I QM: Interesting View - Get the Inside Scoop

[vanhees71]

This is for two reasons :

1. The first is political, since there are many like you who take offence at that dirty word.
2. The second is pragmatic, since Dirac collapse is somewhat too special for the needs of quantum information applications.

But Dirac's collapse is precisely the special case of a pure quantum channel where the transmission operator $T$ is a projector, corresponding to a von Neumann projective measure-and-prepare situation.

There's nothing against this. It's just a special case, depending on the equipment used to prepare the system. It's nothing foundational and it's not anything outside what's described by the quantum formalism.

For me the collapse assumption is the claim that there is "something" (usually not specified by the proponents of collapse interpretations) outside the quantum formalism preparing a system in the eigenstate of the meausured observable. This is not true in most of real-world measurements and also not necessary in the quantum foundations.

If I put a filter, it's simply another macroscopic lump of matter interacting with the quantum system such that it "absorbs" this system under certain conditions and "lets ti through" under other conditions (as in the SG experiment, where the location of the particle is entangled ~100% with the specific spin state, such that I can block particles with those spin states on wanted and keeping only those with one specific spin states. This as not achieved by some magical collapse but simply by the interaction of the blocked particles with the blocking material.

 

[A. Neumaier]

But how could a microscopic theory ever be found if you insist that it be rigorously derived from classical physics using logical deduction?

You might insist; I don't since it is futile. The relation between reality and the mathematics used to describe physics can never be rigorous. Indeed, rigor using logical deduction always entails mathematics, hence is divorced from reality.

The microscopic theory called quantum mechanics was actually found by nonrigorous thinking of physicists like Bohr, Einstein, Born, Heisenberg, and Schrödinger.

John Bell wrote: "And does not any analysis of measurement require concepts more fundamental than measurement? And should not the fundamental theory be about these more fundamental concepts?" (Quantum mechanics for cosmologists)

In practice, the analysis of measurement (as opposed to postulates like Born's rule, which has limited applicability) requires the fundamental theory called quantum field theory. It is about the more fundamental concept of a quantum field. These explain the properties of macroscopic equipment used to define the meaning of measurements to a highly satisfactory extent. Thus we have what John Bell was asking for in this quote.

 

[vanhees71]

After the encounter with Ballentine's Rev.Mod.Phys. article I thought I had understood QM. And I'm still convinced that QM is a statistical (stochastic) theory and not deterministic. (I'm astonished that so many people take Schrödinger's equation to be the pinnacle of quantum theory -- it is just a piece of a bigger mathematical machinery that creates the illusion of determinism.)

Of course Bell's inequalities are problematic also for the statistical interpretation if you believe in particles having definite properties at all times. But you don't have to believe in "particles", which are a classical concept anyway. To me, the Aspect et al. experiments show that it is a conceptual dead end to think that "something" travels from the source to the detectors while engaging in superluminal communication. And QFT as a microscopic theory cannot be grounded on a macroscopic concept like "measurement".

Sure, Ballentine is usually associated with the minimal interpretation, and that's all that's needed to use QT as a physical theory.

I don't believe in "particles having definite properties at all times", because this is disproven by all the Bell tests confirming Q(F)T. QFT is in accordance with all experiments, particularly with these Bell tests and that's why there's no need for the assumption of non-local interactions. One of ther cornerstones of the successful relativistic QFT is locality and microcausality implying the cluster decomposition principle.

The upshot is: The only valid description of properties of particles is what's encoded in the statistical operator describing their "preparation". These described properties are probabilistic and nothing else.

 

[A. Neumaier]

This as not achieved by some magical collapse

This is called collapse by everyone except you. No magic was ever claimed to be involved.

If I put a filter, it's simply another macroscopic lump of matter interacting with the quantum system such that it "absorbs" this system under certain conditions and "lets it through" under other conditions

A polarization filter does not do this. It collapses the state without letting particles through under certain conditions (which conditions would this be?) and absorbing them under all other conditions. A quantum channel accounts for this change of state without explaining how it happens.

Your catch-all explanation of this being due to interaction with a macroscopic lump of matter looks like an intuitive explanation but is not a consequence of the statistical interpretation without collapse.

