Are quantum fields real objects in space?

[bhobba]

This is a question which “Physics” cannot answer seriously. One should not extend speculations beyond the range of experiments/observations. The reality is in the "observation" of the moon, not in the moon itself.

Remember the moon is being observed all the time by its environment. How the classical world emerges is discussed by Hartle and Gell-Mann in a famous paper here:
https://arxiv.org/abs/quant-ph/0609190

To 'decipher' it see here (as well as a link to another paper by Hartle and Gell-Mann about it):
https://www.sciencenews.org/blog/context/gell-mann-hartle-spin-quantum-narrative-about-reality

That uses normal QM - not QFT - but of course QM is a limiting case of QFT. Are the fields of QFT real? Well first ask are the fields of EM real. Wheeler and Feynman formulated EM in terms of action at a distance so you do not need fields - so why do physicists believe in them? The answer is Noether - we believe in conservation of energy and momentum. If you move a charged particle then another charged particle does not react straight away due to relativity. But we want energy and momentum to be conserved because of Noether. I read somewhere where Wigner even produced some no-go theorems about it. The answer was to have a field which via Noether (again) has energy and momentum. Well with energy it can in principle be converted to mass - most physicists are not too philosophical and think mass real - whatever real is - so fields are real - even though you never directly observe them - just their effects - and as mentioned you can formulate EM without them. Bohr was an exception - there probably are others as well - but most these days seem to be like Feynman because of his experience with philosophy at MIT - the teacher bored him to death and spent his time in the class drilling small holes in his shoes - thought it all hooey. To add insult to injury, he didn't care what his son studied as long as it was not philosophy. Guess what - he studied philosophy. He later switched to computer science and Feynman was happier. Anyway, to recap, because most physicists consider mass real they consider fields real. You could apply the same argument to Quantum Fields - they in a certain limit become the stuff around us. Its a pretty common sense sort of view - but physicists often are like that. For example read Weinberg on Kuhn and his view of what science is:
http://www.physics.utah.edu/~detar/phys4910/readings/fundamentals/weinberg.html

'I remarked in a recent article in The New York Review of Books that for me as a physicist the laws of nature are real in the same sense (whatever that is) as the rocks on the ground. A few months after the publication of my article I was attacked for this remark by Richard Rorty. He accused me of thinking that as a physicist I can easily clear up questions about reality and truth that have engaged philosophers for millennia. But that is not my position. I know that it is terribly hard to say precisely what we mean when we use words like "real" and "true." That is why, when I said that the laws of nature and the rocks on the ground are real in the same sense, I added in parentheses "whatever that is." I respect the efforts of philosophers to clarify these concepts, but I'm sure that even Kuhn and Rorty have used words like "truth" and "reality" in everyday life, and had no trouble with them. I don't see any reason why we cannot also use them in some of our statements about the history of science. Certainly philosophers can do us a great service in their attempts to clarify what we mean by truth and reality. But for Kuhn to say that as a philosopher he has trouble understanding what is meant by truth or reality proves nothing beyond the fact that he has trouble understanding what is meant by truth or reality.'

It's not deep is it? Its pretty common-sense - and that basically is how many (perhaps even most - but probably not all) physicists view it. For a counter view read Penrose - I will say no more - his views are rather unusual - but strangely compelling - one can see why those of a certain 'bent' would gravitate to it - I did at one time.

Thanks
Bill

 

[bhobba]

In the Copenhagen interpretation, an observer is someone or something that collapses the wave function into an eigenstate of the operator observed. How do you ensure that your elementary observer does this?
Surely the interaction of the photon with the Moon does not do this by itself, it just entangles the state of the photon with the state of the Moon.

I think that's one reason Hartle and Gell-Mann developed Decoherent Histories - but they are the first to admit the program is not complete - there are issues remaining that need to be worked out. Maybe they can't in which case - down the gurgler it goes - but as of now they are open questions.

A few of the issues can be found in Omnes book on the subject:
https://www.amazon.com/dp/0691004358/?tag=pfamazon01-20

Thanks
Bill

 

[bhobba]

So how does this interpretation cope with the quantum physics of the early universe, before there were observers? It cannot.

