tag:blogger.com,1999:blog-13869903.post1490530267465653529..comments2021-05-08T11:27:06.192-05:00Comments on nanoscale views: What is a crystal?Douglas Natelsonhttp://www.blogger.com/profile/13340091255404229559noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-13869903.post-12636639513751443932017-01-30T22:22:01.704-06:002017-01-30T22:22:01.704-06:00Anon@12:53, I was thinking of mentioning quasicrys...Anon@12:53, I was thinking of mentioning quasicrystals (see <a href="http://nanoscale.blogspot.com/2011/10/quasicrystals.html" rel="nofollow">here</a>). I believe in that case the atoms are arranged quasiperiodically, in a projection into 3d of an arrangement that would have discrete translational symmetry in four spatial dimensions. As a non-expert on quasicrystals, I don't know what that means for things like wavefunctions - whether or not there is some variant of the Bloch Theorem for quasiperiodic systems.<br /><br />Anon@10:30, the answer by Anon@15:26 is right on. Conceivably spacetime could have some underlying lattice structure, and it would be fun to write a sci-fi novel about the Umklapp Drive, where your spacecraft scatters off the fundamental periodicity of the universe and acquires momentum in units of the Planck momentum. A serious challenge of lattice theories is to construct versions that don't break Lorentz invariance (and thus special relativity).Douglas Natelsonhttps://www.blogger.com/profile/13340091255404229559noreply@blogger.comtag:blogger.com,1999:blog-13869903.post-9256208814015720312017-01-30T15:26:23.934-06:002017-01-30T15:26:23.934-06:00^^ This is the strategy of lattice field, which si...^^ This is the strategy of lattice field, which simulates quantum field theories on a discretized spacetime lattice, then takes the limit as the lattice spacing goes to 0 go recover the continuum theory. It is currently an open question as to whether a true theory of quantum gravity implies that spacetime is fundamentally discrete and grainy.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-13869903.post-60272134015179810552017-01-30T10:30:28.064-06:002017-01-30T10:30:28.064-06:00The crystalline structure and your comparison of i...The crystalline structure and your comparison of it to space-time symmetries are really interesting. You mentioned that space-time is invariant under continuous translation and rotation, while the crystal is not, but it isn't really the case if we assume that space-time is also quantized with the frequency of the Planck length. Could a crystal be the background of our space-time? Or could we study the structure of space-time in a crystal model?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-13869903.post-45748984598977955982017-01-30T00:53:56.506-06:002017-01-30T00:53:56.506-06:00A crystal necessary has to have a discrete diffrac...A crystal necessary has to have a discrete diffraction spectrum, but does it necessarily have to have discrete translational symmetry? I'm thinking about quasicrystals in particular here. Anonymousnoreply@blogger.com