Interpretations (Continued Discussion)

[jambaugh]

I'm starting this thread to continue a tangential discussion of interpretations, specifically Bohmian vs Copenhagen from https://www.physicsforums.com/showthread.php?t=324790".

Remember CI doesn't so much assert the absence of e.g. pilot waves or even multiple worlds. It rather insists on agnosticism about these theological speculations. It is the same as SR's agnosticism about the unobservable luminiferous aether, or science's general agnosticism about God & friends. Assertions about the nature of reality beyond the observable is a departure from the domain of science.

Let me ask you a personal question:
Do you believe that the universe existed even before humans (or animals) have started to observe it? Or are you completely agnostic about that?

As a class of phenomena "Yes" of course. As an object "No", nor do I believe in the existence of "The Universe" as a real object now.

Your question shows a misunderstanding of CI or more generally of its positivism. It is as much an error to deny the existence of the moon (as an object) when it is not observed as to assert the existence of the moon (as an object) when is not observed. But there is "moon as object" and "moon as process". And the physical process we have repeatedly observed as the moon along with the observed cause and effect of physics which dictates how observations are implemented show that "the moon has not suddenly ceased to exist" by virtue of our continued existence. We can infer from experiment that a sudden failure of the moon to continue its journey about the Earth would cause such upheavals, said upheavals which we continually fail to see, that we effectively are continually observing the moons existence. When collections of phenomena behave so ponderously as to be effectively in continual interaction with their environment and thus are continuously under observation of their gross properties we can then treat such as objects and utilize the reality model of classical mechanics to describe those objects at the resolution which is significantly meaningful to them.

"Reality" is a model of phenomena as behaving objects with properties whose values (objective state) are always well defined. Below the level of this model is the phenomena themselves which "happen". In describing those phenomena at the classical level a "reality model" is appropriate but it is still a model. At the quantum level the use of a reality model breaks down and we should stick to the more operational description of the phenomena themselves.

But don't confuse the positivism used in CI with nihilism. CI does not make assertions about the nature of reality or its absence. CI is not a philosophical theory at all. Tt rather is --as stated-- an interpretation giving the meaning of the terms and constructs in QM. It is not (as with MW or BPW) a general philosophical statement about the universe.

The principle point is that in CI the wave-function we right down is "the wave function we write down" and should not be asserted to be a physical object. You are free to go beyond CIQM and assert in addition to the computational wave function a physical one. But understand that you are then going beyond QM into a realm of metaphysics. Similarly if you postulate a reality of many-worlds. If you wish to talk of such within the realm of science then you should seek empirically testable hypotheses such as means to directly observe pilot waves or communicate between parallel worlds.

An unfortunate product of the historic development of QM and grappling with its interpretation is the use of terms with implicit meaning such as "state vector" or "wave function".

It would be helpful if we distinguished the mathematical wave-function interpreted as CI interprets it as our representation of knowledge about a physical system from the physical wave-function asserted by other "interpretations".

Those other interpretations do not deny that one in addition to thinking about physical wave-functions out there also work with the body of knowledge about the physical system which we encapsulate in a mathematical wave-function. They thus do not really deny the CI interpretation of the (mathematical) wave-function but rather overlay additional meaning.

And I think we can agree that those other interpretations can accept collapsing these mathematical wave-functions as a method of calculation, just as one would collapse a classical probability distribution to a new conditional distribution (Bayesian inference) when new information is asserted. They are free to assert anything they like about their physical wave-functions.

I would similarly parse through the remaining points of CI and assert that really the other "interpreters" are not denying the assertions of CI but rather overlaying (for their own reasons) additional "baggage" which for the most part does not add to the predictions of QM.

Finally I would assert that these other "interpretations" should instead be referred to as "models" unless and until they either contradict or append on to the predictions of QM.

CI is the "shut up and calculate" interpretation.

These models did not supplant the Euclidean case as natural science their appearance rather show that natural science is not the proper context to study geometry. One is in the context of logic rather than science and one is thus free to choose axioms freely (within the constraint of consistency).

But we have a very physical theory - general relativity - that tells us that geometry may be an important part of a natural science. In particular, it is possible to decide by an experiment whether the universe is curved or not.

No! the theory of general relativity --properly parsed-- tells us the behavior of physical objects (now that we're on the classical level I'll use a "reality" model and speak of classical test bodies or EM waves as objects). It may be described in terms of geometry but that is a choice of model.

The equivalence principle goes both ways. We can interpret the regional gravity as a dynamic force in a regionally flat geometry or as an absence of dynamic forces in a regionally curved geometry or any of a continuum of possible mixtures. This is a "choice of gauge" roughly analogous to choosing the potential of a charged particle to be zero at infinity. The physical quantity is not the value of the potentials but differences in potential between distinct space-time events.

Indeed you may reformulate GR in terms of a anisotropic variable speed of light field expressible via an refractive tensor. It is just a relabeling of the same mathematical entities used in calculating the behavior of physical objects. Ultimately geometry is a mathematical construct not an observed phenomenon.

