"Let a drop of wine fall into a glass of water; whatever be the law that governs the internal movement of the liquid, we will soon see it tint itself uniformly pink and from th at moment on, however we may agitate the vessel, it appears that the wine and water can separate no more. All this, Maxwell and Boltzmann have explained, but the one who saw it in the cleanest way, in a book that is too little read because it is difficult to read, is Gibbs, in his Principles of Statistical Mechanics." (Henri Poincaré, "La valeur de la science" ["The Value of Science"], 1904)
"Newton was the greatest creative genius physics has ever seen. None of the other candidates for the superlative (Einstein, Maxwell, Boltzmann, Gibbs, and Feynman) has matched Newton’s combined achievements as theoretician, experimentalist, and mathematician. […] If you were to become a time traveler and meet Newton on a trip back to the seventeenth century, you might find him something like the performer who first exasperates everyone in sight and then goes on stage and sings like an angel." William H Cropper,"Great Physicists", 2001)
"Replacing particles by strings is a naive-sounding step, from which many other things follow. In fact, replacing Feynman graphs by Riemann surfaces has numerous consequences: 1. It eliminates the infinities from the theory. [...] 2. It greatly reduces the number of possible theories. [...] 3. It gives the first hint that string theory will change our notions of spacetime." (Edward Witten, "The Past and Future of String Theory", 2003)
"Physics reduces Moonshine to a duality between two different pictures of quantum field theory: the Hamiltonian one, which concretely gives us from representation theory the graded vector spaces, and another, due to Feynman, which manifestly gives us modularity. In particular, physics tells us that this modularity is a topological effect, and the group SL2(Z) directly arises in its familiar role as the modular group of the torus." (Terry Gannon, "Moonshine Beyond the Monster: The Bridge Connecting Algebra, Modular Forms and Physics", 2006)
"Among the differences that will always be with you are the small overshoots and oscillations just before and after the vertical jumps in the square waves. This is called 'Gibbs ripple' and it will cause an overshoot of about 9% at the discontinuities of the square wave no matter how many terms of the series you add. But [...] adding more terms increases the frequency of the Gibbs ripple and reduces its horizontal extent in the vicinity of the jumps." (Daniel Fleisch & Laura Kinnaman, "A Student’s Guide to Waves", 2015)
"Combining the ideas of thermodynamics and Hamiltonian mechanics Gibbs. introduced into statistical physics a remarkable mathematical structure - the Hamiltonian system endowed with a measure evolving (sometimes toequilibrium which is of particular interest) under the action of a Hamiltonian flow in the phase space of the system." (Vladimir Zorich, "Mathematical Analysis of Problems in the Natural Sciences", 2010)
"Clausius, Maxwell, Boltzmann and Gibbs had a feeling for the statistical interpretation of the second principle of thermodynamics and defended it. But their explanations were based on thought experiments coming from the postulate of the existence of molecules. Only after the discovery of Brownian motion does the interpretation of the second principle of thermodynamics as an absolute law become impossible. Brownian particles rising and falling as a result of the thermal motion of the molecules is a clear demonstration for us of a perpetual motion machine of the second kind. Therefore at the end of the 19th century the investigation of Brownian motion acquired enormous theoretical significance and attracted the attention of many theoretical physicists including Einstein." (Vladimir Zorich, "Mathematical Analysis of Problems in the Natural Sciences", 2010)
No comments:
Post a Comment