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

[PeterDonis]

Wikipedia says

You've been here long enough to know not to use Wikipedia as a reference, particularly for a topic like this.

how do you define the "measurement problem"?

The measurement problem is the problem of why we observe single definite outcomes when we do experiments on quantum systems. In the basic math of QM, this is simply put in by hand as the projection postulate: there is nothing anywhere else in the math that predicts it. The rest of the math says that when you do an experiment to make a measurement you entangle the system being measured with the measuring device and end up with a superposition of different possible outcomes. The only way to get a single definite outcome out of that in the basic math is to put in the projection postulate by hand--i.e., just declare by fiat that we collapse the wave function in the math whenever we have to to make predictions for future experimental results come out right.

On a collapse interpretation, the projection postulate becomes an actual physical law and wave function collapses become actual physical events (instead of just mathematical devices to make correct predictions for future experimental results). But then they have to explain how these collapse events happen and how correlations between spacelike separated measurements on entangled particles can violate the Bell inequalities without actual faster than light signaling.

On a no collapse interpretation like the MWI, the projection postulate remains just a mathematical device, and the rationale for applying it is that, once decoherence happens after a measurement, the different branches of the wave function can never interact with each other again, so in each individual branch we can apply the projection postulate to get an "effective" wave function for that branch that works for predicting future measurement results in that branch, even though we "know" (if we accept the MWI as true) that there are other branches in the overall wave function. But this requires one to accept all of the other things that come along with the MWI and all of the other issues that have been raised with it.

On an interpretation like the Bohmian interpretation, while collapse of the wave function is not an actual physical process (the full wave function is always there), measurements have single outcomes because those outcomes are determined by the underlying, unobservable particle positions, and each particle always has a single definite position. But the equation of motion for these definite particle positions is highly nonlocal, which many people find very difficult to accept. Also, on this interpretation, when you dig into the details of how measurements of anything other than position actually work, you realize that what you are actually measuring when you think you are measuring, say, the spin of an electron, looks nothing like what you expect a spin measurement to look like.

 

[Sunil]

On an interpretation like the Bohmian interpretation, while collapse of the wave function is not an actual physical process (the full wave function is always there), measurements have single outcomes because those outcomes are determined by the underlying, unobservable particle positions, and each particle always has a single definite position.

I think the "unobservable" is misleading, given that all what we see are those positions - of macroscopic devices, but those macroscopic devices consist of particles as well.

But the equation of motion for these definite particle positions is highly nonlocal, which many people find very difficult to accept. Also, on this interpretation, when you dig into the details of how measurements of anything other than position actually work, you realize that what you are actually measuring when you think you are measuring, say, the spin of an electron, looks nothing like what you expect a spin measurement to look like.

Given the violation of Bell's inequalities, "nonlocality" (which is only non-Einstein-causality) is simply the explanation which is most compatible with common sense. Everything else - giving up realism (the extremely weak EPR criterion) and causality (in particular necessarily Reichenbach's common cause principle - astrologers will be happy) would be no alternative in normal life. So why should it accepted as making sense in science?

That "measurement" is a misleading word has been criticized already by Bell in the paper "against measurement". The "measurement result" is the result of an interaction, not a property of one of the interacting systems.

 

[timmdeeg]

It is important to distinguish the wave function of the alpha-particle from the wave function in the 3 * (N+1) dimensional configuration space of the "whole" system including the gas of the cloud chamber. Tracing out the uninteresting coordinates of the gas molecules is certainly a non-unitary operation, and the result for the alpha-particle would again have spherical symmetry (and it would be misleading to still call it a "wave function").

What the formalism tells us is that the drops are vastly more likely to form straight lines than erratic zig-zag curves. Similarly the Feynman path integral tells us that the points at which the alpha-particle interacts are likely to be very close to a path that has the least action. Wave function collapse is just a figure of speech that has no basis in the formalism.

Thanks, great explanation.
Could one - to simplify a little - say that the straight lines are based on the equations of motion? But then this result can be expected. I was wondering why they call it "a highly non trivial result without having any recourse to the wave packet reduction rule" .

 

[timmdeeg]

You've been here long enough to know not to use Wikipedia as a reference, particularly for a topic like this.

