I What does it take to solve the measurement problem? (new paper published)

[A. Neumaier]

There cannot be a generally valid collapse postulate, because it depends on your experimental setup, what happens to the measured object.

There can be, and in fact there is:

The dependence of the collapse on the setup is correctly accounted for by the notion of a quantum instrument (or quantum operation, or quantum channel), which generalizes the Heisenberg collapse in the same way as the POVM concept generalizes the Born rule.

The quantum instrument formalism is routinely taught in quantum information theory. For example, the well-known textbook

• M.A. Nielsen and I.L, Chuang, Quantum computation and quantum information: 10th Anniversary Edition, Cambridge Univ. Press, Cambridge 2011.

introduces them (in Section 2.2.3 on quantum measurement, without introducing a name for the concept) even before defining the traditional projective measurements.

I also discuss them in Section 6.6 of my paper

• Quantum tomography explains quantum mechanics.

 

[gentzen]

(in Section 2.2.3 on quantum measurement, without introducing a name for the concept)

See also section 8.2.4 (because it "explains something about the interpretational background" of that concept) ...

 

[Morbert]

There cannot be a generally valid collapse postulate, because it depends on your experimental setup, what happens to the measured object. E.g., if you detect a photon with a photo detector you use the photoelectric effect, i.e., the photon is absorbed by the detector and for sure not in an eigenstate of the measured quantity (e.g., the polarization in a given direction). Of course there are (approximations of) ideal von Neumann "filter measurements", e.g., using a polarization filter, which lets through only photons with linear polarization in a given direction. Then the projection postulate holds, and you have a kind of "collapse of the state".

Adding to the point made by A. Neumaier above, we can also recover a collapse postulate if we generalise our description of the experiment to possible histories $\{C_\alpha\}$ of the joint system (measured system + instrument). Collapse is the change $\rho \rightarrow \frac{C_\alpha \rho C^\dagger_\alpha}{\mathrm{tr}C_\alpha \rho C^\dagger_\alpha}$

https://arxiv.org/abs/gr-qc/9210010

I don't know, what you mean here. There is no problem with filter measurements nor with other kinds of experiments. The "proof" is simple: QT works with great success whereever it is applied!

What Hossenfelder is arguing (unsuccessfully imo) is that, without a collapse postulate, QM's inability to account for the realisation of one possibility over others is a point of incorrectness of the theory.

 

[vanhees71]

What is meant by "QM's inability to account for the realization of one possibility over others"? QT describes, in accordance with all observations, the probabilities for the outcome of any possible measurement, given the state of the system. Which outcome is realized in each individual measurement is inherently random. That's an observed elementary fact about how Nature behaves, and this inherent randomness in Nature was a big problem for physicists used to the classical, deterministic picture of classical physics, and the quest for finding some deterministic description of the random behavior was in vain until today. So far nobody could find any deterministic description of this random behavior. Of course, you cannot exclude the possibility that we simple haven't been clever enough to find such a description, but according to today's knowledge there's not the slightest hint that there exists one.

 

[Morbert]

Actually, to her credit, she clarifies in the very next sentence, the ambiguity I raised. I should have been more patient.

"This means quantum mechanics without the Collapse Postulate is not wrong, but it describes less of what we observe. The Collapse Postulate is hence useful, and part of the axioms because it increases the explanatory power of the theory. It cannot simply be discarded."

 

[vanhees71]

What is it that's observed, which needs a collapse to describe it? These pseudophilosophical texts are all too enigmatic to make sense.

 

[PeterDonis]

What is it that's observed, which needs a collapse to describe it?

The fact that we only observe single outcomes. For example, we observe Schrodinger's cat to be either alive or dead, but without the collapse postulate, unitary QM predicts that it ends up in a superposition of alive and dead.

