The discussion between @Demystifier and @A. Neumaier might have some relevance to consistent histories.

For every possible preparation of a microscopic system $s$, the detector response theorem let's us compute the mean rates $p_k$ of measurement outcomes $k$ from a quantum measure $P_k$ like so $$p_k = \mathrm{tr}_{s}\rho_sP_k$$ Luis and Sanchez-Soto give a similar expression, but they consider a Hilbert space that includes both the microscopic system and ancilla $a$ relevant to the measurement process $$p_k = \mathrm{tr}_{s,a}\rho_s \rho_aU^\dagger|k\rangle\langle k|U$$My understanding is that @A. Neumaier maintains that there is not necessarily a physical ancilla $a$ that would let us recover projectors $|k\rangle\langle k|$ from the measure $P_k$ for every physical measurement scenario. i.e. $$P_k = \mathrm{tr}_a\rho_aU^\dagger|k\rangle\langle k|U$$This is actually something that consistent histories relies upon, as physical properties are associated with projective decompositions of the identity (PDI), not POVMs. If there are measurements for which there is no PDI, then that wold mean trouble for consistent histories, as we would have physical properties (the macroscopic measurement outcomes) that have no representation in consistent histories quantum theory.

 

[A. Neumaier]

There are two ancillas, they are called meters in the paper, see the sentence after Eq. (1).

No, these are meters that produce the measured results, not ancillas in the sense Peres (and everyone else) is using the term.

 

[A. Neumaier]

If this is your POVM for a joint measurement of $x$ and $p$, so how is this concretely realized in an experiment? Maybe it's easier to give the POVM (math) first, and then give a measurement device?

A concrete experimental realization is given in the paper Demystifier referred to in post #379; see also #399.

 

[A. Neumaier]

My understanding is that @A. Neumaier maintains that there is not necessarily a physical ancilla a that would let us recover projectors

Yes. It is a one-way street.

If you happen to have an ancilla in an environment and use it to define a measurement process, you get a POVM.

But given an arbitrary experimental arrangement for quantum detection one always has a quantum measure (by my detector response theorem) and hence a POVM , but usually no ancilla in the quantum description of the whole experiment. One can construct an associated ancilla by Naimark's theorem, but this ancilla does not live in the Hilbert space of the environment one started with but in an artificially constructed Hilbert space.

 

[Demystifier]

No, these are meters that produce the measured results, not ancillas in the sense Peres (and everyone else) is using the term.

Well, those meters are "ancillas" in the sense I used that term in post #374, for which you asked me to give a specific model. Maybe others don't use the word "ancilla" in that sense, but in that sense the ancilla is manifestly physical. If it's really so non-standard to think of "ancilla" in that sense, maybe I should write a paper about it, titled something like "Measurement apparatus as ancilla".

 

[vanhees71]

A concrete experimental realization is given in the paper Demystifier referred to in post #379; see also #399.

In #379 it's just standard QT. No POVM is constructed.

 

[Demystifier]

In #379 it's just standard QT. No POVM is constructed.

No POVM is explicitly constructed in that paper, but POVM is implicitly there as I explained in #374.
I also discuss this stuff briefly in my "Bohmian mechanics for instrumentalists", Sec. 3.3.

 

[vanhees71]

From our discussion here, I've gotten once more the impression that the POVM approach is entirely theoretical. Concrete understanding of measurement protocols is rather modeled by standard theory of open quantum systems and thus entirely within the standard interpretation of the quantum state using Born's rule.

 

[Morbert]

Yes. It is a one-way street.

If you happen to have an ancilla in an environment and use it to define a measurement process, you get a POVM.

But given an arbitrary experimental arrangement for quantum detection one always has a quantum measure (by my detector response theorem) and hence a POVM , but usually no ancilla in the quantum description of the whole experiment. One can construct an associated ancilla by Naimark's theorem, but this ancilla does not live in the Hilbert space of the environment one started with but in an artificially constructed Hilbert space.