Yes, therefore I wrote "Wikipedia says simply".

The measurement problem is the problem of why we observe single definite outcomes when we do experiments on quantum systems. In the basic math of QM, this is simply put in by hand as the projection postulate: there is nothing anywhere else in the math that predicts it. The rest of the math says that when you do an experiment to make a measurement you entangle the system being measured with the measuring device and end up with a superposition of different possible outcomes. The only way to get a single definite outcome out of that in the basic math is to put in the projection postulate by hand--i.e., just declare by fiat that we collapse the wave function in the math whenever we have to to make predictions for future experimental results come out right.

On a collapse interpretation, the projection postulate becomes an actual physical law and wave function collapses become actual physical events (instead of just mathematical devices to make correct predictions for future experimental results). But then they have to explain how these collapse events happen and how correlations between spacelike separated measurements on entangled particles can violate the Bell inequalities without actual faster than light signaling.

On a no collapse interpretation like the MWI, the projection postulate remains just a mathematical device, and the rationale for applying it is that, once decoherence happens after a measurement, the different branches of the wave function can never interact with each other again, so in each individual branch we can apply the projection postulate to get an "effective" wave function for that branch that works for predicting future measurement results in that branch, even though we "know" (if we accept the MWI as true) that there are other branches in the overall wave function. But this requires one to accept all of the other things that come along with the MWI and all of the other issues that have been raised with it.

So in the MWI the projection postulate isn't in conflict with unitarity (though "put in by hand") because the wavefunction doesn't collapse. It confirms nothing more than what we observe, single definite outcomes".

Having searched the web I couldn't find any comparable comprehensive form explaining the meaning of the "Measurement Problem". Perhaps you should think to add it to the FAQ list.

Thanks!

 

[WernerQH]

Could one - to simplify a little - say that the straight lines are based on the equations of motion? But then this result can be expected.

What is non-trivial depends very much on how you look at it. :-)
The equations of motion can be derived from the action principle, so it's basically the same argument.

I think the wave function (whether in 3 or more dimensions) is a red herring. The Heisenberg picture offers a more sensible view of the quantum formalism: the states are constant. There's no mention of collapse. A |ket> by itself is meaningless; it always has to be combined with a <bra| and a trace be taken. One always considers ensembles, and nobody has ever suggested that an operator, rather than a wave function, represents an individual system. In the Heisenberg picture you can consider the evolution over a certain period of time and compute expectation values of operator products at different times. Averages, and the likelihood of particular histories are the natural output of the formalism. Nobody has to clarify which "quantum state" the system is "really" in at any particular moment. Quantum theory is silent on that.

 

[PeterDonis]

I think the "unobservable" is misleading, given that all what we see are those positions - of macroscopic devices

Exactly: we see positions of macroscopic devices, not positions of individual particles. (Btw, the "particles" in question aren't necessarily any of the particles that appear in our fundamental theories--they're not necessarily quarks or leptons. They could be some other kind of particles at a deeper level.) The individual particle positions, which are the basic ontology of the Bohmian interpretation, are unobservable.

 

[EPR]

The only theory that unites the quantum world with the "classical" scale is QFT. Out of it, it's known that the world is not made of classical objects but of the 18 quantum fields. The fields are the fundamental nature of reality. At least as far as science goes.
Gravity isn't expected to change the fields nature of reality either.
At least we now know how the world isn't.

To tackle the enigma of classical perception, physicists have conjured up fantastic ontologies: higher-dimensional space-time or the multiverse, in which our universe is just one instance out of an infinitude. Other physicists have resorted to mysticism. There are more ontological questions than answers, but it's better to not know than be fooled.

 

[timmdeeg]

This article seems to question the universal validity of the projection postulate.

If correct would this affect the interpretations of QM?

https://link.springer.com/article/10.1007/s10701-021-00452-x

"Specifically, quantum computing algorithms make heavy use of the projection postulate [2], the axiom that every measurement is strictly equivalent to random application of one of a set of mathematical projection operators, with probability governed by the Born rule.
...
So, is the projection postulate or any related measurement axiom fundamentally and literally true if you look closely enough? In this paper, I will attempt to analyze the internal dynamics of a specific real single-quantum detector, the cloud chamber.
...
I have formulated a mechanism for how the Hamiltonian structure of quantum decay, the physics of droplets in supersaturated vapors, and the mathematics of quantum Coulomb scattering from degenerate states can together account for the observed phenomenology of track origination in cloud chambers, without having to invoke measurement axioms."

