What Defines the Standard and Realist Views in Quantum Mechanics?

[vanhees71]

Of course the single photons are simply unpolarized and prepared in the corresponding mixed state. The state of a subsystem is given by the partial trace (i.e., tracing out the other subsystem). As I said the state of the full system as well as all of its subsystems is fully determined by the preparation of the photon pair in an entangled pair. The general quantum state is of course a mixed state.

What's real are the observable facts about the system, and these are the detector clicks for the photons.

 

[WernerQH]

Of course the single photons are simply unpolarized

Most physicists think of the polarization of a photon as real. It can be measured, after all. Talk of a property that a combination of these objects must have, but not the two objects individually until some intervention occurs, doesn't make sense to me. I know the formalism and that (after years of habituation!) it "suggests" the wording used in discussing the experiments. But I can't find it a reasonable use of language to talk of "photons" as objects. I know you dislike the word "photon" and prefer to speak of quanta (or $\gamma$'s), but it doesn't make the awkwardness go away.

 

[vanhees71]

Of course, polarization of photons is an observable and thus they are "real". As any observable within QT polarization (to be concrete take helicity as the observable) doesn't need to take a definite value. Whether that's the case depends on the state the photon is prepared in. I've never understood all the "hype" about what's "real" and what's "not real" in QT. It's not a very sharply defined notion anyway. For me, simply everything that can be observed and measured is real.

 

[lodbrok]

Whatever it might be, what's "beyond the observations" it's not, what's studied within the natural sciences. With this you clearly go into other realms of human experience than objective observations of phenomena.

Isn't the electromagnetic field between the source and the detector "beyond the observations"? It appears to be an appropriate subject of the natural sciences. Sure, you can place a detector there and detect it, but once you take that detector away, it appears you believe there's something there beyond the observations -- that's Camp A.

 

[vanhees71]

Sure is there something, namely the em. field. We can observe it through its interaction with charged particles, which is the case within both classical and quantum electrodynamics. It seems to me that philosophers tend to overcomplicate things rather than clarifying them.

 

[lodbrok]

Sure is there something, namely the em. field. We can observe it through its interaction with charged particles, which is the case within both classical and quantum electrodynamics. It seems to me that philosophers tend to overcomplicate things rather than clarifying them.

On the contrary, Philosophy is important for Science: https://www.pnas.org/doi/10.1073/pnas.1900357116

A knowledge of the historic and philosophical background gives that kind of​

independence from prejudices of his generation from which most scientists​

are suffering. This independence created by philosophical insight is—in my​

opinion—the mark of distinction between a mere artisan or specialist and a​

real seeker after truth.​

— Albert Einstein, Letter to Robert Thornton, 1944​

Still very relevant to this generation.

 

[Demystifier]

So you are finally outing yourself as a realist!

@vanhees71 is sometimes realist and sometimes non-realist, but he is consistent because he is never both at the same time. His philosophy of QM is contextual, it depends on the question one asks him. Nevertheless his brain is classical, because it does not produce long-range correlations. For example, if you ask him a) Is it true that only measurable things are real?, and if in another post you ask him b) Is it true that electromagnetic field between two measurements is real?, there will be no correlation between the two answers.

 

[vanhees71]

I am a realist, if "realism" refers to objectively observable, quantitative facts about phenomena in Nature. I don't understand, why you think there's no correlation between the answers a) and b). The electromagnetic field is real, because it is measurable through its interactions with other fields, describing charged particles. For me on the most fundamental level physics is described by a spacetime model (the most comprehensive one is General Relativity or, most probably, some extension of it including torsion like Einstein-Cartan theory) and local relativistic QFT. Within this scheme, though incomplete, because the gravitational interaction with its strong correlation to spacetime structure is not yet fully understood within quantum (field?) theory, it's very clear what's "real", i.e., observable and what is not. The electromagnetic field is clearly observable and thus real (the electromagnetic potentials are not, because they are not gauge invariant).

 

[WernerQH]

I've never understood all the "hype" about what's "real" and what's "not real" in QT. It's not a very sharply defined notion anyway.

Ignoring a problem is an option. But being unable to perceive it can be a disadvantage.

 

[martinbn]

@vanhees71 is sometimes realist and sometimes non-realist, ...