But two physicists understanding all of this can still discuss "how matter bends space-time" because the geometry model is the most efficient at encoding the physics. They use the terms always in a tentative non-literal meaning. They are using the language of the model since the model encapsulates the predictions of the theory (but not necessarily uniquely).

At the same time physicists must be careful using "language of the model" short hand because one may (and I have seen this happen many times) get caught up in arguments about differences in model components which do not upon careful investigation yield differences in observations.

 

[zenith8]

Hi James,

I think you're off-base here in a number of ways.. You don't even appear to understand what the Copenhagen interpretation actually is - rather you seem to be mixing it all up with the basic instrumentalist assertions of QM and bits of the ensemble interpretation.

Cutting and pasting from http://en.wikipedia.org/wiki/Interpretation_of_quantum_mechanics" (we're at that level here):

"An interpretation of quantum mechanics is a statement which attempts to explain how quantum mechanics informs our understanding of nature."

This is not to be confused with an instrumentalist description of the theory which:

"relates the mathematical formalism to experimental practice and prediction." (i.e. shut up and calculate).

Copenhagen does in fact attempt to make philosophical statements about nature. That is why it is called an interpretation.

Again http://en.wikipedia.org/wiki/Copenhagen_interpretation" [note to moderator: it's hard finding a definitive statement of Copenhagen in the peer-reviewed literature, and anyway, the article is rather good]:

Here are the ideas normally associated with the Copenhagen interpretation:

1. A system is completely described by a wave function ψ, which represents an observer's knowledge of the system. (Heisenberg)

2. The description of nature is essentially probabilistic. The probability of an event is related to the square of the amplitude of the wave function related to it. (Born)

3. Heisenberg's uncertainty principle ... it is not possible to know the values of all of the properties of the system at the same time; those properties that are not known with precision must be described by probabilities.

4. Complementarity principle: matter exhibits a wave-particle duality. An experiment can show the particle-like properties of matter, or wave-like properties, but not both at the same time.(Niels Bohr)

5. Measuring devices are essentially classical devices, and measure classical properties such as position and momentum.

6. The correspondence principle of Bohr and Heisenberg: the quantum mechanical description of large systems should closely approximate the classical description.

Furthermore, given that the time-development of the solution to the Schroedinger equation predicts that all possible events will happen (the measurement problem) we need to supplement the above with statements about how we get rid of the unwanted eigenvalues (usually by some 'collapse' process where the Schroedinger equation stops working for a moment). Thus standard QM is fundamentally not consistent (a problem solvable, incidentally, only by granting real physical existence to theory objects).

Now most of these things are philosophical statements about how things are, and one can quite clearly disagree with just about all of them. Let's take, for the sake of [relative] brevity, just the first one:

The wave function represents knowledge of system i.e. the central dynamical object of QM refers exclusively to a human mind. The problem here is the rather preposterous notion that this interpretation is uniquely unburdened by any prior philosophical world view. One then often hears, as here, that the 'standard view is perfectly consistent and free of extraneous metaphysical concepts other interpretations attach to theory. Encumbering QM with hidden variables, multiple worlds, or spontaneous collapse, without any improvement in its predictive power, only gives illusion of a better understanding'. This is just a different, equally philosophical view involving unsupported metaphysical and fundamentally anti-scientific assumptions.

Let's keep going with this idea that the wave function represents knowledge or information about the system:

- Whose knowledge?

- Information about what?

- What about quantum interference? How can terms of a quantum superposition interfere with each other, producing an observable interference pattern, if such a superposition is just an expression of our ignorance?

- QM is supposed to be a fundamental physical theory. As such it should be precise. But if it is fundamentally about information, then it is presumably concerned directly either with mental events - which is weird - or, more likely, with the behaviour of macroscopic variables. But the notion of 'macroscopic' in QM is intrinsically vague.

- Simple physical laws are to be expected, if at all, at the most fundamental level - of the basic microscopic entities - and that messy complications should arise at level of larger complex systems. It is only at this level that talk of information, as opposed to microscopic reality, can become appropriate.

- The very form of the Hamiltonian and wave function strongly points to a microscopic level of description. Why else [tex]\Psi(\bx_1,\bx_2,\ldots,\bx_N)[/tex]?

You can criticize these objections, if you want - sometimes legitimately - but the point is that it is not 'obvious' that the assertions of Copenhagen are the greater truth which other interpretations just add to, as you imply. That's true about the basic instrumentalist assertions of the theory, but that is something else.

[Note before anyone objects: when talking loosely, I am sometimes guilty of this error myself - see previous posts].

"Reality" is a model of phenomena as behaving objects with properties whose values (objective state) are always well defined. Below the level of this model is the phenomena themselves which "happen". In describing those phenomena at the classical level a "reality model" is appropriate but it is still a model. At the quantum level the use of a reality model breaks down and we should stick to the more operational description of the phenomena themselves.

