Quantum measurement of a Strontium ion

[PeterDonis]

ontological theories (such as Bohmian mechanics) are also "local" in the QFT sense

Yes, "QM" here includes any interpretation of QM, since all of them make the same predictions, and therefore all of them satisfy the property that spacelike separated measurements commute for the case under discussion.

 

[Demystifier]

Why aren't the correlations there?

I already said, because correlations are in the observed objects, not in the Hilbert space.

If you have a two-spin state like the singlet state $|1/2,-1/2 \rangle-|-1/2,1/2 \rangle$, then ... you have a 100% correlation:

No, as long as you only talk about the state in the Hilbert space, you cannot talk about correlation at all.

Whenever you measure $\sigma_z=1/2$ on particle 1, you'll measure $\sigma_z=-1/2$ on particle 2 or vice versa.

Yes, "measure" is the key word. To paraphrase Peres, measurement doesn't happen in the Hilbert space, it happens in the laboratory.

As long as you ensure that nothing disturbes the state, the entanglement is preserved,

But measurement does disturb the state.

 

[vanhees71]

I already said, because correlations are in the observed objects, not in the Hilbert space.

Sure, but the quantum state is formulated in Hilbert space. It describes the probabilities for the outcome of measurements, and the correlations described by entangled states are measurable, and they are in the objects.

No, as long as you only talk about the state in the Hilbert space, you cannot talk about correlation at all.Yes, "measure" is the key word. To paraphrase Peres, measurement doesn't happen in the Hilbert space, it happens in the laboratory.

Sure, but were do I claim something else? The polarization of the single photons in a typical Bell experiment with photon pairs are measured in the lab, and the correlations are revealed by such measurements when comparing the outcome of these measurements for each photon pair (for which you need an adequate measurement protocol to enable this comparison for the outcome of local single-photon measurements belonging to each pair; usually that's done by sufficiently precise "time stamps" of the single-photon measurement events.

But measurement does disturb the state.

Of course, when doing a measurement on at least one of a single photon you usually destroy the entanglement and another measurement after that won't show the correlations described by the original entangled state but something different, depending on how you changed the state by the first measurement.

I don't see any contradiction between what you and Peres say with my very simple point of view. It just takes the quantum state with its solely probabilistic meaning seriously. Indeed the formalism is a formalism not the real world, but that's true for any physical theory. In Newtonian mechanics the Earth in its Orbit around the Sun is also not a triple of real numbers used to describe the Earth's position in terms of some coordinates.

 

[Demystifier]

It just takes the quantum state with its solely probabilistic meaning seriously. Indeed the formalism is a formalism not the real world, but that's true for any physical theory.

I agree that the formalism is not the real world. But at least the real world should be represented by a formalism. The problem is that the quantum state does not represent the real world (except in the collapse interpretations and many world interpretations). The quantum state represents the probability, but probability is not the real world. The real world is the thing which we observe in a single measurement, and probability does not represent a single measurement. A click in the detector is not represented by a number $p\in[0,1]$. So we need some additional formalism and some additional variables that represent a single measurement. Bell calls such additional variables $\lambda$ and shows that they must obey some nonlocal laws in the sense of action at a distance, even if those laws are probabilistic.

But you refuse to even think about an additional variable $\lambda$. So the problem is not that you take the probabilistic meaning of the quantum state seriously. The problem is that you refuse to take anything else seriously. The probability $p$ is a probability of some event mathematically represented by some variable $E$, so we really have $p(E)$. The Bell theorem asks: OK, if we have $p(E)$, then what does it tell us about $E$? The minimal interpretation, by contrast, talks about $p(E)$, but refuses to talk mathematically about $E$. The minimal interpretation talks about events informally, but refuses to talk about them mathematically. That's why the minimal interpretation is incomplete and that's why (your version of) the minimal interpretation cannot see the implications of the Bell theorem.

 

[vanhees71]

The quantum state represents the real world in the sense that it predicts probabilities for the outcome of measurements, given the preparation of the measured system. One should not forget the instrumental definition of the quantum state as a preparation procedure (or an equivalence class of preparation procedures) for ensembles enabling one to check the probabilistic predictions of the theory.

