A Quantum measurement of a Strontium ion

[Killtech]

I don't know where you are getting all this from; it's nothing like the standard description of a Stern-Gerlach device. Do you have a reference? Or is it just speculation on your part?

sorry, this is just my intuition of QM. Am i so hopelessly wrong with that? For me this is kind of the canonical attempt to try explain the results. But it's just an idea/ansatz where i would start. Normally i try to google such stuff but it's usually not helpful in figuring out how good that intuition is... (Neither is working in insurance away from physics) so no, i haven't found a reference that tells either way how well this idea works. but aren't the forums a place to help with that out? i mean i wouldn't ask if i knew and i don't know where else to ask.

 

[PeterDonis]

this is just my intuition of QM. Am i so hopelessly wrong with that?

Yes. I strongly suggest that you spend some time learning about how a Stern-Gerlach apparatus actually works and how it is modeled mathematically in QM. I briefly described it in words in post #48; notice how what I said in that post looks nothing at all like what you said.

Btw, since the Stern-Gerlach experiment was one of the classic experiments that showed that QM is necessary for describing how subatomic particles like electrons work (because the prediction of classical physics for the result was shown to be false), you have to be very careful not to use classical ideas when analyzing it.

 

[vanhees71]

Any physicist who does not support the MWI is (at least implicitly) denying that unitary time evolution is always valid, because if you assume that unitary time evolution is always valid, the MWI is what you get.

You should not put words in my mouth I didn't say! I said for any CLOSED SYSTEM unitary time-evolution is valid. It's analogous to classical mechanics, where the fundamental Hamilton canonical equations also hold for closed and/or non-dissipative systems only. When you treat open quantum or classical systems the time evolution is no longer unitary, and you describe among other things decoherence. There's no need for the assumption that there's a quantum-classical cut (including an instantaneous collapse). That's all I'm saying. I don't think that this is MWI, but I don't care how you call any interpretation, because it's anyway imprecise to name any interpretation by a single word.

In the SGE you send an Ag atom through a magnetic field taylored such that you prepare position-spin entangled states. This is indeed described by the unitary time evolution, i.e., by the time-dependent Pauli equation, which is a manifestation of unitary time evolution in the position-spin (or if you prefer momentum-spin) representation.

You are right in saying that, within collapse interpretations, the collapse occurs when the Ag atom hits the screen. Then it's stuck there and its position (a macroscopic variable!) can be measured (or rather the distribution of many Ag atoms hitting the screen) by observing it under a microscope (at least that's how it was done in 1921).

I don't see, how you can claim that here a collapse assumption is necessary. As well I can argut that the Ag atom interacts with the screen, and the apparent collapse simply comes from the very coarse-grained description and from looking at one (macroscopic) observable only, namely the single-Ag-atom distribution on the screen. Why do you think that's a non-orthodox interpretation? Only because I avoid the very problematic idea of an instantaneous collapse?

 

[Lord Jestocost]

When you treat open quantum or classical systems the time evolution is no longer unitary, and you describe among other things decoherence.

When quantum mechanics is applied uniformly at all levels, to the apparatus and its environment as well as to the system, the time evolution is always unitary as all entangles to each other. Decoherence changes nothing (see "Why Decoherence has not Solved the Measurement Problem: A Response to P.W. Anderson" by Stephen L. Adler).

 

[vanhees71]

Well, but the classical behavior of macroscopic systems is convincingly described by quantum statistical mechanics, at least FAPP. What's the physical (sic! I mean rather than philosophical) problem left concerning the so-called "measurement problem"? Can you point to the specific article you have in mind?

 

[Lord Jestocost]

Joos, E. (1999) ‘Elements of Environmental Decoherence’, in P. Blanchard, D. Giulini, E.
Joos, C. Kiefer and I.-O. Stamatescu (eds.), Decoherence: Theoretical, Experimental, and
Conceptual Problems (New York: Springer), pp. 1-17:

“Does decoherence solve the measurement problem? Clearly not. What decoherence tells us is that
certain objects appear classical when observed. But what is an observation? At some stage
we still have to apply the usual probability rules of quantum theory.”

