New numerical algorithms

Two recent developments on numerical analysis have called my attention

A new very efficient sparse Fourier transform
http://web.mit.edu/newsoffice/2012/faster-fourier-transforms-0118.html

A significantly faster algorithm for matrix multiplication
http://www.newscientist.com/article/mg21228422.500-mathematical-matrix-multiplier-sees-first-advance-in-24-years.html

De Broglie waves and relativity

Another extremely interesting connection between relativity and quantum mechanics is that the quantum De Broglie waves can be understood as an effect of the relativistic desynchronization of clocks given that the clocks rotate with a frequency proportional to the total energy of the particle.   

Imagine a train with a long chain of synchronized clocks from one extreme to the other with the synchronization established according to an observer moving along with the train. Another person standing still on the train station will conclude that the clocks are actually not synchronized (what he would see is a different thing). If the train is moving to the right, the clocks on the right will be ahead respect to the clocks on the left. The De Broglie wave length will be the length that stretches 12 hours of desynchronization.   

[1] W. Baylis, Canadian Journal of Physics, 2007, 85:(12) 1317-1323, 10.1139/p07-121

The ball is round!

The first thing we learn in a course of relativity is the relativistic length contraction effect for moving objects relative to an observer. However, what one would actually see is a different thing ! because another important effect must be considered; the time required for the light to arrive from the different points of the observed object to our eyes. The combined effect of the Lorentz contraction along with the time delay was investigated reaching to curious results. For example, a relativistic ball remains with a round appearance!, as discussed by Penrose in the following paper

http://adsabs.harvard.edu/abs/1959PCPS...55..137P

A nice visulaization can be found at

http://www.spacetimetravel.org/ueberblick/ueberblick1.html

Thermodynamical entropy and Shannon information

The moment I read about information theory I thought that it was evident that the thermodynamical entropy  was completely equivalent; the same thing, just measured in different units with the Boltzmann constant in the middle. I was shocked when I read that this issue is still under debate today. There are two books that share the idea that the thermodynamical entropy is fundamentally a measure of information

• A Farewell To Entropy: Statistical Thermodynamics based on Information. By Arieh Ben-Naim

• E.T. Jaynes: Papers on Probability, Statistics and Statistical Physics. By R.D. Rosenkrantz (Editor)
  

The main issue is that the Shannon information is fundamentally conserved, while  the thermodynamical entropy  may describe irreversible systems where it is not conserved. More about this topic can be found at

• http://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_information_theory

PyNewtonCUDA

Denys Bondar and I, just released to the public: PyNewtonCUDA

https://code.google.com/p/py-newton-cuda/

This program is able to propagate a large number of classical particles using  GPU technology. The code is written in Python and PyCUDA, which allows to write high-level code for GPU programming while maintaining very high performance.


You can download the code with the following command

svn checkout https://py-newton-cuda.google.com/svn/trunk PyNewtonCUDA

I found a book on the interesting and very difficult topic of many-body classical relativistic theory

Classical Relativistic Many-Body Dynamics

Trump, M.A., Schieve, W.C
Springer, Fundamental Theories of Physics, Vol. 103

This relativistic covariant many-body formulation overcomes the no go theorem by Jordan and Sudarshan [1] by giving up the locality of the interactions and the individual mass-shell conditions. These are not simply cosmetic upgrades but have serious consequences on how we should understand classical physics.

"The single particle has no significance; it is the whole system that counts" --Lanczos


[1] FROM CLASSICAL TO
QUANTUM MECHANICS
Giampiero Esposito, Giuseppe Marmo

Geo-coordinates for citations on scientific papers

Here I draw a map for the places that either published a paper mentioning the word Bures measure or were referenced by somebody who used the word Bures measure

The corresponding plot with the citations as links was created by my brother Ruben Cabrera

The total number of papers in consideration were 662. The extraction of coordinates from heterogeneous references is an expensive computational task.