In general QT doesn't tell you much about the outcome of a single measurement, but only about the statistical properties of ensembles of equally (in a stochastic sense!) prepared systems. Whether or not this is a "complete" description of the world is a philosophical debate going basically on since Born's probability-interpretation footnote. I think from a physical point of view you can never prove whether any theory is "complete". As far as we know today, QT is complete in the sense that it describes all observations right it can describe. As it seems the room for any deterministic (then necessarily nonlocal!) theory seems to be very small given all the stringent Bell-test experiments we have for some decades now.

As long as there's no nonlocal deterministic theory which describes as much as QT, I don't consider it very interesting to think about it. For me it's enough to see that local deterministic theories in Bell's sense are ruled out, while Q(F)T, which deals with local interactions only and is causal within the relativistic spacetime description and at the same time describes the observed inseparability and long-distance correlations in the sense stated in my previous posting.

I don't believe in scholastic approaches. The strong belief even in "physics beyond the standard model" hasn't lead to success yet. I think we need clear hints of observations to see even the standard model fall yet. So I've not much hopes that one can come up with a possible successor of QT on an even more fundamental level by pure thought.

 

[pinball1970]

The quantum state represents the real world in the sense that it predicts probabilities for the outcome of measurements, given the preparation of the measured system. One should not forget the instrumental definition of the quantum state as a preparation procedure (or an equivalence class of preparation procedures) for ensembles enabling one to check the probabilistic predictions of the theory.

In general QT doesn't tell you much about the outcome of a single measurement, but only about the statistical properties of ensembles of equally (in a stochastic sense!) prepared systems. Whether or not this is a "complete" description of the world is a philosophical debate going basically on since Born's probability-interpretation footnote. I think from a physical point of view you can never prove whether any theory is "complete". As far as we know today, QT is complete in the sense that it describes all observations right it can describe. As it seems the room for any deterministic (then necessarily nonlocal!) theory seems to be very small given all the stringent Bell-test experiments we have for some decades now.

As long as there's no nonlocal deterministic theory which describes as much as QT, I don't consider it very interesting to think about it. For me it's enough to see that local deterministic theories in Bell's sense are ruled out, while Q(F)T, which deals with local interactions only and is causal within the relativistic spacetime description and at the same time describes the observed inseparability and long-distance correlations in the sense stated in my previous posting.

I don't believe in scholastic approaches. The strong belief even in "physics beyond the standard model" hasn't lead to success yet. I think we need clear hints of observations to see even the standard model fall yet. So I've not much hopes that one can come up with a possible successor of QT on an even more fundamental level by pure thought.

I am reading the comments as they come through and will continue to do so, I do not want you thinking I have posted this then ran.

Obviously my understanding of the discussion is limited as the points are technical / subtle but there are recurring themes that I can investigate further.

Thanks

 

[Lord Jestocost]

...but only about the statistical properties of ensembles of equally (in a stochastic sense!) prepared systems.

One has to talk about a collective of identically prepared systems. Nothing differentiates the members of the collective from each other in a stochastic sense. Don't draw naively the wrong conclusion that the post-measurement situation mirrors the pre-measurement situation; in case you understand - within the framework of QM - a collective of identically prepard systems in the pre-measurement situation as a statistical collective, you touch down in the hidden variable camp.

 

[vanhees71]

I don't understand. What's the difference between "collective" and "ensemble"? Aren't these synonyms in this context. I also don't understand what you mean by "you touch down in the hidden variable camp". To the controrary I follow the minimal interpretation and say that there's nothing else than these probabilities, because all observables that are not determined are really not determined, i.e., there are no hidden variables that would determine them.

 

[Lord Jestocost]

Ensemble is a collection of large number of systems which are macroscopically identical but microscopically different.

 

[vanhees71]

Ok, that's a very strict definition. Usually it's also used in quantum-theory textbooks concerning microscopic systems like a single particle.

 

[Lord Jestocost]

I think we have a comletely different view regarding the terms "probabilistic" and "statistical". My point of view becomes accessible from the following quotes.