 

[vanhees71]

What has this to do with the collapse? The collapse occurs when the measurement result is obtained, simply as a postulate, i.e., if the state before the measurement is $\hat{\rho}$ and you measure the observable $A$ with the outcome $a$ (an eigenvalue of the corresponding self-adjoint operator $\hat{A}$), and the eigenspace is spanned by the CONS $|a,\alpha \rangle$, then it's assumed that after the measurement the state has to be descibed by
$$\hat{\rho}'=\frac{1}{\mathrm{Tr} (\hat{P}_a \hat{\rho} \hat{P}_a)} \hat{P}_a \hat{\rho} \hat{P}_a) \quad \text{with} \quad \hat{P}_a =\sum_{\alpha} |a, \alpha \rangle \langle a,\alpha|.$$
This doesn't explain, why there is "a single outcome".

For me this holds true for very specific kinds of measurements, which can only quite rarely realized for very simple systems. One example are single photons run through a polarization filter. Then FAPP there is a collapse in the above described sense, i.e., if a specific photon goes through the filter it's in a linear-polarization state given by this projection, but in no way can this description explain, whether and why a given specific photon goes through the filter or not. All I can say, given the state before the photon hits the filter is the probablity that it will go through.

For me all this refers to the fundamental postulates of the quantum formalism, which cannot be explained by simpler assumptions of some more comprehensive theory (yet). The fundamental postulates have been figured out by a lot of intertwined observation-model-building processes, and they cannot be mathematically proven or otherwise be inferred. It's as with Newtonian mechanics, where you also have Newton's postulates, which cannot be explained by anything but by the fact that they work (within their realm of applicability).

 

[PeterDonis]

What has this to do with the collapse?

You can't get single outcomes without it. With just unitary evolution you don't get single outcomes.

This doesn't explain, why there is "a single outcome".

Whether it "explains" it depends on what you consider to be an "explanation". But mathematically, the state after applying the collapse postulate describes a single outcome having happened. The state before applying the collapse postulate does not.

I suppose one could say all this is interpretation dependent, since on an ensemble interpretation states don't apply to individual runs of experiments anyway.

 

[vanhees71]

My question is simply, what has to be explaned?

For me the alleged interpretation of the collapse postulate doesn't make sense. It doesn't explain the single outcome but the preparation procedure by filtering, and whether this is realized in a specific experiment depends on the measurement procedure/manipulation of the object under investigation and cannot be stated as a generally valid postulate.

E.g., you can also prepare a linearly polarized photon by using a polarizing beam splitter (like a birefringent) crystal. This entangles the polarization (H or V wrt. the chosen orientation of the crystal) with the momentum of the photon. Also here you cannot predict, which momentum and thus polarization any given photon will take (except if it's prepared already as being H or V polarized before), and this is not described by a projection but by a unitary operator (for an ideal PBS).

 

[PeterDonis]

My question is simply, what has to be explaned?

That's going to depend on what you think needs to be explained.

It doesn't explain the single outcome but the preparation procedure by filtering

A measurement with a single outcome is a preparation procedure by filtering. If I pass a photon through a horizontal polarizer and it is transmitted (instead of absorbed), I can either say I've measured its polarization and the result (single outcome) is "horizontal", or I can say I've filtered it so that only horizontally polarized photons get through. It's the same thing either way.

And either way I need the collapse postulate to get to the final state where I just have a horizontally polarized photon in the output beam of the polarizer. If I just use unitary evolution, I get a superposition of "horizontally polarized photon in the output beam of the polarizer" and "vertically polarized photon absorbed by the polarizer".

 

[vanhees71]

No, it doesn't need to be a preparation procedure. E.g., a photon usually a photon is detected via the photoelectric effect and then is gone and not prepared in another state. Of course, when doing a filter measurement, it's described FAPP by the projection/collapse postulate. This is of course not described by a unitary evolution, since it's described within the "open-quantum-system formalism", i.e., you "trace out" the equipment the photon is interacting with to be measured and, maybe, prepared in a new state.

 

[PeterDonis]

Of course, when doing a filter measurement, it's described FAPP by the projection/collapse postulate.

This is also the case for a photon measured (and destroyed) by a detector. Otherwise you wouldn't be able to explain why just one detector fires in any experiment with multiple detectors (for example, a beam splitter with a detector in each output arm). Unitary evolution predicts a superposition of "detector A fires" and "detector B fires" for a case like that.

