Is the Wave Function Real? Evidence from the Frankenstein Photon Experiment

[RUTA]

I agree with your perspective about context of experiment. What I am questioning is the issue about components, even in a relational format. I would say that all components of the wave functions contribute to the outcome, even when classical logic would say that only the "selected" component did.

What do you mean by "contribute?" Formally, all the components contribute to the unique specification of the wave function, so you certainly don't mean "contribute" in the mathematical sense. Are you making the ontic case for Hardy's "half-empty waves" as in the context of interaction-free measurement (IFM)?

 

[Demystifier]

DrChinese, if I understood you correctly, you suggest that your (proposed) experiment gives STRONGER evidence (for wave-function reality) than other existing experiments. If I am right, it suggests that you CAN imagine how other experiments could be true without reality of the wave function, but you just cannot imagine how your particular experiment could be that.
If this is so, could you explain how the standard double-slit experiment could be true without the wave function being real? If you could explain that, I believe it would be much easier to answer your questions on this thread.

 

[RUTA]

DrChinese, if I understood you correctly, you suggest that your (proposed) experiment gives STRONGER evidence (for wave-function reality) than other existing experiments. If I am right, it suggests that you CAN imagine how other experiments could be true without reality of the wave function, but you just cannot imagine how your particular experiment could be that.
If this is so, could you explain how the standard double-slit experiment could be true without the wave function being real? If you could explain that, I believe it would be much easier to answer your questions on this thread.

There is a detailed explanation of the twin-slit experiment without invoking any "quantum entities" (waves, particles, or anything else) in “Reconciling Spacetime and the Quantum: Relational Blockworld and the Quantum Liar Paradox,” W.M. Stuckey, Michael Silberstein & Michael Cifone, Foundations of Physics 38, No. 4, 348 – 383 (2008), quant-ph/0510090. We have also done it using path integrals over graphs, see section 3.4 of arXiv 0908.4348.

 

[LostConjugate]

Can the lack of any angular momentum in the hydrogen atom ground state be explained without the wave function?

 

[RUTA]

Can the lack of any angular momentum in the hydrogen atom ground state be explained without the wave function?

We need wave functions (or path integrals) to generate the probability amplitude, so I assume that "without the wave function" is an ontic statement. The answer would probably be "no" because what is meant by "a hydrogen atom in its ground state" entails a wave function (or equivalent) perspective (model). If you rather ask about the nature of "sources" and the measurement of quantum angular momentum per experimental observations, then, yes, one can avoid wave function realism. Essentially, you have to define what you mean by "a hydrogen atom in its ground state" via experimental observations (which is true of all physics, but most such identification is tacit).

 

[LostConjugate]

We need wave functions (or path integrals) to generate the probability amplitude, so I assume that "without the wave function" is an ontic statement. The answer would probably be "no" because what is meant by "a hydrogen atom in its ground state" entails a wave function (or equivalent) perspective (model). If you rather ask about the nature of "sources" and the measurement of quantum angular momentum per experimental observations, then, yes, one can avoid wave function realism. Essentially, you have to define what you mean by "a hydrogen atom in its ground state" via experimental observations (which is true of all physics, but most such identification is tacit).

Instead of saying in it's ground state what if I just said how can a particle be some distance r from the nucleus with no angular momentum if it were not a wave or membrane of sorts.

 

[DrChinese]

DrChinese, if I understood you correctly, you suggest that your (proposed) experiment gives STRONGER evidence (for wave-function reality) than other existing experiments. If I am right, it suggests that you CAN imagine how other experiments could be true without reality of the wave function, but you just cannot imagine how your particular experiment could be that.
If this is so, could you explain how the standard double-slit experiment could be true without the wave function being real? If you could explain that, I believe it would be much easier to answer your questions on this thread.

Yes, good point. I think the double slit explanation tends to invoke the idea of interference of the various paths the particle takes to the screen. I.e. there is self interference. And you could say that proves the reality of the wave function, with the logic that the photon took a discrete path. For the Bohmian, there is a pilot wave portion and that is real as well.