Consider a microscopic system $s$ being measured, and the pointer $M$ doing the measuring

Premise 1)
The pointer must be describable with quantum mechanics. I.e. There must be a Hilbert space $\mathcal{H}_s\otimes\mathcal{H}_M$ in principle.

Premise 2)
Given some POVM $P_k$, there must be an associated measure $E_k$ for the pointer positions

Premise 3)
If the pointer really does measure the microscopic system, then it must be the case that rates are given by $$p_k = \mathrm{tr}_s\rho_{s}P_k = \mathrm{tr}_{s,M}\rho_{s,M} E_k = \mathrm{tr}_{s,M}P^\dagger_k\rho_{s,M}P_k E_k$$ I.e. The rates must be repoducible by both measures $P_k$ and $E_k$

Premise 4) Since the pointer positions are mutually exclusive, it must be the case that $E_kE_{k'} = \delta_{k,k'}$

I think premises 1 + 2 would give us an quantum mechanically describable ancilla that must exist and premises 3 + 4 would say the measurement scenario involving this ancilla must also be describable with a projective decomposition. Which of these would you take issue with?

 

[A. Neumaier]

Premise 2)
Given some POVM $P_k$, there must be an associated measure $E_k$ for the pointer positions

I don't understand the precise intended meaning of 'associated'?

Premise 4) Since the pointer positions are mutually exclusive, it must be the case that $E_kE_{k'} = \delta_{k,k'}$

If the $E_k$ are measures, how can their product be a number?

In practice, pointers on a continuous scale are readable only approximately. Hence the actual measurements average over some neighborhood, which most likely spoils exact orthogonality of whatever you precisely mean by $E_k$

 

[Morbert]

Oops, yes I meant $E_kE_{k'} = \delta_{k,k'}E_k$ or $\mathrm{tr}\rho E_kE_{k'} = \delta_{k,k'}\mathrm{tr}\rho E_k$. And yes continuous measurement would need a clearer treatment.

 

[Morbert]

I don't understand the precise intended meaning of 'associated'?

I'm trying to relate the POVM used to predict the mean rates, with a "pointer observable" the experimenter directly looks at (like a dial position) to read off results, as I think that is the pointer system is the ancilla that can be added to recover projective measurement. So this association would be an isometry $J:\mathcal{H}_s\rightarrow\mathcal{H}_M$ such that $J^\dagger E_k J = P_k$.

 

[A. Neumaier]

I'm trying to relate the POVM used to predict the mean rates, with a "pointer observable" the experimenter directly looks at (like a dial position) to read off results,

So the preparation of the projective measurement may involve computer calculations that go into computing the pixels that determine the number on an electronic display which the experimenter looks at?

as I think that is the pointer system is the ancilla that can be added to recover projective measurement. So this association would be an isometry $J:\mathcal{H}_s\rightarrow\mathcal{H}_M$ such that $J^\dagger E_k J = P_k$.

So $E_k$ is a projection matrix, not a measure?

 

[Morbert]

So the preparation of the projective measurement may involve computer calculations that go into computing the pixels that determine the number on an electronic display which the experimenter looks at?

So $E_k$ is a projection matrix, not a measure?

Yes, sorry I though the former was a special case of the latter

 

[A. Neumaier]

Yes, sorry I though the former was a special case of the latter

well, not quite. There is an isomorphism (though not s canonical one) between measures on the set of values and projection valued measures indexed by the set of values. This means that, informally, there are many more PVMs than measures, though each PVM defines a measure.

But whereas before you had used set brackets to distinguish sets from individuals, you now talked about $E_k$ without brackets, which would be single projections. These have no relation to measures.

 

[Morbert]

But whereas before you had used set brackets to distinguish sets from individuals, you now talked about $E_k$ without brackets, which would be single projections. These have no relation to measures.

After I looked through your paper I tried to adopt the convention used there but I should have been explicit in this change. E.g. This sentence

is defining a quantum measure as the collection of $P_k$s right?

