tag:blogger.com,1999:blog-5439168179960787195.post2059340179659874884..comments2024-03-28T17:13:01.117+10:00Comments on Condensed concepts: The theory of everythingRoss H. McKenziehttp://www.blogger.com/profile/09950455939572097456noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-5439168179960787195.post-18945450394502635802009-06-30T09:31:33.372+10:002009-06-30T09:31:33.372+10:00Another (non argumentative) comment: I would be re...Another (non argumentative) comment: I would be really interested to see in detail how the principle of broken symmetry leads to exact flux quantisation. Is there any chance you could write an accessible blog exposition of this?<br /><br />Thanks,<br />Sean BarrettSean Barretthttps://www.blogger.com/profile/06411871490316449827noreply@blogger.comtag:blogger.com,1999:blog-5439168179960787195.post-87428435856426240162009-06-30T09:21:04.120+10:002009-06-30T09:21:04.120+10:00Hi Ross,
This is a great blog, full of informativ...Hi Ross,<br /><br />This is a great blog, full of informative and thought provoking posts. Sorry to be commenting on a slightly old post, but you update this much more frequently than I have time to visit!<br /><br />I have a couple of comments on this post. Firstly, while I agree that computer simulations might not, of themselves, give much insight into the origin of a particular phenomena, I think they can still be extremely useful. It seems to me that they ought to be able to be of some use in uncovering phenomena such as broken symmetry - surely if a numerical simulation is `just like doing an experiment,' it can be no worse than an experiment in uncovering some observable phenomenon. (This leaves aside, for now, the question of how long the simulation takes to run, but see my comments further down on this). In particular, experimentalists can, in a sense, observe a broken symmetry in an experiment on a finite sized system. Arguably, all such experiments have been performed on finite systems; and yet the existence of broken symmetry phases (or at least the validity of the concept as a useful limiting case) is not in dispute.<br /><br />Furthermore, there are circumstances where a computer simulation might be more useful than a particular experiment, in terms of determining an explanation for a particular phenomenon. This is because modern digital computers hardly ever make mistakes - noise acting on the computer causes a change in the state of the computer only very, very rarely. So, if a computer simulation gives an answer that disagrees with what is observed in experiment, this can only be for two reasons: either the algorithm we used has some inherent numerical instabilities, or the assumptions that we put into our physical model were incorrect. The former can often be ruled out by a sort of mathematical reasoning that is quite independent of the phenomenon under consideration. This means that computers can be very useful in testing our intuitions about what should go into the `essential physics' of the phenomenon we are trying to understand.<br /><br />I believe this is somewhat different from actual experiments - in a given experiment one can never be sure wether one is observing the `true' effect, or some artifact of the particular setup (which could be due to the way noise is affecting the system). For this reason, it is useful to have multiple probes of a particular phenomenon.<br /><br />To give an example, it seems to me (as a casual outside observer) that there has been significant debate between condensed matter physicists as to whether the essential physics of high temperature superconductors is contained within the 2D Hubbard model, or whether additional interactions are required. If we could simulate the Hubbard model on a computer, such questions could be settled immediately, and theorists could focus their efforts in explaining *how* superconductivity arises from such a model.<br />One could call this a (weak) form of reductionism, which does not `explain' an emergent phenomenon, but does use a `lower strata' to glean some useful information about it.<br /><br />The obvious issue with the above is that modern digital computers are not really up to the task of exactly simulating (for example) 2D Hubbard models with sufficient numbers of particles to see emergent phenomena like superconductivity. However, we know that, in principle, quantum computers can be made to have the equivalent property as classical digital computers of being robust to the noise acting on them (provided it is sufficiently weak, of course). Thus, if we had a QC, we could run simulations of model systems such as Hubbard models, and reasonably confident that the output of the simulation is not some artifact of the noise acting on the computer. To my mind, this is one of the most important motivations for developing quantum computers.Sean Barretthttps://www.blogger.com/profile/06411871490316449827noreply@blogger.comtag:blogger.com,1999:blog-5439168179960787195.post-55105096352984857252009-06-23T00:04:24.733+10:002009-06-23T00:04:24.733+10:00We are a group that is challenging the current par...We are a group that is challenging the current paradigm in physics which is Quantum Mechanics and String Theory. There is a new Theory of Everything Breakthrough. It exposes the flaws in both Quantum Theory and String Theory. Please Help us set the physics community back on the right course and prove that Einstein <br />was right! Visit our site The Theory of Super Relativity: <a href="http://www.superrelativity.org/" title="Super Relativity" rel="nofollow">Super Relativity</a>mmfiorehttps://www.blogger.com/profile/07649185144011409332noreply@blogger.com