In my Frankenstein version, we must have an interaction between the probability from Alice and the probability from Bob to get entangled Chris. Similar for Dale. I don't see how that would occur if the probabilities represented knowledge of the system and nothing else.

I guess you could say that this is just words, and doesn't mean anything. Sorta like the "entangled photons that have not interacted in the past". On the other hand, that is a pretty interesting experiment and certainly worthly of consideration when thinking about entanglement.

 

[Fredrik]

What does any of this have to do with the wavefunction being "real" or not? What does that even mean?

 

[DrChinese]

What does any of this have to do with the wavefunction being "real" or not? What does that even mean?

My question has to do with the idea that state has to do with knowledge of the system. I think the state is an accurate and complete description of the system.

 

[RUTA]

My question has to do with the idea that state has to do with knowledge of the system. I think the state is an accurate and complete description of the system.

By "system" do you mean the experimental devices or "a quantum entity" or some combination thereof or ...?

 

[RUTA]

Yes, good point. I think the double slit explanation tends to invoke the idea of interference of the various paths the particle takes to the screen. I.e. there is self interference. And you could say that proves the reality of the wave function, with the logic that the photon took a discrete path. For the Bohmian, there is a pilot wave portion and that is real as well.

The wave function need not have any ontic status, e.g., the pilot wave. You don't even need a "wave" function, i.e., you can compute the twin-slit outcome using the transition amplitude from the path integral. So, the twin-slit experiment doesn't imply the wave function is "real" in the ontic or formal sense.

 

[DrChinese]

By "system" do you mean the experimental devices or "a quantum entity" or some combination thereof or ...?

Ha! I am not sure... I guess what I am saying is that the probability function (WF) can be manipulated in all kinds of strange ways.

1. The WF can be split, recombined, combined with the WFs from other particles, entangled with particles it has never been in contact with, including those that have never even existed at the same time. I guess that makes it pretty real. I realize that is a subjective statement.

2. If it can be recombined, I guess I would say that collapse is NOT an irreversible process. At least not at the point that the WF is split, so it would need to be later - when the complete final context has been determined.

So imagine entangled Alice: We run Alice through a PBS oriented at 0 degrees, getting 2 outputs. We run each of those outputs through PBSs oriented at 45 degrees. We then recombine the 4 outputs into 2 using 2 reverse splitters (a la the Eberly article quoted previously). And finally, recombine these 2 outputs with another suitably oriented reverse splitter. What do we have now? We have our original entangled Alice (at least we hope so).

3. And similarly, we should be able to mix and match any similar permutations of Alice and Bob so we can get Frankenstein photons Chris' and Dale', as long as everything sums to 100% and we have no idea which paths were traced.

So I am asking, if you are a believer of MWI for example (which of course you are not): how does all this splitting and mixing and matching go on and the entanglement can be restored? How does the universe know not to split because we are going to put everything back together again when we are finished with the manipulations? You don't think that might be a tall order for that interpretation?

 

[SpectraCat]

The wave function need not have any ontic status, e.g., the pilot wave. You don't even need a "wave" function, i.e., you can compute the twin-slit outcome using the transition amplitude from the path integral. So, the twin-slit experiment doesn't imply the wave function is "real" in the ontic or formal sense.

That last part seems like semantics ... AFAIK the path integral approach is formally equivalent to solving the Schrodinger equation in the normal way. Also, there are certainly wave-like entities involved in the path integral approach, since each individual path is represented by an amplitude times a complex exponential of the classical action. So, while it may be strictly true that the path integral doesn't involve the wave function as we usually think about it, it does involve wave-like entities.

So all this just moves the discussion to being about the reality of the path-integrals. Perhaps this is worthwhile ... I guess no one would dispute the reality of the paths themselves, since they are physical trajectories in space and time. Furthermore, the classical action along a given path also seems like a real thing, since it is just a time integral over the kinetic and potential energies along that path. Still, I guess that doesn't answer the question of how "real" the path integrals themselves are. They certainly seem real to me though, for all the same reasons that the wave-functions do. I guess that is what I meant when I said it seems like you are drawing a semantic distinction.

