# System that is more efficient to simulate than to compute

I know some physics calculations require alot of computing to solve.

Are there currently systems where it is more logical to do an experiment to "let the universe simulate the experiment for us" and measure the outcome instead of calculating it out of time/resource concerns?

Note i do not mean the complexity of the experiment or number of independent variables but solely out of a mathematical standpoint.

• Wind tunnels are still in widespread use. – CuriousOne Jul 4 '16 at 22:10
• @CuriousOne, true, but there are also computer programs that do the same thing more efficiently...autodesk.com/products/flow-design/features/all/list-view is one example – heather Jul 4 '16 at 23:02
• @heather: Ask Boeing what they think about using autodesk for their next airliner.... :-) – CuriousOne Jul 4 '16 at 23:03
• @heather: You mean less efficiently. At a high enough level of detail, a 1 hour wind tunnel experiment may require a month long simulation. That's why simulations are always used for "rough draft" during the design phase where you can simulate at lower resolutions and/or with simplified physics but never during the actual verification phase of the design (once you've made your mind up on your design) - it's simply faster to run a wind tunnel test. – slebetman Jul 5 '16 at 3:32
• @heather there are 2 distinct problems in simulation verification and validation. We can validate a model but not verify it without a experiment in a real wind tunnel. But yes a real wind tunnel is much faster than a simulation, also we dont know how turbulence really works. So without real testing we dont know of real emergent features of the system and obviously a simulation does not know how to simulate features you did not know to account for. – joojaa Jul 5 '16 at 6:59

## 2 Answers

Virtually all experiments (at least in condensed matter physics) fall under this category. Unlike in high energy, where we're actually testing fundamental physical theories, at the energy scales of condensed matter, we are quite confident that in principle, the many-body nonrelativistic Schrodinger equation runs the whole show. (Perhaps with relativistic corrections in the case of the heavier atoms, where spin-orbit coupling can be significant.) In Dirac's famous words, "The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble." Since we can't solve the $10^{23}$-body Schrodinger equation, we still do experiments. (This is even more the case in the case of cold atoms, where we can precisely control the Hamiltonian itself, but the field of cold atom experiment is flourishing.)

• +1, with the caveat that many important experiments are not done to give us solutions for the known, they are being done to explore the unknown. – CuriousOne Jul 4 '16 at 22:28
• I believe this (my original answer) is also the case in high-energy experiment at heavy ion colliders like RHIC at Brookhaven. I think it's quite solidly believed that all the important physics in these processes can in principle be captured by QCD, but the calculations are far too difficult to do in practice. – tparker Jul 4 '16 at 22:33
• You are wrong about that. Nobody (of any importance) in the theory community thinks that QCD, or even QFT as a general theory is even close to the final result. The standard model is basically just a low energy fit up to approx. one TeV and it doesn't even contain dark matter. At this point it's hardly bette than epicycles were 400 years ago. – CuriousOne Jul 4 '16 at 22:36
• @CuriousOne Of course the Standard Model isn't anywhere close to the final result. I was just saying that the specific case of heavy ion collisions have low enough energy that they can be described within the Standard Model – tparker Jul 4 '16 at 22:38
• That doesn't help because we already know that the standard model doesn't explain anything, and it certainly doesn't explain QCD. In any case, these experiments are not being done because we are just mopping up a few remaining bread crumbs, they are being done because we genuinely don't know what's going on. In other words: try to get an experiment approved for which you can't, at least tentatively, demonstrate new discovery potential. Nobody will give you money for that in physics. – CuriousOne Jul 4 '16 at 22:43

A very well-known example is atomic weapons. It is much easier to build a device and test it than it is to simulate it: it took a very long time before simulations of existing designs and small variations on them became convincing enough that people had any faith in them at all, and I believe that we can really only use simulations now because it became clear that small variations on existing designs were adequate, and radical innovations were no longer needed (no-one wanted suitcase nukes or hundred-megaton devices to exist). Even now there are many physical tests of critical aspects of weapon systems (some of this sort of thing goes on at the National Ignition Facility).

Of course full tests of nuclear weapons have several undesirable side-effects, so people were eventually pushed into simulations combined with physical tests of things that were too hard to simulate.

More generally almost any complex system -- which is almost any system -- is generally either ludicrously hard or completely impractical to simulate numerically.

More generally still, if you are just doing simulations, you're not actually doing physics: you're testing a model you've made, which can be interesting in itself, but to do physics you need to be comparing the model with the world.