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There is some current work on interpretations of quantum mechanics. How do you think can interesting results in that area help physics? Can it change quantum physics or make it easier? Which interpretation has to potential to change practical QM calculations? I mean if MWI turns out the best, then so what? It neither provides more intuition nor makes it calculations easier.

If there are axioms and QM is derived from these, is there any practical value from this mathematical approach? I thought a statement like "it's the only mathematically consistent solution to the axioms", would provide no practical value?

How is knowledge about QFT important to interpretations of QM or is QFT merely a handy mathematical framework?

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FYI: MWI may not be that useless. DavidZaslavsky proved(not exactly proved) something I'd asked on chat using MWI. According to him, the normal proof would be quite tedious.So I guess it has its uses... – Manishearth♦ Mar 7 '12 at 13:26
If I remember correctly I basically used MWI to make it seem more intuitively understandable, but I highly doubt that the actual result would be any different in any other interpretation. That's basically what the different interpretations are good for: sometimes it's easier to figure something out using one or the other, but the actual result doesn't depend on which you use. (Like the different branches of string theory/M-theory) – David Zaslavsky♦ Mar 7 '12 at 23:36
By the way, Gerenuk, try to avoid "What/How do you think...?" questions. A question that invites people's individual opinions is usually not the best fit for this site. – David Zaslavsky♦ Mar 7 '12 at 23:37
@Zaslavsky: Sure, but it's up to the reader to read the full question with all explanations. I could add: Does any of the interpretations potentially help advancing technology? That's all what matters really, unless you are researcher who is getting paid. It's about practicality and results and not fancy mathematical frameworks which lose imaginability of reality. – Gerenuk Mar 8 '12 at 9:39
What "new interpretations"? I dispute that there are any new interpretation. The last significant work on this was in the 1980s, perhaps earlier. Perhaps you mean things like what 'tHooft is doing, which is not supposed to be an interpretation, but a new theory. – Ron Maimon Aug 24 '12 at 19:43
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Different viewpoints might highlight different aspects of quantum mechanics. In this way they may provide a starting point to extend quantum mechanics or deepen our understanding of related theories (specially the relationship between classical and quantum mechanics). Let me give you some examples of recent reformulations of quantum mechanics and their importance.

Feynmann path integrals: They provide the reinterpretation of transition probabilities being the 'sum' over all possible paths connecting the initial and the final state. Without this reformulation of qm and the associated Lagrangian-techniques much of QFT would be ridiculous to formulate/calculate.

Geometric quantum mechanics: In this language ones identify all the rays of hilbert space and considers the resulting infinite dimensional manifold (the quantum phase space). By doing this, one can find some 'axioms', which characterize the quantum phase space (these are not axioms in the general meaning; they are more or less properties of the manifold and it is not yet proven, that they define it uniquely). Then one can examine weaker axioms and so extend quantum mechanics in some way. (I think extending a existing theory is the most profound intension behind axiomatization.) See eg http://arxiv.org/abs/gr-qc/9706069

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Can you think of interpretation which potentially could make the most difference? Does QFT offer any insights into the simple double slit experiment? I mean saying the particle considers all paths and then behaves accordingly is even less intuitive than non-locality etc?! Later I'll have a look at geometric QM. But at first glance it seems like mathematical reformulation which makes is mathematically nicer but physically less understandable?! – Gerenuk Mar 8 '12 at 8:55
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Interpretations make no difference at all to practical quantum mechanical (QM) calculations. However, they affect a lot how QM is taught and hence how it is understood. Better interpretations would imply less confusion, faster understanding, more conceptual clarity, and therefore correct understanding for more people.

Axioms can be extremely useful if they are clear and simple, as they allow one to get to the heart of a concept without much ado. (Compare the beauty and simplicity of special relativity with the situation in quantum mechanics.)

Quantum field theory (QFT) is QM applied to fields. Thus it is part of QM, though for technical reasons it is usually treated separately. A knowledge of some QFT is extremely helpful when doing statistical quantum mechanics. Also, the particle concept is far less paradoxical when one keeps in mind that from the point of view of QFT, particles are just localized excitations of the corresponding field.

