Sunday, November 20, 2011

What is "Field Momentum"

I remember hearing about "Field Momentum" - the idea that the electromagnetic fields (e.g. radiation) could have momentum and not understanding how that could be possible.  Particles / matter have momentum.  I've seen the equation and heard that photons have momentum, but did not understand.  But reading today I remembered / rediscovered some understanding.

If you have 2 particles (A and B), uncharged, then you can completely describe the state of the system by the position and momentum of each particle.

However, if the particles are charged, you need more information.  Imagine that a and b are not close to each other and are moving slowly.  Since these particles are charged, their motions affect each other.  The mechanism is through the electromagnetic field - as particle A moves, the electromagnetic field changes.  This change propagates away from particle A at the speed of light.  Particle B is affected by the motion of A sometime later depending upon its distance away from A.  So if you have a snapshot of the position and momentum of A and B, there could still be "information in transit" from A to B (or vice-versa) that has not yet affected their momentum/position, and you need to capture that information in order to fully describe the system.

Field momentum captures this information, and it tries to do it in a way that is similar (symmetric) with the way it is captured for the particles.

Some examples:
Example 1 - in the snapshot, A and B are slow moving and far apart.  Prior to the snapshot they were also slow moving and far apart.  A and B continue their slow motions.

Example 2 - A and B are slow moving in your snapshot, but immediately prior to the snapshot A was oscillating rapidly.  Not captured by the position and momentum of A and B are the electromagnetic waves that currently propagating from A to B.  Without these waves, A and B would continue as in example 1 (slow regular motion) - which would be incorrect, because when the waves reach B, B will begin to oscillate (perhaps rapidly if the mass to charge ratio of B is similar to A).

Wednesday, March 30, 2011

With notably rare exceptions...

Alan Greenspan: complete a*****e:

Alan Greenspan, regarding modern finance:
With notably rare exceptions (2008, for example), the global “invisible hand” has created relatively stable exchange rates, interest rates, prices, and wage rates

 I've extracted my favorites from the comment section in the original

With notably rare exceptions, Newt Gingrich is a loyal and faithful husband.

Though unredeemably(sic) opaque, Mr. Madoff’s operations delivered excellent returns, with notably rare exceptions.

With notably rare exceptions, the levees protecting New Orleans have held fast in the face of major hurricanes.
With notably rare exceptions, petroleum extraction has minimal environmental impact.

With notably rare exceptions, the New England Patriots were undefeated in the 2007-2008 season.

With notably rare exceptions, Ted Kennedy’s driving was superb.

With notably rare exceptions, Achilles was invincible.

With notably rare exceptions, atomic energy has been used to the benefit of mankind.

With notably rare exceptions (1940, for example), the Tacoma Narrows Bridge is impressively stable.

With notably rare exceptions, allowing Ayn Rand’s acolytes to serve as Federal Reserve chairmen has worked out well, both for the nation and the world.

With notably rare exceptions (e.g. 2004, 2011), living on the shores of the Pacific Ocean is perfectly safe.

Monday, March 7, 2011

Notes on Real Genius

At the end of the movie they mount a small optical component on Prof. Hathaway's house.  It looks like a retroreflector. That didn't make sense to me, at first.  But then I considered that they may have intended to fire the beam back at the source, damaging it.  This could explain why the laser fails catastrophically at the end of the movie.

Saturday, January 1, 2011

The chandelier needed something...

The chandelier needed something to make it mine:


This guy was in a Roomba I've had for over a year and hadn't gotten around to using:

I wonder what he was living on in there?