Is wave function a real physical thing?

[Nick V]

Is the wave function ( ex. electron wave function) just a mathmatical equation or a real physical object? I know that it's widely known that it's just an equation however some researchers say that they have proof that it's real.
Here is the link.
http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392
Does this prove that wave function is a real physical object after all?

 

[orsanyuksek]

Thanks for sharing the article, it is really interesting.

To your question: The wave equation conventionally is not considered "real". Rather, its square gives the probability.

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

Örsan Yüksek

 

[atyy]

No, this does not show that the wave function is real. It only shows it under some assumptions, which are not obviously required. Counterexamples to a real wave function have been constructed: http://arxiv.org/abs/1201.6554, http://arxiv.org/abs/1303.2834.

There is also the interesting comment in http://arxiv.org/abs/0706.2661 that Wiseman suggests that even within Bohmian Mechanics, the wave function is not necessarily real - this was highlighted to me by Bohm2: "Inspired by this pattern, Valentini has wondered whether the pilot-wave (and hence ontic) nature of the wave function in the deBroglie-Bohm approach might be unavoidable [77]. On the other hand, it has been suggested by Wiseman that there exists an unconventional reading of the deBroglie-Bohm approach which is not ψ-ontic [78]. A distinction is made between the quantum state of the universe and the conditional quantum state of a subsystem, defined in Ref. [79]. The latter is argued to be epistemic while the former is deemed to be nomic, that is, law-like, following the lines of Ref. [80] (in which case it is presumably a category mistake to try to characterize the universal wave function as ontic or epistemic)."

 

[James_Harford]

The article is dated November 2011. So, I would think any question about its importance would be settled by now.

 

[bhobba]

Its the well known and important PBR theorem:
http://lanl.arxiv.org/pdf/1111.3328v3.pdf

Note what the paper says:
'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.'

Both Copenhagen and the Ensemble interpretation reject exactly that assumption.

Indeed more work has been done clarifying it eg:
http://arxiv.org/abs/1203.4779

It turns out for every model where it holds you can find one that evades it and conversely.

Thanks
Bill

 

[atyy]

Both Copenhagen and the Ensemble interpretation reject exactly that assumption.

Of course, such a rejection is unscientific. Consequently, there are flavours of Copenhagen that do not reject such an assumption.

 

[Nugatory]

Is the wave function ( ex. electron wave function) just a mathmatical equation or a real physical object? I know that it's widely known that it's just an equation however some researchers say that they have proof that it's real.
Here is the link.
http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392

This article is way better than most (not surprising, as Nature is a source way better than most) in that it includes a link to the actual work being discussed: http://lanl.arxiv.org/abs/1111.3328. It's a preprint, and a final version of the paper (sadly, behind a paywall) was published in 2012. Googling for "PBR theorem" will find some more discussion since then.

Does this prove that wave function is a real physical object after all?

Getting a paper through peer review and into publication doesn't automatically establish the paper as truth. Instead it starts the process of connecting the new insight to what is already understood, working out the implications across various fields of study, seeing where the new insight can shed new light on previously intractable problems, discovering what we can build on top of it.

So, no, this paper does not prove that the wave function is a real physical object. It does provide a serious argument and a proof by example that there is something new to say on the subject.

 

[Nick V]

This article is way better than most (not surprising, as Nature is a source way better than most) in that it includes a link to the actual work being discussed: http://lanl.arxiv.org/abs/1111.3328. It's a preprint, and a final version of the paper (sadly, behind a paywall) was published in 2012. Googling for "PBR theorem" will find some more discussion since then.Getting a paper through peer review and into publication doesn't automatically establish the paper as truth. Instead it starts the process of connecting the new insight to what is already understood, working out the implications across various fields of study, seeing where the new insight can shed new light on previously intractable problems, discovering what we can build on top of it.

So, no, this paper does not prove that the wave function is a real physical object. It does provide a serious argument and a proof by example that there is something new to say on the subject.

So what do you personally think, do you think the wave function is real and physical, or just a mathematical tool?

 

[Nugatory]

So what do you personally think, do you think the wave function is real and physical, or just a mathematical tool?

I neither know nor care. The question will only become interesting when someone can:
1) Clearly define exactly what the words "real and physical" mean.
2) Clearly define exactly what the words "just a mathematical tool" mean.
3) After these terms have been defined, describe an experiment that will produce different results if the wave function is real and physical than if it just a mathematical tool.