 

[vanhees71]

We always detect one photon only once (as also with massive particles). That's why Born introduced the probability interpretation of the quantum state in contradiction with Schrödinger's original interpretation as a classical-field description of particles. Born's rule, in my opinion, is also simply one of the other independent postulates of QT, and it has nothing to do with the collapse postulate.

 

[PeterDonis]

We always detect one photon only once

Of course, I'm not saying we don't. I'm saying that if we only use unitary evolution and do not use the collapse postulate, QM does not predict this. It predicts a superposition of detection by different detetors, not a single detection by just one detector.

 

[PeterDonis]

That's why Born introduced the probability interpretation of the quantum state

Yes, but that "interpretation" still doesn't narrow down very much. Advocates of all of the known QM interpretations say that they are consistent with Born's probability interpretation of the state and the Born rule.

Born's rule, in my opinion, is also simply one of the other independent postulates of QT, and it has nothing to do with the collapse postulate.

Yes, that's how we view them in our 7 Basic Rules.

 

[vanhees71]

It's of course again a matter of interpretation. For me the meaning of the state is strictly probabilistic, i.e., a single-photon state tells me the probability to find the photon with a detector at a given position (note, it's not the position of the photon, because a photon has no position observable in the usual sense) and, if I bother to measure it, a given polarization. It's not to be interpreted in a classical-field sense. This was the original interpretation by Schrödinger of his wave function for a (nonrelativistic massive) particle, i.e., Schrödinger thought he could describe the electron as a classical field rather than as a classical point particle, but of course pretty soon it turned out that this is incompatible with what's observed, i.e., an electron is detected always as a point but not as a continuously smeared charge distribution as is predicted by the Schrödinger equation, when interpreting the wave function as a classical field with $-e|\psi(t,\vec{x})|^2$ as a continuous charge distribution. That's why Schrödinger introduced the probabilistic interpretation, and it's the only consistent interpretation of the quantum state until today. As with any fundamental law you can only explain how the physicists historically came to this theory, including its interpretation (in the sense of how the mathematical description has to be applied to the description of real-world observations and measurements), but you cannot explain "why it must be so", except you find some new, more comprehensive theory, for which QT follows in some approximate sense. So far we neither have such a more comprehensive theory nor do we have any idea, whether there's any need for it.

The one big issue, of course, is the question of quantum gravity (or in your preferred geometric interpretation of gravity a quantum theory of spacetime), but I don't think that this has anything to do with the measurement (pseudo-)problem of the philosophers. It's simply lack of empirical guidance that pushes some theorists into the right ansatz for the resolution of this quibble.

 

[Demystifier]

Of course there are (approximations of) ideal von Neumann "filter measurements", e.g., using a polarization filter, which lets through only photons with linear polarization in a given direction. Then the projection postulate holds, and you have a kind of "collapse of the state".

What about the Stern-Gerlach apparatus that measures spin of a massive particle? Would you say that the projection postulate holds in this case?

 

[Demystifier]

This doesn't explain, why there is "a single outcome".

The minimal statistical interpretation also does not explain why there is a single outcome.

 

[Fra]

My question is simply, what has to be explaned?

From my perspective, the collapse just declares in a simplified way that the agents expectation is changed after an information update. It is just a "reset" required before again applying unitary evolution. What needs to be explained is the detailed HOW the interaction/observation by the agent is processed and revise the expectation of the agent.

As the unitary evolution only defines the agents expectations - in between - information updates, what happens AT the "information updates" is like some boundary process, that is left unexplained in QM.

I view this missing thing as an internal process of the agent. And the process of how the agents state is "changed" by post-processing new input, seems to me to be like a "repreparation". But without ensembles. The preparation refers then not to an ensemble, but to the single agents state. That view can still view the agents "state" as isomorphic to the "information about an ensemble" in some cases, but the state of a single agent makes sense always, even when the ensemble realization does not.

Also, if one like I do, think that agents are simply matter systems interacting, what is missing in QM is ultimately to understand how the hamiltonian emerges as two agents interact. The postulated hamiltonian evolution in between measurements, must then be in principle sequence of "collapses".

