Interpretations of Quantum Mechanics (is there a general consensus?)

[Vectronix]

Hi :)

I recently read a book that states that most scientists believe the wave function represents a real field (i.e., one that possesses energy and momentum). I think this is part of the transactional interpretation of QM but not sure... can anyone confirm whether the book I read is right about this or not?

 

[martinbn]

I don't know what most scientists believe, but I find that statement strange. I would have thought that the one thing, about the wave function, they would agree on, is that it doesn't represent a real field.

 

[phyzguy]

From my experience, I would say there is not a general consensus on this point, and most scientists seem to take the view of SUAC - Shut Up And Calculate - which means they know how to do the calculations and just don't worry too much about the interpretation.

 

[juanrga]

Hi :)

I recently read a book that states that most scientists believe the wave function represents a real field (i.e., one that possesses energy and momentum). I think this is part of the transactional interpretation of QM but not sure... can anyone confirm whether the book I read is right about this or not?

You would fill some money refund form

 

[jtbell]

I recently read a book

Which book?

 

[Ken G]

Not only don't I think there's a consensus on that, I'm not even sure what the statement means. A field is real if it carries energy and momentum? How does one know if a field carries energy and momentum? I would say that thinking is backward-- we don't ask if it carries energy and momentum, and then decide we think it's real, we ask if we think it's real, and then decide it carries the energy and momentum. In other words, we all know we wish to associate energy and momentum with the wavefunction, whether we regard it as real or not, so we first have to ask if we regard it is real before we can decide whether or not it "carries" that energy and momentum, instead of just "associates with" that energy and momentum. So the field is not real if it carries energy and momentum, the field carries energy and momentum if it is real.

 

[Vectronix]

Yeah, what you said makes sense, Ken. I would have thought that most scientists don't believe the wave function is real, too, martin. I may have mis-stated the part about the wave function a bit, but here's a quote from the preface of the book:

"...if someone, not a theoretical physicist and not thoroughly acquainted with modern methods of analysis, were to attempt to digest a current article dealing with nuclear forces or cosmic rays, relying for help on the available books on the subject, he would discover to his dismay that modern quantum mechanics differs radically from that which he finds in the textbooks... More confusing to him is the interpretation of a field in the new mechanics. It seems evident that what is meant is a real field possessing energy and momentum. Yet the textbooks attach a purely symbolic meaning to the wave field of a particle, picturing the field concept merely as a probability function."

...and there you have it.

You would fill some money refund form

lol I got it from Borders bookstore before they went out of business, so... :P

Which book?

It's called Quantum Mechanics of Particles and Wave Fields, by Arthur March.

 

[juanrga]

lol I got it from Borders bookstore before they went out of business, so... :P

Try the Book publisher then

 

[Vectronix]

hehe... Do you seriously think I should? :)

 

[bhobba]

Hi :)I recently read a book that states that most scientists believe the wave function represents a real field (i.e., one that possesses energy and momentum). I think this is part of the transactional interpretation of QM but not sure... can anyone confirm whether the book I read is right about this or not?

Most probably believe it has a real existence like say an electric field does - not as an actual field - but as something that exists out there because they think a wave-function collapse is an issue. The interpretation that probably demands it is one based on quantum decoherence for that collapse and its variants - don't know about the transactional interpretation.

I personally don't believe it does - I think its like classical probability theory - its simply a device for calculating statistical outcomes. Check out:
http://arxiv.org/pdf/quant-ph/0111068v1.pdf

Thanks
Bill

 

[stevendaryl]

There is something about the wave function that makes a completely different kettle of fish than fields such as the electric field. That is, that unlike the electric field, the wave function is not a field in the physical world. It's a field in configuration space.

The distinction is this: In the case of an electric field, I can point to a particular spot, and ask "What is the value of the electric field right there?" You cannot ask the analogous question about the wave function, because it is not a probability amplitude on points in space. To see why not, consider a two-particle wave function. In general, It would be written as (simplifying to the case of 1 spatial dimension): ψ(x₁, x₂), the square of which gives the probability density of finding the first particle at position x₁ and the second particle at position x₂. It doesn't make any sense for me to point to a particular point and ask what the value of the wave function is at that point.

I don't know what the implications of this physical-space versus configuration space distinction is for whether the wave function is "real", but it certainly shows that the wave function cannot be considered an ordinary field like the electric field.

 

[Ken G]

Yet you can point to a box in real space and ask "what is the probability of finding a particle in that box", even for multiple-particle wave functions (if the particles are distinguishable, you can also specify which type of particle you are asking about). You can also ask about correlations like "what is the probability of finding particles in both of these two boxes", and so on. So it's a more sophisticated kind of field, but it seems to me one can still imagine it "exists" in real space if one wants to. True, it is kind of a "question answering field", but then, so are they all. Does one want to attribute independent existence to question-answering fields? No less so in quantum than classical physics, it was always something of a stretch in my view!

