Motivated by this question (and the P. W. Anderson article linked in that question, which I came across here somewhere today and just read) I wonder about something, which is somewhat bordering an inverse idea of effective field theories:

Can a theory of a microscopic scale accurately describe microscopic effects, if it is known that the macroscopic behaviours predicted by it don't correspond with observation?

Maybe the answer is a trivial no. After all, the "classical limit" is ofter a guiding principle. But I can't really show it.

I can think of possibilities where such a scenario might be realized. For example I could imagine a microscopic theory A which has been introduced to describe a certain phenomenon, but which neglects some things on the same scale level as the one of the property of interest (in which the physicist is not interested though) and where these second effect determine more global or macroscopic behaviour. The second effect would be unforseen by the theory A. Are there examples for this?

And if so, is there a guiding principle, which says, that a parallel or even more detailed and so called fundamental theory B must become that theory A, if the degrees of freedoms in B (maybe e.g. some vector field components), which the first theory A never contained, are then neglegted?

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    $\begingroup$ I think you have a really lovely question hidden here, but you should restructure your post in order not to lose it. There is a difference between: 1) We neglected something microscopically and it worked, but macroscopically we couldn't neglect and it didn't work. Consider any long-range forces, e.g. gravity, and you are there. 2) We used a physical model for micro, it worked, then we used it for macro and it didn't work. Question 2) is much better. $\endgroup$ – Alexey Bobrick Apr 13 '12 at 0:15
  • $\begingroup$ I would still wonder, what do you mean by microscopic model working. Is it that we zoom in sufficiently deep, or is it about modelling some isolated chunk of material? The answers may be rather different in the two cases. $\endgroup$ – Alexey Bobrick Apr 13 '12 at 0:17
  • $\begingroup$ @AlexeyBobrick: additionally, there could be a question about emergent properties hidden here. The fact that you have things like phase transitions hidden in the Ising model is not at all obvious by naively looking at the microscopic Hamiltonian. $\endgroup$ – Jerry Schirmer Apr 13 '12 at 12:31

As long as the theory is correct in every way, it should work for microscopic and macroscopic worlds. So if the rule doesn't work for both micro and macro, then the rule of wrong.

Consider weather prediction. We look at data from the Earth and space now and then try to predict what it will do globally. However, if we didn't look at how the other objects in space and our star interfered, the predictions would be all wrong. Even a star thousands of light years away will change our weather just a small amount. There is an expedential scale of how accurate you want your results and how much data to process.

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