Undergrad Are there signs that any Quantum Interpretation can be proved or disproved?

[A. Neumaier]

What above and similar types of reasoning miss completely is that pointer states are ensembles with huge numbers of states that are exponential in $N=10^{20}$.

Nonsense. A pointer state is a single state, not an ensemble of states. For the latter you need an ensemble of pointers. But experiments are made with single pointers.

This is the source of exponentially small overlap of classical histories of collective coordinates. Now, Banks's book (Chapter 10) has not one but three different arguments to show the exponentially small overlap.

This misses the point. The tiny overlap of nearly classical macroscopic states of a classical pointer has nothing to do with the huge uncertainty of the nonclassical macroscopic states of the pointer that arise from an assumed unitary dynamics of a detector for a spin variable. Thus Banks arguments in Chapter 10 contribute nothing to the explanation of the measurement process.

The sloppiness of Bank's arguments in general, and the resulting low quality, can also be seen from other strange assertions that he makes, full of confidence in his magical powers of reasoning by pure assertion:

This violates only one rule of classical logic: The Law of the Excluded Middle. That law takes as the definition a state that one cannot be in two states simultaneously. Ultimately, like any other law in a scientific theory, the Law of the Excluded Middle must be tested by experiment, and it fails decisively for experiments performed on microscopic systems.

A microscopic system is never in two different states simultaneously. Being in a superposition of classical states is a very different property, which does not contradict the law of excluded middle. The law of excluded middle (not not A =A) is perfectly valid in quantum logic, with a trivial proof: $1-(1-P_A)=P_A$.

Instead, what fails decisively in quantum logic is that one cannot define a meaningful notion of implication with the properties needed for logical reasoning. Indeed, physically relevant reasoning in quantum physics has always been done exclusively with classical logic (including the law of excluded middle), not with quantum logic.

experimental results are quoted with “error bars.” This means that the results of any experiment are themselves given by a probability
distribution.

Not at all. Error bars only mean that the results of experiments are given with an indication of uncertainty. This is far from giving a probability distribution, which cannot be reliably given in many circumstances. It is usually non-Gaussian and hence unknown, unless a huge number of experiments are evaluated together.

Our insistence that there are only a finite number of states means that we can only contemplate discrete time evolution

Banks admits here that his powers of contemplation are far too little developed to cope correctly with quantum phenomena. Clearly, Banks has never heard of shot noise, a 2-state stochastic process in continuous time common in quantum experiments.

A source that makes without hesitation several such strange assertions in the first few pages of the book - a chapter titled ''What you will learn from this book'' - cannot be taken seriously. One can be sure that one learns a lot of wrong things, alongside the standard material - without any guidance of how to separate the wheat from the chaff.

 

[PeterDonis]

you used the word "reality" which is a heavy loaded term. Given that we are in the "quantum interpretation" branch of the forum, you may want to define what you mean by that, before making conclusions about other people's positions.

I didn't mean to attribute my own personal meaning to the term "reality"; as I have already explained, I meant it to mean "whatever Banks is asserting in the given quote". Again, if you don't like the word "reality" to describe what Banks is asserting, feel free to substitute some other word; my argument was based on the substance of what Banks said in the quote, not on the words I used to describe it.

I suggest you read Banks's paper itself first

Doing that now (thanks for the reference).

 

[PeterDonis]

I suggest you read Banks's paper itself first, so you know in what context that quote was given and what are actual conclusions that he draws from the smallness of the above discussed overlap

Ok, having read the paper, the conclusion he draws is that it's ok to just use the classical calculation since the exponentially small interference terms in the quantum calculation make it "in principle" (his phrase) the same as the classical calculation.

That conclusion is wrong. The quantum calculation does not just give interference terms that are exponentially small; even if we ignore the interference terms, it gives a superposition of multiple classical results. But the classical calculation only gives one classical result. So the two are not the same even if we ignore the exponentially small interference terms.

(Btw, I'm assuming for the sake of argument that Banks is correct that the interference terms are actually exponentially small. I have not checked his argument for that since it doesn't really matter for what I have said above.)

I will agree that my previous post did not correctly capture what Banks was actually saying in the quote I referenced earlier. However, that doesn't really help you here, since, when correctly captured, as above, Banks's claim is wrong.