 

[martinbn]

@ Ken_G: The point of stevendaryl is that fields are represented by mathematical object that have domain spacetime not configuration space. I thought this was so obvious, that's why I didn't even say in my post!

 

[stevendaryl]

Yet you can point to a box in real space and ask "what is the probability of finding a particle in that box", even for multiple-particle wave functions (if the particles are distinguishable, you can also specify which type of particle you are asking about). You can also ask about correlations like "what is the probability of finding particles in both of these two boxes", and so on. So it's a more sophisticated kind of field, but it seems to me one can still imagine it "exists" in real space if one wants to. True, it is kind of a "question answering field", but then, so are they all. Does one want to attribute independent existence to question-answering fields? No less so in quantum than classical physics, it was always something of a stretch in my view!​

Well, I don't think there was ever any question about whether the wave function was useful for answering questions. It certainly provides information about the real world. My point is that it isn't something that resides in the real world. It isn't an object that exists in some location, nor is it a field that varies from location to location.

 

[bohm2]

I really like Matt Leifer's suggestion in this post:

Even disregarding the issue of whether the quantum state has to be ontic, Bell’s theorem already implies the same issue with simultaneity. It shows that the ontic state at B must depend on the choice of measurement at A and vice versa, and there are frames of reference in which the measurements occur in either order. There are only two possible responses to this:

1. Reject relativity at the fundamental level. Assume that there is a preferred frame of reference and have the nonlocal influences operate instantaneously in this frame. The frame will be hidden at the statistical level due to the averaging over ontic states, so you will still have Lorentz invariance at the operational level, but it means that you cannot use relativistic arguments to reason about what is happening at the ontic level, so the paradoxes do not arise. This is the solution adopted in Bohmian mechanics for example.

2. Reject one or more of the assumptions of Bell’s theorem (also assumed by PBR). For example, one could adopt a no-collapse interpretation like Everett/many-worlds, which denies the existence of ontic properties localized in spacetime, an assumption that Einstein called “separability” and that is crucial to the derivation of nonlocality. Alternatively, one could adopt one of the “neo-Copenhagen” approaches to quantum theory in which the need for an ontic state is denied. Finally, one could retain realism and single-valuedness of measurement outcomes by adopting ontologies that are not considered in the derivation of Bell’s theorem, e.g. retrocausality.

I already stated in the blog post that I like the retrocausal solution, or at least that I consider it worth investigating in more detail. This is because I prefer to retain realism, fundamental Lorentz invariance and psi-epistemicism, and it is one of the few options on the table that still has a chance of doing that. If the retrocausal program fails then I would have to drop one or more of these requirements and I fluctuate between preferring neo-Copenhagen approaches or Everett depending on whether my psi-epistemic or realist convictions are stronger on any given day. To be convinced to drop fundamental Lorentz invariance, I would have to see violations of it on the statistical level. Valentini argues that this is to be expected in the Bohmian approach for example, since the statistical washing out of nonlocal influence is analagous to being in a state of thermal equilibrium in statistical mechanics, so we should expect to see systems out of this state of equilibrium somewhere in the universe. I consider this to be a firm prediction of all such theories, and so I would need to see empirical violations of Lorentz invariance to be convinced of them.

Can the quantum state be interpreted statistically?
http://mattleifer.info/2011/11/20/can-the-quantum-state-be-interpreted-statistically/

 

[ardenmann0]

Gell-Mann once wrote, ‘Bohr brainwashed a whole generation of physicists into ‘believing' the Copenhagen interpretation of quantum mechanics'.

 

[LaserMind]

So a wave function is not a wave and its not a particle, its an entity of some sort in 'superposition' that spreads out in x,y,z and t. We can only find out if its 'there' by decohering it. Otherwise it is not a physical, real entity.

It behaves as though it were a 'calculation' waiting for its result (at some x,y,z and t) on decoherence. It leaves no track of its path. It simply 'arrives'. We know where it came from but have no idea of its path to its destination.

So what entity can achieve this? Something superposition is not a 'thing' - its not an object that we cannot enclose or put in a container - unless we decohere. And even then decoherence results in 'values observed'.

 

[ardenmann0]

I don't know what most scientists believe, but I find that statement strange. I would have thought that the one thing, about the wave function, they would agree on, is that it doesn't represent a real field.

If it doesn't represent a real field, how can it interfere with itself in the double slit experiment?