It's not impossible that this could happen. In 1935 Einstein posed a then-unanswerable question about quantum mechanics (google for "EPR paper"); thirty years later John Bell (google for "Bell's theorem") proposed definitions and an experiment that could settle the question; and since then the experimental results have been coming in. The question is now largely settled.

But unless and until something like that happens here .. Your question (which in the literature goes by the term "psi-ontic versus psi-epistemic") is sterile except when someone has something new to say. The PBR theorem may be such a thing, but it's way too soon and there is way too little experimental data to know.

 

[bohm2]

re

Does this prove that wave function is a real physical object after all?

The PBR theorem only rules out Ψ-epistemic models. So one can't assume that the wavefunction is just our knowledge about some underlying ontic state. Such models are ruled out by PBR (given a few reasonable assumptions). So, either one must accept the wave function as being ontic or accept non-realism (i.e. Ψ does not represent some deeper underlying reality as per instrumental/Copenhagen-type interpretations).

Having said that, one of the reasonable assumptions of the PBR theorem which has been most questioned by some authors is the Preparation Independence assumption. Leifer goes into a lot of detail of this PBR assumption in his most recent paper on this topic:

Is the quantum state real? A review of Ψ-ontology theorems
http://mattleifer.info/wordpress/wp-content/uploads/2008/10/quanta-pbr.pdf

 

[bhobba]

I neither know nor care. The question will only become interesting when someone can:
1) Clearly define exactly what the words "real and physical" mean.
2) Clearly define exactly what the words "just a mathematical tool" mean.
3) After these terms have been defined, describe an experiment that will produce different results if the wave function is real and physical than if it just a mathematical tool.

Exactly.

Gleason's theorem, by showing the state follows from the properties of observables, suggests the exact oppose:
https://www.physicsforums.com/threads/the-born-rule-in-many-worlds.763139/page-7

See post 137.

Who is right? Blowed if I know - opinions are like bums - everyone has one - it doesn't make it right. What we need is experiment to decide.

Thanks
Bill

 

[bhobba]

So what do you personally think, do you think the wave function is real and physical, or just a mathematical tool?

Personally I find what Gleason says very persuasive - its simply a requirement of non-contextuality - without going into what that is exactly. Its just a mathematical tool that helps calculate the probabilities of outcomes. But that's just my opinion and without experiment to decide it means diddly squat.

Thanks
Bill

 

[bohm2]

Just to add to this topic, 3 experiments have actually been done to test the ontic/epistemic status of the wave function:

Can different quantum state vectors correspond to the same physical state? An experimental test
http://lanl.arxiv.org/pdf/1211.0942.pdf[/B]

Experimentally probing the reality of the quantum state
http://lanl.arxiv.org/pdf/1211.1179.pdf

Measurements on the reality of the wavefunction
http://arxiv.org/pdf/1412.6213.pdf

The last one was just published today. Unfortunately, as Leifer points out there are limitations in all these type of experiments:

Probably the most important issue not discussed so far in this review is the question of whether the reality of the quantum state can be established experimentally...In modern parlance, tests of Bell's Theorem are device independent. In contrast, a test of the reality of the quantum state would not be device independent simply because the "quantum state" is the thing we are testing the reality of, and that is a theory dependent notion. Consequently, one has to assume that our quantum theoretical description of the way that our preparation devices work is more or less accurate, in the sense that they are approximately preparing the quantum states the theory says they are, in order to test the existing ψ-ontology results. Therefore, it is desirable to have a more theory independent notion of whether a given set of observed statistics imply that the "probabilistic state", i.e. some theory-independent generalization of the quantum state, must be real. It is not obvious whether this can be done, but if it can then experimental tests of ψ-ontology results would become much more interesting.

Of course, one can still perform non device independent experimental tests. This amounts to trying to prepare the states, perform the transformations, and make the measurements involved in a ψ-ontology result and checking that the quantum predictions are approximately upheld. Due to experimental error, the agreement will never be exact, but one can bound the overlap between probability measures representing quantum states instead of showing that it must be exactly zero. For the special case of the PBR Theorem given in Example 7.9, this has been done using two ions in an ion trap. However, the experimental result only shows that the overlap in probability measures must be smaller than the quantum probability, and not that it must be close to zero. This is quite far from establishing the reality of the quantum state, since for that one would want to test many pairs of quantum states with a variety of different inner products, and the PBR measurement for states with large inner product requires an entangled measurement on a large number of quantum systems. This is not likely to be feasible until we have a general purpose quantum computer.

http://mattleifer.info/wordpress/wp-content/uploads/2008/10/quanta-pbr.pdf

 

[atyy]

But unless and until something like that happens here .. Your question (which in the literature goes by the term "psi-ontic versus psi-epistemic") is sterile except when someone has something new to say. The PBR theorem may be such a thing, but it's way too soon and there is way too little experimental data to know.

