[lisper]

> Isn't the entire universe one quantum system?

Yes.

> If so, how can we talk about discrete systems.

That is an excellent question! And the answer is that when you do the math, the result of taking a subset of the wave function (the mathematical operation is called a "trace") is something that looks like a classical system. If you want the details, see this paper:

http://www.flownet.com/ron/QM.pdf

Or this video

https://www.youtube.com/watch?v=dEaecUuEqfc

which covers the same material.

[nickpsecurity]

" And the answer is that when you do the math, the result of taking a subset of the wave function (the mathematical operation is called a "trace") is something that looks like a classical system."

Your statement just connected to unrelated subjects in my head that might mean something. As I studied hardware, I found that underneath these nice, mathematical blocks that we build digital with are analog components that appear to operate on messy, kind-of-chaotic waves of electricity they hand-tune into the digital cells. Then, you say the clean building blocks of classical systems are composed of messy waves in quantum. Worded like that, it makes me wonder if analog vs digital could teach us something about quantum vs classical. Or some universal principle at work. Reason I wonder is some of the math keeps showing up in different disciplines.

What you think? Is my brain overreaching on this?

[lisper]

The difference between classical and quantum is not really analogous to the difference between digital and analog, it's the difference between real numbers and Turing machines (classical) and complex numbers (quantum).

But the ability of classical math to model all this is truly extraordinary.

https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.htm...

[nickpsecurity]

Oh OK. Yeah, I assumed quantum did reals for probabilities. Might not apply if using complex numbers.

[lisper]

Probabilities are always real (by definition). QM uses complex numbers for amplitudes, not probabilities. The probability is the square of the absolute value of the amplitude. Why nature should choose such a weird rule is the Big Mystery. The best discussion of this that I know of is this one:

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

[Jcol1]

Can you eli5?