 

[physicsworks]

Nonsense. A pointer state is a single state, not an ensemble of states. For the latter you need an ensemble of pointers. But experiments are made with single pointers.

Nonsense. There is a huge number of linearly independent states that have the same expectation value for the position of the needle on a macroscopic apparatus. Also, you grossly misused the word ensemble in the quote. Furthermore, you don't control microscopic changes in the apparatus, so there is an exponentially vanishing chance for you to start with the same pointer state every time you measure something in a long string of repeated measurements of "identically" prepared systems, which is the only way to check QM predictions.

the conclusion he draws is that it's ok to just use the classical calculation

I don't agree that this is his conclusion, but I'm afraid I'm tired of arguing about what other people say.

 

[A. Neumaier]

There is a huge number of linearly independent states that have the same expectation value for the position of the needle on a macroscopic apparatus.

This does not matter. A single pointer is at any time in a single of these states. The collective position operator is an average over microscopic position operators. But operators are not states, so this average does not make the pointer an ensemble.

If you calculate the expectation value of the pointer position in a nonclassical superposition of classical states you get a value far from the measured values, though consistent with the huge uncertainty.

 

[A. Neumaier]

I'm afraid I'm tired of arguing about what other people say.

You made it your argument by quoting it. So you are tired of defending your own arguments...

 

[PeterDonis]

I don't agree that this his conclusion

From p. 6 of the paper:

For me, these considerations resolve all the angst associated with the Schrodinger's cat paradox. Figurative superpositions of live and dead cats occur every day, whenever a macroscopic event is triggered by a micro-event. We see nothing remarkable about them because quantum mechanics makes no remarkable predictions about them. It never says "the cat is both alive and dead", but rather, "I can't predict whether the cat is alive or dead, only the probability that you will find it alive or dead if you do the same experiment over and over."

It is the classical calculation that says "I can't predict whether the cat is alive or dead, only the probability that you will find it alive or dead if you do the same experiment over and over." The quantum calculation, as Banks himself shows on p. 5 of the paper, does say "the cat is both alive and dead", or more precisely, "the cat is in a superposition of alive and dead, with amplitudes $\alpha$ and $\beta$ that are derived from the initial state". That is what the equations at the top of p. 5 are saying. Note that there are no interference terms in the second equation there, yet that equation still describes a superposition of macroscopically different states. So unless he is claiming that ignoring the interference terms allows you to replace the quantum calculation with the classical calculation, what he says in the quote I gave earlier in this post makes no sense.

 

[vanhees71]

This does not matter. A single pointer is at any time in a single of these states. The collective position operator is an average over microscopic position operators. But operators are not states, so this average does not make the pointer an ensemble.

If you calculate the expectation value of the pointer position in a nonclassical superposition of classical states you get a value far from the measured values, though consistent with the huge uncertainty.

A macroscopic "pointer state" is not described by a single pure state but by a statistical operator close to thermal equilibrium. You have of course thermal as well as quantum fluctuations (quantified as the standard deviations from the mean) which are however very small compared to the accuracy you use to define the macroscopic pointer reading.

It's of course true that nowadays experimentalists are able to prepare also macroscopic (or mesoscopic) systems showing quantum behavior, but that's underlining the point of view given above: As soon as I'm able to resolve quantum behavior, I'll observe it. If I don't I observe classical behavior modulo FAPP negligible fluctuations.

Whether or not you accept this as an explanation for the (apparent) classical behavior of macroscopic systems or not, is of course your personal opinion, and it's hard to argue about it. Of course, if you don't accept probabilistic arguments, it's hard to find a satisfactory argument, but then you also are back to the hitherto unsuccessful attempts to find a comprehensive unified determinstic description of the world like Einstein and Schrödinger in their more mature years. One should note that such attempts seem to be even more hopeless than they seemed to be in those days, because after all the decades of Bell's et al work, making the vague, philosophical EPR ideas scientific and the very successful experimental tests, confirming quantum theory in comparison to local deterministic HV models.

I'm not so sure about Banks's paper (I don't have the book). It seems to make many words with little mathematical analysis. For this topic, I'd rather refer to the book by Joos, Zeh, et al, Decoherence and the Appearance of a Classical World in Quantum Theory, Springer (2003).

 

[A. Neumaier]

A macroscopic "pointer state" is not described by a single pure state but by a statistical operator close to thermal equilibrium.