I view things differently. There already are proposals to test deviations from quantum mechanics such as http://arxiv.org/abs/1407.8262 and http://arxiv.org/abs/1410.0270. I view the PBR theorem and other similar investigations as analogous to the Weinberg-Witten theorem, which is also "sterile" in that it does not point to any specific deviation from quantum general relativity. Yet the Weinberg-Witten theorem is usually not considered sterile, but an important no-go theorem.

 

[TrickyDicky]

I neither know nor care. The question will only become interesting when someone can:
1) Clearly define exactly what the words "real and physical" mean.
2) Clearly define exactly what the words "just a mathematical tool" mean.

It always amazes me when physicists need to have defined the object and tools of their discipline, shouldn't they know what it is they are subjecting to study, and what they are using to analyze it(mathematical tools, right?)
I mean imagine a doctor who gets asked about a possible disease and treatment of a patient, that claims that just to start doing something requires somebody giving exact and clear definitions of disease, medical instruments and patient(like he shoudn't have some notion after years of study), and to any definition the reply was: "That's philosophy, not medicine".
Even more amazing is when this bewilderment is quite often used to to suggest there is not such an object, not realizing that would deny physics as the study of physical phenomena.

3) After these terms have been defined, describe an experiment that will produce different results if the wave function is real and physical than if it just a mathematical tool.

Again, this seems befuddled. Not requiring an experiment, rather the part about the goal of the experiment. Shouldn't the goal of a good experiment serve to ascertain whether or not the wavefunction(that is, the mathematical model) describes accurately and completely the physics, that is, the phenomena we observe? My understanding is that in general this is what experiments are for.

The truth is that the OP question is not well formulated from the start. If we only understand the wave function in statistical terms of states of the system it is too easy to run into trouble, why not stop ignoring that NRQM is currently superseded by QFT as a model of nature? In QFT the wavefunction is not very useful in the way it is described in NRQM, it is not describing a (position eigenvector projection of a) state anymore, since there are no states except for the vacuum, it is an operator(functional) instead, in a particular configuration of field disturbances where Schrodinger space of positions(also remember position is no longer an operator here) picture is not very illuminating nor useful .

 

[bhobba]

It always amazes me when physicists need to have defined the object and tools of their discipline, shouldn't they know what it is they are subjecting to study, and what they are using to analyze it(mathematical tools, right?)

That's not the issue - the issue is getting any kind of agreement on things like that. It's much easier to move forward - and has proven very useful.

Thanks
Bill

 

[vanhees71]

For an experimental physicist it's pretty clear what he is doing when setting up an experiment, say a particle collision at the LHC: He shoots bunches of protons head on and then counts (the part of ) particles emerging by this reaction using a bunch of detectors to figure out, which particles come out, which momenta they have, etc. Then he's doing very many such experiments to "gain statistics" and get a nice bumb in a certain reaction cross section telling him that he has indeed created something that was predicted by his theoretical colleagues using sophisticated math, like Higgs did in the 60ies when he predicted the famous scalar boson named after him. Since the CMS and ATLAS collaboration have achieved this with a pretty high statistical significance of more than 5 standard deviations, it's called a discovery and earned Higgs and Englert the Nobel prize in physics of 2013.

The experimentalist (and to be honest almost all theorists working in this field either) doesn't bother much about the entirely philosophical question, whether there is an ontic interpretation of probabilities (and it all boils down to an ontic interpretation of probabilities since the wave function in non-relativistic quantum theory or more generally the S-matrix elements are a specific way to calculate probabilities for a given setup of the quantum objects under consideration) or not. It's simply irrelevant for physics: There's a clear experimental setup with a well-known characteristics concerning the uncertainties in the "state preparation" and the "measurement" (to know the detector characteristic and have a reliable estimate of its systematic uncertainties is the key work of an experimentalist) with a clear statistical result that can be compared to the probabilities (cross sections) calculated by the theorist within a given model, and this comparison can rule out the model or strengthen our confidence in it. The standard model is good in strengthening our confidence in it although we'd like to find deviations from it, because there are some problems we'd like to solve by finding an even better model, but so far there's no clear result contradicting the standard model (the most promising at the moment seems to be the anomalous magnetic moment of the muon, but (a) the deviation is around 3 sigmas only, which is no discovery but only evidence and (b) there's still some uncertainty concerning the hadronic contributions to the theoretical prediction which is in the same ballpark as the experimental uncertainties). That's what physics is about and not the vague question if some highly abstract Hilbert space structure is "real" ("ontic") or only descriptive ("epistemic").