And the probabilty rules represent nothing else but the non-unitary collapse.

You don't get the problem. Maybe, the following might help you:

"Basically, the quantum measurement paradox is that most interpretations of QM at the microscopic level do not allow definite outcomes to be realized, whereas at the level of our human consciousness it seems a matter of direct experience that such outcomes occur..."
(A. J. Leggett in "The Quantum Measurement Problem")

P.S.: To understand my position: For me there exists no "classical behaviour" as I regard classical concepts as folk science.

 

[vanhees71]

Indeed, I don't get the problem. The first quote by Joos is all I need. Of course QT tells us that nature is inherently probabilistic, and at "some stage we still have to apply the usual probability rules of quantum theory." What else should I apply, given that QT is the best theory we have?

The quote by Leggett is true too, of course, but so what? Human observations do not resolve the "microscopic level", and decoherence tells me satisfactorily why any observation is a definite outcome of macroscopic observables.

Of course, the "classical behavior" is only apparent and due to the necessarily coarse grained observation of macroscopic systems.

 

[PeterDonis]

I said for any CLOSED SYSTEM unitary time-evolution is valid.

But you also claimed that a particle + detector system is closed. It isn't. You even admit that:

When you treat open quantum or classical systems the time evolution is no longer unitary, and you describe among other things decoherence.

Unless you are going to claim that there is no decoherence when an Ag atom hits the detector in a Stern-Gerlach measurement?

Remember that in the Stern-Gerlach measurement, the magnet is not the detector. The detector is the screen that the Ag atoms hit after they have exited the magnetic field. You can treat the atom plus magnet system as closed and undergoing unitary time evolution. You cannot do the same for atom plus detector; that system is not closed, it is open, and undergoes decoherence.

I don't see, how you can claim that here a collapse assumption is necessary.

Now you're the one putting words in my mouth. I never made any such claim.

As well I can argut that the Ag atom interacts with the screen, and the apparent collapse simply comes from the very coarse-grained description and from looking at one (macroscopic) observable only, namely the single-Ag-atom distribution on the screen. Why do you think that's a non-orthodox interpretation?

I never said that this interpretation was non-orthodox. I have simply been trying to get you to explain clearly what interpretation you are actually using. The next question based on your description here is obvious: what happens when the human observer looks at the screen? Is there only an "apparent collapse" there as well? If your answer is "yes", you are describing the MWI. If your answer is "no", you are describing a collapse interpretation. Trying to waffle by saying things like "there's no need for a quantum-classical cut" won't do.

 

[vanhees71]

Ok, if you consider the meausurment device as external (which makes of course sense), then there's no unitary time evolution for the Ag atom alone, but it's also not a spontaneous collapse. It doesn't even make sense, because the Ag atom is for sure not in the "measured" spin state for long but it thermalizes rapidly with the matter making up the detector, where it is stuck after it hit the plate.

As always, it depends on how you split the complete system (Ag atom + detector) into an open quantum system, i.e., which "information you project out/or coarse-grain away". For a closed system, AFAIK there's no clear argument or experimental fact that indicates that the usual dynamical rules of QT were incomplete and some fundamental quantum-classical cut is necessesary. That's all I'm claiming.

 

[Lord Jestocost]

Indeed, I don't get the problem.

To understand my reasoning, there is a simple and fundamental question:

Does a measurement reveal a preexisting value of a measured property (hidden variable reasoning, ensemble interpretations) or is the outcome of a measurement brought into being by the act of measurement itself (Copenhagen interpretation)?

My point of view:

No observable has any value before a measurement: Measurements of an observable thus “create” their outcomes because all of an unmeasured systems‘ possibilities are live possibilities - potentially possible in the instant of a measurement’s onset, not randomly pre-existing just before the measurement.