 

[vanhees71]

An ideal polarization filter let's through the electric-field component in one direction and absorbs the others. It's describable by the interaction of the electromagnetic field with the medium making up the filter. There's no collapse necessary to explain this. It's all described by standard QED.

 

[WernerQH]

Thus we have what John Bell was asking for in this quote.

Obviously we don't. You may be thinking that you've solved the problem. But not everybody shares this view. Why do we have these endless discussions?

 

[Lord Jestocost]

Sure, Ballentine is usually associated with the minimal interpretation, and that's all that's needed to use QT as a physical theory.

Thee are others who usally associate Ballentine with the ensemble interpretation. For example, Maximilian Schlosshauer in „Classicality, the ensemble interpretation, and decoherence: Resolving the Hyperion dispute“ (Found Phys 38, 796–803 (2008)):

"Instead, Wiebe and Ballentine explicitly state that the only role of quantum states is to describe “the probabilities of the various possible phenomena” [13, p. 022109-1]. Thus they presume the ensemble, or statistical, interpretation of quantum mechanics[2].

The key assumption of this type of interpretation is to consider the quantum state as only representing the statistical properties of an ensemble of similarly prepared systems. The ensemble interpretation thus implies that the entire formal body of quantum mechanics (for example, a probability amplitude) has no direct physical meaning, in the sense of having no direct correspondence to the entities of the physical world (see also the comment by Leggett [7]). This interpretation effectively points toward the need for some hidden-variables theory to fully specify the state of individual systems, but it does not actually specify what this “complete theory” would be.“
[bold by LJ]

 

[RUTA]

The devil is in the details. The mathematical characterization of events requires a bit more than time and location. Does your book expand on this, or is it just discussing general principles?

Yes, you still need fields on the lattice (links for gauge fields, nodes for fermion fields). We talk about lattice gauge theory with quantum field theory in general in Chapters 5 and 6.

 

[vanhees71]

Thee are others who usally associate Ballentine with the ensemble interpretation. For example, Maximilian Schlosshauer in „Classicality, the ensemble interpretation, and decoherence: Resolving the Hyperion dispute“ (Found Phys 38, 796–803 (2008)):

"Instead, Wiebe and Ballentine explicitly state that the only role of quantum states is to describe “the probabilities of the various possible phenomena” [13, p. 022109-1]. Thus they presume the ensemble, or statistical, interpretation of quantum mechanics[2].

The key assumption of this type of interpretation is to consider the quantum state as only representing the statistical properties of an ensemble of similarly prepared systems. The ensemble interpretation thus implies that the entire formal body of quantum mechanics (for example, a probability amplitude) has no direct physical meaning, in the sense of having no direct correspondence to the entities of the physical world (see also the comment by Leggett [7]). This interpretation effectively points toward the need for some hidden-variables theory to fully specify the state of individual systems, but it does not actually specify what this “complete theory” would be.“
[bold by LJ]

I can agree with everything except the conclusion in the last bold-faced sentence. Why does this point toward the need for some hidden-variable theory? If one simply takes QT with the probability interpretation of the state a la Born seriously then there is no need for any hidden variables. All there is are the well-known observables, which simply do not take predetermined values but behave as "random variables" in probability theory do, i.e., to analyze there properties, given the quantum state of the system, you have to prepare an ensemble and measure the quantities and do some statistical analysis with the data. That's why you need an ensemble to test QT by experiment. It's implied by the probabilistic interpretation of the quantum state.

So it does not necessarily follow that there must be hidden variables. This only follows under the assumption that the world must behave somehow deterministically on the most fundamental level. The Bell tests tell us that, if this is really true, we'd need a non-local deterministic description. Of course, I cannot disprove yet this possibility, but for sure if one finds any such deterministic theory in accordance with the observations being in accordance with the statistical predictions of QT, it won't be any less strange to our classical-physics-biased "common sense" than QT itself. So even as a philosopher, who has to save his classical prejudices about his worldview, won't be any "happier" with this maybe existing non-local deterministic theory.