 

[mooglue]

I think everyone can at least agree that a wavefunction the square of the probability density for a given system. Would you say "probability" is real? It's not something tangible, but it does carry tangible information. I think that if you can argue that a probability distribution is a real thing, then you can possibly consider the wave function real.

 

[Dmitry67]

No, because in deterministic interpretations there is no 'probability' - at all.

 

[DrChinese]

So all this just moves the discussion to being about the reality of the path-integrals. Perhaps this is worthwhile ... I guess no one would dispute the reality of the paths themselves, since they are physical trajectories in space and time.

This is pretty much the path I am on and hoping to consider. And sincerely, I realize the line between semantics and meaning is razor thin on this one.

If the WF/path is real, then a lot of additional things must be true. For example, a free photon in space that eventually hits my eye must have its WF still propagating in space long after it hits my eye.

 

[Count Iblis]

So I am asking, if you are a believer of MWI for example (which of course you are not): how does all this splitting and mixing and matching go on and the entanglement can be restored? How does the universe know not to split because we are going to put everything back together again when we are finished with the manipulations? You don't think that might be a tall order for that interpretation?

But MWI just assumes that the formalism of quantum mechanics works as usual without invoking a real collapse of the wavefunction after a measurement. It is only that the effective collapse can be pictured as if the universe splits.

 

[RUTA]

That last part seems like semantics ... AFAIK the path integral approach is formally equivalent to solving the Schrodinger equation in the normal way. Also, there are certainly wave-like entities involved in the path integral approach, since each individual path is represented by an amplitude times a complex exponential of the classical action. So, while it may be strictly true that the path integral doesn't involve the wave function as we usually think about it, it does involve wave-like entities.

So all this just moves the discussion to being about the reality of the path-integrals. Perhaps this is worthwhile ... I guess no one would dispute the reality of the paths themselves, since they are physical trajectories in space and time. Furthermore, the classical action along a given path also seems like a real thing, since it is just a time integral over the kinetic and potential energies along that path. Still, I guess that doesn't answer the question of how "real" the path integrals themselves are. They certainly seem real to me though, for all the same reasons that the wave-functions do. I guess that is what I meant when I said it seems like you are drawing a semantic distinction.

One doesn't have to view the path integral Z as involving paths (in configuration space or spacetime). Typically, one sees it explained using paths (thus the name), but that's just a convenient way of ordering all possible values of the integration variable (typically evaluated from -infinity to infinity). One can rather view Z as providing a measure of the symmetry of that part of the integrand stripped of the integration variable (we call it the actional). That's why we call Z the symmetry amplitude in RBW instead of the transition amplitude. And, again, there are no quantum entities represented in the actional -- just the experimental equipment.

 

[Fredrik]

My question has to do with the idea that state has to do with knowledge of the system. I think the state is an accurate and complete description of the system.

In that case I guess I just don't understand the argument. Everyone already agrees that the wavefunction describes the system immediately after a measurement, so what you're getting at must be that it does so at all times. I don't see anything in your argument that we can use to reach that conclusion.

Maybe you're arguing for something else entirely. If you're arguing against the state vector being a representation of our "knowledge" of the system, I think the argument would have to start with an explanation of what that means. Personally, I don't think it makes sense to argue against that particular flavor of the CI, because it's so ill-defined and so poorly explained by its proponents that there's nothing to refute.

 

[Demystifier]

2. If it can be recombined, I guess I would say that collapse is NOT an irreversible process. At least not at the point that the WF is split, so it would need to be later - when the complete final context has been determined.

In my opinion, the collapse is a vague and obsolete concept. A modern much better defined concept that to a large extent replaces the concept of collapse is - decoherence. Decoherence is reversible in principle, but irreversible in practice because decoherence occurs when the system interacts with a LARGE number of environment degrees of freedom. When the wave can be recombined (in practice), it simply means that decoherence has not happened before the recombination.

So, does it say anything about reality of the wave function? Well, certainly not directly. Nevertheless, most physicists working with decoherence like to think in terms of some variant of the "many-world" interpretation, in which the wave function is thought of as something "real". Bohmians also can be counted as belonging to this camp, as Bohmian interpretation can also be thought of as a variant of the "many-world" interpretation.