We can't detect gravitational waves right now, but it does not mean they do not exist.
It just mean our instruments are not sensitive enough to detect them directly right now.

 

[Naty1]

Vectronix:
There are many interpretations...check here in Wikipedia
for background and introduction

http://en.wikipedia.org/wiki/Quantu...ble_functions_-_analytical_calculus_formalism

The wave function is absolutely central to quantum mechanics: it makes the subject what it is. Also; it is the source of the mysterious consequences and philosophical difficulties in what quantum mechanics means in nature, and even how nature itself behaves at the atomic scale and beyond - which continue in debate to this day.

It's probably the 'abstract vector space' formulation that's leads to major disagreements.

Here are a few quotes I saved from QUANTUM MECHANICS by Albert Messiah:

This first may be the most controversial:

In its mature form, the idea of quantum field theory is that quantum fields are the basic ingredients of the universe, and particles are just bundles of energy and momentum of the fields.

The major difficulty of classical theory in explaining submicroscopic phenomena stems from the appearance of discontinuities which result from quantized behavior.
In classical mechanics the evolution in time of physical systems is described by dynamic variables with well defined values at every instant. It became evident around 1900 phenomena on the atomic and sub atomic scale do not fit this framework...The first series of experiments forcing a revision of the wave theory of Maxwell-Lorentz was the photoelectric effect and Compton scattering.

So some new mathematical models became popular:

The Matrix Mechanics of Heisenberg and the Wave Mechanics of Schrödinger are equivalent quantum formulations…non relativistic theories. Wave mechanics (Schrödinger) utilizes the more familiar language of partial differential equations and tends to a simpler introduction to QM (than Heisenberg’s matrix mechanics

The matrix formulation starts from observable quantities...dynamical variables…. and associates with each a matrix; these matrices obey non commutative algebra. It is this non commutative algebra matrix mechanics differs from classical mechanics...In its mature form, the idea of quantum field theory is that quantum fields are the basic ingredients of the universe, and particles are just bundles of energy and momentum of the fields.

It is a POSTULATE that the Schrödinger wave equation [psi] of a quantum system completely defines its dynamical state. [The statistical results of the measurement of a dynamical variable can be deduced from the wave function...but not precisely accurate repeatable results*. ] The central problem of QM is knowing the wave function at some initial time to determine the equation of propagation of the wave [psi] for all later time. “It is quite clear that no deductive reasoning can lead us to that equation.

* This is a 'one liner' referring to the Heisenberg uncertainty principle.

So what we have, in my own words, are models. They provide some great insights, have been shown to offer many experimental predictions which have been verified to great precision, but which still leave remaining interpretational issues.

 

[Ken G]

Well, I don't think there was ever any question about whether the wave function was useful for answering questions. It certainly provides information about the real world. My point is that it isn't something that resides in the real world. It isn't an object that exists in some location, nor is it a field that varies from location to location.

My point is that with multiple particles, complete information in quantum mechanics refers not only to the particles themselves, but also to their correlations. The importance of correlations doesn't mean we are not dealing with things that "reside" in 3-space, it just means that correlations are more sophisticated animals. We would face an analogous issue if we were interested in purely classical correlations between density variations between two species in 3 space, like two types of gas. There our density correlation functions would be mathematically dependent on 3X2 space, not 3 space, because we'd be interested in questions like the probability of finding density increases in one gas given that we have nearby density increases in the other. Yet even so, no one would question that the density distributions themselves "reside" in 3 space. The mathematical animal needed to talk about correlations in 3 space is a higher dimensional object, but I don't see why that needs to compromise our sense of where these correlations "reside." It's like how in relativity, we think of events as residing in spacetime, but the fields in relativity are tensors, not vectors that take on values in spacetime. So they are more sophisticated mathematical objects, to maintain the correct invariances, yet we still think of relativistic fields as "residing" in spacetime.

 

[Ken G]

I really like Matt Leifer's suggestion in this post:

Yes I think that was well put, though I would personally question his adherence to realism at the cost of allowing retrocausality. The reason I think one should hold causation and drop realism is that causation is epistemic and realism is ontic, and I view physics as primarily epistemic, so we should always hold epistemic principles above ontic ones. That might be the most boiled-down way to restate Bohr's approach.

 

[bohm2]

The mathematical animal needed to talk about correlations in 3 space is a higher dimensional object, but I don't see why that needs to compromise our sense of where these correlations "reside."

If one isn't a wave function "realist" it doesn't matter, but if one assumes wave function "realism", doesn't that necessarily also lead to:

1. configuration space "realism" (e.g. if wave function is real, then the 3-D space of our ordinary experience must be an illusion). Or
2. at least a need to explain and find a way to recover 3-D space from configuration space and wave function ontology.