For non-relativistic QM we have such a theory, Bohmian mechanics. Though a deterministic reinterpretation of QM, it doesn't bring back much of the "intuitive" classical picture of particles described as mathematical points following precisely predetermined trajectories.

 

[A. Neumaier]

An ideal polarization filter let's through the electric-field component in one direction and absorbs the others. It's describable by the interaction of the electromagnetic field with the medium making up the filter. There's no collapse necessary to explain this. It's all described by standard QED.

No.

Exercise: If the electromagnetic field is in a pure 1-photon state neither parallel nor orthogonal to the polarization direction - does it absorb the field or let it through?

 

[A. Neumaier]

Why do we have these endless discussions?

Because Bell also wanted other things not in your quote. He wanted foundations completely free of the notion of measurement. All interpretations that provide this are controversial.

 

[vanhees71]

If you have a 1-photon state it gets either absorbed (as a whole) or is let through (as a whole). The probability is given by Malus's law, $P=\cos^2 \theta$, where $\theta$ is the angle of the polarization filter relative to the polarization direction of the photon.

 

[A. Neumaier]

If you have a 1-photon state it gets either absorbed (as a whole) or is let through (as a whole). The probability is given by Malus's law, $P=\cos^2 \theta$, where $\theta$ is the angle of the polarization filter relative to the polarization direction of the photon.

But if it gets through its polarization has changed. This is the collapse!

 

[vanhees71]

Because Bell also wanted other things not in your quote. He wanted foundations completely free of the notion of measurement. All interpretations that provide this are controversial.

This leads to a lot of confusion, because physics is all about measurements (i.e., observations), and a good theory predicts the outcome of measurements for a given experimental setup ("preparation"). I don't know for sure, but I think Bell somehow hoped to find his LHV model class confirmed and quantum theory refuted by the Bell-test experiments. Fortunately, however, rather quantum theory holds true.

 

[A. Neumaier]

This leads to a lot of confusion, because physics is all about measurements (i.e., observations), and a good theory predicts the outcome of measurements for a given experimental setup ("preparation").

Classical physics was also all about measurements but the foundations were independent of it. Nobody had measured (or required an operational measurement procedure) the particles that were posited underlying the fields that Euler and Navier, and Stokes discussed.

Thus measurement-free foundations never lead to confusion, while with the measurement-ridden quantum foundations we have now almost 100 years of manifest confusion!

 

[vanhees71]

But if it gets through its polarization has changed. This is the collapse!

Of course, the polarization has changed. That's why we call a polarization filter a polarization filter. But it's nothing that is outside of the dynamics as described by QED. You don't need an additional vague assumption called "collapse". As we discussed zillions of times, "collapse" is a FAPP description for such situations. It's not to be taken as some additional dynamial law outside of the quantum dynamical laws in the minimal formulation.

 

[A. Neumaier]

As we discussed zillions of times, "collapse" is a FAPP description for such situations.

Just like Born's rule. Being FAPP does not make it unnecessary.

 

[vanhees71]

Classical physics was also all about measurements but the foundations were independent of it. Nobody had measured (or required an operational measurement procedure) the particles that were posited underlying the fields that Euler and Navier, and Stokes discussed.

Thus measurement-free foundations never lead to confusion, while with the measurement-ridden quantum foundations we have now almost 100 years of manifest confusion!

Of course not, because we are so used to that everyday "objects" we handle all the time that nobody thought much about these foundations (though Newton et al did a lot ;-)).

 

[gentzen]

Why do we have these endless discussions?

Perhaps because we enjoy those discussions? If you watch philosophers or mathematicians wonder about Alternatives to Axiomatic Method, then you can get the impression that they are seriously inquiring about a puzzle. They still don't reach definite conclusions, or agree with each other, but at least you don't get the impression that they have endless discussions and go round in circles. In discussions of QM interpretation, there might be some participants that seem to seriously inquire about a puzzle. (For example take RUTA's attempt to give a principle account of QM similar to principal accounts of SR.) But many participants seem to actively deny that there is any puzzle to start with, for which serious inquiry could be useful at all.

