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Comment by whatshisface | Hacker News Reader

There is a bit of a parable I hear told sometimes when this topic comes up: A man is being taught how computers work, and is presented with the design of an adder in the form of a few Boolean logic expressions. Thinking back to the true "reality" of addition, he rejects the design of the adder on the grounds that nand gates have no apparent connection to the sensible reality of having 5 apples and 3 oranges and 8 fruits.

This would be considered a ridiculous objection in every field but physics, where misunderstandings following from it have become the basis of many bestsellers. For some reason, we consider the math involved in physics to be exempt from the otherwise universal sense of abstraction that all the other fields enjoy. We don't go looking for tiny calculators in bacteria capable of plotting out exponential population growth, so why should the weirdness of quantum math cause so much trouble?

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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 a fock space, we just know that it gives us the right results.

I think part of the issue is that Physicists really care about why, not whether something fits the model.

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 you -- without any recourse to experiment -- that quantum mechanics would also have been on God's whiteboard. I'm going to show you why, if you want a universe with certain very generic properties, you seem forced to one of three choices: (1) determinism, (2) classical probabilities, or (3) quantum mechanics. Even if the "mystery" of quantum mechanics can never be banished entirely, you might be surprised by just how far people could've gotten without leaving their armchairs! That they didn't get far until atomic spectra and so on forced the theory down their throats is one of the strongest arguments I know for experiments being necessary."

http://www.scottaaronson.com/democritus/lec9.html

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.

> why should the weirdness of quantum math cause so much trouble?

The deep issue is not the weird math - that's just math and it's not even particularly weird - mostly just differential equations and complex numbers. It's the weird behaviour of physical reality that's puzzling. Take for example entangled photons going through detectors a long way apart. The state of the detector at one end has something like a faster than light effect on the outcome at the other end. It's easy to write equations for it but how on earth does it work?

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