This is your fault(QM foundations community). Because you use the word "real" with different meanings. He is a realist in the sense that objective reality exists, say the em field. He is also an anti-realist in the QM sense that observables have no values unless they are measured.

 

[vanhees71]

Ignoring a problem is an option. But being unable to perceive it can be a disadvantage.

A clear formulation of the question is more than half the way to the solution of the problem!

 

[WernerQH]

The electromagnetic field is real, because it is measurable through its interactions with other fields

It's an abstraction, and by no means dictated by observations, but dependent on your mindset, world view, or preferred theory. Decades before Faraday physicists grappled with electricity and magnetism and did not perceive the field concept as "obvious".

I'm not denying its usefulness and calling it real (far from it!), but it is a classical concept. In my view, just "quantizing" it has not sufficiently refined the concept to satisfy mathematicians. Not to mention baffled students of QED.

A clear formulation of the question is more than half the way to the solution of the problem!

Exactly. Einstein perceived the problems of electrodynamics more clearly than others. (He did not "shut up and calculate".)

 

[vanhees71]

This is your fault(QM foundations community). Because you use the word "real" with different meanings. He is a realist in the sense that objective reality exists, say the em field. He is also an anti-realist in the QM sense that observables have no values unless they are measured.

Observables take not determined values by being measured but by the preparation of the system in a corresponding state. If the system is determined in a state, where the outcome of the corresponding measurement is uncertain, the observable simply doesn't take a determined value and thus the state preparation only provides probabilities for each possible outcome of a measurement of this observable, and that's "real", at least according to all so far known observations.

 

[Morbert]

If the system is determined in a state, where the outcome of the corresponding measurement is uncertain, the observable simply doesn't take a determined value

If by "an observable takes a determined value" you mean the outcome of a future measurement of that observable, if it is performed, is known with certainty, then that is uncontroversial.

If instead you mean the microscopic system has a real property corresponding to an eigenvalue of the observable, regardless of whether or not you measure it, then that is a realist position and is controversial.

 

[vanhees71]

Scripsi scripsi! If the state is such that the observable doesn't take a determined value, then it doesn't take a determined value. The meaning of the state is only that it provides the probability for finding any possible value of any observable (an eigenvalue of the representing self-adjoint operator of this observable) when it is (accurately enough) measured. The observable itself always exists, independent of the state, i.e., it can be measured with an appropriate measurement device indepenent of the state the system is prepared in.

 

[martinbn]

It's an abstraction, and by no means dictated by observations, but dependent on your mindset, world view, or preferred theory. Decades before Faraday physicists grappled with electricity and magnetism and did not perceive the field concept as "obvious".

But they were puzzled by some aspects of electricity and magnetism. For example current in a wire deflects a near by compass without any contact.

Also what is the alternative? If there is no em field, then what accounts for the observations? An action at a distance perhaps, but it is a strange one because it is at a distance and propagates with finite velocity!

 

[vanhees71]

The alternative is "action at a distance". Of course, it's indeed a re-conception to use "fields and the local-interaction principle" instead of the concept of "action at a distance". Interestingly already Newton had his quibbles with his action-at-a-distance description of the gravitational interaction. With Faraday and Maxwell in addition it started to become clear that the "em. field" can be interpreted as a dynamical quantity itself, but initially this was even for such progressive thinkers too far-fetched and thus there was, particularly in Maxwell's case, the idea of an aether, i.e., a "mechanical fluid-like medium" an essential idea to understand what we call nowadays the em. field.

Of course such arguments as about what's a "particle" or "field" "ontology or a "reality criterion" or in general anything concerning our epistemic views are theory driven, and of course one must discuss them within the theory we like to find a epistemic or even "ontological" interpretation for. For me, QT on the fundamental level must be discussed using relativistic QFT, when it comes to the question, what "locality" and "realism" means. For me locality makes only sense within a relativistic theory, and the only "realistic" (i.e., applicable to real-world observations) version of a relativistic QT is local relativistic QFT, is based on the "local-field-interaction concept" to make it consistent with the relativistic causality structure following from the relativistic spacetime model, and indeed there is no question that QFT is "local" in this sense, i.e., that there are no causal connections between space-like separated events, and that's implemented in basic foundation of the theory in terms of the "microcausality constraint" on the operators that represent local observables.

