The announcement the world has been waiting for can now be made: the paper “Morlet wavelets in quantum mechanics” has been updated. The latest version has a much clearer explanation of the point, a number of errors corrected, and some stylistic infelicities eliminated.
This version has been uploaded to the physics archive.
Abstract:
Wavelets offer significant advantages for the analysis of problems in quantum mechanics. Because wavelets are localized in both time and frequency they avoid certain subtle but potentially fatal conceptual errors that can result from the use of plane wave or delta function decomposition. Morlet wavelets are particularly well-suited for this work: as Gaussians, they have a simple analytic form and they work well with Feynman path integrals. To take full advantage of Morlet wavelets we need an explicit form for the inverse Morlet transform and a manifestly covariant form for the four-dimensional Morlet wavelet. We supply both here.
December 12th, 2009
One of the members of my Macintosh programming SIG asked me if for today’s meeting I would talk about Quantum Time, which I was, of course, happy to do. There is nothing like explaining something to a bunch of intelligent listeners for getting it straight in your own head. And if you can get across some of the wonder & the weird that is modern physics, that’s even better!
I’ve got the slides online (see under talks). Summary:
Read more »
Followup post on 12/3/2009.
This coming Sunday, in two days, there will be a panel discussion with the topic:
Towards a Theory of Quantum Gravity
Read more »
Wavelets are like musical notes: they are wave forms limited in both time and frequency. What makes them particularly useful is that any reasonable wave function may be written as a sum over them.
Usually we think of music in terms of pure tones, in terms of its Fourier components. But pure tones can be a bit too pure. For one thing, if a tone is to be completely pure it has to last forever, not a characteristic associated with practical questions. Wavelets are impure tones, and therefore a better match to the real world.
Read more »
I’d like to thank Ferne Welch and Arthur Tansky for copy-editing the previous version of “Quantum Time“. It bears a significantly greater resemblance to English now!
And I would like to thank Jonathan Smith and also Mark West and Ashleigh Thomas for help in getting setup at University of Pennsylvania.
If anyone knows a bibtex style that handles electronic references well, please let me know. If no suggestions, then I think I will warm up learning Old Kingdom hieroglyphs, then tackle bibtex.
All comments on Quantum Time are very welcome. I’m planning to fold such into the great work of time as appropriate, then, if not too discouraged, push Quantum Time to the archive.
Thanks!
John Ashmead
I’ve set this blog up to explore the intersection between time and quantum mechanics. Both subjects are interesting in their own right, the intersection rich with possibility. No shortage of topics!
Cheers!
John Ashmead
Announcement, Wavelets | John Ashmead | 
December 30, 2009 11:42 pm | 
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