Timeline for How does hyperbolicity of space time affect our lives?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Mar 27, 2013 at 12:44 | comment | added | Anton Galaev | Note that an interesting application of the hyperbolic geometry gives the Luneburg theory, see Rudolf Karl Luneburg, The metric of binocular visual space, J. Opt. Soc. America, 1950, 40, 627-642 that states that 9 from 10 people see the world so as its geometry were hyperbolic, but not Euclidean. | |
| Mar 16, 2013 at 14:22 | comment | added | user21349 | I didn't say they were unrelated. However, they are completely different. | |
| Mar 16, 2013 at 4:49 | comment | added | Delio Mugnolo | Ben Crowell, I am not quite sure the two ways of using that world are actually unrelated. The solvability features of a wave equation (as opposed to, say, a heat equation) actually depend on the fact that the "hyperbolic" wave equation is a PDE whose symbol is a function with certain properties - the same properties that one would need to define a riemannian metric of negative curvature. | |
| Mar 15, 2013 at 22:23 | comment | added | user21349 | Heads up: the way you're using the phrase "hyperbolicity of space time" is completely different than what relativists mean by the same words. To a relativist, a (globally) hyperbolic spacetime is essentially one in which solutions to Cauchy problems (e.g., for a wave equation within that spacetime) exist and are unique. See Hawking and Ellis, p. 206, and Geroch, J Math Phys 11 (1970) 437. | |
| Mar 15, 2013 at 18:33 | answer | added | Y Macdisi | timeline score: 1 | |
| Mar 15, 2013 at 14:54 | vote | accept | Brian Rushton | ||
| Mar 15, 2013 at 12:41 | answer | added | Carlo Beenakker | timeline score: 17 | |
| Mar 15, 2013 at 3:57 | comment | added | Ryan Budney | I think of hyperbolicity as having multi-pronged connections to the real world. It comes up naturally in many situations, especially via the geometrization of 3-manifolds. In practice it seems to be the right object for succinctly describing certain types of "teeming" complexity. | |
| Mar 15, 2013 at 3:55 | comment | added | Ryan Budney | The symmetry group of the Minkowski (vector) space is the same as for hyperbolic space. The hyperbolic space carries all the information of the isometry, well, provided the isometry preserves the sense of time. It's the same idea as how one can study euclidean (vector space) symmetries by studying the action on the sphere. | |
| Mar 15, 2013 at 3:33 | history | asked | Brian Rushton | CC BY-SA 3.0 |