I What Defines the Standard and Realist Views in Quantum Mechanics?

[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.

 

[gentzen]

You can also consider the evaluation 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 enough to give you a function.

Thanks for your answer. Despite reading an "unbelievable amount" about QFT, I still cannot translate such descriptions into a "big picture" of how the math looks like. This may be entirely my own fault. At least I have two basic "big pictures" of how the QFT math looks like at the moment: the "operators depending on space-time like parameters" picture (i.e. what I quoted from my answer), and the "quantum probability amplitudes for field configurations" picture (as explained by Sean Carroll in his books, talks, papers, and blog posts). But I would be willing to read another "huge amount" about QFT, if this would enable me to add another "big picture" of how the math looks like to my repertoire, especially if that would be the picture (from your description) that I initially failed to make sense of, and that I still fail currently to understand.

 

[Demystifier]

At least I have two basic "big pictures" of how the QFT math looks like at the moment: the "operators depending on space-time like parameters" picture (i.e. what I quoted from my answer), and the "quantum probability amplitudes for field configurations" picture (as explained by Sean Carroll in his books, talks, papers, and blog posts).

It may help if you notice that it has an analog in 1-particle QM. There is operators depending on time picture, and there is quantum probability amplitudes for particle positions picture. These are more or less the same as the Heisenberg picture and Schrodinger picture, respectively.

 

[vanhees71]

This mixes up different things. One should stay clear at least about the indisputable math before indulging into philosophical messing.

The QT formalism leads to the same predictions for any choice of the picture of time evolution. The picture of time evolution is just the arbitrary choice, how to distribute the time dependence to observable operators and the statistical operator, given the Hamiltonian $\hat{H}$ of the system. The time evolution equations are given by
$$\dot{\hat{O}}=\frac{1}{\mathrm{i} \hbar} [\hat{O},\hat{H}_1], \quad \dot{\hat{\rho}}=-\frac{1}{\mathrm{i} \hbar} [\hat{\rho},\hat{H}_2],$$
where $\hat{H}=\hat{H}_1+\hat{H}_2$.

For the eigenvectors of the observables you have from this
$$\hbar \partial_t |o,t \rangle=\mathrm{i} \hat{H}_1 |o,t \rangle \; \Rightarrow\; \partial_t \langle o,t|=-\mathrm{i} \langle o,t|\hat{H}_1$$
and for the state ket of a pure state
$$\hbar \partial_t |\psi,t \rangle=-\mathrm{i} \hat{H}_2 |\psi,t \rangle.$$
The Schrödinger equation for the position representation of a pure-state vector is of course the same in any picture of time evolution, because it's the time-picture invariant probability amplitude,
$$\psi(t,\vec{x})=\langle \vec{x},t | \psi,t \rangle,$$
i.e.,
$$\mathrm{i} \hbar \partial_t \psi(t,\vec{x})=\langle \vec{x},t|\hat{H}_1+\hat{H}_2|\psi,t,\rangle=\langle \vec{x},t|\hat{H}|\psi,t \rangle=:\hat{H} \psi(t,\vec{x}).$$
Where the latter notation uses the Hamilton operator in its definition of the position representation.

In QFT the most natural way is to use the Heisenberg picture, where the entire time dependence is on the operators representing observables. Then also the field operators (which don't need to be representants of observables, but by construction all local observables can be built with the field operators and their space-time derivatives) are time dependent, $\hat{\Phi}(t,\vec{x})$ and the states $\hat{\rho}(t)=\hat{\rho}_0=\text{const}$ or in the case of pure states the corresponding state kets $|\psi,t \rangle=|\psi,t_0 =|\psi \rangle=\text{const}$. That's most convenient, because then the field operators obey similar equations as the corresponding unquantized fields (formally the same equations for free fields, which are equations linear in the field operators).

 

[Fra]

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.

Indeed, the puzzle is not if the correlations are really there - we know this empirically. The puzzle is that we do not understand how...

the great achievement by Bell was to provide a clear definition of a "local realistic theory", leading to empirically testable predictions contradicting QT.