Some argue that there are problems with taking option 1. above (e.g. David Albert), however as noted by Maudlin and summarized here by Ney:

Unfortunately, for a view that takes the wave function to be an element of the fundamental ontology, the name ‘configuration space’ is misleading. According to wave function realism, particles in three-dimensional space are not ontologically prior to the wave function, and so the space the wave function inhabits is not fundamentally a space of configurations of particles in three-dimensional space.

So, then what is the "N" of 3-N dimensional space about if not particles?

Ontological Reduction and the Wave Function Ontology
http://www.rochester.edu/college/faculty/alyssaney/research/papers/Ney_ReductionWaveFunction.pdf

 

[bhobba]

at least a need to explain and find a way to recover 3-D space from configuration space and wave function ontology.

Come again - you don't need to recover anything - it makes probabilistic predictions about what happens in 3D space just like for example a probability vector predicts how a dice behaves in 3D space.

Thanks
Bill

 

[bohm2]

you don't need to recover anything - it makes probabilistic predictions about what happens in 3D space just like for example a probability vector predicts how a dice behaves in 3D space.

I'm only talking about one who is a wave function realist.

 

[Pollock]

The original question was Interpretation of QM;is there a general consensus? Why doesn't someone answer that question ?.
Does anyone still take the Copenhagen view as the best available?.What other interpretations are currently favoured?.

 

[bhobba]

The original question was Interpretation of QM;is there a general consensus? Why doesn't someone answer that question ?.Does anyone still take the Copenhagen view as the best available?.What other interpretations are currently favoured?.

No there isn't. And there are people who still adhere to Copenhagen as the best there is. What do you mean by currently favoured? These days with more to choose from its probably even more 'jumbled'. But a new one called Consistent Histories (some people say its Copenhagen done right) now has a lot of adherents and the Ensemble Interpretation of Einstein (also known as shut up and calculate - its my view) has come on strong.

Thanks
Bill

 

[bhobba]

I'm only talking about one who is a wave function realist.

Even then its the same thing - the quantum state resides in 3D space - but its exact nature is an open question.

Thanks
Bill

 

[bohm2]

Even then its the same thing - the quantum state resides in 3D space - but its exact nature is an open question.

The wave function cannot exist in 3-D space. Predictions of QM depend on the 3N-dimensional space that get lost in the 3-D representation (e.g. information about correlations among different parts of the system, that are experimentally observed are left out). For a philosophical discussion of this see the following thread:

The reality of configuration space
https://www.physicsforums.com/showthread.php?t=554543

 

[Ken G]

You're saying that if the wavefunction is regarded as real, then the space on which it takes on values must be the space in which it "lives." If the particles are instead regarded as real, then the wavefunction can just be thought of as a way to organize information about those particles, in which case the particles can still "reside" in 3 space while the wave function takes on values from some information space. I think that's true, I just don't really buy the idea that either the wave function or the particles are real. It's all just the spaces we use to picture the information-- the information of a wave function takes on values from configuration space, but that's nothing new, we have many ways of organizing information about particles that is accessed from configuration space. But even the particle concept, and the 3-space concept, are just more ways of organizing information. Why do we need to say which mode of information is real? All information is real, but it's still just information.

Hence I think a lot of this issue relies on what we think is "existing in" 3D space. The wavefunction of multiple particles is not a function on 3D space, we can agree there, but I don't see that it has any problem referring to other entities that "reside" in 3D space. We are interested in tracking correlations, so the correlations can't exist in 3D space, but what they are correlating can. I don't see why this issue is any different from using phase space to talk about N gas particles in a box, for example. The 6N dimensional phase space of those N particles is also not a 3 dimensional object, but it is clearly referring to particles that can be pictured as "residing" in 3 space, and moving through 3 space. It's just the mathematical treatment, like if we say F=ma we are looking at a second time derivative of a 3D position, but if we say F(x)=dp/dt and p=m*dx/dt, we are looking at two first time derivatives on a 6D space of x and p. No one thinks these two different formulations call into question the reality of whether particles "reside" in 3 space, if one is a realist in regard to particles, there is just a difference between the entities we are interested in versus what space we use to track our information about them. But I don't really see any point in being a realist in regard to either particles or wavefunctions-- physics manipulates information, get over it, is my attitude. (That isn't "shut up and calculate", it's "talk as much as you like, but what you are talking about is information.")

 

[bohm2]

But I don't really see any point in being a realist in regard to either particles or wavefunctions-- physics manipulates information, get over it, is my attitude. (That isn't "shut up and calculate", it's "talk as much as you like, but what you are talking about is information.")

Sure, but then realists are likely to ask "information about what" and "whose information"?