# Enrique Loedel Palumbo

Enrique Loedel Palumbo (Montevideo Uruguay, June 29, 1901 – La Plata Argentina, July 31, 1962) was an Uruguayan physicist.

Loedel Palumbo was born in Montevideo, Uruguay and studied at the University of La Plata in Argentina. His doctoral advisor was the German physicist of Jewish origin Richard Gans. Loedel wrote his Ph.D. thesis in December 1925[1] on optical and electrical constants of sugar cane. An extract of the thesis was published in German in Annalen der Physik in 1926.[2] He then began his career as professor in La Plata.

During Einstein's visit to Argentina in 1925[3] they had a conversation about the differential equation of a point-source gravitational field, which resulted in a paper published by Loedel in Physikalische Zeitschrift.[A 1] It is claimed that this is the first research paper on relativity ever published by a Latin American scientist.[4]

Loedel Palumbo then spent some time in Germany working with Erwin Schrödinger and Max Planck. He returned to Argentina in 1930 and from there on concentrated on teaching. He published several scientific papers during his career in international journals and wrote several books (in Spanish).

## Loedel diagram

The Loedel frame is a resting frame showing two moving frames with equal speeds in opposite directions. The two sets of parallel lines represent simultaneous events, one set for each moving frame.

Max Born (1920) and systematically Paul Gruner (1921) introduced symmetric Minkowski diagrams in German and French papers, where the ct'-axis is perpendicular to the x-axis, as well as the ct-axis perpendicular to the x'-axis (for sources and historical details, see Loedel diagram).

In 1948 and in subsequent papers, Loedel independently rediscovered such diagrams.[A 2][A 3] They were again rediscovered in 1955 by Henri Amar,[5] who subsequently wrote in 1957 in American Journal of Physics: "I regret my unfamiliarity with South American literature and wish to acknowledge the priority of Professor Loedel's work", along with a note by Loedel Palumbo citing his publications on the geometrical representation of Lorentz transformations.[6] Those diagrams are therefore called "Loedel diagrams", and have been cited by some textbook authors on the subject.[7][8]

Suppose there are two collinear velocities v and w. How does one find the frame of reference in which the velocities become equal speeds in opposite directions? One solution uses modern algebra to find it: Suppose ${\displaystyle \tanh \ a\ =\ v/c}$ and ${\displaystyle \tanh \ b\ =\ w/c}$, so that a and b are rapidities corresponding to velocities v and w. Let m = (a + b)/2, the midpoint rapidity. The transformation

${\displaystyle z\mapsto ze^{-mj}}$

of the split-complex number plane represents the required transformation since ${\displaystyle e^{aj}\mapsto e^{(a-b)j/2}}$ and ${\displaystyle e^{bj}\mapsto e^{(b-a)j/2}.}$ As the exponents are additive inverses of each other, the images represent equal speeds in opposite directions.

## Publications

1. ^ Loedel, Enrique (1926). "Die Form der Raum-Zeit-Oberfläche eines Gravitationsfeldes, das von einer punkt-förmigen Masse herrürt". Physikalische Zeitschrift. 27: 645–648.
2. ^ Loedel, Enrique (1948). "Aberracion y Relatividad". Anales Soc. Cient. Argentina. 145: 3–13.
3. ^ Fisica relativista, Kapelusz Editorial, Buenos Aires, Argentina (1955).

## Notes and references

1. ^ Babiloni, A.G. (2007). "La Física en La Plata, del Justicialismo al Desarrollismo pasando por "La Libertadora"". Anales de la Asociación Física Argentina. Retrieved 2016-04-26.
2. ^ "Optische und electrische Konstanten des Rohrzuckers", Annalen der Physik 384(6):533–49 (1926)
3. ^ Thomas F. Glick (1987) "Cultural issues in the reception of relativity", in Glick (ed.) The Comparative Reception of Relativity, D. Reidel ISBN 90-277-2498-9 . "In his trips to Spain, Brazil, Argentina, and Uruguay, Einstein spoke mainly to engineers who comprised the rank-and-file of those with interest in his ideas."
4. ^ Current Literature on Science of Science, volume 20, 1991, pp. 167-169 (Review of Lewis Pyenson's book "Cultural Imperialism and Exact Sciences): p. 168: "Later, in 1925, Einstein visited Argentina, and was met by Enrique Loedel Palumbo, a young Uruguayan physicist then finishing a doctorate at La Plata. Palumbo asked Einstein about a system of differential equations for a point-source gravitational field. Einstein did not know the solution, but was interested in it. Palumbo published on the subject shortly thereafter and was hailed as Argentina's first world-class theoretician."
5. ^ Amar, Henri (1955). "New Geometric Representation of the Lorentz Transformation". American Journal of Physics. 23 (8): 487–489. Bibcode:1955AmJPh..23..487A. doi:10.1119/1.1934074.
6. ^ Amar, Henri; Loedel, Enrique (1957). "Geometric Representation of the Lorentz Transformation". American Journal of Physics. 25 (5): 326–327. Bibcode:1957AmJPh..25..326A. doi:10.1119/1.1934453.
7. ^ Albert Shadowitz (1988). Special relativity (Reprint of 1968 ed.). Courier Dover Publications. pp. 20–22. ISBN 978-0-486-65743-1.
8. ^ E. Beneditto, M. Capriolo, A. Feoli, D. Tucci (2013) Some remarks about underused Loedel diagrams European Journal of Physics 34(1)
9. ^ Loedel Palumbo, Enrique; De Luca, Salvador (1941). Elementos de Cosmografía. Estrada.
10. ^ Loedel Palumbo, Enrique (1955). Física Relativista. Kapelusz.