It did in the 1920s. Not any more.

CI does not make assertions about the nature of reality or its absence. CI is not a philosophical theory at all.

Yes it does..

It would be helpful if we distinguished the mathematical wave-function interpreted as CI interprets it as our representation of knowledge about a physical system from the physical wave-function asserted by other "interpretations".

We do. If you like, let the 'wave field' be the thing that exists, and the 'wave function' its mathematical representation. Just to be clear.

Your quotes around interpretations are unnecessary - the word is used in its correct context here.

You are free to go beyond CIQM and assert in addition to the computational wave function a physical one. But understand that you are then going beyond QM into a realm of metaphysics. ... If you wish to talk of such within the realm of science then you should seek empirically testable hypotheses such as means to directly observe pilot waves..

Let's be clear: 'going into the realm of metaphysics' is merely slightly wearying jargon for 'making a clear statement about what exists'. As I have argued in another thread - ['Spooky action at a distance' p. 6 onwards] - for anyone who keeps up with modern developments in experimental physics, the evidence for the fact that 'the wave field exists' (for example) is unequivocal.

In matter-wave optics experiments for example - we find that it is possible to diffract, reflect, focus, interfere, do stimulated emission with the wave field (the thing that is mathematically represented by the wave function). This is clear experimental evidence for the objective existence of the wave. If the wave can be subject to and utilized in such a process, it logically follows that the wave field must exist in order to act and be acted upon.

There is other evidence that particles exist as well (which is why I like the de Broglie-Bohm version of wave-particle duality - waves and particles exist! - then everything puzzling just becomes perfectly ordinary statistical mechanics with a non-classical dynamics) - see the other thread.

I would similarly parse through the remaining points of CI and assert that really the other "interpreters" are not denying the assertions of CI but rather overlaying (for their own reasons) additional "baggage" which for the most part does not add to the predictions of QM.

Yes they are denying them. As well as the knowledge thing, one can dispute Copenhagen assertions such as:

- The uncertainty principle has something fundamental to say about a single experiment, rather than an ensemble of them (e.g. the electron does not actually 'have' a well-defined position and momentum until they are measured.).

- Classical measuring devices measure classical properties such as momentum, and this refers to a property that the quantum object actually had before the experiment was performed (hence the word 'measurement'). [This effectively assumes that mass times velocity is conserved (which it isn't if there is a fundamental non-classical dynamics as in de Broglie-Bohm)].

etc. etc.

Finally I would assert that these other "interpretations" should instead be referred to as "models" unless and until they either contradict or append on to the predictions of QM.

Why? Your only purpose in stating this appears to be asserting the superiority of the Copenhagen interpretation and doing down the people who, quite legitimately, study these other "interpretations", as you call them. Why make them feel small? They probably have wives, children, careers to nurture.. Can't you just let them be happy?

CI is the "shut up and calculate" interpretation.

Not so. And even if it were, so what? Does it want a round of applause? If that's what you're interested in, then why don't you just go and do exactly that, and leave the rest of us to worry about conceptual problems.

My final point (and I apologize for the length of the post): experimental physics is moving on; there are now many suggestions for how to distinguish experimentally between different interpretations. Let's engage with them. It is no longer appropriate to use an old-fashioned interpretation of a theory designed to alleviate confusion in an era 80 years ago when experiments involving quantum objects were incredibly unsophisticated. Let's try to think about what this is all telling us, instead of collectively sticking our fingers in our ears, closing our eyes, and shouting 'MEANINGLESS! MEANINGLESS!' whenever anyone asks what it all means. Bah..

 

[jambaugh]

Hi James,
I think you're off-base here in a number of ways.. You don't even appear to understand what the Copenhagen interpretation actually is - rather you seem to be mixing it all up with the basic instrumentalist assertions of QM and bits of the ensemble interpretation.

Your synopsis below is pretty dead on. The wikipedia article http://en.wikipedia.org/wiki/Interpretation_of_quantum_mechanics" lists three versions. The first "Copenhagen Interpretation, (wave function not real)" is what I think of as the Copenhagen Interpretation as I understand the final version of the discussions between Bohr and Heisenberg.

Cutting and pasting from http://en.wikipedia.org/wiki/Interpretation_of_quantum_mechanics" (we're at that level here):

"An interpretation of quantum mechanics is a statement which attempts to explain how quantum mechanics informs our understanding of nature."

Quite right. And via CIQM we limit our "understanding of nature" to processes and reject the paradigm of objective states of reality (a classical physics concept). QM is a paradigm shift. The derivation of Bell's inequality has nothing to do with locality per se and everything to do with deriving probabilities from a distribution over a set of objective physical states.

This is not to be confused with an instrumentalist description of the theory which:

"relates the mathematical formalism to experimental practice and prediction." (i.e. shut up and calculate).

And prediction is not "informative of our understanding of nature"?

Copenhagen does in fact attempt to make philosophical statements about nature. That is why it is called an interpretation.