 

[gentzen]

This article seems to question the universal validity of the projection postulate.

If correct would this affect the interpretations of QM?

Hard to say. Some physicists reject the projection postulate (as generally valid), but don't expect this to be a big deal:

Where I strongly differ with the orthodox/minimal view (aka the 7 rules agreed on by the majority in this forum) is only in refusing the collapse/projection postulate as a fundamental generally valid postulate.

Arnold Neumaier's thermal interpretation also comes to the conclusion that Born's rule (and the projection postulate) are not universally valid, but seems to attach more importance to this:

Then I prove that under certain other circumstances and especially for ideal binary measurements (rather than assume that always, or at least under unstated conditions), Born's interpretation of the formal Born rule as a statistical ensemble mean is valid. Thus I recover the probabilistic interpretation in the cases where it is essential, and only there, without having assumed it anywhere.

Maybe the attached importance is more related to the Born rule itself, than to the projection postulate.

Edit: I should probably clarify that my answer just tries to point out that practical implications of the non-universality of the projection postulate will be very limited, because it is well known already that you should not interpret it too literally. So my guess is that the implications for quantum computing will be minimal. For interpretations on the other hand, stressing its non-universality might be important.

 

[vanhees71]

For me the question whether or not the Born rule can be derived from other postulates is secondary. You can come to the same mathematical formalism via different heuristic routes. I'm not too convinced by the alternative @A. Neumaier calls "thermal interpretation".

What's for sure clear is that the projection postulate is not needed and in almost all real-world experiments not followed or not feasible. It's only a special case of a particular sort of preparation procedure where it is possible to prepare a system in a pure quantum state by measurement of a certain observable (or a set of compatible observables) to a resolution such that all but one outcome are filtered away. This is possible e.g., for the Stern-Gerlach experiment, where a beam of silver atoms is split in two entangeling the spin component chosen by the direction of the magnetic field with the position almost ideally and thus being able to prepare a pure spin-component eigenstate. Another example are polarization states of single photons just using a good polarization filter. It depends on the feasibility of such a high-resolution measurement and filtering, whether you can prepare a certain given pure quantum state, and most measurements are far from this. I don't think that such an exceptional case should be taken as one of the fundamental postulates of a general physical theory.

 

[timmdeeg]

Hard to say. Some physicists reject the projection postulate (as generally valid), but don't expect this to be a big deal:

The projection postulate is not an interpretation of QM, but which importance this postulate has for a physicist perhaps depends on the interpretation he favors.

 

[timmdeeg]

What's for sure clear is that the projection postulate is not needed and in almost all real-world experiments not followed or not feasible.

Would you say that this conclusion is interpretation independent?

 

[EPR]

Would you say that this conclusion is interpretation independent?

It's standard quantum mechanics. Some people don't like it because it leads to the measurement paradox and the issue with the cat.

I think it's the most revealing aspect of all QT.

 

[PeterDonis]

I have formulated a mechanism for how the Hamiltonian structure of quantum decay, the physics of droplets in supersaturated vapors, and the mathematics of quantum Coulomb scattering from degenerate states can together account for the observed phenomenology of track origination in cloud chambers, without having to invoke measurement axioms."

The mechanism described appears to me to be similar to Neumaier's thermal interpretation, which was mentioned in an earlier post. Basically, the mechanism is random variation in the huge number of degrees of freedom of the detector--in this case the molecules in the chamber--which leads to one particular direction for the cloud chamber track being selected out of all the possible ones.

 

[vanhees71]

Would you say that this conclusion is interpretation independent?

Yes, you only have to look, how in practice QT is applied to describe and predict the outcome of real-world measurements within QT.

 

[vanhees71]

The mechanism described appears to me to be similar to Neumaier's thermal interpretation, which was mentioned in an earlier post. Basically, the mechanism is random variation in the huge number of degrees of freedom of the detector--in this case the molecules in the chamber--which leads to one particular direction for the cloud chamber track being selected out of all the possible ones.

