Leo Philip Kadanoff

LPK

We have lost a great scientist.

Michael Fisher, and him, revolutionized theoretical physics when I started my studies at UCSB in 1973. I was lucky to have had Robert Brout telling us at CINVESTAV, Mexico, that phase transitions were the best subjects to study.

Water boiling as temperature goes up, and magnetism arising as temperature goes down. All around this beautiful Universe, this is happening, you don't need to only look at CERN, and Fermilab.

One idea I want to emphasize here is that of fractal curves.

Critical exponents are hard to measure, because they depend logarithmically on macroscopic variables. One has to change the control variable by orders of magnitude to observe the predictions.

Nevertheless critical exponents exist.

My friend John L. Cardy  understood that expanding protons, could be explained by critical phenomena ideas, the size of proton-proton cross sections is  proportional to the logarithm of the  energy .

To this day, the Ultra High Energy Cosmic Rays (UHECR) have been observed to obey this law.


 Behind all these logarithms there are critical exponents, best explained by fractal motion.

According to Quantum Mechanics, particles do not follow classical paths, they can be best described by density functions. These functions inform us of the most likely place to find them.

Kadanoff-Fisher-Wilson are the authors of these foundational ideas. To understand the motion of a quantum particle one has to use fractal paths. These curves are continuous, but do not have derivatives on any point. These paths can be best described by their critical exponents. Their lenght is infinite, but their fractal dimension is not.