It doesn't, and is a known problem.

Thanks
Bill

 

[Demystifier]

But it doesn't mean "is not" i.e. the object doesn't exist. Copenhagen is open on that part.

As I stressed many times, there are several different versions of "Copenhagen" interpretation. Some versions are, as you say, open to it. Some are not.

More importantly, if one accepts that properties of the object exist even before observation, and that measurement just changes (rather than creates) those properties, then the Bell theorem implies that those changes obey non-local (deterministic or stochastic) laws. It is inconsistent to think that nature is both local and existing without observations. Some Copenhagenians are aware of that, which is why, by insisting on saving locality, they argue that objects don't exist before observation.

 

[DarMM]

Some Copenhagenians are aware of that, which is why, by insisting on saving locality, they argue that objects don't exist before observation.

I think the most common version of this today is denying that the quantum probabilities are set by some hidden variable $\lambda$ of the system in question, though the system itself exists.

 

[Demystifier]

I think the most common version of this today is denying that the quantum probabilities are set by some hidden variable $\lambda$ of the system in question, though the system itself exists.

But probabilities must be determined by something. For example, if that something is the wave function $\psi$, that also qualifies as a special case of $\lambda$.

 

[A. Neumaier]

For example read Weinberg on Kuhn and his view of what science is:
http://www.physics.utah.edu/~detar/phys4910/readings/fundamentals/weinberg.html

Nice essay!

 

[A. Neumaier]

Is this is heresy, there must be a name for it. I don't know what it is.

It is the heresy of superficial speculation.

 

[bhobba]

But probabilities must be determined by something. For example, if that something is the wave function $\psi$, that also qualifies as a special case of $\lambda$.

Hmmm. Interesting view. What do you think of probabilities themselves - do you reach the same conclusion?

Thanks
Bill

 

[bhobba]

Is this is heresy, it must be a name for it. I don't now what is.

As has been correctly pointed out there are different versions of Copenhagen and each version has different issues. These days many Copenhagenists have moved over to Consistent/Decoherent Histories calling it Copenhagen done right - you can read about its basics here:
http://quantum.phys.cmu.edu/CQT/index.html

But there is no free lunch - as I mentioned it is more concise than general Copenhagen, eg no issues with measurement because it is replaced by the concept of history. So far so good - but as I mentioned before there are some issues in principle not yet worked out fully. Only the future will tell us how it fares. If its of any value Murray gave a lecture on it when his friend (the friendship cooled towards the end - but the respect never did - nor did Feynman's respect for Murray - calling him the worlds best living physicist) Feynman was alive and was in the audience. At the end he got up and everyone thought a ding dong was on - but instead said - I agree with everything said. So he was converted to it towards the end.

Thanks
Bill

 

[Demystifier]

What do you think of probilities themdrlves - do you reach the same conclusion?

I'm not sure what do you mean by probabilities themselves, but I guess the PBR theorem is relevant here.

 

[bhobba]

I'm not sure what do you mean by probabilities themselves, but I guess the PBR theorem is relevant here.

What I meant is one view if you are into Gleason etc is it is simply something that helps in calculating probabilities which are something that simply helps in calculating frequencies of observations. In a sense you can look on both as just calculational devices for the reality which is observations. I personally do not believe that - there is more to it eg how a mixed state becomes a proper mixed state - just interested in what you think. BTW I have never thought of the wave-function itself as a hidden variable - but now you have placed the idea in my mind I think it deserves serious thinking about.

And PBR is definitely relevant - if it is not just some abstract calculational device its pretty hard to deny its reality in the sense of the theorem.

Thanks
Bill

 

[Demystifier]

BTW I have never thought of the wave-function itself as a hidden variable - but now you have placed the idea in my mind I think it deserves serious thinking about.

And PBR is definitely relevant - if it is not just some abstract calculational device its pretty hard to deny its reality in the sense of the theorem.

The PBR theorem can be stated as follows. If there is some $\lambda$ at all, then either $\psi$ is $\lambda$, or $\psi$ is uniquely determined by $\lambda$.