David Mermin in "What Is Quantum Mechanics Trying to Tell Us?"

“The view that probabilistic theories are about ensembles implicitly assumes that probability is about ignorance….”V. A. Fock in “ON THE INTERPRETATION OF QUANTUM MECHANICS”, Czech J Phys (1957) 7: 643

“The deeper reason for the circumstance that the wave function cannot correspond to any statistical collective [AKA “ensemble”, LJ] lies in the fact that the concept of the wave function belongs to the potentially possible (to experiments not yet performed), while the concept of the statistical collective belongs to the accomplished (to the results of experiments already carried out).”

 

[vanhees71]

I do not understand this statement by Mermin. An ensemble is in the usual understanding within QT equally prepared independent realizations of an observational/experimental setup. E.g., at the LHC they provide beams of protons colliding head on at about 14 TeV center-of-momentum energy. This can of course be more quantitatively specified by giving the corresponding particle distributions within the bunches, etc.

Probabilities are for me theoretically calculated predictions for the frequency with which I get a given outcome of an measurement on an ensemble (I use the frequentist interpretation of probabilities since this is how it's used in real-world experiments; one can argue about other interpretations like Bayesian, but that obscures the discussion usually even further).

Statistics are measured and quantified frequencies for outcomes of measurements on an ensemble prepared in the lab in the above sense. They can be formally tested against the predicted probabilities in the sense above, which includes a detailed error analysis and a determination of the statistical significance.

The statement by Fock is interesting. As I said, so far I understand under ensemble what he calls a collective.

It's of course clear that you can perform only one measurement at each individual realization of the ensemble, i.e., in general you cannot measure sharply incompatible observables (except in a weak sense, which then needs the use of more complicated (and usually also more realistic) descriptions of the measurement in terms of POVMs; remember the discussion we had about this aspect some time ago).

 

[Demystifier]

As it seems the room for any deterministic (then necessarily nonlocal!) theory seems to be very small given all the stringent Bell-test experiments we have for some decades now.

It doesn't make sense. The Bell test experiments are not an evidence against nonlocal deterministic theories at all. Just the opposite, they are evidence for nonlocal (either deterministic or stochastic) theories. The only assumption in the Bell theorem (that the minimal interpretation may deny) is some weak assumption of realism, essentially saying that measurement outcomes exist even when nobody observes them. Sure, it's a philosophical assumption, one cannot prove by the scientific method that measurement outcomes exist when nobody observed them. But this is the assumption that you actually accept. You just don't accept the logical consequences of the assumption that you accept.

 

[vanhees71]

Which logical consequences do you think I don't accept. For me QT is a satisfactory description of the known empirical facts (except gravity of course, and that's the only point where it is incomplete). I don't need deterministic (or "realistic" though I don't know what's meant by this word anymore, because philosophers have blurred its meaning to an extent making the word useless because it expresses everything and nothing) theories, because we have QT.

Of course, I don't need a human observer that measurement outcomes exist. Storing the result in a computer, as is the modern way of storing experimental outcomes, is enough to fix the outcomes.

My quoted sentence is unfortunate gibberish indeed. What I wanted to say is that (a) if there's a deterministic theory as successful in explaining all observed facts (except gravity) must be nonlocal (in the sense that QFT explicitly is not) and (b) that this makes possibilities for a consistent relativistic deterministic model very narrow since then you have a real tension between nonlocal interactions and relativistic causality (which local, i.e., microcausal, QFT by construction cannot have).

 

[Demystifier]

Which logical consequences do you think I don't accept.

The Bell theorem, namely that any theory (satisfying some weak assumptions of realism) consistent with QM must be nonlocal. For the assumptions of the Bell theorem see http://de.arxiv.org/abs/1501.04168

My quoted sentence is unfortunate gibberish indeed. What I wanted to say is that (a) if there's a deterministic theory as successful in explaining all observed facts (except gravity) must be nonlocal (in the sense that QFT explicitly is not)

That's a gibberish again. In the sense in which QFT is local, deterministic theories such as Bohmian mechanics are local too. For instance, field operators commute at spacelike distances in Bohmian mechanics just as they do in standard QFT. Bohmian mechanics is nonlocal in a different sense.

and (b) that this makes possibilities for a consistent relativistic deterministic model very narrow since then you have a real tension between nonlocal interactions and relativistic causality (which local, i.e., microcausal, QFT by construction cannot have).