Realism is even less clearly defined in the philosophers' literature. It's not entirely clear to me, what they really mean. For me the most rational definition is that realism assumes as a given fundamental fact that there are "observables", i.e., quantifiable descriptions of phenomena and that these observables always take determined values. Both non-relativistic AM and relativistic QFT clearly contradict the reality criterion, i.e., observables take only determined values when the system under consideration is in a corresponding state. Otherwise there are only probabilities for the outcome of measurements on the system, and that's not a lack of information as in classical statistical mechanics ("subjective probabilities") but inherent in the very definition of "state" and "observable" within quantum theory ("objective/irreducible probabilities").

Since relativistic QFT is strictly "local" in the above sense but for sure not "realistic" and in accordance with all (objective quantitative) observations made so far, my conclusion is that Nature behaves according to the concept of locality (realized through local-field descriptions of interactions) but not according to the "realistic description" of classical physics (be it Newtonian point-particle or continuum mechanics or relativistic field theory).

 

[DrChinese]

Observables take "not determined" values by being measured but by the preparation of the system in a corresponding state. If the system is determined in a state, where the outcome of the corresponding measurement is uncertain, the observable simply doesn't take a determined value and thus the state preparation only provides probabilities for each possible outcome of a measurement of this observable, and that's "real", at least according to all so far known observations. ... If the state is such that the observable doesn't take a determined value, then it doesn't take a determined value. The meaning of the state is only that it provides the probability for finding any possible value of any observable (an eigenvalue of the representing self-adjoint operator of this observable) when it is (accurately enough) measured. The observable itself always exists, independent of the state, i.e., it can be measured with an appropriate measurement device independent of the state the system is prepared in.

This frightens me... I actually agree with all of the above. I better understand your terminology now, as you use the concept of Observable to include both cases: when the outcome is certain, and when it is not.

Now: if we could agree the Observable goes from having a "not determined" (completely uncertain) value to having a specific value for that Observable, well... that sounds discontinuous to me. (I call that "Collapse".) Which then begs the question of "when" and "where" that happens, and whether it is the local measurement that causes it or if it is "something else".

QM itself is silent on these points. Presumably the "Collapse" occurs between the Preparation (not determined) and the Measurement (value measured/recorded). But even that is not a requirement of QM (due to existence of delayed choice experiments that blur the usual ordering). And presumably, the "collapse" occurs near (i.e. local to) the Observable. And again, that is not a requirement of QM (due to quantum nonlocality, which blurs where the "cause" originates and the "effect" appears).

 

[WernerQH]

But they were puzzled by some aspects of electricity and magnetism. For example current in a wire deflects a near by compass without any contact.

Also what is the alternative? If there is no em field, then what accounts for the observations? An action at a distance perhaps, but it is a strange one because it is at a distance and propagates with finite velocity!

Ampere developed an accurate theory for the force of one current element on a distant one. At the time he was dealing with what we now call magnetostatics, and all of the experiments seemed to indicate that the action is instantaneous.

 

[WernerQH]

... observables take only determined values when the system under consideration is in a corresponding state. Otherwise there are only probabilities for the outcome of measurements on the system ...

This only makes sense when you talk about the experiment as a whole, i.e. including "state preparation" and "measurement" (none of which happen in an instant). But with the word "state" most physicists associate something that refers to a specific instant in time (and often changes with time). It is unfortunate that you use the word "state" as synonymous with "object". The rules of QM (including the Born rule, of course) give us the frequencies with which certain patterns of events can be expected to occur in a small region of spacetime. Unfortunately many have the desire to think of a "system" and how its "state" evolves with time. I think Consistent Histories was introduced to counter this misrepresentation of QM.

"System", as well as "measurement", was among the terms that John Bell was hoping to ban from the foundations of QM.

 

[Peter Morgan]

As you may have noticed, I am obsessed with understanding the difference between two views of quantum mechanics, one of which can be called the "standard" view, and the other the "realist" view. The difference, of course, is very complicated, but I believe that the essence and origin of the difference must be simple. In this thread I am trying to explain the difference in terms of two simple schemes, corresponding to two approaches to theoretical physics as a science.