Again http://en.wikipedia.org/wiki/Copenhagen_interpretation" [note to moderator: it's hard finding a definitive statement of Copenhagen in the peer-reviewed literature, and anyway, the article is rather good]:

Here are the ideas normally associated with the Copenhagen interpretation:

1. A system is completely described by a wave function ψ, which represents an observer's knowledge of the system. (Heisenberg)

2. The description of nature is essentially probabilistic. The probability of an event is related to the square of the amplitude of the wave function related to it. (Born)

3. Heisenberg's uncertainty principle ... it is not possible to know the values of all of the properties of the system at the same time; those properties that are not known with precision must be described by probabilities.

4. Complementarity principle: matter exhibits a wave-particle duality. An experiment can show the particle-like properties of matter, or wave-like properties, but not both at the same time.(Niels Bohr)

5. Measuring devices are essentially classical devices, and measure classical properties such as position and momentum.

6. The correspondence principle of Bohr and Heisenberg: the quantum mechanical description of large systems should closely approximate the classical description.

Personally I lump 3 and 4 together.

Furthermore, given that the time-development of the solution to the Schroedinger equation predicts that all possible events will happen (the measurement problem)...

Huh??
The Schrodinger equation predicts how the wave function will evolve over time. How that relates to possible events depends on the interpretation. There is no measurement problem in CI since CI does not assert that the wave-function is a physical object.

we need to supplement the above with statements about how we get rid of the unwanted eigenvalues (usually by some 'collapse' process where the Schroedinger equation stops working for a moment). Thus standard QM is fundamentally not consistent (a problem solvable, incidentally, only by granting real physical existence to theory objects).

You are assuming your premise. Only if you grant the wave-function "real status" do you get the inconsistency you need to "cure" with granting the wave-function "real status".
In CI since the wave-function is not real the collapse prescription is just our updating of our representation to fit the newly incorporated data (outcome of a measurement).

You continue to misread CI. You continue to think of the Schrodinger eqn as an equation for the physical evolution of the system. It is an equation for the evolution of our probability amplitudes which represent our knowledge of probabilistic behavior of the system when measurements are made:

1. A system is completely described by a wave function ψ, which represents an observer's knowledge of the system. (Heisenberg)

Here is where you are misunderstanding the CI. Point 1 ! The wave function represents our knowledge about the system.

Now most of these things are philosophical statements about how things are, and one can quite clearly disagree with just about all of them. Let's take, for the sake of [relative] brevity, just the first one:

The wave function represents knowledge of system i.e. the central dynamical object of QM refers exclusively to a human mind. The problem here is the rather preposterous notion that this interpretation is uniquely unburdened by any prior philosophical world view. One then often hears, as here, that the 'standard view is perfectly consistent and free of extraneous metaphysical concepts other interpretations attach to theory. Encumbering QM with hidden variables, multiple worlds, or spontaneous collapse, without any improvement in its predictive power, only gives illusion of a better understanding'. This is just a different, equally philosophical view involving unsupported metaphysical and fundamentally anti-scientific assumptions.

Huh? The wave-function refers to the system but does not model the system. We express our knowledge of the system with a wave-function. We can't do physics without the "We". You still insist that since we update our understanding of what a given system
does by updating our representation of the system that this update is modeling a physical change of the system. No. The break in the Schrodinger evolution is due to the assumption while that equation holds that no measurement is being made.

Here's another analogy. I'm watching my stock ticker right now. I see a stream of transactions for a given stock at various prices. Sometimes the ticker slows and there's several seconds between transactions. The value of the stock between ticks is not perfectly well defined but we can assume that this value will be close to the last transaction price. As time passes without an update our assumption weakens and the probabilistic expectation value of how far away the next transaction will be from the last grows. We could model this and write a "wave" equation. Once a new transaction ticks we "collapse" this growing uncertainty because we have new data. Nothing mysterious or unreasonable in this provided we understand our representation to be encoding our knowledge about how the stock will behave and not assume this representation is describing some physical model of what the stock is.

Let's keep going with this idea that the wave function represents knowledge or information about the system:

- Whose knowledge?

Whose wave-function?

- Information about what?

The system. If you like "the system of phenomena" e.g. an electron or a photon or an ensemble of photons or a cavity with varying number of photons. But like the two physicists discussing the geometry of space-time I am using nouns here loosely... best to stick with "system of phenomena" or simply "the quantum".

- What about quantum interference? How can terms of a quantum superposition interfere with each other, producing an observable interference pattern, if such a superposition is just an expression of our ignorance?

We see interference in the evolution of the wave function and the wave function tells us probabilistically where we are likely to see the quantum if we choose to measure position.
But the interference we see is not in quality the same as what we see with classical waves. By the same token by virtue of seeing the interference, or by seeing e.g. diffraction we are not observing a classical point particle when we make a position measurement.