As long as we don't understand this better, the collapse postulate seems required, but it does itself not really "explain" anything. It's just required to "reset" the evolution after measurements. But the physics of this reset is not understood. This is also the sense is which I see this as connected to the unification quest.

/Fredrik

 

[martinbn]

I don't understand the issue with single outvomes. How can there be anything else? What is a multiple outcome?

 

[Fra]

As I see it:

Given the hamiltonian and unitary evolution (this is input; not "explained") and an initial state, QM just predicts probabilities. So what happens when we make an observation; then obviously we gain new information, that must revise our expectations of the future. This is not explained or described in depth as a physical phenomena in QM - this is "missing". Lacking this, we throw in the "collapse postulate" which explain nothing, but it declares the supposed influence of a single observation of the future expectations, but leaving you unsatisfied.

I think this part in QM leaves alot of space to wish for more.

The heart of the matter is the causal connection between single events and expectations of the future. Ie. how single events, forges the "dice". And the "dice" is in my thinking implicitly defined by the state of the agent. This is the connetion between single event events, and guiding or normative probabilities that we still miss. You can simply assume that you just instantly revise the state after some idealised observation. But I think this glosses over some deeper dynamics. IT describes was is supposed to happen, but not why or how.

So when the agent corresponds to the usual "classical laboratory" watching an atom, then the "dice" is indeed made up by massive amounts of statistics or repeats which matches well the ensemble interpretation. Then a single events will not deform the dice, it takes massive statistics to do so. But this view gets problematic when the "classical agent" is then part of the system, such as the schrödinger cats etc. Resorting to decoherence explanations is I think just a way to curing something with more of the same.

/Fredrik

 

[vanhees71]

From my perspective, the collapse just declares in a simplified way that the agents expectation is changed after an information update. It is just a "reset" required before again applying unitary evolution. What needs to be explained is the detailed HOW the interaction/observation by the agent is processed and revise the expectation of the agent.

In my opinion it has nothing to do with the agent, which state I associate with the system after a measurement but with the specific experiment I'm doing, i.e., with how the measured system interacts with the measurement device. The collapse assumption is only then the right choice for the update of the state after the measurement, if the equipment is realizing (with some good approximation) a filter measurement. Otherwise you have to think about another update of the state.

As the unitary evolution only defines the agents expectations - in between - information updates, what happens AT the "information updates" is like some boundary process, that is left unexplained in QM.

The unitary evolution describes the time evolution of the states (probability amplitudes) for a closed system. What happens to the partial system of interest, follows by "tracing out" the other parts (measurement devices, "environment") and is not a unitary time evolution anymore, and this time evolution includes dissipation and decoherence. The "information update" for us is completely irrelevant to this dynamics. It's just reading off a measurement result from a scale or from a computer file.

 

[A. Neumaier]

What is a multiple outcome?

If one particle is sent and several detectors respond.

 

[martinbn]

If one particle is sent and several detectors respond.

That is still a single outcome.

 

[gentzen]

I don't understand the issue with single outvomes. How can there be anything else? What is a multiple outcome?

There certainly can be other "classical outcomes," which are not single outcomes. You would probably classify such measurements as "weak measurements," and only regard the projective measurements with "single outcomes" as true measurements. Noisy detector readings are sometimes better interpreted as approximations to the expectation value (which could even evolve in time) of the measurement operator, instead of interpreting each individual noisy measurement record as a "single outcome".

Of course, those other "classical outcomes" still don't quality as "multiple outcomes," and especially not as complex superpositions of "single classical outcomes". But this has "theoretical" issues anyway, first it would need a "physically" preferred basis of the Hilbert space, and second some "physical" distinction between i and -i. Both are certainly "doable" to a certain extent, for example i and -i are often associated with time direction, and absorption processes often translate into an imaginary part of some "nearly classical quantity". Still, the whole setup is missing gauge invariance, and even so specific experimental arrangements often come with their preferred gauge fixing, it is still a hard call to claim that quantum mechanics by default would predict such gauge dependent measurement outcomes.