The standard approach:
1. Write down the equations.
2. Make the measurable predictions implied by the equations. That's the most important part to do if you aspire to be a scientist, rather than just a mathematician.
3. If you can, try to say what does it all tell us about what the world is made of. But if you are not sure, stay silent about it.

The realist approach:
1. Say what is the world made of.
2. Write down the corresponding equations. That's the most important part to do if you aspire to be a scientist, rather than just a philosopher.
3. If you can, try to make the measurable predictions implied by the equations. But if you are not sure, stay silent about it.

I suggest the standard approach can be twisted around:

1. Construct and perform experiments, as a result of which we have some number of Gigabytes or Exabytes of (noisy) data (it seems to me notable that in modern times we often generate that data at ~MHz rates, far faster than any real-time intervention by people.) We take that actually recorded experimental data to be "real" (I suppose that's Bohr's view when he says, in 1949, "It is decisive to recognize that, however far the phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms.") Certainly, if we don't have credible data available in computer memory, a journal editor will not publish an article about the experiment so that other physicists will take the experiment really seriously.
2. Find ways to systematize that noisy experimental data. Statistics (and probability as an idealization) seem to be more-or-less essential because of the noise. It turns out that Fourier analysis and Hilbert spaces are rather good mathematical tools (the "equations"), but they go beyond the tools we have in ordinary Classical Physics (I suppose that's what Dirac suggests when he says, in 1949, "My own opinion is that we ought to search for a way of making fundamental changes not only in our present Quantum Mechanics, but actually in Classical Mechanics as well.")
3. Use our various systematizations to predict statistics for the results of new experiments. Adjust as necessary.
4. Understand how the ways in which Fourier analysis and Hilbert spaces go beyond ordinary Classical Physics are classically natural, without twisting one's classical intuition very much.

How (4) works is too much to rehearse here. I gave a talk two weeks ago to the Lisbon Philosophy of Physics Seminar, "A Field & Signal Analysis Approach to Quantum Measurement",
(which points to articles in Physica Scripta 2019, Annals of Physics 2020, and Journal of Physics A 2022) that I hope gives some indication of how I think this can be made to play out. The PDF for the talk, which is on Dropbox, https://www.dropbox.com/s/nh4504m6tjrejaa/Lisbon 2023 (as given).pdf?dl=0, has DOIs for those papers and can be skipped through more quickly than listening to me talking round it. I hope a few people here might find it stimulating even though of course nobody will agree with all of it.

 

[Peter Morgan]

This only makes sense when you talk about the experiment as a whole, i.e. including "state preparation" and "measurement" (none of which happen in an instant). But with the word "state" most physicists associate something that refers to a specific instant in time (and often changes with time). It is unfortunate that you use the word "state" as synonymous with "object". The rules of QM (including the Born rule, of course) give us the frequencies with which certain patterns of events can be expected to occur in a small region of spacetime. Unfortunately many have the desire to think of a "system" and how its "state" evolves with time. I think Consistent Histories was introduced to counter this misrepresentation of QM.

"System", as well as "measurement", was among the terms that John Bell was hoping to ban from the foundations of QM.

That seems to me remarkably close to the view I express in the video and papers I refer to in the comment I just posted.

 

[Demystifier]

If there is no em field, then what accounts for the observations?

If there is em field (even when we don't measure it), what is its mathematical representation?
a) A real valued function of ${\bf x},t$.
b) A self-adjoint operator valued function of ${\bf x},t$.
c) A vector in the Hilbert space on which the operator in b) acts.
d) Something else - what?
e) Something as yet unknown.
f) It doesn't have a mathematical representation at all.
g) Prefer not to say.

 

[martinbn]

If there is em field (even when we don't measure it), what is its mathematical representation?
a) A real valued function of ${\bf x},t$.
b) A self-adjoint operator valued function of ${\bf x},t$.
c) A vector in the Hilbert space on which the operator in b) acts.
d) Something else - what?
e) Something as yet unknown.
f) It doesn't have a mathematical representation at all.
g) Prefer not to say.

In the classical theory a) in the quantum b) (may be a distribution rather than a function, and may be not necessarily self-adjoint). But why do you ask me! You tell me what the physical theories say.

 

[Demystifier]

in the quantum b) (may be a distribution rather than a function, and may be not necessarily self-adjoint). But why do you ask me! You tell me what the physical theories say.

