xcthulhu
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Joined: December 14th, 2006, 12:55 pm
Location: Cambridge, MA
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April 2011
Notes on Category Theory and Quantum Mechanics
April 10th, 2011, 9:23 am

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So I was recently curious about Quantum Logic, and I discovered that it basically takes "Propositions" to be self adjoint operators, like so:

$\langle P x | y\rangle = \langle x | P y\rangle$

Immediately, I thought: "Just like self-adjoint endofunctor!"

Being not a physicist, but having basic graduate category theory behind me, I thought maybe that the categorical perspective would be a way to crack the subject for me. So I immediately found this little article by John Baez.

There's also this really old paper from the 1970s by Holdsworth. I haven't read it - don't want to bother with remote accessing my university account to retrieve it: ...

[ continued ]

Lately I've been studying quaternions for some software I'm writing to do space-craft attitude simulation. This involves brushing up on my basic mechanics, as well as my algebra - because the standard in aerospace is to represent rotations in terms of quaternions which do not have coordinate singularities.

Now one thing I need to do in my simulations is to approximate the instantaneous angular velocity tensor $\omega$, which is obtained from the momentum vector $L$ and the moment of inertia tensor $I$, which I am to be provided by my engineering friends. Specifically, the equation relating these is:

$L = I \cdot \omega$

Not really all that relevant, just background :D

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Moreover, we may observe that the rotation $A$ obeys the following:

(1) $\frac{\partial A}{\partial t} = \omega \cdot A$...

[ continued ]

Hey All,

This summer, I will be working with Thomas Hales on his work to proof of the Kepler conjecture. He'll be based out of Hanoi, Vietnam.

Now, sadly University of Pittsburg, which is arranging the research program this summer, couldn't arrange for a flight to Vietnam for me from Amsterdam, since it was out of budget. They could only manage a flight out of the US. However, I had a frequent flyer ticket out of Amsterdam to Logan Airport, so I'll be flying to the US before flying to Vietnam.

This flight plan is kind of crazy:
Schiphol, Amsterdam, NL -> O'Hare, Chicago, IL
O'Hare, Chicago, IL -> Logan, Boston, MA
Logan, Boston, MA -> JFK Intl Airport, New York, NY
JFK Intl Airport, New York, NY -> Hong Kong Intl. Airport, Hong Kong, China
Hong Kong Intl. Airport, Hong Kong, China -> Noi Bai, Hanoi, Vietnam

And here's the path on google maps... estimated around 13,700 miles......

[ continued ]

Last edited by xcthulhu on May 23rd, 2009, 1:50 pm, edited 4 times in total.