On top of this irrelevance of these metaphysical problems for physics it's also quite unsharply formulated, i.e., it's not clear from a physical point of view, what's meant by these notions. It indeed only becomes an interesting physical question, when one can find an experimental setup to distinguish between these two possibilities, but as far as I can see from all these debates, it's not even clear, what's the difference between the two in this physical hard sense of a question!

 

[atyy]

That's what physics is about and not the vague question if some highly abstract Hilbert space structure is "real" ("ontic") or only descriptive ("epistemic").

On top of this irrelevance of these metaphysical problems for physics it's also quite unsharply formulated, i.e., it's not clear from a physical point of view, what's meant by these notions. It indeed only becomes an interesting physical question, when one can find an experimental setup to distinguish between these two possibilities, but as far as I can see from all these debates, it's not even clear, what's the difference between the two in this physical hard sense of a question!

Well, is the Weinberg-Witten theorem also "metaphysical" and addressing a problem that is unsharply formulated?

 

[vanhees71]

The Weinberg-Witten theorem is a mathematical statement about (asymptotic free!) single-particle states in connection with the existence of a covariant conserved current carried by massless particles. It's a clear statement and a not too difficult proof, which you can even find in the Wikipedia:

http://en.wikipedia.org/wiki/Weinberg–Witten_theorem

It's not about some vaguely defined philosophical idea.

 

[atyy]

The Weinberg-Witten theorem is a mathematical statement about (asymptotic free!) single-particle states in connection with the existence of a covariant conserved current carried by massless particles. It's a clear statement and a not too difficult proof, which you can even find in the Wikipedia:

http://en.wikipedia.org/wiki/Weinberg–Witten_theorem

It's not about some vaguely defined philosophical idea.

It's about a vaguely defined philosophical idea called Wilsonian renormalization and effective field theory. According to Wilson, non-renormalizable theories like general relativity are acceptable as effective theories, and there are "hidden variables" or more fundamental degrees of freedom at energies near the Planck scale. The Weinberg-Witten theorem shows that the hidden variables of Wilson cannot be described by a relativistic 4 dimensional quantum field theory.

 

[vanhees71]

Hm, the Wilsonian renormalization group is not vaguely defined but in a clear mathematical way. Of course, you may argue that QFT (Dyson renormalizable or "effective") of interacting particles are not well-defined. From a mathematical point of view this is a quite unsatisfactory affair of state :-(.

 

[atyy]

Hm, the Wilsonian renormalization group is not vaguely defined but in a clear mathematical way. Of course, you may argue that QFT (Dyson renormalizable or "effective") of interacting particles are not well-defined. From a mathematical point of view this is a quite unsatisfactory affair of state :-(.

Well, it's vague in the sense that we don't know what the more fundamental theory is from which the non-renormalizable theory of quantum general relativity emerges. However, in the Wilsonian view there is no problem with the non-renormalizability of quantum general relativity because it is only an effective theory. The concept of effective theory means that there are "hidden variables" that are important near the Planck scale. So these "hidden variables" are crucial to Wilson's argument. The Weinberg-Witten theorem rules out a wide class of hidden variable theories for quantum general relativity, just like PBR rules out a wide class of hidden variable theories for quantum mechanics.

But my point is not really that Wilsonian renormalizatio is vague. My point is that PBR is like the Weinberg-Witten theorem in that both are about hidden variables that solve a conceptual problem. Hidden variables are a potential solution to the measurement problem in QM, while hidden variables are a potential solution to non-renormalizability in quantum general relativity. Both PBR and Weinberg-Witten rule out large classes of hidden variable theories. The PBR theorem is as sharp a theorem as the Weinberg-Witten theorem.

 

[vanhees71]

Now I understand what you mean. That's of course true. Of course for a physicist it's a goal to find more comprehensive models of phenomena yet discribed only by effective theories. In looking for such more comprehensive theories "no-go theorems" like the Weinberg-Witten theorem or the Coleman-Mandula theorem (leading to the idea to extent the usual symmetries of particle physics to supersymmetric ones to look for models that solve or at least weaken some of the problems of the Standard Model like the hierarchy problem). I'd also not say that PBR is vague or anything (although I'm not very familiar with the argument). I referred to the idea of the quantum state's status as an "ontic" or "epistemic" quantity. That sounds quite vague to me. First of all one would have to give it a clear meaning in terms of mathematics and then determine whether it can be decided by experiment whether the state is "ontic" or "epistemic" in this mathematically sharpen sense. Mathematics only becomes physics when you can provide a (gedanken) experiment that can (at least in principle) be made in the lab or by observation in the real world (as is often the case in cosmology)!