 

[bhobba]

The PBR theorem can be stated as follows. If there is some $\lambda$ at all, then either $\psi$ is $\lambda$, or $\psi$ is uniquely determined by $\lambda$.

Yes.

Just for those not aware of it here is the paper:
https://arxiv.org/pdf/1111.3328.pdf

The out is what is mentioned in the paper - some for some reason seem to forget it, even though its clearly stated it in the original paper:
'The argument depends on few assumptions. One is that a system has a “real physical state” – not necessarily completely described by quantum theory, but objective and independent of the observer. This assumption only needs to hold for systems that are isolated, and not entangled with other systems. Nonetheless, this assumption, or some part of it, would be denied by instrumentalist approaches to quantum theory, wherein the quantum state is merely a calculational tool for making predictions concerning macroscopic measurement outcomes.'

You are right - if you do not invoke the out then the wave-function is clearly a hidden variable - I just never thought of it that way.

Thanks
Bill

 

[Demystifier]

Yes.

Just for those not aware of it here is the paper:
https://arxiv.org/pdf/1111.3328.pdf

The out is what is mentioned in the paper - some for some reason seem to forget it, even though its clearly stated it in the original paper:
'The argument depends on few assumptions. One is that a system has a “real physical state” – not necessarily completely described by quantum theory, but objective and independent of the observer. This assumption only needs to hold for systems that are isolated, and not entangled with other systems. Nonetheless, this assumption, or some part of it, would be denied by instrumentalist approaches to quantum theory, wherein the quantum state is merely a calculational tool for making predictions concerning macroscopic measurement outcomes.'

You are right - if you do not invoke the out then the wave-function is clearly a hidden variable - I just never thought of it that way.

Thanks
Bill

Exactly. After all, nobody ever measured $\psi$ by a single measurement, so it is hidden. In fact, Bohmians often say that it is $\psi$, not the particle position, which is really "hidden".

 

[DarMM]

The PBR theorem can be stated as follows. If there is some $\lambda$ at all, then either $\psi$ is $\lambda$, or $\psi$ is uniquely determined by $\lambda$.

But probabilities must be determined by something. For example, if that something is the wave function $\psi$, that also qualifies as a special case of $\lambda$.

$\psi$ itself being the only hidden variable is the subset of psi-ontic interpretations known as psi-complete interpretations. The usual phrasing of the PBR theorem is that if $\Lambda$ is the space of hidden variables and

1. $\Lambda$ is measureable
2. Experiments have one outcome
3. There is no retrocausality
4. There is no superdeterminism
5. $\Lambda$ has a product structure on two systems, i.e. $\Lambda_{AB} = \Lambda_A \times \Lambda_B$

Then at the very least $\Lambda = \mathcal{H} \times \mathcal{A}$, with $\mathcal{H}$ the quantum mechanical Hilbert space.

Axioms 1-4 are called the ontological framework axioms, with interpretational models obeying it called ontological models. So the theorem may be stated as any ontological model whose state space has a product structure for two systems (i.e. two systems can be prepared independently) must have the wavefunction as a subset of its hidden variables.

One can reject this by rejecting axioms 1-4 of course (I've seen no serious attempts at 5) or one can take the AntiRealist view and reject the existence of $\Lambda$.
This basically views quantum probabilities as not arising from mathematical properties of the quantum system itself. As mad as it sounds one must acknowledge that all realist views (i.e. ones with a $\Lambda$) suffer from fine-tuning problems such as those mentioned in the Pusey-Leifer theorem (a development of Price's theorem).

 

[DarMM]

BTW I have never thought of the wave-function itself as a hidden variable - but now you have placed the idea in my mind I think it deserves serious thinking about.

It's standard in modern quantum foundations to view $\psi$ as a special case of hidden variables.

The best review article on all this stuff is Matt Leifer's:
https://arxiv.org/abs/1409.1570

 

[rrogers]

I have a more elaborated answer to this in a paper I currently write. Would you like me to send you a draft of the paper?

