# Angel "Java" Lopez en Blog

### Publicado el 20 de Diciembre, 2013, 10:03

Sigo presentando y comentando esta "Introduction" del comienzo del libro de 1929, "The electromagnetc field", Ed. Dover, escrito por Max Mason y Warren Weaver:

Kirchoff in 1857 noticed the coincidence between the value of the velocity of light and that of the ratio of the electrical units.

Esa relación era completamente inesperada. Pero no parece que fuera Kirchoff el que la descubrió. Leo en:

http://en.wikipedia.org/wiki/Speed_of_light#Connections_with_electromagnetism

### Connections with electromagnetism

In the 19th century Hippolyte Fizeau developed a method to determine the speed of light based on time-of-flight measurements on Earth and reported a value of315,000 km/s. His method was improved upon by Léon Foucault who obtained a value of 298,000 km/s in 1862.[91] In the year 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch measured the ratio of the electromagnetic and electrostatic units of charge, 1/√ε0μ0, by discharging a Leyden jar, and found that its numerical value was very close to the speed of light as measured directly by Fizeau. The following year Gustav Kirchhoff calculated that an electric signal in aresistanceless wire travels along the wire at this speed.[122] In the early 1860s, Maxwell showed that, according to the theory of electromagnetism he was working on, electromagnetic waves propagate in empty space[123][124][125] at a speed equal to the above Weber/Kohrausch ratio, and drawing attention to the numerical proximity of this value to the speed of light as measured by Fizeau, he proposed that light is in fact an electromagnetic wave.[126]

Sigamos con la "intro":

In 1858 Riemann presented a paper to the Gottingen Academy in .which he assumed a finite velocity of propagation, and deduced that this rnust.be equal to the ratio of the units, and hence to the velocity of light. In 1867, Lorenz, of Copenhagen, extended the theory of Neumann, obtained expressions for the retarded vector and scalar potentials which are equivalent to the forms commonly used today, and was led independently of Maxwell to the conception of light as an electromagnetic phenomenon. The difference in viewpoints is, however, striking; for Lorentz considered that if light were shown to be electromagnetic in nature there was no longer the necessity for maintaining the hypothesis of an aether. The action at a distance theory was thus moving certainly toward the discovery of time lag in. effects and toward the electromagnetic theory of light. Maxwell reached this goal, however, by an attack from quite a different angle, and in the glare caused by his brilliant investigations much of the work just mentioned was lost sight of.

No conocía el trabajo de Riemann. Vean que los autores escriben "Lorenz, of Copenhagen", y luego "Lorentz". Por lo que veo, no se refieren al Hendrick Lorentz, mencionado en el título de este post, sino a:

http://en.wikipedia.org/wiki/Ludvig_Lorenz

Ludvig Valentin Lorenz (January 18, 1829 – June 9, 1891) was a Danish mathematician and physicist. He developed mathematical formulae to describe phenomena such as the relation between the refraction of light and the density of a pure transparent substance, and the relation between a metal's electrical and thermal conductivity and temperature (Wiedemann–Franz–Lorenz law).

Lorenz was born in Helsingør and studied at the Technical University in Copenhagen. He became professor at the Military Academy in Copenhagen 1876. From 1887, his research was funded by the Carlsberg Foundation. He investigated the mathematical description for light propagation through a single homogeneous medium and described the passage of light between different media. The formula for the mathematical relationship between the refractive index and the density of a medium was published by Lorenz in 1869 and by Hendrik Lorentz (who discovered it independently) in 1870 and is therefore called the Lorentz–Lorenz equation. Using his electromagnetic theory of light he stated what is known as the Lorenz gauge condition, and was able to derive a correct value for the velocity of light. He also developed a theory of light scattering, publishing it in Danish in 1890 and in French in his Collected Works, published in 1898. It was later independently rediscovered by Gustav Mie in 1908, so it is sometimes referred to as Lorenz–Mie theory. Additionally, Lorenz laid the foundations for ellipsometry by using Fresnel's theory of refraction to discover that light reflected by a thin transition layer between two media becomes elliptically polarized.[1]

Conocía a Mie, pero pensé que sus ideas estaban asociadas al "otro" Lorentz. Como casi siempre en la física moderna, empieza a aparecer la palabra "gauge".

Encontré una referencia al trabajo de Riemann en la cita de Google Books en Intellectual Mastery of Nature:

... Riemann generalized Poisson's equation for the electrostatic potential by adding to it a second-order time derivative of the potential to arrive at an equation of propagation, a wave equation with a source term. Riemann solved the equation using a so-called retarded potential, which he showed leads to experimentally confirmed results. Riemann  did not publish the paper, and when it appeared posthumously it was immediately criticized by Clausius, who pointed out a mathematical error in it and suggested that Riemann had withdrawn the paper because of it. But the theory was widely noticed, and, as we will see, Carl Neumann, for one, found it a stimulus to develop his own electrodynamic theory.

¿Será el Neumann mencionado en el fragmento de arriba? En una nota de este fragmento, leo:

Riemann was apparently the first to use a retarded potential, but because of the delay in the publication of the work, the first published use of it was by Ludwig Lorenz in 1861. Rosenfeld, "The Velocity of Light," 1635.

También leo en esta cita de Google Books:

In his lectures of Gottingen in 1861, which were published in 1876, Riemann proposed a new "fundamental law" of electrodynamics. This law was another variation of Weber's, differing from Weber's in that the total relative velocity of a pair of electric masses enters in place of the relativity velocity only along the line between the masses. This time Riemann did not derive the electrodynamic action from a finite propagation of the potential function but from Lagrange's law, which he constructed from the kinetic energy T of electrical system, an electrostatic part S of the potential depending only on position, and an electrodynamic part D of the potential depending on both position and velocity.

El que hubiera un potencial que dependiera de la velocidad era algo, digamos, novedoso. El potencial más usado hasta entonces, el gravitatorio, sólo dependía de la posición. Como pasa frecuentemente, aparece Lagrange en un problema físico.

En el próximo post, seguiré con el trabajo de Maxwell, mencionado en el fragmento de hoy.

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com