 

[TrickyDicky]

Well, it's vague in the sense that we don't know what the more fundamental theory is from which the non-renormalizable theory of quantum general relativity emerges. However, in the Wilsonian view there is no problem with the non-renormalizability of quantum general relativity because it is only an effective theory. The concept of effective theory means that there are "hidden variables" that are important near the Planck scale. So these "hidden variables" are crucial to Wilson's argument. The Weinberg-Witten theorem rules out a wide class of hidden variable theories for quantum general relativity, just like PBR rules out a wide class of hidden variable theories for quantum mechanics.

I referred to the idea of the quantum state's status as an "ontic" or "epistemic" quantity. That sounds quite vague to me. First of all one would have to give it a clear meaning in terms of mathematics and then determine whether it can be decided by experiment whether the state is "ontic" or "epistemic" in this mathematically sharpen sense. Mathematics only becomes physics when you can provide a (gedanken) experiment that can (at least in principle) be made in the lab or by observation in the real world (as is often the case in cosmology)!

Yes, assuming a more fundamental theory all these debates in the vein of "real vs. statistical" will dissolve and makes little sense to spend effort on disentangling them unless they come in the form of theorems.

 

[atyy]

I referred to the idea of the quantum state's status as an "ontic" or "epistemic" quantity. That sounds quite vague to me.

"Ontic" and "Epistemic" are technical terms in PBR, and have strict definitions which were proposed by Harrigan and Spekkens http://arxiv.org/abs/0706.2661. Roughly, to continue with the idea that QM might be an emergent theory like gravity, PBR addresses constraints on the possible "coarse-graining" from more fundamental degrees of freedom to the wave function. If given a particular state of the underlying variables, the "coarse-graining" leads to a unique wave function, then the wave function is defined to be "ontic". But if the "coarse-graining" does not lead to a unique wave function, then the wave function is defined to be "epistemic".

I put "coarse-graining" in quotes, because this is not standard Kadanoff-Wilsonian coarse-graining over scale. Of course, the Weinberg-Witten theorem shows that gravity itself, if it is emergent is probably not a standard coarse-graining over scale, and the gauge/gravity conjecture shows that the emergence might be holographic. So neither quantum mechanics nor gravity are necessarily coarse-grained effective theories in the strict sense, but they are still probably emergent in some sense, so I have abused the term "coarse-graining" since the idea is the same, although the technicalities are vastly different.

 

[vanhees71]

Very interesting! I've to read the paper carefully first, but I think that's indeed at least a clear mathematical specification of what's meant by "ontic" and "epistemic". Then you are more in the realm on "physics" in the same sense as the Weinberg-Witten no-go theorem is "physics". As I said before, the importance of such no-go theorems is to direct your search for new theories in the right direction.

On the other hand no-go theorems have to be taken with a grain of salt. E.g., the Higgs mechanism was a way out to a pseudo no-go theorem at the time of its discovery: Nambu and Goldstone have shown that spontaneous symmetry breaking of global symmetries leads to the existence of massless Nambu-Goldstone bosons. The idea to get massive non-abelian gauge theories by "spontaneous symmetry breaking" seemed to be ruled out since no such Nambu-Goldstone bosons were seen in the particle spectrum.

What then was found by Andersen as an effective model for superconductivity, namely "Higgsing the electromagnetic interaction", as we'd call it today, was different: There's no Nambu-Goldstone boson in such a model but the "would-be Goldstone modes" get "eaten up" by the gauge fields to give them the necessary 3rd polarization degree of freedom of a massive vector field, at least in a special gauge, called "unitary gauge", because then all fields present in the gauge-fixed Lagrangian represent physical particles. Of course, there are also the Faddeev-Popov ghosts in the non-abelian case, but these are simply there to cancel unphysical degrees of freedom still present in the gauge fields as represented by Lorentz four-vector fields.

