Physics is now a solved problem. All experiments agree that the standard model of particle physics (unchanged since 1973) is correct, and that general relativity (from 1915) is correct. The ad-hoc equations specifying which of the two work when are also unchanged. That leaves dark matter as the only remaining unknown, let’s ignore that here.

Therefore in theory, as a corollary, all chemistry, biology and psychology is solved (TIC). Only minor issues left to solve.

Anyway, taking that as given, I looked up quantum physics to see if I could understand how it worked, and quickly ran across the Numerical sign problem , sometimes just called the “sign problem”.

“The numerical sign problem in applied mathematics refers to the difficulty of numerically evaluating the integral of a highly oscillatory function of a large number of variables. Numerical methods fail because of the near-cancellation of the positive and negative contributions to the integral. The sign problem is one of the major unsolved problems in the physics of many-particle systems. It often arises in (Monte-Carlo) calculations of” lattice QCD.

I may just be in a position to contribute here. I’ve done work on optimal lattices in n-D for n=1 to 4. I’ve done work in speeding up Monte-Carlo methods. And my work on infinite numbers gave me a unique insight into finding the limits of divergent sequences and into eliminating oscillating components from calculations of limits of infinite sequences (such as one generated by Riemann sums of an integral).

One the other hand I’ve never understood the difference between a “bra” and a “ket” in elementary quantum mechanics, and would have to look up the meanings of: Lagrangian, Hamiltonian, unitary, Dirac matrix, etc., in order to use them.

So, how would you go about finding a computer program that illustrates the numerical sign problem for quantum mechanics, a program that I could perhaps reverse engineer to understand it?

mollwollfumble said:

Physics is now a solved problem. All experiments agree that the standard model of particle physics (unchanged since 1973) is correct, and that general relativity (from 1915) is correct. The ad-hoc equations specifying which of the two work when are also unchanged. That leaves dark matter as the only remaining unknown, let’s ignore that here.

Therefore in theory, as a corollary, all chemistry, biology and psychology is solved (TIC). Only minor issues left to solve.

Anyway, taking that as given, I looked up quantum physics to see if I could understand how it worked, and quickly ran across the Numerical sign problem , sometimes just called the “sign problem”.

“The numerical sign problem in applied mathematics refers to the difficulty of numerically evaluating the integral of a highly oscillatory function of a large number of variables. Numerical methods fail because of the near-cancellation of the positive and negative contributions to the integral. The sign problem is one of the major unsolved problems in the physics of many-particle systems. It often arises in (Monte-Carlo) calculations of” lattice QCD.

How would you go about finding a computer program that illustrates the numerical sign problem for quantum mechanics, a program that I could perhaps reverse engineer to understand it?

Well, at least now I have a starting point. “Lattice QCD for novices”, June 2005.
“These lectures are for novices to lattice QCD. They introduce a set of simple ideas and numerical techniques that can be implemented in a short period of time and that are capable of generating nontrivial, nonperturbative results from lattice QCD.”
http://arxiv.org/pdf/hep-lat/0506036v1.pdf

mollwollfumble said:

I looked up quantum physics to see if I could understand how it worked, and quickly ran across the “Numerical sign problem”.

“The numerical sign problem in applied mathematics refers to the difficulty of numerically evaluating the integral of a highly oscillatory function of a large number of variables. Numerical methods fail because of the near-cancellation of the positive and negative contributions to the integral. The sign problem is one of the major unsolved problems in the physics of many-particle systems. It often arises in (Monte-Carlo) calculations of” lattice QCD.

I may just be in a position to contribute here. I’ve done work on optimal lattices in n-D for n=1 to 4. I’ve done work in speeding up Monte-Carlo methods. And my work on infinite numbers gave me a unique insight into finding the limits of divergent sequences and into eliminating oscillating components from calculations of limits of infinite sequences (such as one generated by Riemann sums of an integral).

Well, at least now I have a starting point. “Lattice QCD for novices”, June 2005.
“These lectures are for novices to lattice QCD. They introduce a set of simple ideas and numerical techniques that can be implemented in a short period of time and that are capable of generating nontrivial, nonperturbative results from lattice QCD.”
http://arxiv.org/pdf/hep-lat/0506036v1.pdf

I’ve now read “Lattice QCD for novices” and my respect for those who do lattice QCD calculations has increased enormously. Most of the numerical tricks and techniques that I’ve learnt with computational fluid dynamics (CFD) and elsewhere are already being implemented in lattice QCD, and a few that I’ve never heard of before as well (such as tadpole correction). The slow speed and crude discretisation of QCD calculation is understandable when I compare the time required for CFD (N^5 to N^6) with that required for QCD (up to N^24) where N is the number of elements in any one direction.