Finally

Quantum Time now up on the physics archive.

Dissertation complete

I’ve finished re-checking the dissertation:  629 equations, 188 references, 110 pages, 83 input files, 48 lists, 36 footnotes, 28 quotes, 17 figures, 6 chapters (counting the appendix), 5 requirements, 1 idea.  It should be up on the physics archive in a day or two.

Now drops shoe the 3rd …

Give me the child. Through dangers untold and hardships unnumbered, I have fought my way here to the castle beyond the Goblin City to take back the child that you have stolen. For my will is as strong as yours, and my kingdom is as great…

Or, less poetically, I have (finally) finished checking the calculations in my dissertation.  The checked version is up & I hope to have it uploaded to the physics archive by the end of the weekend.

The Other Shoe Drops

I’ve just finished the cross checks on my dissertation “Quantum Time“.

The dissertation asks “what happens if measurements in the time dimension are fuzzy, just as we know they are in the space dimensions”?  Another way to put this is “what if particles are spread out in time, not just fixed in the present instant, but extending a bit into future and past”?

The question is motivated by relativity:  From relativity we know that time and space are interchangeable.  Even if a particle should happen to be flat in one frame, with no extension into past or future, in another frame it will have such an extension.  Therefore it is simplest to assume any particle is always extended a bit in time, just not so much that we notice it.

But to work out specific predictions from this is tricky:  how do you give an experimentalist something to chew on?

I was able to work out the rules for this by rewriting quantum mechanics in a way that doesn’t favor space over time.  But even with that part done, it was still tricky to apply these rules to specific experimental cases and be confident that I had used the rules consistently and correctly.

Eventually what I hit on is a set of principles (aside from being as careful as possible about the algebra!):  when the extension in time goes to zero, we should get exactly the standard result.  And every experiment should morph smoothly into its neighbors.  For instance, if we are working on a double slit experiment, and we separate the two gates far enough, the results should look like those for two separated single gates.

I’ve spent the last two months working on this & as of yesterday the analysis seems complete.

In general, of course, everything gets fuzzier in time.  If you send a particle through a “chopper”, a gate in time, then the pattern it leaves in time at the detector will be more spread out if time is fuzzy.

There were some surprises of course.  For instance, the classic double slit experiment normally produces an oscillating comb-like pattern at the detector.  If time is fuzzy, not only does each tooth of the comb get wider (we knew that was coming) but the teeth get more spread out.  And shorter.  So there are three different effects to look for.

All three effects are subtle, so it is possible that the effects of quantum time have already been seen, but racked up to experimental noise.

I’m letting the latest version of the paper cool off for a week, then giving it a quick double check & submitting it to the physics archive next weekend.

“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.

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.

Paradox Noise

“YOUR ONLY CHANCE LIES IN PREVENTING THE ASSASSINATION OF PRESIDENT ABRAHAM LINCOLN . . .” “What?” 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

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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

‘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

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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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