Yes, the tentative "mechanism" (namely the naive ignorance type, combined with normal causal rules implied by bells anzats) obviously does not work. So Bell killed one possible soluton to the puzzle.

But the orignal puzzle is still there! Unless you denied the original puzzle in the first place, then there was no puzzle from the beginning.

/Fredrik

 

[Fra]

As I see it, QM is pursely descriptive, as the hamiltionian, state space and initial state, are "inputs". The initial state or hamiltonians are inferred in principled from tomography.

Once done, we have a descriptive system, but this for this system only. If we have a new system, or combines system previously unrelated, i think "in principle" the new composite system has to undergo the same tomography etc.

In this sense, the explanatory value is low. But the predictive value for repeated processes are high, but only valid for that system.

Einsteins ambition to understand how probably went beyond that, and I am symphatetic to that and I think this "issue" transcends the notion of "bell realism". I neither need nor want bell realism, but a puzzle is still there.

/Fredrik

 

[vanhees71]

Indeed, the puzzle is not if the correlations are really there - we know this empirically. The puzzle is that we do not understand how...

At the time of the EPR paper it was not clear, whether the correlations described by entangled states (btw. the much more concise description is by Schrödinger written at about the same time as the EPR paper) "are really there". This was established only much later after Bell opened the door with his famous idea on "local realistic hidden-variable theories" and his inequality. The first experimental works were done by Clauser and Aspect with entangled photon pairs from atomic cascades. I'm not sure, but reading Bell's papers, I had the impression that he expected not a confirmation of QT but of local realistic theories ;-).

Yes, the tentative "mechanism" (namely the naive ignorance type, combined with normal causal rules implied by bells anzats) obviously does not work. So Bell killed one possible soluton to the puzzle.

But the orignal puzzle is still there! Unless you denied the original puzzle in the first place, then there was no puzzle from the beginning.

/Fredrik

There is indeed no puzzle, because QT provides a perfect description of these phenomena (at least as far as we know today, but we know it with great precision and for various quite different systems). It's only a puzzle from a classical worldview, but Nature behaves not according to any of our epistemological prejudices. Science is the only way to overcome such prejudices to get ever closer to the discovery of "what's really going on". The most "realistic theory" we have today is QT, which paradoxically is "not realistic", because the word "realistic" is defined to have a classical meaning, which however is disproven by all these "Bell tests".

IMHO we can go on, and indeed that's what happens right now: What was a fundamental question 40 years ago, today is the basis for new developments in engineering. A strong indication for this is that for some years the "Universities of Applied Sciences" develop curricula in quantum (information) theory for their students!

 

[Fra]

There is indeed no puzzle

I see a puzzle still, but the perspective where the puzzle exists is I think different than yours. So it makes sense to me after all that you deny the puzzle.

It seems for the same reason that you reject or postpone the foundational problems of QM/QFT with the motivation that there isn't much experimental problems. Even though concpetually and logically it almost certainly exists when one wants to complete unification of all interactions.

To relate this still to concepts of "science" as that is what the thread is about, I think your stance is constrained to the set of existing effective theories? While I like to understand the motivation of the theories, beyond empirics.

Another example would be, suppose you ask an AI for a solution to a problem. We get the answer and can experimentally "verify" that it is correct. For some this is enough. But while others are really not just seeking the answer, but seeks to understand the process where by the solution emerges. Ie. the "algorithm" of the AI.

So I am not just interested in certained fixed effective theories with a limited domain of applicability. I rather want to understand why these theories are constructed as they are, and i think this answer exists, we just don't have it yet.

/Fredrik

 

[gentzen]

It may help if you notice that it has an analog in 1-particle QM. There is operators depending on time picture, and there is quantum probability amplitudes for particle positions picture. These are more or less the same as the Heisenberg picture and Schrodinger picture, respectively.

This mixes up different things. One should stay clear at least about the indisputable math before indulging into philosophical messing.