 

[A. Neumaier]

After I looked through your paper I tried to adopt the convention used there but I should have been explicit in this change. E.g. This sentence

View attachment 316289

is defining a quantum measure as the collection of $P_k$s right?

Yes, but you forgot to add the term quantum, which makes a difference. Without that qualification, measure has the standard meaning as everywhere in mathematics. (A measure may be considered as a quantum measure where all $P_k$ are multiples of the identity.)

 

[Demystifier]

The editors of high impact journal Nature Physics explain why the field of quantum foundations is important for physics.
https://www.nature.com/articles/s41567-022-01766-x

As a reaction to this, another paper in the same journal is published yesterday. I can't see the whole paper (behind the paywall), but given the authors it must be about superdeterminism.
https://www.nature.com/articles/s41567-022-01831-5

 

[A. Neumaier]

As a reaction to this, another paper in the same journal is published yesterday. I can't see the whole paper (behind the paywall), but given the authors it must be about superdeterminism.
https://www.nature.com/articles/s41567-022-01831-5

the observed violations of Bell’s inequality can be said to show that maintaining local causality requires violating statistical independence. [...] Types of local hidden variables theories that violate statistical independence include those that are superdeterministic, retrocausal [or] supermeasured.

 

[physika]

But what's wrong with that? In certain cases the wavefunction is sharply peaked, which means that the quantum particle exhibits "classical behaviour". But that doesn't make it a "classic particle".

Just because a sheep can be fluffy it doesn't mean it's a pillow; we just perceive that in that case (unshaved) it shows "pillow-like behaviour".

Maybe it's nomenclature, but the wave-particle duality is not a statement about the ontology of quantum particles, afaik. That's why I'm surprised by VanHees' adament statement.

But maybe this is off-topic.

Indeed.

https://opg.optica.org/oe/fulltext.cfm?uri=oe-26-4-4470&id=381585"we demonstrate the new measure of wave-particle duality based on two kinds of coherence measures quantitatively for the first time. The wave property, quantified by the coherence in the l1-norm measure and the relative entropy measure, can be obtained via tomography of the target state, which is encoded in the path degree of freedom of the photons. The particle property, quantified by the path information, can be obtained via the discrimination of detector states, which is encoded in the polarization degree of freedom of the photons. Our work may deepen people’s understanding of coherence and provide a new perspective regarding wave-particle duality.".

 

[physika]

Q1A: Do the [far-distant] parts have definite values from the moment they leave the preparation device and along their travel towards the measurement devices of Alice and Bob, with the correlations being explained by virtue of their shared preparation?

as symmetrical law.

.

 

[Demystifier]

Indeed.

https://opg.optica.org/oe/fulltext.cfm?uri=oe-26-4-4470&id=381585"we demonstrate the new measure of wave-particle duality based on two kinds of coherence measures quantitatively for the first time. The wave property, quantified by the coherence in the l1-norm measure and the relative entropy measure, can be obtained via tomography of the target state, which is encoded in the path degree of freedom of the photons. The particle property, quantified by the path information, can be obtained via the discrimination of detector states, which is encoded in the polarization degree of freedom of the photons. Our work may deepen people’s understanding of coherence and provide a new perspective regarding wave-particle duality.".

The notion of wave-particle duality is still quite popular in experimental physics, but not in theoretical physics. This notion describes well how objects appear in experiments, but is not very useful in explaining why they appear so.

 

[Demystifier]

As a reaction to this, another paper in the same journal is published yesterday. I can't see the whole paper (behind the paywall), but given the authors it must be about superdeterminism.
https://www.nature.com/articles/s41567-022-01831-5

Today the arxiv version appeared. https://arxiv.org/abs/2211.01331

 

[Lynch101]

Today the arxiv version appeared. https://arxiv.org/abs/2211.01331

There seems to be a typo in the arxiv version "hidden variable theories quantum mechanics" should be "hidden variable theories that reproduce quantum mechanics", sorry about that

 

[martinbn]

Today the arxiv version appeared. https://arxiv.org/abs/2211.01331

off topic
Why is that a paper!? Surely it is just a comment. Also how is it that so many papers in the foundations are a 5 page blow up of something that can be said in a paragraph!