The measurement process in quantum mechanics by default is modelled by Hermitian measurement operators and "possible classical outcomes" that can be associated with such operators. Interpretations like MWI that claim one could do without should be suspicious, by default...

 

[A. Neumaier]

That is still a single outcome.

It depends how one counts. Those discussing the unique outcome problem say that there are two outcomes, one at each detector. This is not observed, hence should be explained. The quest for an explanation is the unique outcome problem.

If you count differently, the problem still persists, but there is no longer a simple word for it.

 

[vanhees71]

But the "unique outcome problem" is solved by Born's probabilistic interpretation of the state. So, where's the problem?

 

[gentzen]

I don't understand the issue with single outvomes. How can there be anything else? What is a multiple outcome?

… many different answers and discussions by different people …

This is not observed, hence should be explained. The quest for an explanation is the unique outcome problem.

But the "unique outcome problem" is solved by Born's probabilistic interpretation of the state. So, where's the problem?

I guess martinbn asked why we need an axiom like Born‘s in the first place. And now you come and ask „where‘s the problem“, the „unique outcome problem“ is solved by Born‘s …

Independent of the quality of the different answers and discussions, this reaction feels very strange to me.

 

[A. Neumaier]

I guess martinbn asked why we need an axiom like Born‘s in the first place.

No, he explicitly asked for the issue with single outcomes:

I don't understand the issue with single outcomes. How can there be anything else? What is a multiple outcome?

the „unique outcome problem“ is solved by Born‘s …

Born's rule doesn't solve this issue but simply postulates it away!

This is the simple-minded way of solving all unexplained issues in physics: simply postulate what needs to be explained! But it gives a false sense of accomplishment.

 

[vanhees71]

… many different answers and discussions by different people …I guess martinbn asked why we need an axiom like Born‘s in the first place. And now you come and ask „where‘s the problem“, the „unique outcome problem“ is solved by Born‘s …

Independent of the quality of the different answers and discussions, this reaction feels very strange to me.

Why? Physics is an empirical science, and Schrödinger's interpretation of the physical meaning of his wave function was not in accordance with the observations, i.e., single electrons were not detected as little "smeared clouds of continuous charge distributions" but as dots on a photoplate. On the other hand Schrödinger's $|\psi(t,\vec{x})|^2$ were correctly describing the distributions of these dots when applying his wave equation. So Born draw the conclusion that $|\psi(t,\vec{x})|^2$ describes the probability density for finding an electron at the place $\vec{x}$ (when measured at time $t$). That with one ingenious insight resolved the wave-particle duality of the old quantum theory. Obviously even today the prize to pay, i.e., that nature is inherently behaving probabilistically, seems to be too high, so that they look for other (deterministic?) "explanations", but that's a philosophical (religious?) rather than scientific issue.

 

[vanhees71]

No, he explicitly asked for the issue with single outcomes:
Born's rule doesn't solve this issue but simply postulates it away!

This is the simple-minded way of solving all unexplained issues in physics: simply postulate what needs to be explained! But it gives a false sense of accomplishment.

Born's rule indeed does solve this issue by a postulate, which, as anything in the natural sciences, is justified by its consistency with all observations. That's all you need for an accomplishment in physics and, btw, to get a (somewhat belated) Nobel prize ;-)).

 

[Fra]

In my opinion it has nothing to do with the agent, which state I associate with the system after a measurement but with the specific experiment I'm doing, i.e., with how the measured system interacts with the measurement device.

It's not unexpected that you see it differently. How the measured system interacts with the measurement device is in my view simply "how the measured system interacts with the agent".

The key difference is the "measurement device" is part of the macroscopic world, which is for all practical purposes never saturated with information about the quantum system. In my general view, this assymmetry holds only as a exceptional limiting case.

The collapse assumption is only then the right choice for the update of the state after the measurement, if the equipment is realizing (with some good approximation) a filter measurement. Otherwise you have to think about another update of the state.

Thinking about this general update of the state is what understanding the state of the agent is about for me.

The unitary evolution describes the time evolution of the states (probability amplitudes) for a closed system.

The general inside agent/observer is always an open system - except in between information updates - where there is unitary evolution IMO, whose form should be followed be selfconsistency of the prior information (state + hamiltonian). This holds until the agent is perturbed again.

