What Defines the Standard and Realist Views in Quantum Mechanics?

[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!