3 ms·
The funny thing is, besides this one you picked out, pretty much all the rest of these either are continuity assumptions or follow from continuity. I think tha
by pmiller2 6y ago
The funny thing is, besides this one you picked out, pretty much all the rest of these either are continuity assumptions or follow from continuity. I think that's because physicists tend to dismiss discontinuities and singularities as "unphysical," but it does make good intuitive sense.
I suspect that "all equations have one solution" is a lot easier to satisfy when all functions are continuous, or otherwise nice, as well.
- efavdb 6y agoThat's mostly true -- however, physicists devote a lot of time to studying phase transitions and characterizing the kinds of discontinuities that are possible etc in that context.
- pmiller2 6y agoAh, yes, I forgot about phase transitions. Those are actually interesting discontinuities. It seems to me the uninteresting ones are the ones that have roughly the same behavior all around them (e.g. poles of complex functions are not that interesting). Would you say that's an accurate characterization?
- efavdb 6y agosorry don't have much more insight here. I think the goal is to generally make any approximation that isn't relevant to the physical behavior one is trying to model. if a pole sitting somewhere isn't related to the phenomenon you're trying to explore, ignore it!
- pmiller2 6y agoGreat point. There are a ton of good models that break down in certain regions (e.g. quantum mechanics and general relativity at large and small physical scales, respectively).