But I admit that this esotheric things supposedly become relevant only when considering unification of forces. IF one simply postulates(or experimentally findeS) a hamiltonian, none of the above I write makes sense, because then we are considerinf only effective theories (where the implict observer is FIXED and not actively participating in the interactions except in the idealised way of measuremtns we are used to).

/Fredrik

 

[martinbn]

It depends how one counts. Those discussing the unique outcome problem say that there are two outcomes, one at each detector. This is not observed, hence should be explained. The quest for an explanation is the unique outcome problem.

If you count differently, the problem still persists, but there is no longer a simple word for it.

Then the question is why some outcomes dont occur, rather than why a single outcome occurs.

 

[CoolMint]

Then the question is why some outcomes dont occur, rather than why a single outcome occurs.

Conservation laws apply at all scales. When you send 1 electron, you detect 1 electron.

 

[CoolMint]

The real question is how can the circumstances of these measurements be related to anything else than us? Given that without the collapse postulate and measurement, Nature is fundamentally indeterminate.
*Us is a collective term for agents who can record outcomes in memory for storage

 

[Morbert]

Then the question is why some outcomes dont occur, rather than why a single outcome occurs.

Conservation laws apply at all scales. When you send 1 electron, you detect 1 electron.

I think the issue is, if you have an experiment that concludes with either detector 1 or detector 2 going off, QM will give you probabilities for these events. But it will also give you probabilities for complementary events built from superpositions, though they do not have to correspond to "both detectors go off". E.g. Considering the state $\frac{1}{\sqrt{2}}(|D_1\rangle + |D_2\rangle)$ $$p(D_1) = \mathrm{tr}|D_1\rangle\langle D_1|\rho$$ $$p(D_2) = \mathrm{tr}|D_2\rangle\langle D_2|\rho$$ $$p(?) = \frac{1}{2}\mathrm{tr}|D_1+D_2\rangle\langle D_1+D_2|\rho$$The third outcome never occurs even though its probability is nonzero.

 

[A. Neumaier]

Conservation laws apply at all scales. When you send 1 electron, you detect 1 electron.

But unitary quantum mechanics implies conservation laws only for the quantum expectations!

 

[vanhees71]

No, quantum mechanics implies conservation laws event by event. There was a short debate about this in connection with the (infamous) Bohr-Kramers theory. This was disproven by Bothe with his coincidence measurements concerning Compton scattering: As to be expected energy-momentum conservation was fulfilled event by event.

 

[A. Neumaier]

No, quantum mechanics implies conservation laws event by event.

Can you point to a theoretical argument proving this?

There was a short debate about this in connection with the (infamous) Bohr-Kramers theory. This was disproven by Bothe with his coincidence measurements concerning Compton scattering: As to be expected energy-momentum conservation was fulfilled event by event.

This is an experimental proof, not a consequence of quantum mechanics.

Moreover, the argument by @CoolMint was about particle number conservation, for which this experimental proof says nothing.

 

[vanhees71]

It's in any textbook of quantum theory or quantum field theory. There is an energy-momentum conserving $\delta$-distribution in the S-matrix.

 

[A. Neumaier]

It's in any textbook of quantum theory or quantum field theory. There is an energy-momentum conserving $\delta$-distribution in the S-matrix.

Together with the probabilistic interpretation of the S-matrix, this gives indeed energy-momentum conservation violations with probability zero. (Thus finitely many exceptions are still allowed, and we can do only finitely many observations.)

But

the argument by @CoolMint was about particle number conservation,

for which the S-matrix argument does not apply. $N$ photons in does not imply $N$ photons out.

 

[vanhees71]

Of course not. The photon number is not conserved. Nobody has ever claimed this.

 

[CoolMint]

Photons are the entities resembling particles the least.

 

[A. Neumaier]

Photons are the entities resembling particles the least.

Gluons, W-bosons, Higgs, etc. are also not conserved but are still considered particles.

 

[gentzen]

It depends how one counts. Those discussing the unique outcome problem say that there are two outcomes, one at each detector. This is not observed, hence should be explained. The quest for an explanation is the unique outcome problem.