According to the standard view, the true state of the pointer is pure, and only our ignorance turns it into a density operator.

But when coupled for measurement with a spin even a pointer described statistically by a density operator close to equilibrium turns under the now appropriate von-Neumann dynamics into a nonclassical very out-of equilibrium mixture with huge uncertainty for the pointer position.

This is because in repeated experiments (which are necessary to apply the statistical interpretation), the pointers point in 50% of the experiments to the left, and in the other 50% to the right, so that their expectation is in the middle and the uncertainty is macroscopic.

Unexplained (and simply assumed in the statistical interpretation) is why nevertheless the pointer has a nearly definite position in each single experiment. This is the ''problem of definite outcomes'' - the part of the measurement problem unsolved by decoherence.

 

[A. Neumaier]

I'm not so sure about Banks's paper (I don't have the book). It seems to make many words with little mathematical analysis.

Banks adheres to the many words interpretation of quantum mechanics. It is immune against criticism since (due to the lack of a conservation law for words) one can always create more words out of nothing.

 

[vanhees71]

According to the standard view, the true state of the pointer is pure, and only our ignorance turns it into a density operator.

But when coupled for measurement with a spin even a pointer described statistically by a density operator close to equilibrium turns under the now appropriate von-Neumann dynamics into a nonclassical very out-of equilibrium mixture with huge uncertainty for the pointer position.

This is because in repeated experiments (which are necessary to apply the statistical interpretation), the pointers point in 50% of the experiments to the left, and in the other 50% to the right, so that their expectation is in the middle and the uncertainty is macroscopic.

Unexplained (and simply assumed in the statistical interpretation) is why nevertheless the pointer has a nearly definite position in each single experiment. This is the ''problem of definite outcomes'' - the part of the measurement problem unsolved by decoherence.

I don't know any "standard view", which describes a macroscopic observable as a pure state. You cannot even write it down, because of the many microscopic degrees of freedom you'd have to consider.

Your description of a spin measurement contradicts the observations. A silver atom, being prepared in a thermal state (coming out of the hole of an oven kept at some temperature) running through a Stern-Gerlach magnet leaves one spot on a photo plate defining its position within the position resolution of the plate. There are two spots after a large number of silver atoms has hit the screen, with 1/2 probability for ending up in each of the spots due to the entanglement between the spin component determined by the direction of the magnetic field. It's pretty easy to describe this measured distribution within, and that's all what QT promises to predict. What is unsolved is not clear to me.

 

[Lord Jestocost]

This is the ''problem of definite outcomes'' - the part of the measurement problem unsolved by decoherence.

What is unsolved is not clear to me.

Maximilian Schlosshauer in „Quantum Decoherence“ (Phys. Rep. 831, 1-57 (2019)):

„Application of the unitary Schrödinger evolution to a measuring apparatus interacting with a system prepared in a quantum superposition state cannot dynamically describe the stochastic selection of a particular term in the superposition as the measurement outcome (the ‚collapse of the wave function‘); rather, system and apparatus end up in an entangled state, with all terms of the original superposition still present and quantum-correlated with different apparatus states. This is the measurement problem: the question of how to reconcile the linear, deterministic evolution described by the Schrödinger equation with our observation of the occurrence of random measurement outcomes….

…. The measurement problem as just defined cannot be solved by decoherence.“

 

[A. Neumaier]

I don't know any "standard view", which describes a macroscopic observable as a pure state. You cannot even write it down, because of the many microscopic degrees of freedom you'd have to consider.

The standard view (e.g., Landau and Lifschitz) is that all quantum systems (hence also macroscopic ones) are described by a wave function, which is the most complete description of the state. In your lecture notes on quantum physics you also introduce this standard view when you discuss the postulates of quantum mechanics.

Getting from the standard view a density operator is an additional step involving incomplete knowledge.

 

[dextercioby]

The distinction between „macroscopic observable/state” and „microscopic observable/state” doesn't pertain to axiomatic Quantum Mechanics, but to those foundations of classical/quantum statistical mechanics which attempt to explain from statistical principles the phenomenological principles of quasistatic/equilibrium thermodynamics.
So in the Copenhagen/orthodox/textbook formulation, "the state of a quantum system" is always a clear mathematically well-defined object. "microscopic"/"macroscopic" are not words in a QM axiom, i.e. QM is universal.

