Angel "Java" Lopez en Blog

13 de Octubre, 2012

Publicado el 13 de Octubre, 2012, 11:20

Estoy estudiando bastante de física cuántica, sus conceptos, historia, desarrollo conceptual y su relación con la filosofía y el realismo. Es un tema fascinante, pero que lleva su tiempo, y su costo, para alguien como yo aún afectado por el efecto Coto :-). Hay varias razones para que me resulte fascinante, y una es la relación que la física, en general, y la física cuántica, en particular, establece con las matemáticas. Para realmente entender física cuántica, hay que conocer bastante de matemáticas y mucho de física clásica. Por ejemplo, trozos de física matemática clásica traida de nuevo a la cuántica, se ven en el caso de la necesidad de usar lagrangianos y hamiltonianos, o series e integrales de Fourier.

Así que estoy repasando temas viejos y estudiando temas nuevos (para mí) de física y matemáticas. Uno de los libros que más me está ayudando es un clásico, el Methods of Mathematical Physics, en dos volúmenes, de Richard Courant y David Hilbert (tengo pendiente de leer otro libro que tengo, una biografía de los dos). En mi vida, mi primer contacto con la obra de Courant fue con su popular What  is Mathematics? en coautoría con Herbert Robbins, habrá sido en los ochenta. Sólo mucho más adelante conocí de su relación con David Hilbert.

Tengo la edición de 1953, revisada por Courant. La versión original en alemán fue publicada en 1924. Curiosamente, a pesar que el gran salto en la mecánica cuántica fue en 1925-26, con los trabajos de Heisenberg y Schrödinger, el contenido del libro me sirve para empaparme de varios de los temas que son necesarios para entender el desarrollo de la mecánica cuántica de entonces, y luego, de la física cuántica en general, como es el caso de las series de Fourier mencionadas, y cálculo de variaciones. Hasta estudiar álgebra lineal tiene un gusto distinto en este libro. Leo en el artículo de la wikipedia sobre el libro:

The material of the book was worked up from the content of Hilbert's lectures. While Courant played the major editorial role, many at the University of Göttingen were involved in the writing-up, and in that sense it was a collective production.

On its appearance in 1924 it apparently had little direct connection to the quantum theory questions at the centre of the theoretical physics of the time. That changed within two years, since the formulation of Schrödinger's equation made the Hilbert-Courant techniques of immediate relevance to the new wave mechanics.

Es bueno recordar el prefacio de la primera edición en inglés de este excelente libro, escrito por Courant:

The first German edition of this volume was published by Julius Springer, Berlin, in 1924. A second edition, revised and improved with the help of K. O. Friedrichs, R. Luneburg, F. Rellich, and other unselfish friends, followed in 1930. The second volume appeared in 1938. In the meantime I had been forced to leave Germany and was fortunate and grateful to be given the opportunities open in the United States. During the Second World War the German book became unavailable and later was even suppressed by the National Socialist rulers of Germany. Thus the survival of the book was secured when the United States Government seized the copyright and licensed a reprint issued by Interscience Publishers, New York. Such a license also had to be obtained from the Alien Property Custodian for the present English edition.

Un ejemplo de la estupidez humana ha sido prohibir este libro. Leo en la wikipedia:

An Alien Property Custodian was an office within the Government of the United States during World War I and again during World War II, serving as a Custodian of Enemy Property to property that belonged to US enemies.

Sigue Courant:

This edition follows the German original fairly closely but contains a large number of additions and modifications. I have had to postpone a plan to completely rewrite and modernize the book in collaboration with K.O. Friedrichs, because the pressure for publication of an English "Courant-Hilbert" has become irresistible. Even so, it is hoped that the work in its present form will be useful to mathematicians and physicists alike, as the numerous demands from all sides seem to indicate. The objective of the book can still today be expressed almost as in the preface to the first German edition.

Es interesante leer que una de las motivaciones para el libro fue la separación entre física y matemáticas, dado la aparición de estructuras abstractas y formalismo en estas últimas, donde curiosamente Hilbert tuvo mucho que ver.

"Since the seventeenth century, physical intuition has served as a vital source for mathematical problems and methods. Recent trends and fashions have, however, weakened the connection between mathematics and physics; mathematicians, turning away from the roots of mathematics in intuition, have concentrated on refinement and emphasized the postulational side of mathematics, and at times have overlooked the unity of their science with physics and other fields. In many cases, physicists have ceased to appreciate the attitudes of mathematicians. This rift is unquestionably a serious threat to science as a whole; the broad stream of scientific development may split into smaller and smaller rivulets and dry out. It seems therefore important to direct our efforts toward reuniting divergent trends by clarifying the common features and interconnections of many distinct and diverse scientific facts. Only thus can the student attain some mastery of the material and the basis be prepared for further organic development of research.

Es placentero leer este libro, porque libros más modernos están más orientados a enunciar rápidamente algunos teoremas y reglas, para formar ingenieros, o están orientados a estructuras abstractas, para formar matemáticos.

"The present work is designed to serve this purpose for the field of mathematical physics. Mathematical methods originating in problems of physics are developed and the attempt is made to shape results into unified mathematical theories. Completeness is not attempted, but it is hoped that access to a rich and important field will be facilitated by the book.

"The responsibility for the present book rests with me. Yet the name of my teacher, colleague, and friend, D. Hilbert, on the title page seems justified by the fact that much material from Hilbert's papers and lectures has been used, as well as by the hope that the book expresses some of Hilbert's spirit, which has had such a decisive influence on mathematical research and education."

I am greatly indebted to many helpers in all phases of the task of preparing this edition: to Peter Ceike, Ernest Courant, and Anneli Lax, who provided most of the first draft of the translation; to Hanan Rubin and Herbert Kranzer, who have given constructive criticism; to Wilhelm Magnus, who is responsible for the appendix to Chapter VII; and to Natascha Artin and Lucile Gardner, who carried the burden of the editorial work. Most cordial thanks also are due to Interscience Publishers for their patient and helpful attitude and to my old friend and publisher, Dr. Ferdinand Springer in Heidelberg, the great pioneer of modern scientific publishing, for his sympathetic understanding of the situation, which has so greatly changed since the old days of our close cooperation.

JUNE 1953

Post relacionados, con respecto a las dos guerras, la persecución del nacionalsocialismo, la ciencia y las matemáticas:

Físicos cuánticos en 1933
Einstein: ciencia más allá de la guerra
Ciencia en guerra
Felix Hausdorff

Sobre Hilbert:

Los problemas de Hilbert
Imágenes y símbolos, según Hilbert
David Hilbert, según Jean Dieudonné
Formalismo en matemáticas
David Hilbert, por Richard Courant

Nos leemos!

Angel "Java" Lopez

Por ajlopez, en: Ciencia