But the "unique outcome problem" is solved by Born's probabilistic interpretation of the state. So, where's the problem?

And now you come and ask „where‘s the problem“, the „unique outcome problem“ is solved by Born‘s …
..., this reaction feels very strange to me.

Why?

Because the discussion seemed to be about "what is the unique outcome problem" or "why should there be a unique outcome problem," and not about solving it by experimental observations or by postulating specific (reasonable) axioms.

Physics is an empirical science, and Schrödinger's interpretation of the physical meaning of his wave function was not in accordance with the observations, i.e., single electrons were not detected as little "smeared clouds of continuous charge distributions" but as dots on a photoplate.

I don't think that Schrödinger's "very first" interpretation was the subject of this discussion. Additionally, dots on a photoplate without further context cannot "solve" the problem either. All they do is exhibit a context where the "smeared clouds of continuous charge distributions" interpretation is not applicable. Of course, that naive "smeared" interpretation is almost never a good interpretation, even so smeared charge distributions do occur in the density functional theory.My overall problem with this "strange style" of discussion is that it makes it difficult for me to dive into subtle issues in details. For example, the discussion has now touched topics like "conservation laws event by event" or that "photons are the entities resembling particles the least". As we have seen in discussions with RUTA, boundary conditions can sometimes prevent conservation laws from holding event by event, while still enforcing conservation laws for the quantum expectations.

Also with respect to solving the "unique outcome problem" by "postulating specific (reasonable) axioms," there would be interesting subtle details: What sort of postulate would that be? Would it be more of the "2+2=4" type, the "ZFC is consistent" type, or rather the "PA is consistent" type? You see, "2+2=4" is simply true, and "ZFC is consistent" is simply undecidable. But "PA is consistent" is subtle. It is true, it can be proved true in at least three fundamentally different informal ways, but it must be postulated nevertheless.

Maybe more fundamental, I would have found it nice to clarify A. Neumaier's view on Ensembles in quantum field theory. I don't even understand why he thought that you have to "repeatedly prepare a quantum field extending over all of spacetime" in order to use an ensemble interpretation of QFT. But if already the fact that an ensemble interpretation is not universally applicable is never acknowledged, not even in simple examples, then this makes it difficult for me to dive into such subtle issues.

 

[vanhees71]

"Particle" has a very specific meaning in modern relativistic QFT.

I don't think that Schrödinger's "very first" interpretation was the subject of this discussion. Additionally, dots on a photoplate without further context cannot "solve" the problem either. All they do is exhibit a context where the "smeared clouds of continuous charge distributions" interpretation is not applicable. Of course, that naive "smeared" interpretation is almost never a good interpretation, even so smeared charge distributions do occur in the density functional theory.

The dots on the photoplate are the empirical facts, and your mathematical framework of the theory supposed to describe these facts together with the "interpretation" of this framework has to be consistent with these observations. Indeed, the distribution of many equally prepared electrons on the photoplate is given by $|\psi(t,\vec{x})|^2$, the solution of Schrödinger's equation, but the single electron is not detected as a smeared charge distribution but as a dot. This apparent contradiction (known as the "wave-particle dualism" in the old quantum theory) is resolved by Born's interpretation of $|\psi(t,\vec{x})$ as the probability density for the position of the electron, when it is detected at time $t$. No observations so far contradict this interpretation and it has nobody come up with a satisfactory alternative description. That's why I consider the statistical interpretation of the quantum state a la Born as the solution of the wave-particle-dualism as well as the unique-outcome problem. The unique outcome of measurements, given appropriate measurement devices, are an empirical fact too, and again all there is according to the best currently available theory, QT, are the probabilities for these outcome as predicted by this theory.

My overall problem with this "strange style" of discussion is that it makes it difficult for me to dive into subtle issues in details. For example, the discussion has now touched topics like "conservation laws event by event" or that "photons are the entities resembling particles the least". As we have seen in discussions with RUTA, boundary conditions can sometimes prevent conservation laws from holding event by event, while still enforcing conservation laws for the quantum expectations.

