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

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Naty1
#19
Feb12-12, 04:10 PM
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Vectronix:
There are many interpretations...check here in Wikipedia
for background and introduction

http://en.wikipedia.org/wiki/Quantum...ulus_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 thats 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 Schrodinger are equivalent quantum formulations…non relativistic theories. Wave mechanics (Schrodinger) 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 Schrodinger 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
#20
Feb12-12, 09:37 PM
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Quote Quote by stevendaryl View Post
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
#21
Feb12-12, 09:46 PM
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Quote Quote by bohm2 View Post
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
#22
Feb12-12, 10:46 PM
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Quote Quote by Ken G View Post
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/fac...veFunction.pdf
bhobba
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Feb13-12, 02:58 AM
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Quote Quote by bohm2 View Post
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
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Feb13-12, 08:49 AM
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Quote Quote by bhobba View Post
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
#25
Feb13-12, 04:59 PM
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The original question was Interpretation of QM;is there a general concensus? Why dosen't someone answer that question ?.
Does anyone still take the Copenhagen view as the best available?.What other interpretations are currently favoured?.
bhobba
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Feb13-12, 06:17 PM
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Quote Quote by Pollock View Post
The original question was Interpretation of QM;is there a general concensus? Why dosen'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
#27
Feb13-12, 06:24 PM
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Quote Quote by bohm2 View Post
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.

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Bill
bohm2
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Feb13-12, 09:40 PM
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Quote Quote by bhobba View Post
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
http://www.physicsforums.com/showthread.php?t=554543
Ken G
#29
Feb13-12, 10:02 PM
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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
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Feb13-12, 10:44 PM
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Quote Quote by Ken G View Post
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"?
StevieTNZ
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Feb13-12, 11:16 PM
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Quote Quote by bohm2 View Post
Sure, but then realists are likely to ask "information about what" and "whose information"?
Here is a paper by Renato Renner and co, entitled: Completeness of quantum theory implies that wave functions are physical properties

Given the wave function associated with a physical system, quantum theory allows us to compute predictions for the outcomes of any measurement. Since, within quantum theory, a wave function corresponds to an extremal state and is therefore maximally informative, one possible view is that it can be considered an (objective) physical property of the system. However, an alternative view, often motivated by the probabilistic nature of quantum predictions, is that the wave function represents incomplete (subjective) knowledge about some underlying physical properties. Recently, Pusey et al. [arXiv:1111.3328, 2011] showed that the latter, subjective interpretation would contradict certain physically plausible assumptions, in particular that it is possible to prepare multiple systems such that their (possibly hidden) physical properties are uncorrelated. Here we present a novel argument, showing that a subjective interpretation of the wave function can be ruled out as a consequence of the completeness of quantum theory. This allows us to establish that wave functions are physical properties, using only minimal assumptions. Specifically, the (necessary) assumptions are that quantum theory correctly predicts the statistics of measurement outcomes and that measurement settings can (in principle) be chosen freely.
http://arxiv.org/abs/1111.6597
bhobba
#32
Feb13-12, 11:23 PM
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Quote Quote by bohm2 View Post
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
http://www.physicsforums.com/showthread.php?t=554543
Cant follow that one. It can be considered a complex function f(x1,....,xn) - the xi are positions of n particles in ordinary 3d space - it doesn't have to emerge from anything. f gives the probability amplitudes of the particles having those positions. Such functions can be expanded in terms of a infinite but countable basis for theoretical convenience but that does not mean it literally resides in such abstract spaces. If you consider the f real then there is an issue exactly where it resides - it may reside just as a conjecture in some rolled up higher dimensional space that the xi are also in - but 3d space does not have to emerge from anything - its existence is built into the xi.
martinbn
#33
Feb14-12, 03:13 AM
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I am with bohm2 on this one. And I am puzzled about what the meaning of 'real' is to people that say that the wave function is real! Usually it is said that it is real in the same way as the electromagnetic field is, but it is obviously not real in that way. To me real means that there is an object that is in 3D space that intereacts with other objects. Then clearly the wave function is not such a thing. So what does real mean to those poeple?
bhobba
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Feb14-12, 03:53 AM
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Quote Quote by martinbn View Post
I am with bohm2 on this one. And I am puzzled about what the meaning of 'real' is to people that say that the wave function is real! Usually it is said that it is real in the same way as the electromagnetic field is, but it is obviously not real in that way. To me real means that there is an object that is in 3D space that intereacts with other objects. Then clearly the wave function is not such a thing. So what does real mean to those poeple?
Real means it has an external existence and not just a calculational device. In saying it is real like an electromagnetic field it is meant it has an external existence. There are all sorts of possibilities of how that can be - here is an interesting one:
http://arxiv.org/pdf/1104.2822v1.pdf

You mentioned Bohm2 - Bohms pilot wave would be something that also had real existence - the theory is a bit vague about exactly what it is.

Thanks
Bill
martinbn
#35
Feb14-12, 03:58 AM
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Quote Quote by bhobba View Post
Real means it has an external existence and not just a calculational device. In saying it is real like an electromagnetic field it is meant it has an external existence. There are all sorts of possibilities of how that can be - here is an interesting one:
http://arxiv.org/pdf/1104.2822v1.pdf

You mentioned Bohm2 - Bohms pilot wave would be something that also had real existence - the theory is a bit vague about exactly what it is.

Thanks
Bill
Yes, the pilot wave would be an example, but my puzzlement remains. How can something have and external existence and its mathematical discription be a function defined on configuration space?! I think that is what bohm2 is saying also.
bhobba
#36
Feb14-12, 07:27 AM
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Quote Quote by martinbn View Post
Yes, the pilot wave would be an example, but my puzzlement remains. How can something have and external existence and its mathematical discription be a function defined on configuration space?! I think that is what bohm2 is saying also.
The same way the Bohm pilot wave, which can also be viewed the same way can:
http://www-physique.u-strasbg.fr/cou.../Nine_form.pdf
'The quantum potential Q(x1,x2,t) changes instantaneously throughout configuration space whenever the wavefunction changes, and this mechanism is responsible for the nonlocal correlations that are so characteristic of quantum mechanics. A rather natural mechanism prevents human beings from tapping into this instantaneous change for the purpose of faster-than-light communications.'

Interestingly that paper discusses another equivalent formulation of Quantum mechanics, the Second Quantization Formulation, usually associated with QFT, but can also be a formulation for bog standard QM, which can be viewed as a field of creation and annihilation operators at all points of space.

Thanks
Bill


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