It's not narrow at all. It's in fact quite easy to construct nonlocal Bohmian-like theories that make the same measurable predictions as standard QFT. See my lecture 5 in https://www.physicsforums.com/threads/reading-materials-on-quantum-foundations.963543/post-6299524

 

[vanhees71]

Yes, and my point is that QM is fulfilling everything a good theory needs. I don't need "realism" of whatever kind, if QM describes the observational facts! That's what I understand as "realistic" in the natural sciences.

Concerning Bohmian mechanics, I'm not convinced yet that it works in the relativistic context. That may well be due to my ignorance though.

 

[Demystifier]

Yes, and my point is that QM is fulfilling everything a good theory needs. I don't need "realism" of whatever kind, if QM describes the observational facts! That's what I understand as "realistic" in the natural sciences.

If it was true that you don't need "realism", then the Bell theorem would indeed be irrelevant to you. But I can prove that you actually need realism (even though you say that you don't).

Proof 1: You believe that the Moon is there even when nobody observes it. (You usually say that you believe it due to the conservation laws, but that's nonsense because the conservation only proves that something must be there, not that this something must have all the detailed characteristics of the Moon. For instance, the Moon has a spherical shape, but there is no conservation law that guarantees a conservation of the shape.) Therefore, you believe in reality that cannot be directly tested by measurements. Q.E.D.

Proof 2: You often emphasize that the Bell theorem is important because it replaces vague philosophy with a measurable prediction. But the theorem itself depends on a philosophical assumption, namely that a certain kind of reality exists. Therefore you need Bell theorem (because it makes a measurable prediction) and Bell theorem needs realism, from which it follows that you need realism. Q.E.D.

Concerning Bohmian mechanics, I'm not convinced yet that it works in the relativistic context. That may well be due to my ignorance though.

Fair enough! But you can reduce your ignorance without spending much time on it by reading the lecture I mentioned.

 

[vanhees71]

No, I just draw the conclusion that the Bell tests empirically show that the world is not described right by a local realistic theory. Thus I've two choices: to give up realism or locality. Since there's no nonlocal theory consistent with relativity I rather give up realism and simply stay with relativistic local QFT, which works very well as the Standard Model of elementary particles.

 

[Lord Jestocost]

...I rather give up realism...

Now you're talking!

 

[Morbert]

Proof 1: You believe that the Moon is there even when nobody observes it. (You usually say that you believe it due to the conservation laws, but that's nonsense because the conservation only proves that something must be there, not that this something must have all the detailed characteristics of the Moon. For instance, the Moon has a spherical shape, but there is no conservation law that guarantees a conservation of the shape.) Therefore, you believe in reality that cannot be directly tested by measurements. Q.E.D.

A possible reply: Antirealism in QM is not a rejection of reality itself. Instead it's a rejection of the claim that what QM offers is an ontology. We can believe that the moon is real, and also believe that QM is only concerned with the likelihood that we will see it when we look up.

 

[Demystifier]

there's no nonlocal theory consistent with relativity

There are peer-reviewed papers which claim the opposite. Can you pinpoint what exactly is wrong in those papers? If you can't, then how do you know that there is no such theory?

I rather give up realism

You only give up realism when you must choose between that and giving up locality. In all other contexts you accept realism.

 

[vanhees71]

I don't understand what "realism" means. I thought QT is considered unrealistic, and my simple view is that QT (particularly for the special case as local and microcausal relativistic QFT) is the right theory (as far as we can say today) and since QT is considered "not realistic", then I happily give up "realism", because I consider QT the most successful description we have today.

I'm not aware of any peer-reviewed paper that provides a relativistic nonlocal but causal theory. If in addition such a theory were as comprehensive as standard QFT, why then is it not known to every physicist?