 

[DrChinese]

In that case I guess I just don't understand the argument. Everyone already agrees that the wavefunction describes the system immediately after a measurement, so what you're getting at must be that it does so at all times. I don't see anything in your argument that we can use to reach that conclusion.

Maybe you're arguing for something else entirely. If you're arguing against the state vector being a representation of our "knowledge" of the system, I think the argument would have to start with an explanation of what that means. Personally, I don't think it makes sense to argue against that particular flavor of the CI, because it's so ill-defined and so poorly explained by its proponents that there's nothing to refute.

Fredrik, thanks for your comments.-DrC

 

[DrChinese]

In my opinion, the collapse is a vague and obsolete concept. A modern much better defined concept that to a large extent replaces the concept of collapse is - decoherence. Decoherence is reversible in principle, but irreversible in practice because decoherence occurs when the system interacts with a LARGE number of environment degrees of freedom. When the wave can be recombined (in practice), it simply means that decoherence has not happened before the recombination.

So, does it say anything about reality of the wave function? Well, certainly not directly. Nevertheless, most physicists working with decoherence like to think in terms of some variant of the "many-world" interpretation, in which the wave function is thought of as something "real". Bohmians also can be counted as belonging to this camp, as Bohmian interpretation can also be thought of as a variant of the "many-world" interpretation.

Demystifier, thanks for your comments as well. I know the question was a bit ambiguous, I was curious to see what others thoughts in this area might be.

I still can't get around the idea that: A particle's WF expands in free space even after a particle is detected. (It would do this because there are still path alternatives in existence.) It seems like any point in open space would have a large number of these alternative paths coming through. And that would lead to physically detectible effects of some sort. Or maybe not. I know I'm rambling... maybe I had too much coffee this morning.

 

[my_wan]

Interesting thread. I operate under the assumption of an ontic wavefunction. I also agree with RUTA that these frankenstein particles don't actually provide an empirical distinction that circumvents prior arguments. However, I am impressed with its potential to articulate the distinctions between these opposing viewpoints.

No, because in deterministic interpretations there is no 'probability' - at all.

In principle yes, in practice 'probability' is unavoidable in the formalism. Even classical thermodynamics unavoidably relies on 'probability' in the formalism. Even a basic dice role can only be predicted by probability. My personal sense, given my assumptions, is that the wavefunction is an amalgamation of both ontic and epistemic elements. In the dice case an ensemble can be trivially decomposed into real and epistemic parts. In the wavefunction case even our notions of what constitutes a fundamental physical property fails to maintain a distinct identity like dice, as if the realness we empirically percieve in the things around us are epistemic rather than ontic. The only class of theories I know to get around this considers measured properties as emergent, rather than inate.

Local theories that maintain local realism and escape both the Bell and Kochen-Specker Theorems exploit contextuality. Consider how we operationally define Einstein Realism in the context of BI. In essense we take some measurable value, often labeled Alice and Bob, and use them as a proxy for ontic values. Thus any localy realistic theory that doesn't violate these theorems must contextualize these measured values as emergent global properties of an underlying physics. This seems to imply that the wavefunction is, at least in part, a real wave of some sort, with emergent properties we measure and mistakenly assume are inate to the ontic parts. Relational QM is predicated on a similar viewpoint. A lot of abstract models have been formulated in an attempt to demonstrate feasibility, but to date no such model uniquely or fully recovers the formalism of QM.

Although this approach to circumventing the no-go theorems works in principle, it hasn't been demonstrated to be feasible to empirically replicate QFT. Thus my presumptions are just that, presumptions. Yet any argument that attempts to articulate a case for the wavefunction being real is of interest.

Here's the objection I would pose to RUTA's argument. It's true we don't have to view the path integral Z as involving paths, but this presumes the variable we associate with the path is itself not an ontic entity. Fair enough, as this so far would be true for both CI and the contextual relational interpretation mentioned above. Yet what is implied by presuming no ontic entities are involved in defining these properties? It implies that none of the everyday things we interact with are fundamentally ontic in nature. Most of us I presume reject this right or wrong, but once we reject epistemic properties without ontic elements of some sort to define them how do we then reconcile certain physical variables not requiring them. It seems silly to presume that certain physical properties lack an ontic basis at some level yet still cling to the notion that our everyday world contains ontic entities.