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Is there really no interpretation which one day would make calculations better? What is the easiest QM interpretation to teach? What are axioms good for if the imply derivations which you cannot follow in physical understanding? OK, I see where QFT is used. But I guess it will not make the double slit experiment physically more intuitive? – Gerenuk Mar 8 '12 at 10:16
Calculations simplified over the years; but this has nothing to do with interpretation - which is about the meaning of what you calculate. - QFT makes double slit experiments indeed more intuitive, as everything becomes local when the photon is not regarded as a particle. See my FAQ page mat.univie.ac.at/~neum/physfaq/topics/doubleSlit.html - The easiest interpretation to teach is the statistical interpretation, though it has limitations as we now can routinely measure single systems where there is no ensemble anymore. – Arnold Neumaier Mar 8 '12 at 11:12
I feel that interpretation makes a difference regarding how to figure out what "in reality" is to be modelled by what mathematical objects. (On that note, I can't say I have clear picture about how that's done, it mostly seems like trial and error to me.) – Nick Kidman Aug 23 '12 at 20:01
@NickKidman: I rather think that what is modelled by what is a matter of matching experimental data to theories in the most parsimonious way. On the other hand, interpretations explain (often after having created a good theory), what intuitive meaning should be given to the mathemtical ojects used in the theor, in order that intuitive reasoning may support the understanding of the formal side, and sometimes lead to useful generalizations, or adaptations of the models to different situations. – Arnold Neumaier Aug 26 '12 at 9:59
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The most interesting development in interpretations of QM would be a true resolution of the EPR paradox, which most people either completely fail to understand, or choose to ignore the consequences of. After Bell's theorem, we have to accept that our world is non-local. Yet, what does this mean for relativity? What I hope to see, is a new theory which accounts for the non-locality in a relativistic way (e.g. there has to be the same causal description for all frames, something which is lacking in the current description), that is what Bell hoped for, and I conclude with a quote:

"During a colloquium organized in the CERN on January 22, 1990, John Bell has been asked whether he thought that relativity and quantum mechanics could be incompatible. John Bell answered:

"No, I can't say that, because I think someone will find one day a way to demonstrate that they are compatible. But I haven't seen it yet. To me, it's very hard to put them together, but I think somebody will put them together, and we'll just see that my imagination was too limited."

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there is a true resolution of the EPR "paradox"; it is given by correctly interpreting measurements as entanglements between systems and observers; all measurement results exists, conservation of the global invariants makes sure which observer superpositions are allowed and which are not – lurscher Aug 23 '12 at 19:52
@lurscher: While I agree with you within standard QM, the idea people have when making these types of statement is that it goes without saying that you have realism, meaning that all the results of experiments are determined in advance. People think this is so obvious that they don't even question it philosophically, although it isn't true in standard QM or in standard interpretations. – Ron Maimon Aug 24 '12 at 6:23
@RonMaimon, i think that realism is nothing but the new geocentrism; 'here and now is the only thing real' is its dogma. But i guess everyone is entitled to their religion, as long as it is not confused with physics – lurscher Aug 24 '12 at 15:51
@ Lurscher, you fall precisely into category 1: those who have completely failed to understand the essence of Bell's theorem. Please see Bertlemann's socks. What is really interesting is how one can combine non-locality with the revolutionary idea that there can never be agreement on the simultaneity of spacially separated events. – user7348 Aug 24 '12 at 18:23
This answer is a bit of a politician's answer--- anyone can read anything they want. What is this "essence of Bell's theorem"? That signals go faster than light? What is it precisely? The Bell quote is replying to a vague question--- he probably means precisely special relativity is incompatible with hidden-variable quantum mechanics. This is because Bohm is naively incompatible with relativity, although if you formulate the right variables, it is not clear at all. On questions like this, it is best not to be vague. – Ron Maimon Aug 24 '12 at 19:51
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One could conjecture that two physically significant differences might show up in the near future, between rival interpretations. a) How quantum noise reacts as people try to scale up quantum computers. The physical basis of quantum noise is something that might depend on these seemingly philosophical differences. b) decoherence says that quantum measurement depends on a physical interaction with the environment as a kind of thermodynamic reservoir; rival interpretations differ. If the rapidity of decoherence and the noisiness of quantum measurements at the mesoscopic scale were studied under different conditions of shielding from the environment, it might, conceivably, allow of deciding between rival views. Most measurement apparatuses rely on the electromagnetic force for coupling the apparatus to the micro-system being measured. This same force is the main coupling with the environment. In theory, people such as Bohr have sometimes tried to imagine a measurement apparatus based on gravity as a coupling. Now, this would be of no use for discriminating between the rival theories, since gravity also couples to the environment equally. But if a measurement apparatus were based on, say, nuclear spin interactions, then the coupling with the microsystem could possibly be arranged to be much stronger than the coupling to the environment. As far as I can tell, very few people have concerned themselves with this, so far. (And the conjectures I throw out here are not worth very much, but are only meant to be provoking.)

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