I also think that the one thing we cannot give up as natural scientists is the believe in causality, because if the world would behave completely acausal there'd be nothing to be investigated for a natural scientist to begin with, i.e., there'd not be natural laws at all and thus no natural science.

 

[Demystifier]

I don't understand what "realism" means. ... I happily give up "realism",

So you give up something which you don't understand.

I'm not aware of any peer-reviewed paper that provides a relativistic nonlocal but causal theory.

Fine, but don't say that it doesn't exist just because you are not aware.

If in addition such a theory were as comprehensive as standard QFT, why then is it not known to every physicist?

Because physicists don't want to seriously read this even when you give them the reference. Why do they not want to read it? Because they have already decided that the standard QM/QFT is all they need to know.

I also think that the one thing we cannot give up as natural scientists is the believe in causality, because if the world would behave completely acausal there'd be nothing to be investigated for a natural scientist to begin with, i.e., there'd not be natural laws at all and thus no natural science.

So you believe in quantum causality but not in quantum determinism. How would you explain the difference between causality and determinism?

 

[vanhees71]

In the usual way:

Causality: If the state of a system is known in the past it's also known in the future.

Determinism: All observables take certain values at any time. In a causal deterministic world thus, if the values of the observables are known in the past they are also known in the future.

Quantum theory is causal but not deterministic, since not all observables of a system can take certain values, i.e., an observable can be "undetermined", and then the state implies "only" probabilities for any possible measurement outcome.

On the fundamental level of our contemporary theories causality is valid in an even stronger sense, because you don't need to know the entire history of the state but the state at only one point in time. Then it's known at any later time.

 

[Demystifier]

Causality: If the state of a system is known in the past it's also known in the future.

For instance, suppose that at time $t_0$ you prepare the spin-1/2 system in the known superposition of |up> and |down>. Then at $t_1>t_0$ the spin is measured by a Stern-Gerlach apparatus, but you don't look at the apparatus. Do you know the state at $t_2>t_1$?

Determinism: All observables take certain values at any time.

That's not called determinism. That's called naive realism. If you said "some" instead of "all", it would be just realism.

In a causal deterministic world thus, if the values of the observables are known in the past they are also known in the future.

That's OK.

 

[vanhees71]

For instance, suppose that at time $t_0$ you prepare the spin-1/2 system in the known superposition of |up> and |down>. Then at $t_1>t_0$ the spin is measured by a Stern-Gerlach apparatus, but you don't look at the apparatus. Do you know the state at $t_2>t_1$?That's not called determinism. That's called naive realism. If you said "some" instead of "all", it would be just realism.That's OK.

On the fundamental level the time evolution is given by unitary time evolution with the Hamiltonian of the closed system consisting of the particle and the complete SG apparatus. So yes, according to QT you know the state given the initial condition from the von Neumann equation
$$\mathring{\hat{\rho}}=\frac{1}{\mathrm{i} \hbar} [\hat{\rho},\hat{H}] + \partial_t \hat{\rho}=0.$$

Well, what I quoted is determinism as in classical physics. If that's "naive realism", fine with me. Better naive than undefined!

A very concise discussion about this distinction between determinism and causality is in

J. Schwinger, Quantum Mechanics, Symbolism of Atomic
Measurements, Springer, Berlin, Heidelberg, New York (2001).

 

[PeroK]

For instance, suppose that at time $t_0$ you prepare the spin-1/2 system in the known superposition of |up> and |down>. Then at $t_1>t_0$ the spin is measured by a Stern-Gerlach apparatus, but you don't look at the apparatus. Do you know the state at $t_2>t_1$?

My understanding of SG is that the spin state is essentially unchanged by the magnet, but that the different components of the spin state have become coupled (I think the term "entangled" has been used previously, but I thought coupled was correct) with different spatial wavefunctions. E.g. in the case where the electron was originally x-spin-up and the magnet is oriented in the z-direction, then the spin state is still a 50-50 superposition of spin up and down in the z-direction after passing through the magnet.

In this case, there is no collapse of the wavefunction (only unitary evolution under the magnetic Hamiltonian) until the electron's position is measured at the screen.

If you have a sequence of SG appartuses, then the behaviour of the electron through successive magnets is consistent with no intermediate collapse.

