When physicists were figuring out quantum mechanics, one of the major constraints was that it had to reproduce classical mechanics in all of the situations where we already knew that classical mechanics works well—i.e. most of the macroscopic world.
Well, that’s false. The details of quantum to classical transition are very much an open problem. Something happens after the decoherence process removes the off-diagonal elements from the density matrix, and before only a single eigenvalue remains; the mysterious projection postulate. We have no idea at what scales it becomes important and in what way. The original goal was to explain new observations, definitely. But it was not “to reproduce classical mechanics in all of the situations where we already knew that classical mechanics works well”.
Your other examples is more in line with what was going on, such as
for special and general relativity—they had to reproduce Galilean relativity and Newtonian gravity, respectively, in the parameter ranges where those were known to work
That program worked out really well. But that is not a universal case by any means. Sometimes new models don’t work in the old areas at all. The free will or the consciousness models do not reproduce physics or vice versa.
The way I understand the “it all adds up to normality” maxim (not a law or a theorem by any means), is that new models do not make your old models obsolete where the old models worked well, nothing more.
I have trouble understanding what you would want from what you dubbed the Egan’s theorem. In one of the comment replies you suggested that the same set of observations could be modeled by two different models, and there should be a morphism between the two models, either directly or through a third model that is more “accurate” or “powerful” in some sense than the other two. If I knew enough category theory, I would probably be able to express it in terms of some commuting diagrams, but alas. But maybe I misunderstand your intent.
In one of the comment replies you suggested that the same set of observations could be modeled by two different models, and there should be a morphism between the two models, either directly or through a third model that is more “accurate” or “powerful” in some sense than the other two. If I knew enough category theory, I would probably be able to express it in terms of some commuting diagrams, but alas.
Yes, something like that would capture the idea, although it’s not necessarily the only or best way to formulate it.
Well, that’s false. The details of quantum to classical transition are very much an open problem. Something happens after the decoherence process removes the off-diagonal elements from the density matrix, and before only a single eigenvalue remains; the mysterious projection postulate. We have no idea at what scales it becomes important and in what way. The original goal was to explain new observations, definitely. But it was not “to reproduce classical mechanics in all of the situations where we already knew that classical mechanics works well”.
Your other examples is more in line with what was going on, such as
That program worked out really well. But that is not a universal case by any means. Sometimes new models don’t work in the old areas at all. The free will or the consciousness models do not reproduce physics or vice versa.
The way I understand the “it all adds up to normality” maxim (not a law or a theorem by any means), is that new models do not make your old models obsolete where the old models worked well, nothing more.
I have trouble understanding what you would want from what you dubbed the Egan’s theorem. In one of the comment replies you suggested that the same set of observations could be modeled by two different models, and there should be a morphism between the two models, either directly or through a third model that is more “accurate” or “powerful” in some sense than the other two. If I knew enough category theory, I would probably be able to express it in terms of some commuting diagrams, but alas. But maybe I misunderstand your intent.
Yes, something like that would capture the idea, although it’s not necessarily the only or best way to formulate it.