 

[WernerQH]

you don't get the impression that they have endless discussions and go round in circles

I was asking a rhetorical question in response to Arnold Neumaier's statement that "[quantum fields] explain the properties of macroscopic equipment used to define the meaning of measurements to a highly satisfactory extent". Not everybody seems to be highly satisfied.

I'm participating in the discussion because I do think that there is a puzzle. The partipants have widely divergent views what the problem is, and which part of theory space is the most promising to look for a solution. There is indeed some overlap between RUTA's ideas and mine, but in my view they do not go far enough.

 

[WernerQH]

Yes, you still need fields on the lattice (links for gauge fields, nodes for fermion fields).

I'm aware of lattice theories. It is quite the opposite of what I have in mind. In those theories you still think of a field as a continuum. You discretize it only for computational reasons. I think of a field as a coarse-grained description of a fundamentally discrete reality, much like "density" refers to an average over discrete atoms. The photon field is not continuous -- photons can be counted! There is not an event at every point in spacetime; absorption and emission events can be far apart. The picture I have in mind is that of events spread out over the spacetime continuum like grains of sand. QFT is a theory describing the statistical regularities we observe in the patterns formed by those grains.

 

[PeroK]

The question remains why there are so many competent quantum physicists who disagree.

Because they are human beings. And I don't mean this flippantly.

 

[gentzen]

Arnold Neumaier's statement that "[quantum fields] explain ... to a highly satisfactory extent". Not everybody seems to be highly satisfied.

Probably because they neither know which puzzle was solved by A. Neumaier, nor what was the special role played by quantum fields for his solution.

There is a puzzle I had for a long time which is solved by A. Neumaier's ideas and elaborations. (I am not sure how many people realize that this puzzle even existed, and that he has indeed solved it.) But he obviously wanted more, i.e. the solution of a much harder puzzle. My own guess would be that the special role of quantum fields for his solution was to bring back space and locality into the picture. (Maybe their contribution to the solution is also related to their high energy / high frequency unobservable degrees of freedom and the associated dissipation.)

 

[vanhees71]

I'm one of those stupid people, who don't see, where the "puzzle" is. There was a serious and well-formulated puzzle for Einstein, which was inadequately (for me not at all) answered by Bohr concerning entanglement, and it's not in the EPR paper (which Einstein didn't like, exactly because of its unclear philosophical rather than physical statements). For Einstein the real issue was "inseparability", i.e., the fact that entangled states can be prepared such that far-distant well-separable parts of a system (e.g., two photons in an entangled polarization-momentum Bell state such that you can measure clearly the single photons by putting detectors far away from each other), which for themselves are totally indetermined (the single photons have utmost indetermined polarization, i.e., they are ideally unpolarized) while they still have 100% certain correlations (e.g., in the polarization singlet state, if A measured "H", with certainty B measures "V" and vice versa).

Now, indeed, Einstein was right in criticizing the Copenhagen interpretation, at least those which add a "collapse assumption" as a physical process outside of the quantum theoretical description of the dynamics, in calling this "action at a distance". His proposal famously was that there might be "hidden variables" which are not observed (or maybe even not observable at all) but provide the probabilistic description of an underlying deterministic theory due to incomplete knowledge as in classical statistics.

Then Bell formulated this philosophical quibbles in terms of truly scientific question, i.e., he made a prediction under general assumptions about what he called "local realistic theories", which is basically the assumption that all observables are in fact determined but their values for a specific system are unknown due to the unobserved "hidden variables". This lead to his famous inequality, which however is contradicted by quantum theory precisely for entangled states we know call Bell states. Now the philosophical quibbles were formulated as an experimental challenge, i.e., a true scientific statement decidable by observations, and starting with Aspect et al the issue was resolved completely with very high accuracy and statistical significance in favor of quantum theory.

For me the problem is thus completely solved as far as QT as a natural science theory is concerned. We are indeed now a step further, being already in the middle of the transformation of an academic puzzle, which is now solved towards having now a theory applicable in the sense of engineering, i.e., the results are now used to construct new technology like quantum cryptography and quantum computers. As in the case of electricity and magnetism, for which Faraday predicted that once the politicians could take taxes for its use, there's a lot money invested with high prospect to earn a profit from it.