I have now carefully processed what you wrote. To understand what you wrote about QFT, I did reread some passages in "QFT books" I had first read in 2018. I now see that they use "regularization by periodic boundary condition" to avoid the need to discuss the stuff in martinbb's answer, which still confuses me today. Even so it is true that in simple cases, this regularization converges against distributions, in all practically relevant cases I had to deal with so far, I quickly ended up with products of distributions, which are no longer well defined mathematically. And indeed on all those cases, I fell back to "regularization by (not necessarily periodic) boundary conditions," simply because I had no better idea. (Even so I did spend quite some time searching.) It worked, but had some practical drawbacks.

Let me say some words on what you wrote about the normal QT formalism. You basically combined the "textbook" way of how to become independent from whether you compute in momentum space or position space, with A. Neumaier's way of how to become independent of your "quantum picture" (i.e. Heisenberg, Schrödinger, or Dirac picture). You nicely executed that idea, I have not yet seen it before. However, let me try to put it in perspective: While A. Neumaier used "his way" to translate into the Ehrenfest picture, your translation is into the Schrödinger picture. This raises the question whether "this way" also allows a similar translation into the Heisenberg picture. (I believe a translation into the Dirac picture would make less sense, but perhaps I am wrong.)

Let me finally come back to the "indulging into philosophical messing" part. You seem to suggest that one can translate into ones preferred picture only at the end, when all the messy computations have already been done in the picture most convenient for them. So just because Sean Carroll needs the Schrödinger picture for his MWI interpretation, this should not limit him in any way on how he uses and explains QFT. And in your opinion, Demystifier "mixes up different things," when he equates my "operators depending on space-time like parameters" picture with the Heisenberg picture, because what I describe is basically just some math used in some practical computations, and not any specific quantum picture.

 

[Demystifier]

@gentzen if you think that is the most confusing thing about quantum physics, then wait to see this:
https://www.physicsforums.com/threads/what-is-quantum-theory-about.767672/

 

[vanhees71]

I have now carefully processed what you wrote. To understand what you wrote about QFT, I did reread some passages in "QFT books" I had first read in 2018. I now see that they use "regularization by periodic boundary condition" to avoid the need to discuss the stuff in martinbb's answer, which still confuses me today. Even so it is true that in simple cases, this regularization converges against distributions, in all practically relevant cases I had to deal with so far, I quickly ended up with products of distributions, which are no longer well defined mathematically. And indeed on all those cases, I fell back to "regularization by (not necessarily periodic) boundary conditions," simply because I had no better idea. (Even so I did spend quite some time searching.) It worked, but had some practical drawbacks.

I don't know, what you are referring to. Which specific problem is puzzling you? Here are just some hints:

The introduction of a "quantization volume" is a regularization that indeed deals with some problems with distributions. E.g., if you have the S-matrix elements, using in the usual naive way plane-wave initial and final states, and you want to square them you have the problem what to do with the energ-momentum conserving $\delta$ function. This can be cured by introducing a quantization volume to get a discrete set of momenta and Kronecker-$\delta$'s instead of $\delta$-distributions. The infinite-volume limit is then taken at the end to get transition-probability-density-rates to evaluate cross sections. Of course, this is just one pretty convenient mathematical way. A more physically intuitive way is to use true asymptotic free states, i.e., square-integrable functions instead of plane waves, which are no true states, because they are not square integrable. They are indeed distributions. That's also so in first-quantized non-relativistic QM.

All this has, of course, nothing to do with the foundations of QT but are mathematical issues, which are pretty well understood.

Let me say some words on what you wrote about the normal QT formalism. You basically combined the "textbook" way of how to become independent from whether you compute in momentum space or position space, with A. Neumaier's way of how to become independent of your "quantum picture" (i.e. Heisenberg, Schrödinger, or Dirac picture). You nicely executed that idea, I have not yet seen it before. However, let me try to put it in perspective: While A. Neumaier used "his way" to translate into the Ehrenfest picture, your translation is into the Schrödinger picture. This raises the question whether "this way" also allows a similar translation into the Heisenberg picture. (I believe a translation into the Dirac picture would make less sense, but perhaps I am wrong.)

I don't know, what you are referring to. The transformation between different pictures of time evolution is well understood since the very beginning of QT. I also don't know, what you mean by "Ehrenfest picture".

