Silas R. Beane, Zohreh Davoudi, Martin J. Savage
2012 · arXiv
Observable consequences of the hypothesis that the observed universe is a numerical simulation performed on a cubic space-time lattice or grid are explored. The simulation scenario is first motivated by extrapolating current trends in computational resource requirements for lattice QCD into the future. Using the historical development of lattice gauge theory technology as a guide, we assume that our universe is an early numerical simulation with unimproved Wilson fermion discretization and investigate potentially-observable consequences. Among the observables that are considered are the muon g-2 and the current differences between determinations of alpha, but the most stringent bound on the inverse lattice spacing of the universe, b^(-1) >~ 10^(11) GeV, is derived from the high-energy cut off of the cosmic ray spectrum. The numerical simulation scenario could reveal itself in the distributions of the highest energy cosmic rays exhibiting a degree of rotational symmetry breaking that reflects the structure of the underlying lattice.
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In that direction there was an idea a few years ago about detecting if on a very small scale we can observe any grid-alignment effect. https://arxiv.org/abs/1210.1847 I think there was another paper about similar grid-alignment idea for some properties of galaxies, but I can't find it now.
> The apparatus would necessarily exist within the closed system. does being in a multiverse influences our world in any way using current theories? yes > we can eventually figure out and run an experiment no > then studying it is as productive as searching the Russel's teapot this is how you set apart a theory from speculation, a falsification test. i.e. > http://arxiv.org/abs/1210.1847
The cost of simulating entire universe becomes increasingly expensive to the point you need a universe of energy to simulate a universe. Daniel Dennet in his "Consciousness Explained" makes a good argument why this is so. Also there was some research done on the constraints on the universe as a numerical simulation http://arxiv.org/abs/1210.1847 telling us that we can do experiments to detect if we are living in a simulation (but the simulators always have a freedom to "increase the resolution" of their simulation to thwart our efforts). The paper does not discuss if there are limits on how far this game can be played on either side.
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 [1] https://en.wikipedia.org/wiki/Action_(physics) [2] https://en.wikipedia.org/wiki/Quantum_chromodynamics
ArXiv paper: http://arxiv.org/abs/1210.1847 This work attempts to draw out the presence of a simulation by looking for tiny violations of known/expected symmetries, which is always worth doing. We should note, however, that an excellent simulation could exactly cover its tracks, lest the underlying architecture cause unintended artifacts. From a CS perspective, the simulation's developer might create unit tests that guarantee the preservation of symmetries. A theorist who develops an experimental test that could prove we do not live in a simulation should be lauded. There are experimentalists (like me) just waiting for such guidance. John Bell's theorem [1] was/is a shining guidestar for physics. [1] http://en.wikipedia.org/wiki/Bells_theorem
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