3 ms·

Not an answer to your question, but it reminded me of something one of my quantum mechanics professors said during undergraduate physics. Paraphrasing: "Quantu

Not an answer to your question, but it reminded me of something one of my quantum mechanics professors said during undergraduate physics. Paraphrasing: "Quantum physics may seem hard, but it's much easier than classical physics. We can describe a quantum system using a finite set of integer (or half-integer) quantum numbers. In classical physics the properties are continuous, and describing the deeper decimal places would require knowing the entire history of all the objects involved. We could also never repeat an experiment exactly, due to these infinite decimals." Of course, we're not totally screwed in classical systems; the far decimals are only a problem in chaotic systems. Still, might be related to the author's claim.

gowld 8y ago
Of course that argument is silly, because if you tried to compute the quantum physics of a simple object like a pair of spheres in a vacuum, you'd be hopelessly lost. Classical physics is only hard (in the given sense) if you care about computing infinite decimal details, which no one does.
- hpcjoe 8y ago
  Not quite ... classical orbits over extended time periods (T >> 1 orbital period) tends to require significant precision thanks to the "chaotic" aspects of the diffeqs. See [1] for some additional details. Many orbital sims use high order methods, predictor-corrector type approaches. As for "quantum physics of a simple object like a pair of spheres in a vacuum" ... I gotta say, as a (non-practicing) physicist, I haven't the foggiest notion about what you are thinking of. Do you mean the collective wave function of the entire ensemble of atoms? Or the valence/band electrons? Or something else? Basically, we've been exploiting symmetries for many years to reduce insanely hard problems to less insanely hard problems. For crystalline material, we exploit periodic boundary conditions to reduce the size of the Hamiltonian to something reasonable. We still have to deal with O(N^3) and higher multicenter matrix elements like <phi_i(R1) | Operator_k(R2) | phi_j(R3)>. This is computationally hard for anything but small N (say 1000-10000). [1] http://carma.astro.umd.edu/nemo/pitp/papers/gd2_s3.4.pdf http://carma.astro.umd.edu/nemo/pitp/papers/gd2_s3.4.pdf

gowld 8y ago

Of course that argument is silly, because if you tried to compute the quantum physics of a simple object like a pair of spheres in a vacuum, you'd be hopelessly lost. Classical physics is only hard (in the given sense) if you care about computing infinite decimal details, which no one does.

hpcjoe 8y ago
Not quite ... classical orbits over extended time periods (T >> 1 orbital period) tends to require significant precision thanks to the "chaotic" aspects of the diffeqs. See [1] for some additional details. Many orbital sims use high order methods, predictor-corrector type approaches. As for "quantum physics of a simple object like a pair of spheres in a vacuum" ... I gotta say, as a (non-practicing) physicist, I haven't the foggiest notion about what you are thinking of. Do you mean the collective wave function of the entire ensemble of atoms? Or the valence/band electrons? Or something else? Basically, we've been exploiting symmetries for many years to reduce insanely hard problems to less insanely hard problems. For crystalline material, we exploit periodic boundary conditions to reduce the size of the Hamiltonian to something reasonable. We still have to deal with O(N^3) and higher multicenter matrix elements like <phi_i(R1) | Operator_k(R2) | phi_j(R3)>. This is computationally hard for anything but small N (say 1000-10000). [1] http://carma.astro.umd.edu/nemo/pitp/papers/gd2_s3.4.pdf http://carma.astro.umd.edu/nemo/pitp/papers/gd2_s3.4.pdf