Wikipedia comparison of interpretations of QM

[greypilgrim]

Hi,

I'm studying
http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics#Comparison_of_interpretations
but have trouble with the apparent differences of the key concepts:

* deterministic - unique history
* wavefunction real - hidden variables - counterfactual definiteness

I thought that all terms in one of the above lines mean the same, or very similar and consistent concepts, but in the table I can always find interpretations where they don't agree. In what way do they differ?

 

[Quantumental]

Deterministic unique history = de-Broglie Bohm
Deterministic WF is real = MWI

 

[bhobba]

Deterministic - has its usual meaning - some interpretations like DBB and MWI only have probabilities entering into it in a derived sense like they enter into statistical mechanics - its not fundamental - in others like the Ensemble interpretation and Copenhagen its fundamental.

A unique history is relevant to MWI and similar interpretations which has many histories happening simultaneously - with most there is only one - hence unique. The Wikipedia article suggests Consistent histories doesn't have unique histories - I think its a bit more subtle than a yes or no answer to that in that interpretation - its clouded by its concept of frame-work.

A wavefunction can be interpreted as real like say an electric field (eg MWI, DBB) or simply as a device to help in describing the outcomes of observation like probabilities are in probability theory eg the Ensemble Interpretation and Copenhagen.

Hidden variables are things, not directly measurable, that are introduced into interpretations to give them aspects those that introduce them like eg in DBB a pilot wave is introduced to keep our usual view of reality existing independent of us.

Counterfactual definiteness is a bit more subtle and I will simply give a link to it.
http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Counterfactual_definiteness.html

Thanks
Bill

 

[greypilgrim]

Thanks, that helps me a lot.

Still a few unclarities:

1. How can a theory be deterministic, but not have hidden variables? Many-worlds and many-minds are apparently of this kind. In a theory that allows to tell the future from the current state, all information has to be somewhere, right?

2. In what way is an electric field more than a device to help in describing the outcomes of measurements? I mean we cannot measure an electric field, but only how it acts on charges. How does that differ from the Ensemble or Copenhagen interpretation of the wavefunction?

3. What about "realism", e.g. used in "local realism" in Bell context. It's not written explicitely in the table. Is "realistic theory" = "hidden variable theory" or "realistic theory" = "wavefunction real", or is it something different? I might be confusing "real" and "realistic" here.

 

[bhobba]

All actually deep questions.

In MWI, and if you want the detail you will need to read articles on it, the wavefunction of the entire universe simply evolves deterministically. Observations are associated with decoherence and each world as a result of that simply keeps evolving. For more detail see:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

In EM theory it is assumed the field is a real thing that pervades space - its required to conserve momentum and energy. If fields weren't real when radio waves for example radiate you need somewhere for the energy to go - it is assumed to reside in the fields. Its an interesting fact, first figured out by Feynman, that you can formulate EM without fields as a real thing - but sort of a bookkeeping device on how particles interact - but the resulting theory is rather wacky having weird stuff such as influences traveling back in time - and we do not have conservation laws in the usual sence:
http://physics.fullerton.edu/~jimw/general/
'Wheeler-Feynman absorber theory was developed as an "action-at-a-distance" explanation for electromagnetic radiation reaction forces (based on earlier work by Dirac). In action-at-a-distance theories "fields" have no real existence apart from the interacting sources. And radiation reaction, instead of being assumed a force produced by a charge acting on itself in the process of launching radiation, is explained as a seemingly instantaneous interaction between a local accelerated charge and the distant matter in the universe (the "absorber") mediated by retarded and advanced disturbances. Fields are just book-keeping devices for the (delayed) interaction of sources. Wheeler-Feynman theory works very neatly.'

But possibly even worse, despite trying for ages, he could never figure out a quantum version. It would seem fields are necessary for consistency and to have a 'reasonable' view of the world. The same with some interpretations of QM - the wavefunction is assumed real. You can't prove it is - that's why its called an interpretation - but those that advocate it use the assumption to give the particular world view that appeals to them.

Realism has a meaning at a number of levels. In relation to QM it usually means the existence of a quantum world out there independent of observation. Local realism means realism and locality.

Thanks
Bill

 

[kith]

1. How can a theory be deterministic, but not have hidden variables? Many-worlds and many-minds are apparently of this kind. In a theory that allows to tell the future from the current state, all information has to be somewhere, right?

All information is contained in the wave function of the universe but not all questions are sensible. It doesn't make sense to ask "what is the spin of the electron?" after a measurement if there are two worlds each of which includes one possibility. The question makes only sense if it is asked from within a world.

2. In what way is an electric field more than a device to help in describing the outcomes of measurements? I mean we cannot measure an electric field, but only how it acts on charges. How does that differ from the Ensemble or Copenhagen interpretation of the wavefunction?

The wavefunction is complex while the electromagnetic field is real. So you cannot measure the wavefunction by by its action on a testparticle. Also, the influence of a changing wavefunction at one place may have an instantaneous effect on the wavefunction at another place.

3. What about "realism", e.g. used in "local realism" in Bell context. It's not written explicitely in the table. Is "realistic theory" = "hidden variable theory" or "realistic theory" = "wavefunction real", or is it something different? I might be confusing "real" and "realistic" here.

If you consider the MWI to be realistic (as I do), "realistic" is broader than "hidden variables". The recent PBR theorem states that "realistic theory" => "wavefunction real". Also I think there is no difference between real and realistic.

 

[greypilgrim]

Counterfactual definiteness is a bit more subtle and I will simply give a link to it.
http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Counterfactual_definiteness.html

I know how to derive the Bell inequality assuming a hidden variable and locality. However this link says that counterfactual definiteness together with locality leads to the Bell inequality. How does one derive this?
And doesn't this also imply that hidden variables and counterfactual definiteness are something very similar?

 

[bhobba]

I know how to derive the Bell inequality assuming a hidden variable and locality. However this link says that counterfactual definiteness together with locality leads to the Bell inequality. How does one derive this? And doesn't this also imply that hidden variables and counterfactual definiteness are something very similar?

No it doesn't. For example looking at it very carefully Feynmans Sum Over Histories approach is a hidden variable interpretation but of a rather non trivial type. Hidden variables are simply things that are not directly observable an interpretation uses - conterfactual definiteness is the ability to speak meaningfully about measurements you haven't performed.

Since in Counterfactual Definiteness you are talking about properties independent of measurements you haven't performed that is one of the key assumptions in deriving Bells inequality:
http://www.drchinese.com/David/Bell_Theorem_Easy_Math.htm
'I call this assumption "Bell Reality". And... this assumption is the equivalent of assuming that the moon is there when no one looks.'

You seem to be getting hung up on the definition of terms. That's usually a philosophers game. In physics and applied math people are not usually that pedantic being a bit looser and using context to work out meaning.

Thanks
Bill