ZapperZ said:
Or what about 3) that collective phoenomena cannot be deduced from knowledge at the reductionism level. This is different than your Point 2, because to be able to say that
There is something potentially misunderstandable here.
To make it clear, this knowledge is NOT practical knowledge on how to handle the formidable mathematical problem. The knowledge is just the axioms of "reductionist" physics at an appropriate level (say, non-relativistic quantum mechanics). So, in the case of condensed matter, it is the masses, charges and spins of the nucleae, the charge and spin of the electron, the EM interaction (maybe treated semi-classically, maybe some elements of QED have to be included).
In that case, I don't understand what you mean by "point 3)" because my points 1) and 2) are logically complete:
point 1) says that the fundamental laws as we know them, are responsible for the collective phenomena
and point 2) says that they aren't.
I don't see room for a point 3), except if it would mean some necessary change in our understanding of our fundamental "reductionist" laws, but that brings us back to point 1) ! We then simply didn't have the correct laws to start with, then, and once we're using the correct ones, we ARE back in the reductionist scheme.
It is just that accounting for all of them, as "fully" as one can, doesn't mean you can get to the collective phenomena. Again, I have mentioned this earlier, that at this point, we are in a similar stage as the EPR-type experiment before Bell.
I don't see the relationship with Bell. Before Bell, people thought that there was always the possibility of an underlying classical, deterministic theory that explained their QM probabilities.
Bell cleared out the following issue: "in order to have an underlying deterministic, classical theory that produces the same probabilities as QM, your deterministic, classical theory must contain non-local interactions".
So it suddenly became interesting to look at those specific cases of QM predictions where Bell's theorem explicitly entered in action. Well, it became interesting (just as a matter of principle) to verify QM also in those predictions. But in fact, if you thought QM was a correct theory, you didn't even have to do those experiments. Bell's result only made it a bit harder to deny superposition on a macroscopic scale, as a modification of QM.
I don't see the relationship with our "state of ignorance" concerning collective phenomena ?
If it is really Point 1, then Anderson, Laughlin, Pines, and even S.C. Zhang[1] (who WAS trained as a high energy physicist before jumping over to CM) would not have any issues with Weinberg and Co. But they do. Anderson's review of Weinberg's latest book clearly revealed that. In fact, there are arguments that "elementary particles" may in fact be emergent, collective behavior themselves (quark fractional charges).
Yes, and that's very interesting. It is even generally believed that what we think are elementary particles are just the effective dynamics of something deeper. You even have discussions of phase transformations of the vacuum and so on. But that is the other way around ! It means that what we think, are elementary phenomena, are in fact collective phenomena of a still deeper dynamics. This doesn't mean that building UP from a deeper dynamics is impossible ! The holy grail of particle physics is in fact just to reveil that deeper dynamics. QCD is already full of it.
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