 

[Fra]

the observed violations of Bell’s inequality can be said to show that maintaining local causality requires violating statistical independence. [...] Types of local hidden variables theories that violate statistical independence include those that are superdeterministic, retrocausal [or] supermeasured.

the observed violations of Bell’s inequality can be said to show that maintaining local causality requires violating statistical independence. [...] Types of local hidden variables theories that violate statistical independence include those that are superdeterministic, retrocausal [or] supermeasured.

The normal notion of statistical indepdencence is defined for events that belong to the same sample space. Again here is the question how we map mathematics to reality: Does the sampling at Alice and Bob belong to the same "sample space"? Ie. is this abstracted mapping satisfactory?

I tend not to think so. The only way it can be so, is when you entertain the common idea that Alice and Bob has pointers that store to the common classical environment. But this ignores the "internal inteactions" going on, ie. the physics between observers.

If you think about this, the "violation of statistical independence" is not really something strange, because there is not one sample space to start with. I think we can not avoid the physics of interacting observers, just thinking of the observes are something that "writes to classical memory", isn't satisfactory because it's not subject to an actual sampling process anyway.

/Fredrik

 

[vanhees71]

Without liking to read that "paper", it's clear that you get a usual probability measure in QT only for experiments that can be done in reality, i.e., if you have the joint measurement of the photons' polarization by Alice and Bob for a two-photon system, you get a probability for each possible outcome and these probabilities add up to 1.

If you want to test the Bell inequality you have to repeat the corresponding set of experiments with measuring polarizations in different directions at A and B on an ensemble of equally prepared photon pairs. QT describes only experiments that can be really done in the lab and not fictitious ones that cannot be done in the lab!

 

[Demystifier]

off topic
Why is that a paper!? Surely it is just a comment.

Technically, it's a correspondence.

Also how is it that so many papers in the foundations are a 5 page blow up of something that can be said in a paragraph!

Can you give other examples?

 

[vanhees71]

Well, the EPR paper and even more Bohr's answer to it are examples ;-). SCNR.

 

[physika]

off topic
Why is that a paper!? Surely it is just a comment. Also how is it that so many papers in the foundations are a 5 page blow up of something that can be said in a paragraph!

...that is only one page

 

[martinbn]

Can you give other examples?

Yes, pick three random papers, chances are one will be an example.

 

[Demystifier]

Well, the EPR paper and even more Bohr's answer to it are examples ;-). SCNR.

OK, explain the EPR paper in one paragraph!

 

[Demystifier]

Yes, pick three random papers, chances are one will be an example.

Pick from which sample?

 

[martinbn]

Pick from which sample?

Why, are you going to write a paper on it?

 

[vanhees71]

OK, explain the EPR paper in one paragraph!

"We don't believe in the probablistic behavior of nature as predicted by quantum theory and assume that there may be some other better theory, which we cannot specify in detail though." ;-).

 

[gentzen]

Well, the EPR paper and even more Bohr's answer to it are examples ;-). SCNR.

OK, explain the EPR paper in one paragraph!

"We don't believe in the probablistic behavior of nature as predicted by quantum theory and assume that there may be some other better theory, which we cannot specify in detail though." ;-).

Cool! Can you do the same for Bohr's answer?

 

[vanhees71]

That's an even greater challenge ;-). I've to check, whether today I can interpret something into Bohr's answer. Some years ago, I couldn't make sense of it at all.

 

[Fra]

"We don't believe in the probablistic behavior of nature as predicted by quantum theory and assume that there may be some other better theory, which we cannot specify in detail though." ;-).

Isn't it the explanatory level for the probabilistic behaviour, in a way that complies to both observation and various hailed principles of physical interactions that makes quantum theory is "incomplete"? Quantum theory describes experiments, but does not provide explanations beyond that it follows from the hamiltonian of the complete system[the hamiltonian which is INPUT to the predictions; on par with initial conditions].