One can speculate and/or theorize as to deeper physical processes. But at the level of the quantum mechanics of the electron in a two slit experiment it is sufficient to describe its behavior. That is what the QM of an electron is doing. Picking an ontological model of pilot wave + point particle is at this stage speculation. Viewing the electron as an excitation of a quantum leptonic field is delving a little deeper. But in so doing you are expanding the system and along with it the set of observables. You get testable predictions beyond the single electron QM and thus you are theorizing. And I suspect you get more as yet unexplained (in the sense of the ontological interpretation you seek) phenomena.

- QM is supposed to be a fundamental physical theory. As such it should be precise.

The only "should" of a physical theory is that it be maximally descriptive. Precision is desired but not a criterion. The ultimate "moral" value in physics is the empirical correspondence and if we don't see precision we shouldn't impose it to fit our personal opinions of what the natural world ought to be.

But if it is fundamentally about information, then it is presumably concerned directly either with mental events - which is weird - or, more likely, with the behaviour of macroscopic variables. But the notion of 'macroscopic' in QM is intrinsically vague.

It is fundamentally about information because fundamentally empirically based knowledge is about information. (CI)QM is the first time we've been "forced" to acknowledge and account for the two way action-reaction nature of the measurement process. It is not about weird "mind over matter" but about hard scientific "matter over mind". What we know is derived from what we see. How we look thus affects what we know. And not looking should be acknowledged as ignorance. Since we cannot (both practically and it would seem fundamentally due to physical limitations) look with infinite precision at all variables we must acknowledge in our representation of the system that our representation contains a fundamental component of ignorance. We thus I.) should use a description which quantifies ignorance namely probabilistic and II.) should limit our interpretation of that description to a prediction of what occurs when we actually do derive knowledge directly from the system i.e. the physical interactions we classify asmeasurements.

- Simple physical laws are to be expected, if at all, at the most fundamental level - of the basic microscopic entities - and that messy complications should arise at level of larger complex systems. It is only at this level that talk of information, as opposed to microscopic reality, can become appropriate.

I don't see by what heuristic you expect this. Messy, complicated, these are human values not Natures. We hope for simple physical laws but why should nature oblige us? She couldn't care less whether we understand or not.

- The very form of the Hamiltonian and wave function strongly points to a microscopic level of description. Why else [tex]\Psi(\bx_1,\bx_2,\ldots,\bx_N)[/tex]?

You'll have to elaborate on how it so points. I don't follow. As a side note the wave-function or more generally the Hilbert space vector is not the most descriptive format. We can be more precise (about our level of knowledge about the system) by using density (co)operators because they allow for less precise knowledge about the system itself.

You can criticize these objections, if you want - sometimes legitimately - but the point is that it is not 'obvious' that the assertions of Copenhagen are the greater truth which other interpretations just add to, as you imply. That's true about the basic instrumentalist assertions of the theory, but that is something else.

CI as I have framed it (unreal wave-function) makes minimal assertions about nature while retaining the predictions of the quantum theory(ies). It makes value judgments about going farther but these are assertions about us not about physical nature.

[...]We do. If you like, let the 'wave field' be the thing that exists, and the 'wave function' its mathematical representation. Just to be clear.

Very nice clarifying semantics. Yes let's adopt it hence and I'll try not to forget to use it.

Let's be clear: 'going into the realm of metaphysics' is merely slightly wearying jargon for 'making a clear statement about what exists'.

Be careful. Existence can be understood in two contexts. Existence of an object with objective state of reality (ontological existence) and Existence of processes which may or may not have an underlying ontological description. I like the way my thesis advisor distinguished these points. He distinguished reality (ontological "what is") from actuality (phenomenological "what happens").

The language of phenomena (or of process) is richer and includes the subset of categorical phenomena for which an underlying objective description is possible. But this is not a proper subset and there are possible phenomenological descriptions which have no (complete) objective descriptions. In order to embed such phenomenological descriptions in an objective description we must multiply without bounds the number of objects and thence the set of possible phenomena. (as occurs most strikingly in MWIQM)

As I have argued in another thread - ['Spooky action at a distance' p. 6 onwards] - for anyone who keeps up with modern developments in experimental physics, the evidence for the fact that 'the wave field exists' (for example) is unequivocal.

I recall visiting your reference and I didn't see unequivocal evidence. Only practical utility in computational methods. Let me revisit it again and get back to you.

In matter-wave optics experiments for example - we find that it is possible to diffract, reflect, focus, interfere, do stimulated emission with the wave field (the thing that is mathematically represented by the wave function).

Until and unless you directly observe "it" you cannot say "it" refracts/reflects/etc. This adds nothing to the debate that wasn't there when "it" interferes or "it" diffracts.

This is clear experimental evidence for the objective existence of the wave. If the wave can be subject to and utilized in such a process, it logically follows that the wave field must exist in order to act and be acted upon.