This has been discussed already in 1929 by Mott in a famous article about, why one sees "straight trajectories" of $\alpha$ particles emitted from a radioactive probe within a cloud chamber. The probability for emission of any individual $\alpha$ particle is random in its direction (in good approximation it's isotropic) and the magnitude of the momentum is determined from the energy of the emitted $\alpha$ particle which is determined at an accuracy which can be estimated by the lifetime-energy uncertainty relation. Mott shows that once the direction of the $\alpha$ particle is given after being emitted by the ionization of the first few droplets of the vapor in the cloud chamber, the probability for ionizing the next droplet in the cloud chamber is sharply peaked around the straight line. It's of course clear that the "trajectory" is never as accurately determined as it would violate the Heisenberg uncertainty relation. This follows without any fancy interpretations from the application of the minimal interpretation as given in the Insights article (you don't even need the projection postulate, which however in this case holds to a pretty good approximation).

 

[A. Neumaier]

What's for sure clear is that the projection postulate is not needed and in almost all real-world experiments not followed or not feasible.

Yes. What is universally true (and therefore should replace the projection postulate and Born's rule associated with it) is the more general POVM view. Simple, elementary foundations for it are given in my paper 'Born's rule and measurement' (arXiv:1912.09906).

I'm not too convinced by the alternative @A. Neumaier calls "thermal interpretation".

But as shown in the above paper, the thermal interpretation matches perfectly with the POVM view.

 

[vanhees71]

Well, as you well know, I've no objections of your formalism, but more when it comes to interpretational issues. What I don't like is that it is not clear, which meaning what you call "expectation values" have. As you want to derive the Born rule, I cannot read it in its usual meaning, namely a probabilistic expectation value. On the other hand the idea that this is actually the "observable" is also not convincing, because that may be true in a "thermal sense", i.e., when you consider macroscopic observables, where the fluctuations are "negligibly small" because you "coarse grain" over large enough space-time volumes, and in this sense your interpretation is indeed really "thermal", but it doesn't apply to microscopic objects, for which we want to use and interpret quantum theory.

That's why I still think from a physicist's point of view the "orthodox minimal interpretation" (no collapse, no quantum-classical cuts on a fundamental level but probabilities and only probabilities a la Born with Born's rule itself a fundamental postulate) is the most "economic approach" to state the scientific part of quantum theory (the only part which in my opinion belongs to physics and not metaphysics).

I'll have a look at your paper as soon as I find the time :-(.

 

[timmdeeg]

That's why I still think from a physicist's point of view the "orthodox minimal interpretation" (no collapse, no quantum-classical cuts on a fundamental level but probabilities and only probabilities a la Born with Born's rule itself a fundamental postulate) is the most "economic approach" to state the scientific part of quantum theory (the only part which in my opinion belongs to physics and not metaphysics).

In his book "Einstein's Schleier" Zeilinger says analogously (? sinngemäß) it is sufficient to understand the wave function just as a mental construct so that its collapse doesn't happen in real space. I was never sure if that is his personal view. It seems to fit though to that what you call "orthodox minimal interpretation", right?

 

[vanhees71]

I think so. I've also read this book, and it's always good to have the view of an experimentalist. I've always talked briefly with Zeilinger after a colloquium some years ago, and there also he told me he's pretty much a "Bohrian Copenhagenian". AFAIK also in his scientific papers, he's pretty much an "orthodox minimal interpreter".

 

[A. Neumaier]

the idea that this is actually the "observable" is also not convincing, because that may be true in a "thermal sense", i.e., when you consider macroscopic observables, where the fluctuations are "negligibly small" because you "coarse grain" over large enough space-time volumes, and in this sense your interpretation is indeed really "thermal",

Thus it applies to the measurement results, which are read off from macroscopic thermal objects...

but it doesn't apply to microscopic objects, for which we want to use and interpret quantum theory.

... even when what is measured is a microscopic degree of freedom, by design of the detector strongly correlated with some macroscopic detector property. This is precisely the condition that allows us to speak of a measurement.