 

[vanhees71]

A measurement does not reveal a preexisting value except the state was such that the measured observable takes a predetermined value (for pure states, if it's represented by an eigenstate). An ideal measurement leads to a result with the probability given by the state the system is prepared in when measured.

So I think we agree. What you formulated in your final sentence is, by the way, Schrödinger's point of view, who was for my taste much more to the point than the Copenhagen gang (particularly Heisenberg), and he was the one who has (besides of course Einstein) seen the true "revolutionary" content (entanglement and inseparability) much more clearly than the "philosophers in Copenhagen" though Schrödinger himself was also much inclined to the philosophical side in his later years, but I think he separated it better from his physics than the Copenhagians.

 

[PeterDonis]

if you consider the meausurment device as external (which makes of course sense), then there's no unitary time evolution for the Ag atom alone

You missed this statement of mine:

Remember that in the Stern-Gerlach measurement, the magnet is not the detector. The detector is the screen that the Ag atoms hit after they have exited the magnetic field. You can treat the atom plus magnet system as closed and undergoing unitary time evolution.

Nobody is arguing that collapse (whether it's viewed as apparent or real) occurs when the Ag atom passes through the magnet. So there is no reason not to consider the magnet as part of the "system" along with the Ag atom, and analyzing the atom + magnet as undergoing unitary time evolution.

For a closed system, AFAIK there's no clear argument or experimental fact that indicates that the usual dynamical rules of QT were incomplete and some fundamental quantum-classical cut is necessesary.

Yes, but with the proper definition of "closed system", any quantum experiment stops being closed as soon as a result is observed (in the case of the SG measurement, this is when the Ag atom hits the detector and makes a bright spot). So the claim you are making here, while true, is much, much less broad than you seem to think it is.

 

[vanhees71]

I think we have just a semantical misunderstanding. Let me try in a different way to make clear what I mean.

On a fundamental level you have quantum theory as the comprehensive theory of physics, including unitary time evolution (of course I neglect gravity here, which is not yet described quantum-theoretically in a satisfactory way). On a fundamental level the SGE from the preparation of the Ag atoms (through letting them out of an oven as a beam) to the detection on the photoplate everything is in principle described by unitary time evolution.

This you can of course never describe in full analytical detail since it would include a huge macroscopic system (the oven with the silver vapor in it, the aperture(s) to shape the beam, the magnet, and finally the photoplate). It is also not necessary to describe all this setup in microscopic detail, and that's why you use effective macroscopic descriptions of the relevant macroscopic observables. In other words you "project on" the relevant information (in the sense of many-body theory), leading to a massive coarse graining. This of course leads to a discription of a huge part of the setup in terms of macroscopic observables and their classical behavior. This classical behavior is emergent in this sense but, at least from a phenomenologist's point of view, complete compatible with the underlying microscopic unitary dynamics. That's why I think there's neither a need for a fundamental quantum-classical cut nor is there any empirical evidence for its existence.

The idea of an instantaneous collapse is of a different caliber: It's contradicting the very foundations of the theory in its form as a relativistic microcausal QFT to begin with. At the same time the collapse proponents claim it's just an interpretational element of this very theory. So, while a "quantum-classical cut" is not principally ruled out based on the theory, the collapse hypothesis is a contradictio in adjecto. An as some of the very recent experimental investigations we discuss here, it seems as if it can now be experimentally demonstrated not to occur at all: There are no instantaneous quantum jumps but just quantum-theoretical time evolution, which can be very rapid on a macroscopic observational scale but are still continuous and smooth at a finer time resolution, and this can even be demonstrated experimentally, including the possibility for "preventing" a "just to appear" quantum jump in the process.

 

[PeterDonis]

On a fundamental level the SGE from the preparation of the Ag atoms (through letting them out of an oven as a beam) to the detection on the photoplate everything is in principle described by unitary time evolution.

