> The beauty and clearness of the dynamical theory, which asserts heat and light to be modes of motion, is at present obscured by two clouds.
Lord Kelvin's two clouds led us to relativity and quantum mechanics.
List of Unsolved Problems in Physics
21–22 of 22 posts
Re: List of Unsolved Problems in Physics
#22Earlier quoted context omitted.
I'm not so sure this is a fair comparison. Anything that grows proportionally to its population will grow exponentially, math just says it will, and you can't avoid that. You can look at the bacteria itself and see that bacteria divide, and so, you expect this sort of growth, and so, it mathematically follows. It just isn't that way for QM, nothing in nature says that systems have to evolve by a hermitian operator on…
I would disagree with you there, actually. As Scott Aaronson says: "Quantum mechanics is what you would inevitably come up with if you started from probability theory, and then said, let's try to generalize it [...] As such, the theory could have been invented by mathematicians in the 19th century without any input from experiment. It wasn't, but it could have been. [...] In this lecture, I'm going to try to convince…
I don't really like arguing back and forth, but the way I read that is he is describing calculations in QM, not the "why" behind QM. QM is not a mystery in calculationally, it is a mystery in interpretation.
The generalization of probability theory to include "negative" probabilities, really, amplitudes is just the method in quantum mechanics. It's like knowing what a derivative is to obtain exponential population growth. That's just mathematics. No one says people who have solved dN/dt=aN predict that bacteria will grow exponentially, it's just how a system acts like that would behave, and we found an example.
But, I've thought a little more about it, I think my original comment was touching a personal bias more than making an argument. I asked, "why does the time evolution operator have to be on a fock space and why do P and X commute like ~i?" I'm not sure physics can answer beyond that at this point, since it matches experiment, we should or could just accept it the way it is.
May be there is no "deeper" reason after all.