 

[Lord Jestocost]

I also think that the one thing we cannot give up as natural scientists is the believe in causality...

The quantum laws for individuals ignore causality.

 

[vanhees71]

But QT is a causal, though nondeterministic, theory. The state develops following the causal dynamics of QT ("causality"). The complete determination of the state does not imply the determination of the values of all observables ("nondeterministic").

 

[vanhees71]

My understanding of SG is that the spin state is essentially unchanged by the magnet, but that the different components of the spin state have become coupled (I think the term "entangled" has been used previously, but I thought coupled was correct) with different spatial wavefunctions. E.g. in the case where the electron was originally x-spin-up and the magnet is oriented in the z-direction, then the spin state is still a 50-50 superposition of spin up and down in the z-direction after passing through the magnet.

In this case, there is no collapse of the wavefunction (only unitary evolution under the magnetic Hamiltonian) until the electron's position is measured at the screen.

If you have a sequence of SG appartuses, then the behaviour of the electron through successive magnets is consistent with no intermediate collapse.

Running through the magnet leads to a spin-component-position (or equivalently a spin-component-momentum) entangled state. Which spin component you measure is simply given by the direction of the magnetic field (given by the large homogeneous part of the magnetic field).

The interaction with the screen is on the fundamental level also just given by a unitary time evolution for a closed many-body system but we cannot resolve that in practice anymore, and that's why it's treated as an open system and that's why the time evolution is no longer "unitary" (it doesn't even make sense to talk about unitarity here, because it's an effective quasiclassical description).

 

[Demystifier]

On the fundamental level the time evolution is given by unitary time evolution with the Hamiltonian of the closed system consisting of the particle and the complete SG apparatus. So yes, according to QT you know the state given the initial condition from the von Neumann equation
$$\mathring{\hat{\rho}}=\frac{1}{\mathrm{i} \hbar} [\hat{\rho},\hat{H}] + \partial_t \hat{\rho}=0.$$

I think I finally know how to classify your interpretation of QM. Your interpretation is not shut up and calculate. Your interpretation is calculate carefully and talk casually.

 

[PeroK]

I think I finally know how to classify your interpretation of QM. Your interpretation is not shut up and calculate. Your interpretation is calculate carefully and talk casually.

I've found that if you look at a description of an experiment, then generally the explanation throws in a number of classical or semi-classical ideas. E.g. the double-slits and SG. If, however, you look for (as far as possible) a purely QM explanation, the less you rely on wavefunction collapse.

I wonder to what extent collapse is only a heuristic of Copenhagen; in the sense that whenever you analyse a specific experiment or scenario, you find that you don't really need to invoke collapse.

 

[Demystifier]

I've found that if you look at a description of an experiment, then generally the explanation throws in a number of classical or semi-classical ideas. E.g. the double-slits and SG. If, however, you look for (as far as possible) a purely QM explanation, the less you rely on wavefunction collapse.

I wonder to what extent collapse is only a heuristic of Copenhagen; in the sense that whenever you analyse a specific experiment or scenario, you find that you don't really need to invoke collapse.

The idea behind using pure QM without classical notions and without collapse is to avoid any talk about measurement, is that right? In principle I am fine with that, but then what is the physical interpretation of $\psi$? Is it something ontological? Is it just a probability amplitude? Probability of what? Does it make sense to have simultaneous probabilities of both $x$ and $p$ without having simultaneous values of both $x$ and $p$?

 

[PeroK]

The idea behind using pure QM without classical notions and without collapse is to avoid any talk about measurement, is that right? In principle I am fine with that, but then what is the physical interpretation of $\psi$? Is it something ontological? Is it just a probability amplitude? Probability of what? Does it make sense to have simultaneous probabilities of both $x$ and $p$ without having simultaneous values of both $x$ and $p$?

I can't claim to have thought about any of those questions!

 

[vanhees71]

I think I finally know how to classify your interpretation of QM. Your interpretation is not shut up and calculate. Your interpretation is calculate carefully and talk casually.

Yeah, and you can judge textbooks pretty well by taking the math to text ratio...