I ask you because I want to know what you mean by that.

My problem with your answer in the quantum case is that it doesn't explain how and why real-valued values (i.e. values $\in\mathbb{R}$) appear when we measure the field. It looks as if, in addition to the field operator, there is also something which exists only when it is measured, but the answer b) doesn't explain why. It doesn't mean that your answer is wrong, but it suggests that something in your answer (which is pretty much standard quantum theory) is still missing. In other words, there is the measurement problem and the answer b) doesn't help to solve it.

If you ask me to explain the standard quantum theory, I don't agree that it says that the field operator exists in the physical sense. It is just a tool for computing the probabilities of measurement outcomes. The standard quantum theory presented correctly, in my view, is completely silent about whether anything exists or not in the absence of measurement. Anyone who is talking something about physical existence in the absence of measurement is either saying something beyond standard quantum theory, or saying nonsense (or both).

 

[vanhees71]

This only makes sense when you talk about the experiment as a whole, i.e. including "state preparation" and "measurement" (none of which happen in an instant). But with the word "state" most physicists associate something that refers to a specific instant in time (and often changes with time). It is unfortunate that you use the word "state" as synonymous with "object". The rules of QM (including the Born rule, of course) give us the frequencies with which certain patterns of events can be expected to occur in a small region of spacetime. Unfortunately many have the desire to think of a "system" and how its "state" evolves with time. I think Consistent Histories was introduced to counter this misrepresentation of QM.

"System", as well as "measurement", was among the terms that John Bell was hoping to ban from the foundations of QM.

The state refers to the preparation procedure, and indeed it's associated with setting the initial conditions for the solutions of the dynamical equations of motion. I don't use the notion of "state" as synonymous with objects but I take it to describe the preparation of the system at the initial time. For me the Heisenberg picture is the mathematical description, which is most clearly reflecting the meaning of the abstract notions of the (Hilbert-space) formalism.

John Bell was great with his discovery of how to make sense to the (wrong) ideas of EPR in terms of a scientifically sensible and thus empirically decidable question. I abhorr his "philosophy" though, which introduces more confusion than it does clarify it.

 

[Demystifier]

John Bell was great with his discovery of how to make sense to the (wrong) ideas of EPR in terms of a scientifically sensible and thus empirically decidable question. I abhorr his "philosophy" though, which introduces more confusion than it does clarify it.

Do you know a reference where the discovery of Bell is explained without using any confusing philosophy?

 

[martinbn]

I ask you because I want to know what you mean by that.

But I didn't say anything about it untill you asked me!

My problem with your answer in the quantum case is that it doesn't explain how and why real-valued values (i.e. values $\in\mathbb{R}$) appear when we measure the field. It looks as if, in addition to the field operator, there is also something which exists only when it is measured, but the answer b) doesn't explain why. It doesn't mean that your answer is wrong, but it suggests that something in your answer (which is pretty much standard quantum theory) is still missing. In other words, there is the measurement problem and the answer b) doesn't help to solve it.

If you ask me to explain the standard quantum theory, I don't agree that it says that the field operator exists in the physical sense. It is just a tool for computing the probabilities of measurement outcomes. The standard quantum theory presented correctly, in my view, is completely silent about whether anything exists or not in the absence of measurement. Anyone who is talking something about physical existence in the absence of measurement is either saying something beyond standard quantum theory, or saying nonsense (or both).

This is a seperate quetion. All I said is that the em field exists. How it is described mathematically is another thing. How rigorous that is, is another. How that relates to observation yet another.

 

[martinbn]

John Bell was great with his discovery of how to make sense to the (wrong) ideas of EPR in terms of a scientifically sensible and thus empirically decidable question. I abhorr his "philosophy" though, which introduces more confusion than it does clarify it.

I am not sure what the probem with EPR is?!

 

[gentzen]

If there is em field (even when we don't measure it), what is its mathematical representation?
a) A real valued function of ${\bf x},t$.
b) A self-adjoint operator valued function of ${\bf x},t$.
c) A vector in the Hilbert space on which the operator in b) acts.
d) ...

In the classical theory a) in the quantum b) (may be a distribution rather than a function, and may be not necessarily self-adjoint). But why do you ask me! You tell me what the physical theories say.