Now certainly there exist many variables that merely encode our state of knowledge, thus require no ontic basis in and of themselves. Yet, if we presume the Universe has an ontic basis, even these variables have ontic underpinnings as some state of knowledge about the ontic elements. Now if we try to maintain an ontic Universe while avoiding any ontic realness contained in the wavefunction, this is only possible by professing ignorance of where the ontic elements are contained, which we are if they exist. Furthermore, any objection to the assumption that the wavefunction has real elements depends on our ignorance to merely claim that we don't have to consider variable X real, which is true, but X can be moved to whatever argument is being made, such as the path integral. Thus it becomes an argument from ignorance. CI requires this very real ignorance to justify moving the goal post at will to maintain cogency without explicitly rejecting the Universe has ontic underpinnings.

It is my opinion that in order to avoid ontic realness associated with the wavefunction at any level requires assuming the Universe or any part of it needs no ontic basis. As a personal preference I'm betting the wavefunction contains real components of some sort, even if no particular variable we use to describe it is explicitly ontic in itself.

 

[Dmitry67]

The very word 'real' is ill-defined.
There is a very good example: BM (Bohmian Interpretation). In BM,there are 2 'real' components: wavefunction (exactly the same as in MWI, with all 'parralel' worlds) and hidden particles guided by this wave.

However, in BM only waves with particles inside (non-empty waves) form what we call reality. If we see a dead cat, then there is definitely a wave of alive one. It is real, but not tagged with particles (which can not be detected!) and hence don't form the reality.

What do you call 'real'?

 

[zonde]

I still can't get around the idea that: A particle's WF expands in free space even after a particle is detected. (It would do this because there are still path alternatives in existence.) It seems like any point in open space would have a large number of these alternative paths coming through. And that would lead to physically detectible effects of some sort. Or maybe not. I know I'm rambling... maybe I had too much coffee this morning.

I am trying to get hold of this question of yours but it does not make much sense for me.
However this comment gives me an idea. Do you consider that requirement for "reality" of wavefunction is "reality" of superposition? Meaning that particles can exist in more than one place before measurement.
If that is so then I can try to defend position that wavefunction is not "real" or even pilot-wave is not "real".

 

[Dmitry67]

Sometimes we can not even isolate 'pure' objects and have to deal with the superposition. Electron may be a lucky exception.

But take proton: (uud). What color is quark d? What we call a proton is actually a superposition of uud having all possible combinations of colors.

 

[Demystifier]

I still can't get around the idea that: A particle's WF expands in free space even after a particle is detected.

What is so strange about it? Isn't the case of quantum non-demolition measurement a clear and well-known example of this?

 

[Demystifier]

It seems like any point in open space would have a large number of these alternative paths coming through.

Oh, perhaps now I see what your problem is. No, the particle does not have a number of alternatives at any point IN SPACE (where "space" means - the 3-dimensional space), simply because the wave function does not live in (this) space. Instead, since the particle is entangled with the environment (because without such an entanglement there would be no decoherence, measurement, or effective "collapse"), the wave function lives in the MULTI-DIMENSIONAL CONFIGURATION space. That's the space in which the alternatives live.

 

[GeorgCantor]

Oh, perhaps now I see what your problem is. No, the particle does not have a number of alternatives at any point IN SPACE (where "space" means - the 3-dimensional space), simply because the wave function does not live in (this) space. Instead, since the particle is entangled with the environment (because without such an entanglement there would be no decoherence, measurement, or effective "collapse"), the wave function lives in the MULTI-DIMENSIONAL CONFIGURATION space. That's the space in which the alternatives live.

Still there must be a correspondence between wavefunctions in configuration space and 3D space. Otherwise, why do we get precise predictions with the SE?

It seems to me the problem lies more with the definition of 3D space. If we do away with it, the MWI takes care of the correspondence in a neat fashion. The 3D problem seems to me to be related more to biology than with physics. This of course is a position assuming the MWI as a starting point.

