Wow, that was quite a tour de force. My mathematics knowledge is woefully inadequate to follow it in detail, but at least I can form a general sense of the richness of the mathematical landscape that sits underneath each of these naive physical concepts. Above all it conveys the sense that even a fairly complete physics education is still nought but a tip of the iceberg as far as our mind's ability to model the phenomena we encounter-- and the "reality" must be orders of magnitude richer still. This seemed a particularly interesting avenue:
Quote:
|
Originally Posted by Chris Hillman
One idea which should rock your universe is a (not entirely rigorous) argument by Ted Jacobson that the EFE can be derived by demanding that dS = dQ/T hold for local "Rindler horizons"; see
http://arxiv.org/abs/gr-qc/9504004
http://arxiv.org/abs/gr-qc/0602001
Another is the suggestion that the gtr can be viewed as a general framework for studying how energy gravitates, in the same sense that thermodynamics can be viewed as a general framework for studying how energy can (cannot) be used to do useful work. |
Also, I agree completely with the following, because "computational convenience" is a lot of what science is, so is nothing to poo-poo:
Quote:
|
I avoid saying that classical mechanics has been -replaced- by quantum mechanics, since it is -appropriate- to use the former in many circumstances not merely for computation convenience but for (valid) theoretical insight. Old bad theories (like N-rays) are well and truly dead, but old good theories never die, they simply are further developed as an important "sector" of science, even if they are in some sense "subsumed" by "more general" theories.
|
Also, when I said that "solutions are emergent of theories, rather than explained by theories", I just meant that we tend to get so enamored of our axioms that when we use them to find a solution that agrees with experiment, we tend to say "those axioms explain that behavior", rather than the more correct "that behavior emerges as a solution from those axioms". To say we have explained something tends to suggest we have plumbed its depths, when in fact we have simply stopped when we got the result we were seeking. It's kind of like the difference between looking for a lost ring and mining for gold-- when you find the ring, you're done, but when you're mining gold, there's only the point where you decide you have "enough gold".