So there obviously was a way out of the dilemma suggested by the Nambu-Goldstone theorem: Try "spontaneous symmetry breaking" of local gauge symmetries. Of course, as a careful analysis shows, there is no spontaneous symmetry breaking of a local gauge theory but a Higgs mechanism making the gauge fields massive and removing the would-be Goldstone degrees of freedom from the physical spectrum. So this was the crucial exception for the no-go theorem.

So one must be careful with no-go theorems not to overlook possible models, but on the other hand they may lead you to the right ideas how to extend models. Maybe that's the case for quantum theory and maybe these PBR ideas lead to something new. Who knows?

 

[atyy]

On the other hand no-go theorems have to be taken with a grain of salt.

Absolutely! The PBR paper should be considered a pair with a paper by LJBR (BR are the same authors on both papers). The PBR paper shows sufficient conditions for the postulated hidden variables that ensures that a given state of the hidden variables uniquely specifies the wave function, so that the wave function is "ontic". However, when the conditions are weakened, LJBR were able to (partially) construct explicit examples in which a given state of the hidden variables do not uniquely specify the wave function, so that the wave function is "epistemic". The LJBR construction is only partial because while the Born Rule is reproduced, as far as I can tell it only talks about a single state without time evolution. Here's the LJBR paper:

http://arxiv.org/abs/1201.6554
Distinct Quantum States Can Be Compatible with a Single State of Reality
Peter G. Lewis, David Jennings, Jonathan Barrett, Terry Rudolph

 

[atyy]

Leifer has reviewed the developments since PBR and LJBR mentioned in post #27. Section 14.4 of Leifer's review discusses other possible assumptions in PBR which if weakened might lead to more models in which the wave function is "epistemic". For example, PBR assumes no retrocausation. However, present retrocausal interpretations treat the wave function as "ontic", so it remains to be seen if these potential loopholes can be exploited to construct models with an "epistemic" wave function.

http://arxiv.org/abs/1409.1570
Is the quantum state real? An extended review of ψ-ontology theorems
M. S. Leifer

 

[Ross D]

Is the wave function ( ex. electron wave function) just a mathmatical equation or a real physical object? I know that it's widely known that it's just an equation however some researchers say that they have proof that it's real.
Here is the link.
http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392
Does this prove that wave function is a real physical object after all?

Personally, I think that it is real. This can be demonstrated by the relationship E=hv, where v is the wave function's frequency. If the wave function was not real, it would be very hard to explain why it's generating a real energy. Therefore, the wave function is probably real, and this can lead to surprising simplifications in quantum physics. For example, a real wave function implies that energy is spread out along its entire volume, and as such you can think of it as having an energy density much like a fluid. Then, you can use equations from fluid dynamics to model it, and get valid results. However, it is important to distinguish between the mathematical treatment of the wave function and the actual thing that is there. Mathematically, the wave function has imaginary components, which are impossible to express in the real world. However, the probability density and the frequency associated with it can be treated as physical quantities (because they are real), thereby allowing new approaches to making computations in quantum physics.

 

[bhobba]

However, it is important to distinguish between the mathematical treatment of the wave function and the actual thing that is there. Mathematically, the wave function has imaginary components, which are impossible to express in the real world.

Why? For example EM can be written in complex form:
file:///C:/Users/Administrator/Downloads/Complex%20Maxwell%2527s%20equations.pdf

Physics is basically a mathematical model - all sorts of things can be used to model it.

Thanks
Bill

 

[jerromyjon]

I believe the wave function of all EM matter exists. It is what determines physical outcomes of interactions. I have faith that the absolute representation when found and proven mathematically will obviously describe what occurs exactly. Just because the math alone isn't as descriptive as english does not mean they are incompatible, some day the equations will "sound" right.

 

[bhobba]

some day the equations will "sound" right.

The modern basis of QM is very elegant - and IMHO sounds very 'right' - just weird until you get used to it:
http://arxiv.org/pdf/quantph/0101012.pdf

That said - nature doesn't have to oblige - in this case it does - but nature is as nature is.