Is it generally possible to get a copy? I would be interested in other opinions (I think I disagree with a lot of them) on what is "real"; but I am always interested in the reasoning behind various viewpoints.
Not dogmatic: just critical :)

 

[drpi]

“…I don't demand that a theory correspond to reality because I don't know what it is. Reality is not a quality you can test with litmus paper. All I'm concerned with is that the theory should predict the results of measurements….” -- Stephen Hawking

https://en.wikiquote.org/wiki/Stephen_Hawking. This was taken from a debate with Roger Penrose in 1994 at the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge, transcribed in The Nature of Space and Time (1996) by Stephen Hawking and Roger Penrose, p. 121.

 

[Demystifier]

fine-tuning problems such as those mentioned in the Pusey-Leifer theorem

I don't know what is the Pusey-Leifer theorem. Can you gave a reference and/or a brief overview?

 

[Demystifier]

Is it generally possible to get a copy?

At some point it will be on arXiv. At the moment, I can tell that the title will be: Bohmian mechanics for instrumentalists

 

[DarMM]

I don't know what is the Pusey-Leifer theorem. Can you gave a reference and/or a brief overview?

https://arxiv.org/abs/1607.07871

In essence Quantum Mechanics has an observed symmetry, Operational Time Symmetry. They basically show that the only way for this symmetry to also hold at the level of the hidden variables is if the hidden variables have retrocausality. If you don't have retrocausality the symmetry can only emerge effectively through some kind of fine tuning or (currently undemonstrated in any model) thermalisation in the early universe. However if you go with the latter version, then the underlying physics (faster-than-light effects in Bohmian Mechanics, evidence of the other Worlds in MWI) should be visible in the early universe and thus one has divergent predictions from QM.

If you do have retrocausality, you get the symmetry, but you run into the same fine-tuning/thermalisation issues with experiments having not yet seen retrocausal signals.

It's an extension of Price's theorem. Price's original proof only covered theories which are Psi-Ontic ($\Lambda = \mathcal{H} \times \mathcal{A}$, i.e. the wavefunction is one of the hidden variables). Leifer and Pusey extended this to Epistemic models of the wavefunction as well.

Of interest to yourself they explicitly discuss Bohmian Mechanics.

 

[Peter Morgan]

FWIW, I think of mathematical models of quantum field theory as like to an experiment rather as a map is like to the landscape to which the map acts as a guide. It takes experience to learn how to use a map that is much less than isomorphically like to the landscape, with some things perhaps rendered almost photorealistically but with other things located on the map only as a symbol, with much variation of style from one map to another.
What the mathematics of QFT says depends on your choice of axioms. Almost universally, there are states over an algebra of operators that is freely constructed using an operator-valued distribution $\hat F(x)$. The operators are of the form $\hat F_{\!f}=\int\hat F(x)f(x)\mathrm{d}^4x$ (where the "test function" $f(x)$ constructs an average of the operator-valued distribution that is differently weighted in different regions of space-time), and satisfy commutation relations $[\hat F_{\!f},\hat F_{\!g}]=(f^*,g)-(g^*,f)$. The standard vacuum state of the free field is $$\langle 0|\mathrm{e}^{\mathrm{i}\lambda\hat F_{\!f}}|0\rangle=\mathrm{e}^{-\lambda^2(f^*,f)/2},$$ which, if $f=f^*$ is real, is the characteristic function of a normal distribution. The inner product $(f,g)$ fixes both the variance of a normal distribution associated with any given operator $\hat F_{\!f}$ and also the commutation relations that determines where Bell inequalities are violated, where Wigner functions take negative values, et cetera. The form of the inner product makes no difference to the algebraic structure, however, only to the geometrical structure. For interacting fields the characteristic function $\langle 0|\mathrm{e}^{\mathrm{i}\lambda\hat F_{\!f}}|0\rangle$ must be deformed to correspond to a different probability distribution, but still there are, in principle, the field operators $\hat F_{\!f}$. [All the above will seem quite distant to anyone who has learned only the path integral approach and works with time-ordered products of operators, but such constructions can be regarded as derived from the construction above.]
How does this structure relate to an experiment? The best approach, again FWIW, is to work with QFT as a signal analysis formalism, where a test function is called a "window function" (I've also seen Chris Fewster call it a "sampling function"), particularly because all the experimental raw data certainly comes to us as voltages on signal lines (think of CERN, with many thousands of measurements of voltages on signal lines being compressed by hardware and software into times and geometries of many events per second, which are then grouped together so that statistics can be compared to the probability distributions that a given theory proposes; but even a very small experiment does the same kind of signal analysis for far fewer voltages on signal lines).
To get back to the original question, the voltages on signal lines can be said to be "real", if you like, although it makes little difference to the world whether you call it names or not, then we might call the operators that are used to describe the signal analysis we do of the records we have of the voltages on the signal lines as not "real" in quite the same sense, because their relationship to the computing and experimental hardware is somewhat more remote (but this is just to say that we have in this a different kind of map of the experiment, which uses different symbols, a little more like an electron microscope and less like a telescope for the sophistication and directness of the transforms that are being applied, say.)
Let me add that a signal analysis approach allows us to say of states other than the vacuum state that they are modulations of the vacuum state. There is a difference from ordinary field theories, because here the modulation is a modulation of probability distributions associated with a signal line voltage, not of a single value for a signal line voltage. Finally, classical signal analysis is very much about Hilbert spaces, because Fourier transforms are very naturally associated with Hilbert spaces, and classical time-frequency analysis is very much used to working with Wigner functions, so that QFT is very close indeed to classical signal analysis.
I imagine no-one will read to here, but to anyone who does, good luck with your own engagement with QFT.

