tag:blogger.com,1999:blog-11295132.post5272508190021055517..comments2014-04-16T10:57:46.206-07:00Comments on A Neighborhood of Infinity: Aliasing and the Heisenberg uncertainty principle.Dan Piponihttps://plus.google.com/107913314994758123748noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-11295132.post-5489021104427121642013-03-03T12:14:40.304-08:002013-03-03T12:14:40.304-08:00David M Rogers makes a good point. The experimenta...David M Rogers makes a good point. The experimental community ran away from the Schwartz-Hora effect and also from the suggestions of Jaynes. Younger folks may not realize why. I think it is due to a prevailing attitude among physicists working post 1980 that "everything had been discovered". This was when the phrase "brilliant confirmation" started popping up in science news articles. XYZ ... and experiment which told us nothing new, became a "brilliant confirmation". This confirmation bias is very human and has been studied a great deal in behavioral finance. Physicists of one generation had a real bad case of this. However, as anybody who knows history will tell you... Science proceeds by "brilliant disconfirmation". It is when we find something new and puzzling that we should pay attention. Things are changing now. Any young experimentalist who would like to win a Nobel Prize should go read Edwin T Jaynes and take the advice of David M Rogers. Like many areas of physics today there is a Nobel Prize going begging here. The older folks were simply too scared to touch this one.Kingsley Joneshttp://www.krwjones.comnoreply@blogger.comtag:blogger.com,1999:blog-11295132.post-50007574894420564222013-01-14T22:57:53.895-08:002013-01-14T22:57:53.895-08:00This is exactly the type of wave packet hypothesiz...This is exactly the type of wave packet hypothesized by Edwin Jaynes when talking about the Schwartz-Hora 'blue electron effect' in "Scattering of Light by Free Electrons as a Test of Quantum Theory". In some experiments, electrons excited by a laser emitted light on collision with a distant conductor. Jaynes speculated that this could be explained by attributing a comb structure at an optical wavelength to the free electron. Hestenes suggested that it may have to do with zwitterbewegung (in which case the extended structure just approximates time-delayed interactions of the electron with its own field). Sounds like we really need an experimental review on the subject, but I have not seen one.David M. Rogershttp://predictivestatmech.weebly.comnoreply@blogger.comtag:blogger.com,1999:blog-11295132.post-72742134929228395362013-01-14T14:54:39.324-08:002013-01-14T14:54:39.324-08:00Ah yes, for optics, one usually uses contact geome...Ah yes, for optics, one usually uses contact geometry which is the odd-dimensional analog of symplectic geometry.Derek Elkinsnoreply@blogger.comtag:blogger.com,1999:blog-11295132.post-57495236047734118782013-01-14T07:13:08.479-08:002013-01-14T07:13:08.479-08:00@Derek,
Symplectic spaces bound how much stuff ca...@Derek,<br /><br />Symplectic spaces bound how much stuff can fit in a 3D space too. I only just learnt about the (very old) concept of etendue: http://en.wikipedia.org/wiki/Etendue In practice it puts practical limits on things like how much light you can collect in a solar cell. Very interesting.Dan Piponihttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-66845372777545294682013-01-14T06:50:37.020-08:002013-01-14T06:50:37.020-08:00@vklj,
Welcome to physics :-)
Physicists tend no...@vklj,<br /><br />Welcome to physics :-)<br /><br />Physicists tend not to worry about such things because there's a variety of different ways to deal with it and they all end up having no impact on the final result (*).<br /><br />The Dirac comb can be seen as an idealised limit of a bunch of well behaved finite models. In this case physicists usually consider a finite region of space L (possibly wrapping around on itself) and allow L to "go to infinity". The Dirac comb can be seen as a limiting case in other ways too.<br /><br />This is a paper that deals explicitly with wavefunctions like this: http://www.cce.ufes.br/jair/estsolpg/PhysRev686_Zak_Dynamics_Bloch_Electrons.pdf<br /><br />(*) Caveat: One of my reasons for thinking about physics at the moment is that I'm trying to understand topological insulators. Part of it is a bunch of phenomena that would have been discovered much earlier if people had realised that finite size assumptions do sometimes have a big impact.Dan Piponihttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-41505469254698801832013-01-14T00:30:49.403-08:002013-01-14T00:30:49.403-08:00I'm not sure that abs(psi(x)^2) is a distribut...I'm not sure that abs(psi(x)^2) is a distribution function. If all deltas are equally weighed, the integral over (-infinity, infinity) is infinite, but, for it to be a probability distribution, it should be equal to 1.<br />Could you make that clearer? vkljhttp://www.blogger.com/profile/14166828860359201624noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-62909963848717970822013-01-13T20:01:20.898-08:002013-01-13T20:01:20.898-08:00I hadn't heard of it until now. It's prett...I hadn't heard of it until now. It's pretty neat.Dan Piponihttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-69111897560916346342013-01-13T19:55:52.861-08:002013-01-13T19:55:52.861-08:00Have you looked in to the symplectic camel?Have you looked in to the symplectic camel?Derek Elkinsnoreply@blogger.com