You feel this is unequivocal but I will debate it. Let's start with whether phonons exist. We can completely describe the quantized dynamics of a crystal via the dynamics of the electromagnetic fields and of the electrons and nuclei. And yet when the crystal is cool enough we can ignore most of this dynamics and resolve the quantized vibrations into "phonons". Do the wave fields of the phonon suddenly pop into existence since we choose this description?
[/QUOTE]

Well I'm running out of steam with this one reply and have not finished with all points. And I see an exponential growth in posts if we don't break things up. So let's do this.

First we need to come to some agreement about what CI says. Or more precisely reconcile what each of us means by "CI" and also what each of us feels is the "correct" interpretation of QM. Until then debating merits hazards endless cycles of semantic precession.

It might even be better to start fresh and reconstruct various interpretations from their basic premises so we can be absolutely clear. I'd suggest say three state modal logic on descriptions of premises "assert" vs "deny" vs "agnostic/irrelevant".

I do sincerely want to make progress in both our understandings rather than just "win an argument".

 

[jambaugh]

I'm going to take a moment and elaborate on my understanding of both classical and quantum mechanics. At this stage I don't want to invoke either forms of field theories. I think it will be helpful in discussions of interpretations of QM (which also require at least in the correspondence principle reference to CM) to have a compatible understanding of what the theories themselves are as a class.

Classical and Quantum Descriptions
---Classical Description---
In classical mechanics we utilize a state manifold S to express the kinematic configuration of a physical system. Coordinates for this manifold correspond to a complete set of physical observables and functions over this state manifold are likewise observables.

Example: Canonical phase space of a particle in the absence of gauge degrees of freedom.
Example: The constraint manifold in the extended phase-space of gauge systems corresponding to a given gauge condition or equivalently the quotient manifold of this extended manifold modulo the gauge orbits.

The possible dynamics of a classical system is then expressed by the Noetherian dual to each observable, a generator of the symmetry associated with conservation of that observable. This is embedded implicitly in the canonical Poisson bracket for the phase-space of a non-gauge system as well as in the Dirac bracket for gauge constrained systems.

But in essence we have a mapping:
[tex] \mathbb{R}^S \to \mathop{\text{Diff}}(S)[/tex]
e.g. for particles:
[tex] p \mapsto [[p,\bullet]] = \partial/\partial x\,\bullet[/tex]
(modulo sign conventions and order conventions.)
We can construct a Hamiltonian from the observables expressing the time evolution of the system i.e. what states later observers see which we associate with the observable of energy.

We can also start with an action functional and action principle which is to say construct the dynamics from a geometry on the state manifold. However ultimately we have a Lie algebra/group of transformations on the manifold of states, a prescription for associating each generator of the Lie algebra with an observable and the determination which observable corresponds to the time evolution (what is the energy as a function of a given complete set of observables).

In short Kinematics = representation of state, Dynamics = Transformation of states and observables.

---Quantum Description----
In quantum theory we begin with the correspondence principle which applies to the observables. However we more closely represent the observables with their associated Noetherian generators. We embed the Lie algebra in an associative algebra with Lie product corresponding to the commutator product (paralleling the canonical embedding of the Lie algebra in a canonical algebra with Poisson bracket.)

To be explicit I will refer to a generic observable with a Roman letter and the Lie generator with a Delta subscript Letter, e.g.:
[tex] X \sim \Delta_X[/tex]
thus for example the time evolution of an observable is expressed via:
[tex] \frac{d}{dt}X = \Delta_H(X)[/tex]
where H is the Hamiltonian.

Again we have the Hamiltonian constructed from observables but with more care in resolving the non-commutativity in the algebraic representation (e.g. where xp is in the classical Hamiltonian we might try the correspondent to xp/2+px/2 ). Again the dynamics will express the evolution of observables.

We may describe the expectation values for observables with co-operators which are linear functionals on the space of operators in the algebra. These are the density (co)operators.
[tex]\rho(X) = \langle X \rangle[/tex]
This gives us a representation of our knowledge about what observed values we are likely (which includes the case of certainty) we are to observe given values. We then get a dual representation of the transformations associated with the observables acting on the co-operators. This tells us how our expectation values evolve as the system evolves dynamically.

Note that at this stage I have not mentioned what values for observables we may actually see, only expectation values. In order to express this we invoke the eigen-value principle which we can derive from necessary behavior of observables. Immediate sequential measurements of the same observable on a given system must yield identical results for the "observable" concept to be meaningful.

Observing how this manifests on the transformation of density co-operators when a specific observable is a component of the Hamiltonian and noting that not only the direction of transformation but the rate is germane we can derive the eigen-value principle:

Given a physical system has observed value x for observable X then its density operator representation must be an eigen-vector a la:
[tex]\Delta_X(\rho_x) = \lambda \rho_x[/tex]
and further the eigen-value must be proportional to the value of the observable in order for observables to transform properly:
[tex]\Delta_X(\rho_x) = \eta x\rho_x[/tex]

Finally for consistency (again in the transformations of observables) this proportionality constant must be universal within the representation i.e. not dependent on the choice of observable.

