“Morlet wavelets in quantum mechanics” updated

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.


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.

Paradox Noise



A burst of audio and visual static reduced reception to unintelligible noise. Then the paradox-generated interference was gone again, as suddenly as it had come.

” . . . Fourteenth of April at Ford’s Theater –” blast, crackle.

“. . . you must be within two meters of the President . . . just before the bullet smashes into Lincoln’s brain. Your total window of opportunity will be three seconds.”

– Fred Saberhagen’s After the Fact

If the block universe view is correct, if time is “nothing but” a space dimension, then we should be able to travel in it. Leaving aside the fact that we don’t quite yet know how to do this (but see some of the books under references) shouldn’t time travel be forbidden by the paradoxes it would otherwise make inevitable?  There are three kinds of paradox to consider:

Three kinds of paradox

Grandfather paradox

Why pick on grandfather? It seems that the only way to prove that time travel is impossible is to cite a case of killing one’s own grandfather. This incessant murdering of harmless ancestors must stop. Let’s see some wide-awake fan make up some other method of disproving the theory.

– 1933 letter to Astounding Stories, as quoted in Nahin’s Time Machines: Time Travel in Physics, Metaphysics, and Science Fiction

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Quantum time talk today

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:
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Why quantum time?

Why quantum time?

A few years ago I was looking for an interpretation/formalism for quantum mechanics which would be manifestly symmetric between time and space. The first question I had was:

Is time already quantized?

Is time treated using the same quantum rules as space is? can quantum mechanics be written in a way which is manifestly covariant?
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The Block Universe

fmany of

‘Can a cube that does not last for any time at all, have a real

Filby became pensive. ‘Clearly,’ the Time Traveller proceeded, ‘any
real body must have extension in _four_ directions: it must have
Length, Breadth, Thickness, and–Duration. But through a natural
infirmity of the flesh, which I will explain to you in a moment, we
incline to overlook this fact. There are really four dimensions,
three which we call the three planes of Space, and a fourth, Time.
There is, however, a tendency to draw an unreal distinction between
the former three dimensions and the latter, because it happens that
our consciousness moves intermittently in one direction along the
latter from the beginning to the end of our lives.’Clearest.

‘Clearly,’ the Time Traveller proceeded, ‘any real body must have extension in four directions: it must have Length, Breadth, Thickness, and–Duration. But through a natural infirmity of the flesh, which I will explain to you in a moment, we incline to overlook this fact. There are really four dimensions, three which we call the three planes of Space, and a fourth, Time. There is, however, a tendency to draw an unreal distinction between the former three dimensions and the latter, because it happens that our consciousness moves intermittently in one direction along the latter from the beginning to the end of our lives.’

– H. G. Well’s The Time Machine

This is still the best single explanation of the idea of the  “block universe”, though Well’s Time Traveller does not use that term. As Julian Barbour puts it his The End of Time: “The objective world simply is, it does not happen. Only to the gaze of my consciousness, crawling upward along the life line of my body, does a section of this world come to life as a fleeting image in space which continuously changes in time.”
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A Typology of Quantum Gravities – Followup on Quantum Gravity Panel

Catherine Asaro, Jay Wile, & I had a good crowd for our quantum gravity panel at Philcon: I was impressed that that many people (perhaps 40 or 50) wanted to hear about a relatively esoteric subject. Esoteric but hot: there are (right now) 663 papers on the physics archive with quantum gravity in the title, in just the last five years!
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The Large Hadron Collider — Followup

Paul Halpern‘s talk on The Large Hadron Collider at Philcon on 11/21/2009 came off well.  I’ve since had a chance to read his Collider: The Search for the World’s Smallest Particles since.  The talk was basically the book light or, if you prefer, the book is the talk heavy.   Good jobs either way.

Paul had  a lot of fun with the idea that someone (from the future) is maliciously trying to keep us pitiful humans from building a high energy collider; first the money difficulties the Superconducting Super-Collider had in Texas and then the explosion at the Large Hadron Collider.  But now that the LHC is in fact colliding (if not yet at full strength), perhaps the little blue men have given all this up as a bad job.
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