Let me finally come back to the "indulging into philosophical messing" part. You seem to suggest that one can translate into ones preferred picture only at the end, when all the messy computations have already been done in the picture most convenient for them. So just because Sean Carroll needs the Schrödinger picture for his MWI interpretation, this should not limit him in any way on how he uses and explains QFT. And in your opinion, Demystifier "mixes up different things," when he equates my "operators depending on space-time like parameters" picture with the Heisenberg picture, because what I describe is basically just some math used in some practical computations, and not any specific quantum picture.

If an interpretation is dependent on the choice of the picture of time evolution, forget about it. All physics, and thus anything that needs "interpretation", is completely picture independent.

What I referred to @Demystifier as "mixing up" was about his statement:

There is operators depending on time picture, and there is quantum probability amplitudes for particle positions picture. These are more or less the same as the Heisenberg picture and Schrodinger picture, respectively.

Indeed, the choice of the picture of time evolution refers to the time evolution of the operators, which represent observables, using a Hamiltonian $\hat{H}_0$ and the time evolution of the state kets (or equivalently the statistical operator of the system), using a Hamiltonian $\hat{H}_1$, where $\hat{H}=\hat{H}_0+\hat{H}_1$ is the Hamiltonian of the system. The split of $\hat{H}$ into $\hat{H}_0$ and $\hat{H}_1$ is completely arbitrary, and nothing of the physics changes. Particularly "the wave function", i.e., the "quantum-probability amplitudes", in the first-quantization formalism of non-relativistic QM is independent of the choice of the picture of time evolution. There's a lot of confusion in the literature, because it's not clearly stated, what "picture of time evolution" means.

 

[gentzen]

I don't know, what you are referring to. Which specific problem is puzzling you? Here are just some hints:

I refer to the part I quoted before in the post to which Demystifier replied:

You can also consider the evaluation 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 enough to give you a function.

 

[vanhees71]

This I also don't understand. In physics observable quantities are always expressed by well-defined numbers and functions. Distributions are calculational tools of the formalism but not directly related to observable phenomena. As I said, one should really be sure about the formalism before starting to discuss "philosophy". One of the main obstacle to get clear answers concerning the philosophical issues of interpretation is that usually philosophers don't care to learn the theory in a sufficiently detailed way and then discuss about something vaguely defined and see problems where there are none.

It's of course also true that physicists tend to be sloppy in dealing with distributions, but in fact this is really completely understood and clarified by mathematicians, who developed a new branch of mathematics called "functional analysis". Distributions have a well-understood meaning, and it's clear that they do not represent physically realizable states. E.g., it is impossible to prepare a particle (even a free one) in a momentum eigenstate ("plane wave"), because it's not square-integrable. The use of plane waves is that you can describe any square-integrable wave function as a "superposition" of them in the sense that
$$\psi(\vec{x})=\int_{\mathbb{R}^3} \mathrm{d}^3 p \frac{1}{(2 \pi \hbar)^{3/2}} \exp(\mathrm{i} \vec{x} \cdot \vec{p}) \tilde{\psi}(\vec{p}).$$

 

[Fra]

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).

As I views it, the "physical basis" that encodes the field operators exist physically on the observer side of the cut, which for normal QFT means in the macroscopic(effectively classical) environment, in other words, on or beyond the boundary of the system we discuss. But conceptually I think wether it's a function, or a function valued function makes no conceptual differense, it's just the "nth quantization" which I think of as different layers or levels of signal processing; but which also is something that happens physically in the macroscopic environment in the standard paradigm.

But in standard QM, the "physics" of the environment(or observer) really isn't take seriously. Which I think it should, but it's a different can of worms.

/Fredrik

 

[Demystifier]

What I referred to @Demystifier as "mixing up" was about his statement

It's hard to be precise and intuitive at the same time. It was my impression that @gentzen knows the precise formalism but lacks an intuitive picture, so I've tried to say something which would make sense to him at an intuitive level.

 

[vanhees71]

Intuitive pictures should not contradict the formalism!