From here we find that the structure of the operator algebra and its co-operator algebra we get all physically predictable quantities including the spectrum of the observables up to dimensional factors and the proportionality constant (essentially Planks constant plus algebra normalization. We can always choose units wherein this constant is one or the imaginary unit i depending on how we wish to express the operators associated with observables.)

Now it is convenient to express the eigen-value principle in terms of left and right ideals of the algebra but this is not necessary nor is it the more general representation of our possible level of knowledge/ignorance about a given class of systems.

Note that from this prescription we can also derive both the uncertainty principle and the born probability formula with little additional addenda for the latter case. We must describe how ensembles of independent systems considered together as a single meta-system is to be represented. It is sufficient to require that their independence implies that their respective observables mutually commute and thus the composite algebra is the tensor product of component algebras. One can then calculate the expectation value for the frequency of a given measurement of the component systems with identical prior knowledge assumed about each as well as the degree of uncertainty in that frequency. In the limit it will approach the value given by the Born probability formula. One is effectively constructing the co-coproduct on the co-operators.

[tex]Pr(X=x|Y=y) \propto (\rho_x^* \cdot\rho_y^*)^*(\mathbf{1})[/tex]
where * is the vector space dual mapping and which (rhs) we usually write as:
[tex]Tr(\rho_x\rho_y)[/tex]
(Note there is a lot of detail hidden in the * mapping and the associative product.)

Now this is as I see it the structure of the theory in general with the Devil being in the details of the representation of a given class of systems. This gets further complicated with quantization and statistics and gauge degrees of freedom.

I think I will writeup a more detailed exposition in the form of a latex article (including my asserted derivations). But that may take some time. What I would like now is critiques of my exposition of the theory and the instrumental interpretation of the formulation without reference to any further interpretation a la CI vs MW vs BPW etc.

 

[Demystifier]

CI is the "shut up and calculate" interpretation.

Either this statement is wrong or you are not an adherent of CI.
Namely, someone who writes so much about CI is certainly not an adherent of the "shut-up" approach.

Anyway, thank you for your detailed and interesting explanations!

 

[jambaugh]

Either this statement is wrong or you are not an adherent of CI.
Namely, someone who writes so much about CI is certainly not an adherent of the "shut-up" approach.

Anyway, thank you for your detailed and interesting explanations!

The "shut-up" applies when one is doing QM. Discussions of QM are another matter.

 

[maverick_starstrider]

In matter-wave optics experiments for example - we find that it is possible to diffract, reflect, focus, interfere, do stimulated emission with the wave field (the thing that is mathematically represented by the wave function). This is clear experimental evidence for the objective existence of the wave. If the wave can be subject to and utilized in such a process, it logically follows that the wave field must exist in order to act and be acted upon.

Hey, could you possible post a link or just the reference numbers of some of these papers? They sound like a good read (assuming I skip over the method/apparatus stuff)

 

[zenith8]

Hey, could you possible post a link or just the reference numbers of some of these papers? They sound like a good read (assuming I skip over the method/apparatus stuff)

Hello Mr. Starstrider. Sorry for the delay in replying - I was out of town.

Here are some relevant references:

"Phase coherent amplification of atomic matter waves" S. Inouye et al Nature 402, 641 (1999)

"Phase coherent amplification of atomic matter waves" M. Kozuma et al
Science 286, 2309 (1999)

"The magic of matter waves", W. Ketterle in MIT Physics Annual 2001, Massachusetts Institute of Technology, Cambridge MA.

"Raman amplification of matter waves", D. Schneble, Phys. Rev. A 69, 041601 (2004)

"Atom nano-optics", V. Balykin et al, Optics and Photonics News, March 2005 (45).

 

[maverick_starstrider]

Much obliged.

 

[jambaugh]

I've experienced hardware failure on my PC and am waiting for parts to upgrade my machine. Apologies for my absence.

Quick note. Observing diffraction, refraction, et al is no different in principle than the original double-slit diffraction of the electron. It doesn't imply a separate Bohmian pilot wave. The electron itself is being Q-diffracted. But note one still only sees in a single instance of such experiments a single electron go "bing" (or not) on the detector.

The issue is one of relativity of the classical description e.g. of the path of the electron-particle or of the diffraction of the electron-wave. Any "absolute reality" description of the process within experiments will lead to conceptual paradoxes in the same way that absolute time descriptions of relativistic twins leads to conceptual paradoxes. Just as we must in SR unlearn our instinctual concept of absolute time and treat time operationally (what a given clock reads) we must in QM unlearn our instinctual concept of absolute state and treat the system operationally (what a given measurement reads).

As in the case of SR you can reject the relativity concept by invoking unobservable extra components namely the aether, you can likewise reject the logical relativity of QM and invoke unobservable extra components e.g. pilot waves or multiverses. But doing so adds nothing to the theory and further obfuscates the physics of the system itself. One in particular must invoke highly questionable one-way coupling between these invisible components and the observable system.