Thanks
Bill

 

[bohm2]

The PBR paper should be considered a pair with a paper by LJBR (BR are the same authors on both papers). The PBR paper shows sufficient conditions for the postulated hidden variables that ensures that a given state of the hidden variables uniquely specifies the wave function, so that the wave function is "ontic". However, when the conditions are weakened, LJBR were able to (partially) construct explicit examples in which a given state of the hidden variables do not uniquely specify the wave function, so that the wave function is "epistemic"...

http://arxiv.org/abs/1201.6554
Distinct Quantum States Can Be Compatible with a Single State of Reality
Peter G. Lewis, David Jennings, Jonathan Barrett, Terry Rudolph

Note that according to one of the authors (Terry Rudolph) of both papers, while ψ-epistemic models can be constructed if no preparation independence assumption, they do not consider such models as serious proposals:

The theorem we prove – that quantum states cannot be understood as merely lack of knowledge of an underlying deeper reality described by some as yet undiscovered deeper theory – assumes preparation independence. It is an important insight that this assumption is necessary for the theorem, and the point of our second paper was to show this explicitly. That second paper is, however, simply making a mathematical/logical point – it is not a serious proposal for how the physical world operates.

http://www.preposterousuniverse.com...-post-terry-rudolph-on-nature-versus-nurture/

Terry Rudolph, argues that this preparation independence assumption of PBR is on par with the experimental free will assumption in deriving Bell's theorem. One can escape Bell's by denying it, but most physicists don't consider such models as serious proposals:

We are in a similar position with Bell’s theorem, which I consider the most important insight into the nature of physical reality of the last century, an honour for which there are some serious competitors! That theorem relies on a presumed ability to make independent choices of measurements at separated locations. Denial of such is the “super-determinism” loophole, and while intelligent people can and do consider its plausibility, and while it is an important insight into Bell’s theorem that this assumption is necessary, the jury is still out (‘t Hoofts efforts notwithstanding) as to whether a super-deterministic theory agreeing with all experiments to date can even be constructed, never mind be a plausible theory of nature.

Denial of preparation independence or invocation of super-determinism throws into question the basic methods of all science carried out to date. Most physicists would, I believe, consider the “cure” (extremely convoluted correlations between seemingly unrelated events leading to a conspiratorial interpretation of the nature of reality) worse than the “disease” (non-locality in the case of Bell’s theorem, the reality of the quantum state in the case of ours). If our theorem fails because the assumption of preparation independence fails, it is a far more amazing insight into nature than the theorem itself provides.

And yet there are a number of papers arguing that this preparation independence assumption is the most controversial assumption of the PBR Theorem. I'm not sure what to make of this? Did the authors of PBR paper underestimate the importance of the preparation independence assumption?

 

[zoki85]

Is the wave function ( ex. electron wave function) just a mathmatical equation or a real physical object?

No function is a real physical object/thing

 

[Marceli]

It is to understand difference between event description and event observation. Both can be accurate having same results! For example experiments are important event observations, measurements.

 

[bhobba]

No function is a real physical object/thing

Neither is any mathematical object - however it can model it.

The EM field is considered real because for the laws of conservation of energy and momentum to hold it has momentum and energy.

The same however may or may not apply to a quantum state (the wave-function is simply the expansion in terms of position eigenstates) - it may or may not be real.

Thanks
Bill

 

[microsansfil]

No function is a real physical object/thing

I am agree here with Nugatory https://www.physicsforums.com/threads/is-wave-function-a-real-physical-thing.788665/#post-4952978.
Depend on the definition you postulate about "real".

For example Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices.

Why not.

This is no more neither no less absurd than to assert the reality of the wave function.

Patrick

 

[zoki85]

Neither is any mathematical object - however it can model it.

The EM field is considered real because for the laws of conservation of energy and momentum to hold it has momentum and energy.

Actually, EM field is considered real becouse we can measure/detect it.

 

[microsansfil]

Actually, EM field is considered real becouse we can measure/detect it.

A lot of "thing" are measurable http://en.wikipedia.org/wiki/Measure_(mathematics)

Patrick

 

[zoki85]

A lot of "thing" are measurable http://en.wikipedia.org/wiki/Measure_(mathematics)

Patrick

How is the wave function measured?

 

[vanhees71]

That's a very good question! Since the physics content of the wave function is probabilistic it can only be "measured" by preparing a lot of independent systems always in the same way (state preparation) and measure the same observable (measurement). Then you do the usual statistical analysis to test the hypothesis that the probabilities are described right by the squared modulus of the wave function.

No matter, what Qbists mumble about the meaning of probabilities for a single event, in the physics lab there's no other way than the frequentist interpretation of probabilities, which BTW is based on the central-limit theorem which is a mathematical fact within the usual axiomatic foundation of probability theory (e.g., the Kolmogorov axioms).

 

[bhobba]

Actually, EM field is considered real becouse we can measure/detect it.

Not quite.

