5 ms·

Isn't the entire universe one quantum system? If so, how can we talk about discrete systems. Also, when you say there are not discrete things, do you mean in t

by Jcol1 10y ago

Isn't the entire universe one quantum system? If so, how can we talk about discrete systems. Also, when you say there are not discrete things, do you mean in the QFT sense of field excitations?

lisper 10y ago
> 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 http://www.flownet.com/ron/QM.pdf Or this video https://www.youtube.com/watch?v=dEaecUuEqfc https://www.youtube.com/watch?v=dEaecUuEqfc which covers the same material.
- nickpsecurity 10y ago
  " 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 10y ago
    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.html https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.htm...
    - nickpsecurity 10y ago
      Oh OK. Yeah, I assumed quantum did reals for probabilities. Might not apply if using complex numbers.
      - lisper 10y ago
        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 http://www.scottaaronson.com/democritus/lec9.html
        Jcol1 10y ago
        Can you eli5?

by Jcol1 10y ago

Isn't the entire universe one quantum system? If so, how can we talk about discrete systems. Also, when you say there are not discrete things, do you mean in the QFT sense of field excitations?

lisper 10y ago

> 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 http://www.flownet.com/ron/QM.pdf Or this video https://www.youtube.com/watch?v=dEaecUuEqfc https://www.youtube.com/watch?v=dEaecUuEqfc which covers the same material.

nickpsecurity 10y ago
" 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 10y ago
  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.html https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.htm...
  - nickpsecurity 10y ago
    Oh OK. Yeah, I assumed quantum did reals for probabilities. Might not apply if using complex numbers.
    - lisper 10y ago
      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 http://www.scottaaronson.com/democritus/lec9.html
      - Jcol1 10y ago
        Can you eli5?