With correct definitions of the two boundaries (the end of preparation and the start of detection), yes. But you immediately make those boundaries too broad:

This you can of course never describe in full analytical detail since it would include a huge macroscopic system (the oven with the silver vapor in it, the aperture(s) to shape the beam, the magnet, and finally the photoplate).

You are misstating this. The correct statement is that the oven and the photoplate are not described by unitary time evolution in our current quantum theory. (See further comments below.) That means we do not know whether unitary time evolution actually applies to the oven and the photoplate. The claim that it does is not a well-tested conclusion of quantum theory. It is an extrapolation of the theory to a domain in which nobody knows how to test it empirically, and in which the straightforward extrapolation, applying unitary evolution to everything, gives answers that seem obviously contrary to observation (i.e., the MWI). This is the reason why there are multiple interpretations of QM and the question of which, if any, of them are correct remains unresolved.

It is also not necessary to describe all this setup in microscopic detail

Not if you just use standard QM, because, as above, standard QM does not describe the oven and the photoplate using unitary time evolution. It just declares by fiat that the oven produces Ag atoms in a particular state, and that the photoplate gives probabilities for showing a bright spot in different places when an Ag atom hits it. Neither of those things are unitary time evolution.

This classical behavior is emergent in this sense but, at least from a phenomenologist's point of view, complete compatible with the underlying microscopic unitary dynamics.

Only if you accept the MWI, since the MWI is what you get when you apply unitary dynamics to everything.

The idea of an instantaneous collapse is of a different caliber: It's contradicting the very foundations of the theory in its form as a relativistic microcausal QFT to begin with.

The simplest version of the collapse interpretation certainly seems that way, yes. That's another reason why there are multiple interpretations of QM and the question of which, if any, of them are correct remains unresolved. Your personal preference is against collapse; that's fine. But it's still your personal preference: it's not an established theoretical conclusion.

as some of the very recent experimental investigations we discuss here, it seems as if it can now be experimentally demonstrated not to occur at all: There are no instantaneous quantum jumps but just quantum-theoretical time evolution

I've already responded to this: these experiments don't show that there is no collapse, because collapse interpretations don't put the collapse where the experimenters are saying they don't observe collapse. These experiments are basically equivalent to demonstrating that the Ag atom + magnet in the SG experiment undergo unitary evolution, and then claiming that shows there's no collapse--when in fact collapse interpretations put the collapse where the Ag atom hits the photoplate.

 

[Demystifier]

The correlations are there because of the preparation in the entangled state at the very beginning of the experiment

I have two problems with this statement.

First, it is not how Ballentine interprets it (nor any other peer reviewed paper AFAIK) , so it's not a part of the minimal statistical ensemble interpretation. It's your own interpretation.

Second, the Bell theorem explicitly rules out such an interpretation. Sure, the Bell theorem rests on some assumptions, so we would like to understand which of those assumptions do you deny. Here is how I see it. When one talks about preparation, Bell assumes that it does make sense to ask - preparation of what? Then Bell assumes that this thing which is prepared can be analysed mathematically and calls it $\lambda$. And from this (and from some additional assumptions that you wouldn't deny) he derives that those $\lambda$ must obey some nonlocal laws. So to avoid the Bell theorem, you deny that the question "Preparation of what?" makes sense to begin with. In other words, you avoid the Bell theorem by refusing to talk explicitly and mathematically about the object which is prepared. In your interpretation, preparation as an action makes sense, but the object which is prepared doesn't.

It's like using the following defense in the court: Yes your honor, I did kill, I don't deny it. But nobody found the murdered body, so it doesn't make sense to say that I killed someone. Therefore I commited no crime, for there is nothing wrong in the act of killing if that act is not applied to any concrete human.