Feel free to speculate about the aether or the pilot waves and see if you can indeed "stabilize" these one-way couplings in a theory which then would make the "invisible" visible. But you are then no longer interpreting the given theory but creating a new speculative one. Propose an experiment distinguishing them and you'll rake in the fame and $$$'s. But don't call it an interpretation of the prior theory.

 

[kote]

In matter-wave optics experiments for example - we find that it is possible to diffract, reflect, focus, interfere, do stimulated emission with the wave field (the thing that is mathematically represented by the wave function). This is clear experimental evidence for the objective existence of the wave. If the wave can be subject to and utilized in such a process, it logically follows that the wave field must exist in order to act and be acted upon.

Unfortunately, saying that something logically follows doesn't make it true. It is not valid to say that if a theory makes accurate predictions then its theoretical structures must exist as basic elements of reality. Anything except for the math itself is arbitrary to the predictive value of a function.

Use the same math but call it the God function instead of the wave function. Waves aren't causing these phenomena to occur, this is just the pattern that God follows when redirecting particles in space. Have I just proven the existence of God and his active involvement in physics?

 

[Demystifier]

Quick note. Observing diffraction, refraction, et al is no different in principle than the original double-slit diffraction of the electron. It doesn't imply a separate Bohmian pilot wave. The electron itself is being Q-diffracted. But note one still only sees in a single instance of such experiments a single electron go "bing" (or not) on the detector.

The issue is one of relativity of the classical description e.g. of the path of the electron-particle or of the diffraction of the electron-wave. Any "absolute reality" description of the process within experiments will lead to conceptual paradoxes in the same way that absolute time descriptions of relativistic twins leads to conceptual paradoxes. Just as we must in SR unlearn our instinctual concept of absolute time and treat time operationally (what a given clock reads) we must in QM unlearn our instinctual concept of absolute state and treat the system operationally (what a given measurement reads).

As in the case of SR you can reject the relativity concept by invoking unobservable extra components namely the aether, you can likewise reject the logical relativity of QM and invoke unobservable extra components e.g. pilot waves or multiverses. But doing so adds nothing to the theory and further obfuscates the physics of the system itself. One in particular must invoke highly questionable one-way coupling between these invisible components and the observable system.

Feel free to speculate about the aether or the pilot waves and see if you can indeed "stabilize" these one-way couplings in a theory which then would make the "invisible" visible. But you are then no longer interpreting the given theory but creating a new speculative one. Propose an experiment distinguishing them and you'll rake in the fame and $$$'s. But don't call it an interpretation of the prior theory.

I must admit, it is a very reasonable attitude.

 

[zenith8]

Unfortunately, saying that something logically follows doesn't make it true. It is not valid to say that if a theory makes accurate predictions then its theoretical structures must exist as basic elements of reality. Anything except for the math itself is arbitrary to the predictive value of a function.

Use the same math but call it the God function instead of the wave function. Waves aren't causing these phenomena to occur, this is just the pattern that God follows when redirecting particles in space. Have I just proven the existence of God and his active involvement in physics?

Look mate, you're coming at this from the wrong angle. I'm not talking about theory or math. I'm talking about experiments.. The matter-wave optics experiments clearly show us that something exists which behaves exactly like a wave, in that it obeys a principle of superposition producing interference patterns, diffraction patterns, it can be amplified etc. etc.

Now if you want to attach a theory to that - which was your idea, not mine - then one finds the wave in question obeys a wave equation, namely the Schroedinger wave equation. That might be useful in order to design better wave-optics apparatus, for example, but it's got nothing to do with my point.

So now you're probably going to say that just because it does everything a 'real wave' does then that doesn't prove such a wave actually exists. But then you could say that about anything in physics, not just QM - and you're veering dangerously close to solipsism.

 

[zenith8]

I must admit, it is a very reasonable attitude.

Come on Demystifier, you can do better than that... are you tired today?

 

[Demystifier]

Come on Demystifier, you can do better than that... are you tired today?

Yes, I am tired of criticizing weak measurements in QM in last few days. (Have you seen that?) Compared with the "mainstream" interpretation of weak measurements, the orthodox interpretation of QM (such as that of jambaugh) is extremely reasonable.

In fact, I do not deny that many other interpretations have some merits. And jambaugh clearly expressed those of the orthodox one, which I respect. Of course, the orthodox interpretation also has some disadvantages and jambaugh have not mentioned them. Nevertheless, I think he is very clever so I believe that he is aware of them too. (Just as I am aware that the Bohmian interpretation also has some disadvantages.) But that's why we are here, to discuss advantages and disadvantages of the imperfect interpretations we like or dislike for various objective and subjective reasons.

Let me make an analogy. When Boltzmann argued in 18th century that thermodynamics is a consequence of motion of little molecules (which were hidden variables at that time), Mach (as well as most of the physics establishment at that time) strongly criticized such a theory. Later, it turned out that Mach was wrong. Nevertheless, the arguments of Mach was very reasonable at that time. And so are the arguments of jambaugh at this time.