 

[A. Neumaier]

classical time-frequency analysis is very much used to working with Wigner functions, so that QFT is very close indeed to classical signal analysis.

Only QFT in a space consisting of a single point only.

 

[Peter Morgan]

Only QFT in a space consisting of a single point only.

How right you are, , although a four-dimensional version of classical signal analysis, which I am won't to call a random field when it is generalized to a probabilistic formalism and presented in a Hilbert space formalism, is rather close to QFT. Close enough that one can in some cases construct isomorphisms between Hilbert spaces, and, with more construction required, between the respective algebras of operators of the quantum and random fields.

 

[A. Neumaier]

a random field when it is generalized to a probabilistic formalism

Random fields, though describable in terms of Fock spaces, correspond to Euclidean space-time field theories only. Analytic continuation to real (Minkowski) space-time drastically changes the operator structure.

 

[martinbn]

As I stressed many times, there are several different versions of "Copenhagen" interpretation. Some versions are, as you say, open to it. Some are not.

Can you give a reference for one that is not.

 

[Peter Morgan]

Random fields, though describable in terms of Fock spaces, correspond to Euclidean space-time field theories only. Analytic continuation to real (Minkowski) space-time drastically changes the operator structure.

Right, it does drastically change the operator structure. One can construct the following for the quantized Maxwell field on Minkowski space in terms of annihilation and creation operators, $\hat F_{\!f}=a_{f^*}+a^\dagger_f$:

• Introduce a nonlocal involution $\widetilde{f^\bullet}(k)=\frac{1}{2}(1+\mathrm{i}\star)\tilde f(k)+\frac{1}{2}(1-\mathrm{i}\star)\tilde f(-k)$, with $\star$ being the Hodge dual applied to the bivector-valued test function $f$, thereby reversing the frequency of one helicity while leaving the other helicity unchanged.
• construct the field $\hat{\sf F}\hspace{-0.35em}{\sf F}_{\!f}=a_{f^{*\bullet}}+a^\dagger_{f^\bullet}$, which satisfies the trivial commutator $[\hat{\sf F}\hspace{-0.35em}{\sf F}_{\!f},\hat{\sf F}\hspace{-0.35em}{\sf F}_{\!g}]=0$, which I therefore take to be a random field.
  