 

[vanhees71]

If you prepare a system (say a two-photon Fock state via parametric down conversion) in an entangled state, it's in this entangled state, isn't it, and the correlations are thus there? What's there left to be interpreted? I'm also not aware, where this view contradicts any textbook formulation, let alone Ballentines, of quantum theory.

 

[Demystifier]

If you prepare a system (say a two-photon Fock state via parametric down conversion) in an entangled state, it's in this entangled state, isn't it,

Yes it is.

and the correlations are thus there?

No they aren't.

What's there left to be interpreted?

Correlations only make sense if one talks about objects which are correlated. Those objects are the things which are left to be interpreted.

Entanglement is in the state in the Hilbert space. Correlation is in the physical things described by this state.

I'm also not aware, where this view contradicts any textbook formulation, let alone Ballentines, of quantum theory.

Ballentine's book, page 607-608:
"Many assumptions, other than locality, that seem to be implicit in Bell’s original argument have been identified, but in every case it has been possible to deduce a contradiction of quantum mechanics without that assumption."

Peres's book, page 173:
"In summary, there is no escape from nonlocality."

 

[PeterDonis]

"In summary, there is no escape from nonlocality."

To be clear, "nonlocality" here means that Bell's "locality" assumption is violated; that assumption is that the function describing the joint probabilities for the two spacelike separated measurements factorizes, i.e., schematically, $P(A, B|a, b, \lambda) = P(A|a, \lambda) P(B|b, \lambda)$, i.e., the probability of a given result for each measurement only depends on the setting of that measuring device (and the hidden variables $\lambda$). The QM probability for an entangled state obviously violates this assumption since it depends on the angle between the two measuring devices (for the case of spin measurements, which is the case Bell treated in his original paper).

However, this definition of "locality" is not the same as the definition of "locality" in QFT. In QFT, "locality" means that spacelike separated measurements commute, i.e., the probabilities are independent of the order in which the measurements are done. The QM probability satisfies this property, so QM is "local" in the QFT sense even thought it is "nonlocal" in the Bell's theorem sense.

 

[vanhees71]

Why aren't the correlations there?

If you have a two-spin state like the singlet state $|1/2,-1/2 \rangle-|-1/2,1/2 \rangle$, then though neither of the single spins has a determined value (but it's described by the mixed state $\hat{\rho}_1=\hat{\rho}_2=\hat{1}/2$) you have a 100% correlation: Whenever you measure $\sigma_z=1/2$ on particle 1, you'll measure $\sigma_z=-1/2$ on particle 2 or vice versa.

As long as you ensure that nothing disturbes the state, the entanglement is preserved, and you can measure the single-particle spins at arbitrary far distance. It's done by local interactions with the measurement device (according to standard relativistic QFT, which has by construction only local interactions, because it obeys the microcausality principle, i.e., the Hamilton density commutes with any local observable at space-like distance of the arguments), but still you find the correlations. There's no spooky action at a distance, since the measurement events determining the outcome of the spin measurements can be spacelike separated. In such a case the microcausality condition rules out an causal effect of one of the single-particle measurements on the other.

So of course there's some kind of "non-locality" here, but it's not non-local interactions but correlations between parts of the entangled system measured at (possible very large) spatial distances. I'd rather use Einstein's word "inseparability" of entangled quantum systems than the somewhat ambiguous word "non-locality".

It's also clear that within the standard interpretation, what the observers measure on the single particles is simply that its unpolarized. As long as you don't polarize the particles before measuring them (and with that of course also destroy the before prepared entangled state) that finding is independent of whatever is measured at the other particle (again at least as long as the measurement events are at spacelike distances).

 

[Demystifier]

The QM probability satisfies this property, so QM is "local" in the QFT sense even thought it is "nonlocal" in the Bell's theorem sense.

I agree. But ontological theories (such as Bohmian mechanics) are also "local" in the QFT sense, so it doesn't make sense to criticize such theories for being incompatible with QFT locality.

 

[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).