 

[gentzen]

Your description of a spin measurement contradicts the observations.

A pointer is not a good picture for a screen. So the mismatch between description and observations is no surprise. Two questions:
1) Is there an experiment (preferably related to spin measurement) where a pointer is a good picture for the physical mechanism of the measurement device?
2) What would be a simple reasonable model for a screen? A 2D non-relativistic quantum field? That seems simple enough, but may be "too coherent".

A silver atom, being prepared in a thermal state (coming out of the hole of an oven kept at some temperature) running through a Stern-Gerlach magnet leaves one spot on a photo plate defining its position within the position resolution of the plate. There are two spots after a large number of silver atoms has hit the screen, with 1/2 probability for ending up in each of the spots due to the entanglement between the spin component determined by the direction of the magnetic field. It's pretty easy to describe this measured distribution within, and that's all what QT promises to predict. What is unsolved is not clear to me.

I am not sure that this is really "all what QT promises to predict". But since you don't want to look at individual silver atoms, there is neither symmetry breaking nor randomness. So you may be right that this specific experiment does not need any interpretative assumptions to match QT predictions to observations. But without a reasonable model for a screen, it is hard to determine the QT predictions.

 

[A. Neumaier]

Your description of a spin measurement contradicts the observations.

I didn't describe Stern-Gerlach but an experiment where a pointer is coupled to a qubit such that it does not move if up is measured but moves when down is measured.

You can take the qubit to be the presence or absence of a photon, and the pointer to be the tip of the needle of a meter measuring the photocurrent generated through magnificaion of the photodetection event.

Unitary dynamics predicts for this setting that the needle will be in a nonthermal state with a macroscopic uncertainty of the pointer.

 

[WernerQH]

You can take the qubit to be the presence or absence of a photon, and the pointer to be the tip of the needle of a meter measuring the photocurrent generated through magnificaion of the photodetection event.

This is an experiment that can only be performed in (some) theoreticians' minds. Experimentalists will laugh at this.

 

[A. Neumaier]

This is an experiment that can only be performed in (some) theoreticians' minds. Experimentalists will laugh at this.

All experiments discussed in this forum are thought experiments. Real experiments are always much more complex than these.

But you can also think of the pointer as a pixel on a screen that turns from white to black when a photon arrives, and position as the grey level rather than a physical position. The presence or absence of a photon is a qubit, The mathematical analysis remains the same.

 

[WernerQH]

The presence or absence of a photon is a qubit, The mathematical analysis remains the same.

A qbit is not the same as a bit. Indeed, that's the mystery: how a qbit gets transformed into a bit. For example, how a circularly polarized photon chooses the path to take in a Nicol prism. In my view neither the qbit nor the wave function are real, only the detection events are real.

 

[A. Neumaier]

A qbit is not the same as a bit.

I didn#t claim they were. Before measurement there is a 2D qubit space of wave functions in superpositions of absent and present, and upon measurement, one of the two materializes and a classical bit results. This is precisely the measurement situation under discussion.

Indeed, that's the mystery: how a qbit gets transformed into a bit.

The mystery - explained neither by the statistical interpretation nor by statistical mechanics added on top.

From the tensor product of a thermal macroscopic state and a qubit state, the von Neumann dynamics produces a complex nonthermal state instead of one of the two observed tensor products of a thermal macroscopic state and a reduced qubit state (unless someone observes the combined system, which leads to von Neumann's regress to consciousness).

In my view neither the qbit nor the wave function are real, only the detection events are real.

But when detection events are real, detectors are real. Now detectors are large quantum systems. How large must a quantum system be in order to count as real? Which of its aspects are then real? Are these determined by its quantum state?

Endless questions for the adherents to this view.

 

[EPR]

But when detection events are real, detectors are real. Now detectors are large quantum systems. How large must a quantum system be in order to count as real? Which of its aspects are then real? Are these determined by its quantum state?

Endless questions for the adherents to this view.

Information availability seems to be key. From my lengthy research on this topic, it's the information availability which acts as a measurement/detection on quantum systems.
And this rule appears to encompass the entire Universe with all quantum systems manifesting as macroscopic detectors, objects, etc with this 'measurement' which in reality is information availability about the quantum system.