 

[zonde]

I think everyone can at least agree that a wavefunction the square of the probability density for a given system. Would you say "probability" is real? It's not something tangible, but it does carry tangible information. I think that if you can argue that a probability distribution is a real thing, then you can possibly consider the wave function real.

I would say that probability is not real because "parallel" probabilities do not interact in physical sense.

 

[Demystifier]

Still there must be a correspondence between wavefunctions in configuration space and 3D space. Otherwise, why do we get precise predictions with the SE?

Of course there is a correspondence. The wave function gives probabilities of particle positions (or, according to BI, guides continuous and deterministic changes of these positions) in the ordinary 3D space. The fact that particles live in a space which is only 3-dimensional is compensated by the fact that there is many (entangled) particles. By contrast, the wave function is only one.

 

[my_wan]

The very word 'real' is ill-defined.
There is a very good example: BM (Bohmian Interpretation). In BM,there are 2 'real' components: wavefunction (exactly the same as in MWI, with all 'parralel' worlds) and hidden particles guided by this wave.

However, in BM only waves with particles inside (non-empty waves) form what we call reality. If we see a dead cat, then there is definitely a wave of alive one. It is real, but not tagged with particles (which can not be detected!) and hence don't form the reality.

What do you call 'real'?

Agreed, real is fought with issues. In the sense I used it here it's ontic, like the particles tucked in the waves in your BM description. I have some difficulty with the BM wave as you've described. This live cat wave has empirical consequences when associated with the cat particles, then loses all empirical meaning when the cat dies even though its existence remains. Almost sounds like a justification for ghosts, if you kept some level of empirical meaning to it. Meanwhile, the cat died and gained a separate concurrently existing dead cat wave from where?

What determines a coupling between a wave and the particles, the location of the particle relative to the waveform? In my reading of BM I didn't get quiet this picture of the wavefunction, but obviously attaching the notion of 'real' to the wavefunction and having it push around particles accordingly isn't going to run into direct empirical falsification. It still seems to me that these BM waves are ad hoc imaginative conveniences, specially crafted so as not to provide any new empirical content.

I have nothing against interpretive or metatheories as such, but I don't see their usefulness as singularly justified metatheories. Rather, as a group of all viable metatheories, they help define a space of viable possibilities which might in part potentially be useful in extending the empirical content of QM itself. Much like the no-go theorems help define what is not viable. For their own sake they seem pretty worthless to me.

 

[eaglelake]

It is sometimes said that wave functions are not real, and simply represent the observer's knowledge of the system. I would like to comment against this point by presenting an experimental setup which would tend to indicate that the wave function is quite real. As far as I know, this setup per se has never been executed (although I am hoping someone might recognize it as something which has been).

To follow the setup, you should be familiar with the following experiment:

Bell inequalities and quantum mechanics, J. H. Eberly (2001)

See Figure 1, the Bell analyzer loop, in which a beam is split into H and V components. Those are then recombined so that the H/V information is erased, leaving a beam with the same properties as it was originally.

So if you took a pair of entangled particles, Alice and Bob, and ran each through a Bell analyzer loop, the recombined Alice and Bob are still entangled. This is what the above paper is saying.

---------------------

Here is my twist:

Frankenstein photons:
=====================

Split Alice into Alice-H and Alice-V. Split Bob into Bob-H and Bob-V. Now recombine Alice-H with Bob-V (which is identical to Alice-V). Recombine Bob-H with Alice-V (likewise identical to Bob-V). You will now have 2 Frankenstein photons that are polarization entangled!

Now, if the above is accurate (I don't see how it could be expected to be otherwise), then you would have to admit that you are mixing the wave functions of different photons to obtain an effect that clearly does not occur with either portion of the component wave functions alone.

So I conclude that the wave function is quite real. Your thoughts?