I understand why Demystifier wrote self-adjoint operator in b), because in section "8.2 Quantum fields" of Quantum mechanics: Myths and facts he writes:

However, the mathematical formalism used in this trick can be reinterpreted in the following way: The fundamental quantum object is neither the particle with the position-operator $\hat{{\bf x}}$ nor the wave function $\psi$, but a new hermitian operator $$\hat{\phi}({\bf x},t)=\hat{\psi}({\bf x},t)+\hat{\psi}^\dagger({\bf x},t). \qquad (76)$$ This hermitian operator is called field and the resulting theory is called quantum field theory (QFT). It is a quantum-operator version of a classical field $\phi({\bf x},t)$.

Remarks like those in the answer by martinbb always deeply confused me, and forced me to read an "unbelievable amount" about QFT, just to get some basic "big picture" of how the math looks like:

In non-QFT quantum physics, time is a parameter. In QFT, both time and space are parameters. In the non-QFT Schrödinger picture, only the Hamiltonian operator is time dependent (i.e. dependent on the time parameter). In QFT, many more operators (creation, annihilation, "measurement," ... operators) are dependent on the time and space parameters. But maybe not even space parameters, frequency parameters, or ... make sense too. So we have many different families of operators, which depend on parameters somehow analogous to the time parameter in non-QFT QM.

Where does this "distribution" in martinbb's answer comes from, and why is it relevant to Demystifier's question? My guess is that martinbb mentions "distribution," because the simple normal functions $\exp(-i(\omega t - {\bf k}{\bf x}))$ representing plane waves will become delta functions (i.e. distributions) in frequency space. From my point of view, those "distributions" are the least of the problems of QFT, and mentioning them is not helpful in discussions of interpretation of QFT.

 

[vanhees71]

The problem with EPR is that it is not very clearly stated. At least Einstein was not satisfied with how it was written (apparently mostly by Podolsky). As he has clarified in his single-authored Dialectica paper of 1948 his concern was about the "inseparability", i.e., the possibility of strong correlations between far-distant parts of a system. The EPR statement about what they considered incomplete in QT is also not a scientific one, i.e., it was not empirically decidable, which is also due to its vagueness, and for me the great achievement by Bell was to provide a clear definition of a "local realistic theory", leading to empirically testable predictions contradicting QT. The writings beyond this hard scientific core of his work is for me more confusing than helpful. Funny words like "beable" instead of "observable" without a clear (operational) definition of it's meaning in the context of real-world observations are just empty phrases and not helpful in clarifying any of the issues some people seem still to have with the "interpretation of QT". For me the interpretation problems are all solved by the result of all the experimental work in testing Bell's local realistic theories against QT, i.e., QT is the correct description, and since its relativistic version, i.e., local relativistic QFT, is local (in the usual scientific sense of the validity of relativistic causality), it's "realism" which must be given up.

 

[Demystifier]

This is a seperate quetion. All I said is that the em field exists. How it is described mathematically is another thing. How rigorous that is, is another. How that relates to observation yet another.

I don't see that as separate. For me, the statement "em field exists" by itself begs those questions.

 

[martinbn]

Where does this "distribution" in martinbb's answer comes from, and why is it relevant to Demystifier's question?

It comes from the fact that in calssical field thoery the state of a field is represented by a function. When you make a measurement at a spacetime point you get the value of the function. You can also consider the eveluation distributions, which assign to a function the its value at a point. And you can use them instead. In this case they vary smoothly enough to for them to form a function. In the quantum case you only have the distributions and they are not regular unough to give you a function. But my understandting of quantum field theory is very limited so take anything I say with a lot of salt.

Why is it relevant? I am not sure whether it is. But I want to be as precise as possible so that there is no confusion, which often happens here when people do not point out what they mean by the terms they use. For example how is @Demystifier 's question relevent?

 

[martinbn]

I don't see that as separate. For me, the statement "em field exists" by itself begs those questions.

But they depend on how much we know. In calssical physics they have answers that are different in quantum physics, which might be different in the next step and so on. But the em field exists remains the same, we just learn more about how it behaves.

 

[martinbn]

The problem with EPR is that it is not very clearly stated.

Many say that, but my opinion is different. I think that EPR is very clear and precise. People may have different views but they shouldn't confuse their own diffrent worldview with the paper being unclear.