Shield the object and it starts to manifest its quantumness.
It's not weird - we just appear to have assumed in the past how the world works on very sketchy and flimsy information.

 

[A. Neumaier]

Information availability seems to be key.

Information is not real. The things the information is about are!

 

[WernerQH]

Before measurement there is a 2D qubit space of wave functions in superpositions of absent and present, and upon measurement, one of the two materializes and a classical bit results.

Endless questions for the adherents to this view.

Obviously you think of the wave function as something physical. And like many physicists you are lured into thinking like this because the wave function has an existence continuous in time, like the "quantum system" that it is supposed to describe. But this is an assumption. If the detector is there whenever we look at it, it is of course an obvious assumption that it is always there. But this need not extend to the smallest scales of space and time. We perceive a motion picture as continuous, although we know it is not. Charge conservation seems to imply that an electron is always there. But there is no experimental evidence that the world-line of an electron must be continuous at the zeptosecond scale. It may in fact be a dotted line; the electron actually being nowhere (rather than "smeared out") between its interaction events.

The notion of an "electron" is, of course, based on a classical concept. It may be more appropriate to see it as a name we attach to a trail of events in spacetime. The essence of an "electron" is the Dirac propagator, and QED is a statistical theory describing correlations between events in spacetime.

I realize that you dislike the statistical interpretation of quantum theory, and I agree that it is unsatisfactory when it is based on an ontology of "particles" with definite properties and existing for finite intervals of time. But you can apply statistics to quite different things!

 

[A. Neumaier]

But you can apply statistics to quite different things!

But wne can apply statistics only to things that exist.

Certain quantum systems consisting of N particles exist and for large N they have properties (such as the center of mass) even when nobody is looking at them - detectors are an example. Decreasing N by one doesn't change the property of existing. By induction, quantum systems exist and have properites (such as the center of mass) down to N=0 (the vacuum), at which point we cannot decrease N anymore.

Or at which N do you suggest that quantum systems stop existing or having a center of mass even when nobody is looking at them? What causes the change in ontology?

 

[WernerQH]

But we can apply statistics only to things that exist.

The click of a Geiger counter is not a "thing". But of course you can do statistics of events. (Queueing theory is just one example!)

If you think that, fundamentally, physics must necessarily be about "things", you are out of luck.

 

[Jarvis323]

The click of a Geiger counter is not a "thing".

What do you mean? Intuitively I wouldn't think that is any less of a "thing" than anything else.

 

[A. Neumaier]

The click of a Geiger counter is not a "thing".

The Geiger counter is the existing thing of which the click is a property. If the quantum system called Geiger counter does not exist, neither the click exists.

If you think that, fundamentally, physics must necessarily be about "things", you are out of luck.

No. I found something innovative this way whereas you only repeat an abstruse tradition. I consider the former to be more lucky than the latter.

 

[PeroK]

Certain quantum systems consisting of N particles exist and for large N they have properties (such as the center of mass) even when nobody is looking at them - detectors are an example. Decreasing N by one doesn't change the property of existing. By induction, quantum systems exist and have properites (such as the center of mass) down to N=0 (the vacuum), at which point we cannot decrease N anymore.

I would say that "centre of mass" is a fuzzy concept. With a large number of particles, the concept is hardly fuzzy at all, but as you remove particles, the property becomes fuzzier and fuzzier.

That's certainly true of other properties: what if we replace "centre of mass" with "age", and apply the same logic? A human being has a well-defined age that cannot be induced into its constituent particles. If you remove the particles that make up me, at what point does what's left stop being 58 years old?

 

[A. Neumaier]

I would say that "centre of mass" is a fuzzy concept. With a large number of particles, the concept is hardly fuzzy at all, but as you remove particles, the property becomes fuzzier and fuzzier.

An object that has a fuzzy property surely exists, no matter how fuzzy the property. And the amount of fuzziness of a property is another (fuzzy) property of the object.

That's certainly true of other properties: what if we replace "centre of mass" with "age", and apply the same logic?

Yes.

A human being has a well-defined age that cannot be induced into its constituent particles. If you remove the particles that make up me, at what point does what's left stop being 58 years old?

When you are dead. There are objective procedures to decide that.

 

[PeroK]

When you are dead. There are objective procedures to decide that.

That's a clever answer, but it doesn't get you round the fundamental problem.