I don't know, what you are referring to here. The conservation laws just say that conserved quantities are conserved. If the system is prepared in an eigenstate of some conserved quantities, then the state at later times stays in such an eigenstate, because the Hamiltonian commutes with the correspond operators representing these conserved quantities. That's a mathematical property of the theory and tells you the event-by-event conservation of conserved quantities. I don't know, which "boundary conditions" you are talking about.

Also with respect to solving the "unique outcome problem" by "postulating specific (reasonable) axioms," there would be interesting subtle details: What sort of postulate would that be? Would it be more of the "2+2=4" type, the "ZFC is consistent" type, or rather the "PA is consistent" type? You see, "2+2=4" is simply true, and "ZFC is consistent" is simply undecidable. But "PA is consistent" is subtle. It is true, it can be proved true in at least three fundamentally different informal ways, but it must be postulated nevertheless.

I don't know, what the fundamental axioms of math have to do with this problem. QT is formulated in terms of standard functional analysis.

Maybe more fundamental, I would have found it nice to clarify A. Neumaier's view on Ensembles in quantum field theory. I don't even understand why he thought that you have to "repeatedly prepare a quantum field extending over all of spacetime" in order to use an ensemble interpretation of QFT. But if already the fact that an ensemble interpretation is not universally applicable is never acknowledged, not even in simple examples, then this makes it difficult for me to dive into such subtle issues.

I've also no clue. Just look at, where (relativistic) QFT is applied to experiments, and you see that the ensemble interpretation perfectly fits. It has a good reason that the LHC and all of its big detectors were upgraded for more luminosity enabling "more statistics"!

 

[gentzen]

Indeed, the distribution of many equally prepared electrons on the photoplate is given by $|\psi(t,\vec{x})|^2$, the solution of Schrödinger's equation, but the single electron is not detected as a smeared charge distribution but as a dot.

The modern formalism assigns physical meaning to quantities that can be associated to self-adjoint measurement operators. As long as no qualification on the physically relevant measurement operators (spin, energy, momentum, ...) and the physically relevant quantities (probabilities for single outcomes, expectation values, ...) are added, this remains a pure description of a mathematical framework (like ordinay differential equations are the framework for classical point particle physics, partial differential equations are the framework for classical field theories, ...), to which the physical content must still be added.

No observations so far contradict this interpretation and it has nobody come up with a satisfactory alternative description.

And still this brute force interpretation might miss some subtle details, like I tried to illustrate above.

(Edit: I remember a huge table from "Quantenchemie: Eine Einführung" by Michael Springborg, where many relevant physical interpretations of quantities occurring in quantum chemistry computations were given. If I can find it again, I will include it in another reply.)

I don't know, what you are referring to here.

The discussions with RUTA about conservation on average only

I don't know, which "boundary conditions" you are talking about.

The easiest way to break a symmetry of the equations of motion is by having physically relevant boundary conditions that are incompatibe with that symmetry, which would have given rise to the conserved quantity. The example from RUTA seem to be easiest explained in terms of such boundary conditions, from my point of view. Of course, symmetries can also be broken for other reasons (at least in classical continuum physics), but those reasons did not apply to his examples, from my point of view.

I don't know, what the fundamental axioms of math have to do with this problem. QT is formulated in terms of standard functional analysis.

They illustrate the subtleties which can still remain despite the agreement that axioms or postulates are indispensible.

I've also no clue. Just look at, where (relativistic) QFT is applied to experiments, and you see that the ensemble interpretation perfectly fits. It has a good reason that the LHC and all of its big detectors were upgraded for more luminosity enabling "more statistics"!

If you always say "it is simple," or "I don't understand your problem," or "...", then this might be harmless as long as your conversation partner is right anyway and doesn't need your input. But you get him into trouble in the occasional cases where he is wrong, and would have benefitted from you input to see this for himself.

 

[PeterDonis]

As we have seen in discussions with RUTA, boundary conditions can sometimes prevent conservation laws from holding event by event

This is a claim RUTA makes, but I don't think it is generally accepted.

 

[vanhees71]

I don't know anybody else, who claims this.