Let us pause for a moment to remind ourselves what we do know about the "wave function", which is more often a "state vector" $$\left| \psi \right\rangle$$.
a) It is defined in a linear vector space: $$\left| \psi \right\rangle = \sum {\left| {\varphi _k } \right\rangle } \left\langle {{\varphi _k }} \mathrel{\left | {\vphantom {{\varphi _k } \psi }} \right. \kern-\nulldelimiterspace} {\psi } \right\rangle$$ where the basis vectors $$\left| {\varphi _k } \right\rangle$$ are the eigenvectors of the observable $$\hat A$$ that is being measured. $$\hat A\left| {\varphi _k } \right\rangle = a_k \left| {\varphi _k } \right\rangle$$.
b) The only "interpretation" that has universal acceptance is the Born postulate: The probability of obtaining the value $$a_k$$ is $$P_k = \left| {\left\langle {{\varphi _k }} \mathrel{\left | {\vphantom {{\varphi _k } \psi }} \right. \kern-\nulldelimiterspace} {\psi } \right\rangle } \right|^2$$.
c) The state vector describes an experiment designed to measure the observable $$\hat A$$. The state vector is determined by the entire experimental arrangement, including the measuring device and the measurement result. Its specific mathematical form is determined by the observable being measured.
d) The state vector satisfies the Schrodinger equation: $$i\hbar \partial \left| \psi \right\rangle /\partial t = \hat H\left| \psi \right\rangle$$.
Thus, the state vector is necessarily complex.
The formalism does not require that $$\left| \psi \right\rangle$$ be "real". In fact, it is silent on the matter. Hence, our present conundrum. The real elements of classical physics are particles and waves which make up all things in the mechanical universe of Newton and Einstein. All (real) things exist in the space-time continuum. Real particles and real waves propagate in 3-space where they interact with detectors designed to measure physical properties possessed by them.
There is no evidence of any kind that state vectors are real in the classical sense. If they are real, then we should be able to design an experiment to detect them. But what are the properties possessed by state vectors that are measureable? We have no idea how to construct a state vector detector. And no one has ever observed state vectors propagating through 3-space, or collapsing, or interacting with any kind of detector known to us. Also, the Eberly paper cited in the OP, yields a contradiction. Its approach assumes a classical-like sequence of events, which does not give the correct quantum results.
So, what is the wavefunction? We only know that it is a mathematical construct used to calculate probabilities. There is no theoretical or experimental evidence that it is anything more!
Dr Chineses asks if the quantum wave function is real. I don't know, but I doubt if they are. I can only give him my own bias on such matters: I am immediately suspicious of anything that cannot be verified experimentally.
Best wishes

 

[Dmitry67]

Whats about first moments from the Big Bang when it was too hot to form any system with stable internal state - so no measurement devices, in principle, could exist?

I believe defining wavefunction in a semi-classical context (observables, Born rule, experiments and measurements) comes from Bohr era. It is very important historically, but it is time to leave it behind.

 

[my_wan]

I read RUTA's paper "http://philsci-archive.pitt.edu/archive/00003247/" ". Very interesting, and gives me a greater perspective of RUTA's perspective here.

This got me to thinking about this question of wavefunction realism both in historical context and a range of other physical parameters. Even Newton had his detractors, most notably wrt gravity, based on the lack of a mechanistic explanation. This was a prime motivation behind the classical ether, even though the empirical absurdities should have effectively killed it even before relativity. With relativity based in kinematics the limit speed C became the de facto proxy for maintaining causality. Yet many remained dissatisfied with the unspecified causal mechanism in pure kinematics. With QM it became even more difficult to maintain this brand of natural philosophy.

The point here is that our questions of realism, wrt to the wavefunction in this case, at some level still points to our predisposition toward real causal actors to underpin dynamics. I think we should continue asking these questions, so long as a priori demands of truth are avoided, like some of the aetherist that are not too uncommon here.

If we consider realism in terms of other phenomena, such as curvature of spacetime, virtual particles, etc., then Frankenstein particles are not so unique. Of course the ontology attached to realness can vary greatly in these cases, and even in various opinions about these cases. Can DrChinese's argument make the case that the wavefuntion has same level of realism as a vacuum? Physically valid or not, these kinds of questions can help define constraints and sort possibly valid solutions that are generally difficult to analyze.