I think critique is still valid. Bell inequality just shot down the simplest possible option for explanation of objective ignorance explanation(ie bell style HV). This also corresponds to the naive form of incompletness. I consider this particular horse beaten dead.

But that does not make the original, deeper concern go away if you think about the whole problem, just because noone yet has a deeper satisfactoty theory at hand. Many use the success to QM as an argument to ignore the subtle issue, but as long as the completion with all forces is missing, I think the whole question is open.

/Fredrik

 

[vanhees71]

Isn't it the explanatory level for the probabilistic behaviour, in a way that complies to both observation and various hailed principles of physical interactions that makes quantum theory is "incomplete"? Quantum theory describes experiments, but does not provide explanations beyond that it follows from the hamiltonian of the complete system[the hamiltonian which is INPUT to the predictions; on par with initial conditions].

Quantum theory is as complete as any other physical theory. As with any physical theory this statement depends on what we know about nature, and it may change when we learn something new, but so far nobody has learnt, what might be incomplete with quantum theory. Everything that is predicted to be random for a given situation concerning quantum systems has always been observed to be random and even the quantitative predictions (probabilities) have turned out right with amazing accuracy.

I think critique is still valid. Bell inequality just shot down the simplest possible option for explanation of objective ignorance explanation(ie bell style HV). This also corresponds to the naive form of incompletness. I consider this particular horse beaten dead.

But that does not make the original, deeper concern go away if you think about the whole problem, just because noone yet has a deeper satisfactoty theory at hand. Many use the success to QM as an argument to ignore the subtle issue, but as long as the completion with all forces is missing, I think the whole question is open.

That's the point! The true problem is not that QT can explain very many things and contradicts our prejudices and classical physics but that there is a piece missing, i.e., the quantum description of the gravitational interaction, and that's where QT is really incomplete as a scientific theory but this seems not to have anything to do with these philosophical quibbles. Maybe a more comprehensive future theory is more satisfactory for philosophers than QT but that's not of any importance for physics as a natural science.

 

[Fra]

the quantum description of the gravitational interaction, and that's where QT is really incomplete as a scientific theory but this seems not to have anything to do with these philosophical quibbles.

I am guessing that many may agree with this, but just to speak for my own understanding and thinking about this, there is a link between this and the "foundational quibbles", but it's visibility is interpretation dependent. But I totally agree that such potential link goes well beyond the bell style HV anyway. Looking for loopholes for the bells inequality will I think not help unify gravity. I also don't think the original debate or Einstein and Bell specifically had unification gravity in mind.

For me the "link" is not that subtle though, it lies in the interaction between different observer backgrounds(which current QM does not treat well, if at all), and these are associated to different spacetime backgrounds, which is the potential link to gravitational inteaction.

/Fredrik

 

[Lord Jestocost]

Also how is it that so many papers in the foundations are a 5 page blow up of something that can be said in a paragraph!

In order to sold "old wine" in "new bottles"!

 

[Fra]

In order to sold "old wine" in "new bottles"!

The old wine is just the hidden variable, you can't assess it without buying the bottle first. Once the news of old wine decohered into the market in enough samples to constitute good evidence(and not only single rumours, _one_ bad bottle proves nothing), the bottled are all sold and newer bottles are out for sale. It's a winning concept no matter how.

It's all driven by expectations which is the core lesson anyway. And the games beats anyone trying to nail the fundamental values in the race.

/Fredrik

 

[physika]

But that does not make the original, deeper concern go away if you think about the whole problem, just because noone yet has a deeper satisfactoty theory at hand. Many use the success to QM as an argument to ignore the subtle issue, but as long as the completion with all forces is missing, I think the whole question is open.

/Fredrik

-
Weinberg’s vision

https://cns.utexas.edu/news/steven-weinberg-s-test-of-quantum-mechanics-might-soon-be-realized

"For many years, Weinberg had been deeply dissatisfied with quantum mechanics and envisioned an experiment that might poke holes in the theory, while also providing clues about what to replace it with."