I find it bizzar in such a situation there are still people not satisfied with quantum theory because of these now solved philosophical quibbles. The real scientific puzzle is rather to find a consistent theory of the gravitational interaction than the philosophical headaches of Einstein and Bohr.

 

[Lord Jestocost]

Now, indeed, Einstein was right in criticizing the Copenhagen interpretation, at least those which add a "collapse assumption" as a physical process outside of the quantum theoretical description of the dynamics...

Sorry, but I have to correct this statement regarding the Copenhagen interpretation. As Cord Friebe et al. put it in “The Philosophy of Quantum Physics”:

"At this point, the infamous collapse of the wavefunction comes into play; however, according to the Copenhagen interpretation, it is either merely methodological, or explicitly epistemological, but in any case not to be understood as ontological." [italics in original, bold by LJ]

 

[WernerQH]

I find it bizarr in such a situation there are still people not satisfied with quantum theory because of these now solved philosophical quibbles.

The puzzle is not "merely" philosophical. It has a profound effect on our thinking and how we teach physics. You may think that the formulation of QFT is an entirely different matter, but it is likely that the problems there have their roots in our imperfect understanding of what a quantum field is.

The real scientific puzzle is rather to find a consistent theory of the gravitational interaction than the philosophical headaches of Einstein amd Bohr.

I don't think gravity needs to be quantized at all. Mostly because of my inability to conceive of a coherent superposition of two different spacetime geometries. Gravity is just too different an animal.

 

[vanhees71]

Sorry, but I have to correct this statement regarding the Copenhagen interpretation. As Cord Friebe et al. put it in “The Philosophy of Quantum Physics”:

"At this point, the infamous collapse of the wavefunction comes into play; however, according to the Copenhagen interpretation, it is either merely methodological, or explicitly epistemological, but in any case not to be understood as ontological." [italics in original, bold by LJ]

Indeed, that's solving the entire problem: you take QT as what it is, i.e., a theory predicting probabilities for the outcome of random random experiments aka. measurements. I think a big part of the problem many people still see in quantum theory is the misinterpretation of the quantum state as describing some ontology. There are no self-adjoint operators on a Hilbert space and Hilbert-space vectors "out there" but particles, many-body systems, etc.

 

[haushofer]

As Ethan Siegel recently puts it:

"Although there are a myriad of interpretations of quantum mechanics that are equally as successful at describing reality, none have ever disagree with the original (Copenhagen) interpretation’s predictions. Preferences for one interpretation over another — which many possess, for reasons I cannot explain — amount to nothing more than ideology."

Ontology is not ideology.

Strange remark imho.

 

[RUTA]

I'm aware of lattice theories. It is quite the opposite of what I have in mind. In those theories you still think of a field as a continuum. You discretize it only for computational reasons.

In our model, (modified) LGT is not an approximation to a continuum reality, but the truth is actually the reverse (see our explanation of regularization, renormalization, and unification). I'm in the process of working up a detailed model for QFT along these lines based on what I now understand about QM via this Insight.

 

[bhobba]

PBut many participants seem to actively deny that there is any puzzle to start with, for which serious inquiry could be useful at all.

I suppose I am close to one of those, thinking it is just a generalised probability theory. To me, the 'puzzle' is from symmetry principles alone; you can derive Schrodihgers equation (Chapter 3 Ballentine). The 'mystery' is taking expectation values; you get the Hamiltonian of classical mechanics suggesting (not proving but just suggesting) to quantize a system, you take the classical Hamiltonian and replace energy etc., with the appropriate operators. It works - but why? Evidently, Dirac thought long and hard about that one as well, except, of course, he used Poisson Brackets:
https://uwaterloo.ca/physics-of-inf...iles/uploads/files/aqm_lecture_notes_10_2.pdf

Yet, I rarely hear anyone discussing that conundrum. To me, it is the central mystery, not the so-called measurement problem, collapse, and other stuff often discussed. That is not to 'trivialise' those issues - I just think the generalised probability theory viewpoint resolves them. But not everyone agrees. Such are the issues with the foundations of QM.

Thanks
Bill