• Then: The Hilbert space generated by the free action of $\hat{\sf F}\hspace{-0.35em}{\sf F}_{\!f}$ on the vacuum vector $|0\rangle$ is isomorphic to the Hilbert space generated by the free action of $\hat F_{\!f}$ on $|0\rangle$.
• And: The algebra of operators generated by the $\hat{\sf F}\hspace{-0.35em}{\sf F}_{\!f}$ and the vacuum projection operator $|0\rangle\langle 0|$ is isomorphic to the algebra of operators generated by the $\hat F_{\!f}$ and the vacuum projection operator $|0\rangle\langle 0|$.

The last bullet point obviously requires the introduction of the vacuum projection operator, which is nonlocal, however the vacuum projection operator is used implicitly in pragmatic physics whenever a transition probability is computed. All the above and more is spelled out in arXiv:1709.06711, of which a current version, in which the math is unchanged but the text has evolved, but not yet enough to be posted to arXiv, can be found on Dropbox here.

 

[DarMM]

Can you give a reference for one that is not.

I'm not aware of a variant that says the objects don't exist before measurement, most posit "something" is there.

However for the properties we measure not existing in any sense before the observation look to Wheeler's writings or QBism.

 

[Demystifier]

Can you give a reference for one that is not.

See refs. [5,6,7] in my http://de.arxiv.org/abs/1112.2034 .

 

[DarMM]

See refs. [5,6,7] in my http://de.arxiv.org/abs/1112.2034 .

For anybody reading these are:

1. Zeilinger-Brukner information interpretation. In this a quantum system has at most one bit of information and if it uses it on one property, it doesn't have a determined value for others. For example a photon entangled with another will use its bit to store the fact that it is entangled (i.e. the form of its relationship with another system), but then the actual polarization bits aren't stored and are thus random. QM's weirdness results from a mismatch from how much information a quantum system has vs how much we expect it logically to have.
2. Mermin's view is QBism. QM's weirdness results because Bayesian reasoning must be modified to take into account the fact that values for certain observables are new elements of the universe introduced at measurements that don't follow from anything previous
3. Rovelli's relational interpretation. Quantum objects don't possesses objective properties, just properties relative to another system, e.g. this electron has spin up for me.

All share the idea that the quantum probabilities are not determined by hidden properties of the object itself in any way. In fact in all of them the probabilities come from the fact that the object doesn't possesses objective properties. Some drop properties existing altogether, others the objective element.

Note that, from having read them, all elements of each interpretation come up in the others. Brukner has recently found his interpretation needs some facts to be relational. In light of the Frauchiger-Renner theorem probably all anti-realist views require this. Their differences are more how primary those elements are, e.g. in the Relational Interpretation the fact that properties are relational is the reason for QM, in the Information interpretation it's just in some cases measurement results have to be relational as the bit of information can't be "read" in a unique way across all environments.

 

[martinbn]

See refs. [5,6,7] in my http://de.arxiv.org/abs/1112.2034 .

Ok, I have them now. Can you point me to the exact part of the text or do I have to read them? I have looked at [5] and [7] before and I don't remember anything about the quantum objects not existing (the moon not being), so I'll have to look again.

 

[vanhees71]

I have a more elaborated answer to this in a paper I currently write. Would you like me to send you a draft of the paper?

Sure, although it'll take some time, until I can have a close look at it, because the semester started, and I've to give two lectures to my teachers students (including one about quantum mechanics ;-)).

 

[vanhees71]

According to some versions of Copenhagen interpretation, the Moon does not exist when nobody looks at it. For instance, Wheeler said that “no phenomenon is a real phenomenon until it is an observed phenomenon.”
I am not defending that interpretation, I am just saying what that interpretation claims.

It's only one more hint at how far idiosyncratic completely overrated philosophical ideas by otherwise ingenious physicists lead, particularly Heisenberg, to a somewhat lesser extent Bohr, although he was even more enigmatic in his writings than Heisenberg, but usually (i.e., at least as far as I can make sense of his mostly non-mathematical writings about the foundations of QT) he had had a sensible physical intuition...

 

[A. Neumaier]

Bohr [...] had a sensible physical intuition...

So had Heisenberg.