 

[Demystifier]

Intuitive pictures should not contradict the formalism!

If a recent paper in Phys. Rev. Lett. can violate this demand,
https://arxiv.org/abs/2305.18521
then so can I in an unformal forum discussion.

 

[Quantum Waver]

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).

In a broader sense, what about when astronomers talk about the larger universe outside our light cone, or the physics inside a black hole?

I watched some lectures by Robert Spekkens on the measurement problem. In the second lecture, he discusses operationalism, then asks the students if any of them have realist objections. He mentioned how Ernst Mach was opposed to the atom in 19th century physics, because it couldn't be observed at the time. Technology has a habit of making the unobservable observable.

 

[Structure seeker]

Nice to see the discussion continue and kind of converge. I think the fact that correlations are real is interesting and inviting for scientists to investigate why they are there. Bell tests show it's not hidden variables and that we need to discard locality or realism.

Discarding realism for me is like giving up that there is something to find. If it's not real anyway, why bother? If you only bother because it's a very respected job that pays well, I ask how wrong conspiracy theorists are for not trusting scientists (ofcourse they are wrong for distrusting science, that's another matter).

Discarding locality is tough; it may be better to view any entangled system as having a wormhole, screwing up our minkowski spacetime. The conundrum is indeed memorable, but: there is clear semi-locality in so far that a wavefunction is only affected where it has density.

As to observables being real and nothing else: I'm afraid progress will be missed when you tie so strongly what you believe to only that which has been observed. As long as you can admit failure, it's better to try to grasp reality your preferred way and then acknowledge that reality proves you wrong than not try at all, because at least you learned something (and a null finding is also a finding).

 

[Structure seeker]

If you only bother because it's a very respected job that pays well, I ask how wrong conspiracy theorists are for not trusting scientists (ofcourse they are wrong for distrusting science, that's another matter).

Or if you focus on applications, that's great! But then avoid theoretical discussions unless you want to also specialize on that part. If you want to spread an interpretation of the theory, I believe there must be an intrinsic motivation tied to the subject matter, not to its reputation, position or gain.

 

[Quantum Waver]

Discarding realism for me is like giving up that there is something to find. If it's not real anyway, why bother? If you only bother because it's a very respected job that pays well, I ask how wrong conspiracy theorists are for not trusting scientists (ofcourse they are wrong for distrusting science, that's another matter).

Agreed, but someone might say that 'realism' is misleading and they just mean giving up on determinate values before a measurement is made. Which sounds fine if there is something that provides the range of possible values. Fields and waves do that. What is hard to understand is treating the math as a tool for making predictions that isn't modeling some physical process. Just talking in terms of preparing experiments to calculate results isn't telling me anything about the world. What makes the experiments work? Why even do the experiments?

It's that kind of anti-realism that bothers me.

 

[Demystifier]

In a broader sense, what about when astronomers talk about the larger universe outside our light cone, or the physics inside a black hole?

Astronomers don't really talk about such unobserved things. Perhaps astrophysicists do, and when they do they do it with a grain of salt, but astronomers don't. One way to frame such questions is to ask what would another observer beyond the horizon observe, if she was there?

 

[vanhees71]

You can ask, but never check the answer :-).

 

[physika]

Agreed, but someone might say that 'realism' is misleading and they just mean giving up on determinate values before a measurement is made.

Right.

just Counterfactual Definiteness, not to be real or not.
or there have to say; is unreal but exist...

​

 

[Quantum Waver]

Right.

just Counterfactual Definiteness, not to be real or not.
or there have to say; is unreal but exist...

One poster in another thread claimed that microphysical objects were non-mathematical (not describable by math, ie wavefunction isn't real). I think they were a QBist. I would put it differently. Quanta aren't particles (classically speaking), they're waves in fields, so their values are spread out until a measurement is made (observationally speaking at least). But whatever the case, something real on the fundamental level gives rise to devices, measurements, observers and makes the formalism work.

 

[Structure seeker]

(I think that:)

Quanta aren't particles (classically speaking), they're waves in fields, so their values are spread out until a measurement is made

Couldn't agree more!