I have no more than glanced at the paper. The following may therefore be a dumb question, in which case I apologize.
It seems as if one of the following must be true. Which?
The arguments of this paper show that classical mechanics could never really have been a good way to model the universe, even if the universe had in fact precisely obeyed the laws of classical mechanics.
The arguments of this paper show that actually there’s some logical incoherence in the very idea of a universe that precisely obeys the laws of classical mechanics.
The arguments of this paper don’t apply to a universe that precisely obeys the laws of classical mechanics, because of some assumption it makes (a) explicitly or (b) implicitly that couldn’t be true in such a universe.
The arguments of this paper don’t exclude a classical universe either by proving it impossible or by making assumptions that already exclude a classical universe, and yet they somehow don’t show that such a universe has to be modelled quantumly.
2 wouldn’t surprise me. A non-relativistic universe seems to have hidden incoherence (justifying Einstein’s enormous confidence in relativity), so while my physics competence is insufficient to follow any similar QM arguments, it wouldn’t shock me if they existed.
There’s a plenty of possible cellular automations that are neither quantum mechanical nor relativistic, and it’s not too hard to construct one that would approximate classical mechanics at macroscopic scale, but wouldn’t in any way resemble quantum mechanics as we know it at microscale*, nor would be relativistic.
caveat: you could represent classical behaviour within quantum mechanical framework, it’s just that you wouldn’t want to.
1 would disappoint me. 2 would surprise me but (for reasons resembling yours) not astonish me. 3 would be the best case and I’d be interested to know what assumptions. (The boundary between 2 and 3 is fuzzy. A nonrelativistic universe with electromagnetism like ours has problems; should “electromagnetism like ours” be considered part of “the very idea” or a further “assumption”?) 4 and 5 would be very interesting but (kinda obviously) I don’t currently see how either would work.
I certainly would not rule out number 5 ;) As for 3, the arguments seem to apply to any universe in which you can carry out a reproducible experiment. However, in a “classical universe” everything is, in principle, exactly knowable, and so you just don’t need a probabilistic description.
Unless there is limited information, in which case you use statistical mechanics. With perfect information you know which microstate the system is in, the evolution is deterministic, there is no entropy (macrostate concept), hence no second law, etc. Only when you have imperfect information—an ensemble of possible microstates, a macrostate—mechanics “becomes” statistical.
Using probabilistic logic in a situation where classical logic applies is either overkill or underconfidence.
In case it’s less than perfectly clear, I am very much not ruling out number 5; that’s why it’s there. But for obvious reasons there’s not much I can say about how it might be true and what the consequences would be.
Even in a classical universe your knowledge is always going to be incomplete in practice. (Perfectly precise measurement is not in general possible. Your brain has fewer possible states than the whole universe. Etc.) So probabilistic reasoning, or something very like it, is inescapable even classically. Regardless, though, it would be pretty surprising to me if mere “underconfidence” (supposing it to be so) required a quantum [EDITED TO ADD: model of the] universe.
I’m not sure if we can say much about a classical universe “in practice” because in practice we do not live in a classical universe. I imagine you could have perfect information if you looked at some simple classical universe from the outside.
For classical universes with complete information you have Newtonian dynamics. For classical universes with incomplete information about the state you can still use Newtonian dynamics but represent the state of the system with a probability distribution. This ultimately leads to (classical) statistical mechanics. For universes with incomplete information about the state and about its evolution (“category 3a” in the paper) you get quantum theory.
[Important caveat about classical statistical mechanics: it turns out to be a problem to formulate it without assuming some sort of granularity of phase space, which quantum theory provides. So it’s all pretty intertwined.]
I have no more than glanced at the paper. The following may therefore be a dumb question, in which case I apologize.
It seems as if one of the following must be true. Which?
The arguments of this paper show that classical mechanics could never really have been a good way to model the universe, even if the universe had in fact precisely obeyed the laws of classical mechanics.
The arguments of this paper show that actually there’s some logical incoherence in the very idea of a universe that precisely obeys the laws of classical mechanics.
The arguments of this paper don’t apply to a universe that precisely obeys the laws of classical mechanics, because of some assumption it makes (a) explicitly or (b) implicitly that couldn’t be true in such a universe.
The arguments of this paper don’t exclude a classical universe either by proving it impossible or by making assumptions that already exclude a classical universe, and yet they somehow don’t show that such a universe has to be modelled quantumly.
I’m confused.
2 wouldn’t surprise me. A non-relativistic universe seems to have hidden incoherence (justifying Einstein’s enormous confidence in relativity), so while my physics competence is insufficient to follow any similar QM arguments, it wouldn’t shock me if they existed.
What would you mean by incoherence, though?
There’s a plenty of possible cellular automations that are neither quantum mechanical nor relativistic, and it’s not too hard to construct one that would approximate classical mechanics at macroscopic scale, but wouldn’t in any way resemble quantum mechanics as we know it at microscale*, nor would be relativistic.
caveat: you could represent classical behaviour within quantum mechanical framework, it’s just that you wouldn’t want to.
1 would disappoint me. 2 would surprise me but (for reasons resembling yours) not astonish me. 3 would be the best case and I’d be interested to know what assumptions. (The boundary between 2 and 3 is fuzzy. A nonrelativistic universe with electromagnetism like ours has problems; should “electromagnetism like ours” be considered part of “the very idea” or a further “assumption”?) 4 and 5 would be very interesting but (kinda obviously) I don’t currently see how either would work.
I certainly would not rule out number 5 ;) As for 3, the arguments seem to apply to any universe in which you can carry out a reproducible experiment. However, in a “classical universe” everything is, in principle, exactly knowable, and so you just don’t need a probabilistic description.
Unless there is limited information, in which case you use statistical mechanics. With perfect information you know which microstate the system is in, the evolution is deterministic, there is no entropy (macrostate concept), hence no second law, etc. Only when you have imperfect information—an ensemble of possible microstates, a macrostate—mechanics “becomes” statistical.
Using probabilistic logic in a situation where classical logic applies is either overkill or underconfidence.
In case it’s less than perfectly clear, I am very much not ruling out number 5; that’s why it’s there. But for obvious reasons there’s not much I can say about how it might be true and what the consequences would be.
Even in a classical universe your knowledge is always going to be incomplete in practice. (Perfectly precise measurement is not in general possible. Your brain has fewer possible states than the whole universe. Etc.) So probabilistic reasoning, or something very like it, is inescapable even classically. Regardless, though, it would be pretty surprising to me if mere “underconfidence” (supposing it to be so) required a quantum [EDITED TO ADD: model of the] universe.
I’m not sure if we can say much about a classical universe “in practice” because in practice we do not live in a classical universe. I imagine you could have perfect information if you looked at some simple classical universe from the outside.
For classical universes with complete information you have Newtonian dynamics. For classical universes with incomplete information about the state you can still use Newtonian dynamics but represent the state of the system with a probability distribution. This ultimately leads to (classical) statistical mechanics. For universes with incomplete information about the state and about its evolution (“category 3a” in the paper) you get quantum theory.
[Important caveat about classical statistical mechanics: it turns out to be a problem to formulate it without assuming some sort of granularity of phase space, which quantum theory provides. So it’s all pretty intertwined.]