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.042117

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.106.032209

.

 

[Fra]

-
Weinberg’s vision

https://cns.utexas.edu/news/steven-weinberg-s-test-of-quantum-mechanics-might-soon-be-realized

"For many years, Weinberg had been deeply dissatisfied with quantum mechanics and envisioned an experiment that might poke holes in the theory, while also providing clues about what to replace it with."

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.042117

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.106.032209

.

I am not sure his ides address the issues I see. Is he looking for modifications of closed QM within the born-markov approxomation? It seem to me that for general stance where the environment(or agent/observer) is a participant and not just a heat bath or passive recorder, such approximations cant hold. Of course a real system is always partially open. Not to mention that you cant screen a system from gravity. But this is to me only half side of the problem.

2 years ago in a webtalk on both hiatory and the future of qft he mentioned asymptotic saftey and string theory and as i recall placed his best on strings, comparing them.

But he also said that ay the fundamental level (including also gravity) he didnt think qft would survive as fundamental best understanding but would remain as an effective tool.

Edit:

/Fredrik

 

[vanhees71]

Well, I don't think that Lindblad equations are a solution. They are approximations to describe the time evolution of open quantum systems enforcing Markovian dynamics for processes that a priori are non-Markovian. It's not even guaranteed to yield the correct equilibrium long-time limit without special care.

 

[LittleSchwinger]

"We don't believe in the probablistic behavior of nature as predicted by quantum theory and assume that there may be some other better theory, which we cannot specify in detail though." ;-).

Hey, I know this is a joke but I thought this was an interesting "challenge" so I thought I'd give my own go.

I'd say the EPR paper is not directly associated with probability but is rather that the combination of:

1. A weak form of realism
2. Locality
3. The correlations in certain entangled states

Implies that quantum mechanics is incomplete. Incomplete meaning that you can derive the existence of facts that the theory should be able to predict that it doesn't.

Bohr's response is basically that even the weak form of realism assumed in (1) is not true in quantum theory and so the EPR theorem has no hold on quantum mechanics.

I would say the GHZ no-go theorem, involving three possible measurements on three spin-1/2 particles, is a better demonstration of the EPR argument and Bohr's rebuttal than the original scenario, which involves two measurements on two spin-1/2 particles*.

I can go into more detail if anybody wants .

*Technically this is Bohm's version of EPR. The original actually involved position and momentum, but mathematically it makes no difference.

 

[bhobba]

But he also said that ay the fundamental level (including also gravity) he didnt think qft would survive as fundamental best understanding but would remain as an effective tool.

That is the well known effective field theory approach that Weinberg was always a proponent of. Actually I cant think of any well known physicist that wasn't. Bohm maybe?

https://arxiv.org/abs/2101.04241

Thanks
Bill

 

[Demystifier]

That is the well known effective field theory approach that Weinberg was always a proponent of. Actually I cant think of any well known physicist that wasn't.

I think anybody who tries hard to make QFT mathematically rigorous is not a proponent of effective field theory approach. Big names include Haag and Wightman. On that matter see also http://philsci-archive.pitt.edu/8890/

 

[Fra]

That is the well known effective field theory approach that Weinberg was always a proponent of.

For me the difference lies more in what to settle with and what to explore more.

For me at least, the stance to see the standard model as an effective theory, is not a final answer to rest with or a disclaimer for not looking further into theory and just stick to experimentally calibrating the models we have. Some may also have the view that renormalization group theory is all the "scaling of theory" we need.

It on the contrary suggests that we should seek further explanatory power is to be found not in the parameters or structure of the current effective theory iteself but in trying to understand the context of where effective theories form and evolve in the bigger context of a theory of theory (of which there are competing ideas). Here I have a feeling physicist take on different stances, but my feeling is that many belong to the first camp that uses the effective view more like an excuse to not look forther. I make the exact opposite conclusion.

/Fredrik