http://arxiv.org/abs/1210.1847 http://arxiv.org/abs/1210.1847 This comment is a response to a bunch of the comments in this thread, but it didn't make sense to

http://arxiv.org/abs/1210.1847 http://arxiv.org/abs/1210.1847 This comment is a response to a bunch of the comments in this thread, but it didn't make sense to scatter the information throughout the page. The way lattice QCD [0] works requires a few approximations in order to fit the problem into your computer. You (1) simulate a universe with finite volume (state-of-the-art calculations have boxes just a few times bigger than a nucleus in each direction), (2) discretize the space into a bunch of points some lattice spacing apart connected by links, and, (3) possibly simulate at values of the quark masses that are not their physical values (this helps make a a matrix you need to invert better-conditioned). Finally, you know what action[1] you want to simulate (that of QCD[2]) and you construct a discretized action that accounts for all of the above approximations that approaches the real action you want to simulate when you take the limits volume --> infinity, lattice spacing --> 0, masses --> physical values. There are many different ways to build such a discretized action (and they go by names like the Wilson action, the Domain Wall action, the Staggered action, and others), but no discretized action is "perfect" in the sense that anything you try to measure can have errors that depend on how different the volume you actually measured is from the infinite-volume limit, how much having a finite lattice spacing changes your answer, and how much unphysical masses matter. We have theory that controls how measured quantities depend on these parameters, and thus can understand, via extrapolation, how lattice artifacts change the quantities we measure from the true continuum limit. You can use this understanding to find out what the answer is in the limit of there being no discretization at all (lattice spacing = 0) and then compare measurements of our world to those predictions. If they match, then the world doesn't really have a grid of points at its bottom, but if they don't match you can find out how finely spaced the grid of spacetime is. Unfortunately, any simulation you do will have error bars, and so in practice all you can say is "the continuum world looks like this ± that", the practical consequence being that you can only put an upper bound on how different the lattice spacing of spacetime is from zero: "If the lattice spacing were bigger than X then we would have conflict between the experimental observations we made of the universe and the simulation. No such conflict is known, so the lattice spacing is smaller than X." Source: I am a postdoc doing lattice QCD, and I have met Martin and Zohreh. [0] https://en.wikipedia.org/wiki/Lattice_QCD https://en.wikipedia.org/wiki/Lattice_QCD [1] https://en.wikipedia.org/wiki/Action_(physics) https://en.wikipedia.org/wiki/Action_(physics) [2] https://en.wikipedia.org/wiki/Quantum_chromodynamics https://en.wikipedia.org/wiki/Quantum_chromodynamics