 

[kith]

@A. Neumaier: If we measure properties of macroscopic bodies, things like expectation values are usually not thought to be beables but epistemic quantities. In principle, such measurement processes should also admit a quantum description where your thermal interpretation treats expectation values as beables. How is this reconciled?

 

[EPR]

In his book "Einstein's Schleier" Zeilinger says analogously (? sinngemäß) it is sufficient to understand the wave function just as a mental construct so that its collapse doesn't happen in real space. I was never sure if that is his personal view. It seems to fit though to that what you call "orthodox minimal interpretation", right?

The detected positions correspond as if the collapse happened in real space. 1:1

That's as good as a model can get.

You can't just brush aside the evidence.

 

[A. Neumaier]

@A. Neumaier: If we measure properties of macroscopic bodies, things like expectation values are usually not thought to be beables but epistemic quantities. In principle, such measurement processes should also admit a quantum description where your thermal interpretation treats expectation values as beables. How is this reconciled?

Nothing in the abstract formalism forces us to interpret the trace of $\rho A$ as an expectation values. A historically unbiased name for this number is 'value of $A$ in the state $\rho$' - this is the literal mathematical meaning when treating the state $\rho$ as a linear functional on an algebra of observables -, leaving the additional qualification 'expectation' to statistical interpretations.

In the thermal interpretation, the traditional name 'expectation value' is therefore just a historical leftover from the old days when the statistical interpretation was thought to be the only reasonable one. I often use 'q-expectation value' to emphasize that quantum expectation values have the name but not the meaning in common with statistical expectation values.

 

[kith]

I'm not sure if I understand this correctly. Does the thermal interpretation say that all quantum mechanical quantities which are traditionally thought of as statistical are beables and that statistics is relevant only in the classical description of measurement devices?

 

[timmdeeg]

The detected positions correspond as if the collapse happened in real space. 1:1

But this notion (in contradiction to special relativity) means that energy spread out in real space would collapse to a point instantaneously. That exactly is Zeilinger's argument. QM doesn't claim the "real space" issue.

 

[A. Neumaier]

I'm not sure if I understand this correctly. Does the thermal interpretation say that all quantum mechanical quantities which are traditionally thought of as statistical are beables and that statistics is relevant only in the classical description of measurement devices?

Not quite.

Whatever is traditionally a statistical expectation value is in the thermal interpretation a q-expectation value and hence a beable. But one can do statistics even on quantum beables, not only on classical ones. In this way one recovers in the thermal interpretation the statistical interpretation of quantum mechanics in those situations where it applies - namely when one has a large supply of instances in identically prepared states.

 

[timmdeeg]

@A. Neumaier: Would you say that the "thermal interpretation" is independent of whether or not the projection postulate holds?

 

[EPR]

But this notion (in contradiction to special relativity) means that energy spread out in real space would collapse to a point instantaneously. That exactly is Zeilinger's argument. QM doesn't claim the "real space" issue.

Yes. If you supposed the system had those properties(e.g. energy) before measurement, you'd get some nonlocality.

 

[vanhees71]

Thus it applies to the measurement results, which are read off from macroscopic thermal objects...

... even when what is measured is a microscopic degree of freedom, by design of the detector strongly correlated with some macroscopic detector property. This is precisely the condition that allows us to speak of a measurement.

My problem with the approach you call "thermal interpretation" still is that it is not clear what the operational meaning of your expectation values is, because you stress several times it's not considered to have the usual probabilistic meaning, but what then is the operational meaning?

What I like about the approach principally is that it makes the attempt to describe the meausurement process on a quantum theoretical basis. If this could worked out to a convincing physical picture, I think it would be real progress.

The advantage of the orthodox minimal interpretation is that it starts from clear operational concepts, i.e., the expectation values have a clear probabilistic meaning, and a measurement device is a real-world physical object not some abstract mathematical construction like a POVM. The latter is needed for the cases that you are qualitatively describing but it's never worked out how to construct the POVM for a given real-world (say quantum optical) apparatus like a beam splitter, mirrors, lenses, a photodector, etc. In the standard approach (see e.g., the textbooks by Scully and Zubairy or Garrison and Chiao), where all these elements are pragmatically described by effective quantized classical models. To some extent you can also derive it from quantum many-body theory from first principles though that is of course pretty tough.