The electric field is defined as the force exerted on a test charge. That doesn't mean there is anything real at that point - it just means there is some other charge around exerting a force on it. The reason its considered real is because of relativity it takes some time for that force to be felt, hence for our conservation laws of momentum and energy to hold there must be somewhere it is held - and that is the field. This is part of some famous no go theorems developed by Wigner and explained in Ohanian's book on Relativity:
https://www.amazon.com/dp/B00ADP76ZO/?tag=pfamazon01-20

A quantum state also can be measured - but, as Vanhees correctly explains - only via a large number of similarly prepared systems the same as the probabilities of a biased coin. However it is not the same as an EM field and similar no-go theorems do not exist. Personally this is part of the reason I do not consider it real - if it was real you could directly measure it rather than having to prepare a large number of systems - it is also one reason I find the minimal statistical interpretation a more direct view.

Measurement is not the requirement for being real in a physical sense.

Thanks
Bill

 

[bhobba]

which BTW is based on the central-limit theorem which is a mathematical fact within the usual axiomatic foundation of probability theory (e.g., the Kolmogorov axioms).

That's true - but I suspect you really meant the strong law of large numbers.

One of my favourite mathematicians, Terry Tao, wrote a nice article on it:
http://terrytao.wordpress.com/2008/06/18/the-strong-law-of-large-numbers/

Just as an aside he also wrote some nice stuff on distribution theory:
http://terrytao.wordpress.com/2009/04/19/245c-notes-3-distributions/
http://www.math.ucla.edu/~tao/preprints/distribution.pdf

Thanks
Bill

 

[vanhees71]

I meant the theorem that the frequencies in a probability experiment converges to the probabilities as predicted by QT in the limit of very many experiments. That's of course the strong law of large numbers. The central-limit theorem explains, why Gaussian distributions occur pretty often in probability problems.

 

[zoki85]

Not quite.

The electric field is defined as the force exerted on a test charge. That doesn't mean there is anything real at that point - it just means there is some other charge around exerting a force on it.

Meaning nothing is real, all the world is illusion. Oh, I can't sleep now :D

 

[TrickyDicky]

That's a very good question! Since the physics content of the wave function is probabilistic it can only be "measured" by preparing a lot of independent systems always in the same way (state preparation) and measure the same observable (measurement). Then you do the usual statistical analysis to test the hypothesis that the probabilities are described right by the squared modulus of the wave function.

No matter, what Qbists mumble about the meaning of probabilities for a single event, in the physics lab there's no other way than the frequentist interpretation of probabilities, which BTW is based on the central-limit theorem which is a mathematical fact within the usual axiomatic foundation of probability theory (e.g., the Kolmogorov axioms).

Exactly, so if the wave function is just a tool to calculate probabilities, i.e. is not something measurable, certainly not when used in this manner, it makes no sense to even ask about the "ontic" nature of such a tool. This would lead to similar considerations about QM states in general.
To me it is salient of QM that its explanatory power for things from tunneling or atomic spectra to chemistry, superconductors or lasers is not directly derived from the probabilistic predictions from wave functions(these applications rely basically on intrinsic quantum properties), rather such predictions are usually more like self-checks for the theory, or for calculating cross-sections in particle physics.

 

[bhobba]

i.e. is not something measurable,

It is measurable - only from a large ensemble of similarly prepared systems, but it is measurable.

Thanks
Bill

 

[TrickyDicky]

It is measurable - only from a large ensemble of similarly prepared systems, but it is measurable.

Thanks
Bill

I suspect you are probably referring here to the mathematical concept of probability measure while I'm referring to measurements in physics.

 

[bhobba]

I suspect you are probably referring here to the mathematical concept of probability measure while I'm referring to measurements in physics.

No - its from the properties of a state.

That said it is indeed different to things like an electric field etc.

Thanks
Bill

 

[stevendaryl]

No matter, what Qbists mumble about the meaning of probabilities for a single event, in the physics lab there's no other way than the frequentist interpretation of probabilities, which BTW is based on the central-limit theorem which is a mathematical fact within the usual axiomatic foundation of probability theory (e.g., the Kolmogorov axioms).

I don't know why you would say that in the lab, there is no other way than the frequentist interpretation. Bayesian probability works perfectly fine in the lab. The differences between bayesian and frequentist really only comes into play at the margins, when you're trying to figure out whether your statistics are good enough to make a conclusion. The frequentists use some cutoff for significance, which is ultimately arbitrary. The bayesian approach is smoother--the more information you have, the stronger a conclusion you can make, but you can use whatever data you have.

Since frequentist probability only applies in the limit of infinitely many trials, there isn't a hard and fast distinction between a single event and 1000 events. Neither one implies anything about the probability, strictly speaking.