Le hasard

by Émile Borel

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

312 pages, Paperback

First published January 1, 1914

About the author

Félix Édouard Justin Émile Borel, né à Saint-Affrique le 7 janvier 1871, mort à Paris le 3 février 1956, est un mathématicien, professeur à la Faculté des sciences de Paris, spécialiste de la théorie des fonctions et des probabilités, membre de l'Académie des sciences, ainsi qu'un homme politique français, député et ministre. Ses actions pour la Société des Nations et au sein de son Comité fédéral de Coopération européenne font de lui un des précurseurs de l'idée européenne.

Reviews

[Randal Samstag · Rating 4 out of 5]

Emile Borel was a prominent French mathematician of the early twentieth century. His 1914 book, Le Hasard or Chance, is credited with an observation that has become a crucial insight in theories of 'decoherence' in modern quantum theory. This is the idea that explains the classical appearance of the observed world in quantum mechanical terms. Borel suggested that a small mass as far away as a distant star could have a significant influence on the motion of gas molecules here on Earth. This is an early statement of the modern quantum mechanical description of entanglement. It is consistent with the quantum mechanical theory that measurement of a quantum system causes entanglement. The ‘coherence’ of the measured system is destroyed by coupling with the environment during a measurement. Borel thus strongly repudiated the idea of determinism in nature.

A quote from Borel (p 178 - 180):

Cherchons à évaluer, en partant de la loi de Newton sur l'attraction universelle, la déviation que ferait subir à une molécule, dans l'intervalle de deux chocs, le déplacement d'une masse extrêmement petite située à une très grande distance. . . . La representation d'une masse gazeuse par une modele unique, forme de molecules dont les positions et les vitessees a un instant donne sont rigoureusement determinees, est donc une pure fiction abstraite; on ne peut se rapprocher de la realite qu'en imaginant un faisceau de moedles, c'est-a-dire en attribuant aus donnees initiales une certain indetermination. Si faibleque soit cette indetermination, si faible aussi que l'on supposes l'indetermination des forces exterieures, le effet des chocs disperse tres rapidement les faisceaux des trajectoires supposes infiniment delies et le probleme du movement ulterieur des molecules devient, en tres peu de secondes, tres indetermine, en ce sense qu'un nombre colossalement grand de possibilites defferentes sont a priori egalement probables.

We seek to evaluate, starting from Newton's law of gravitation, the deviation of a molecule, between two collisions, caused by the displacement of a mass extremely small located at a great distance. . . . The representation of a gaseous mass with a single model, consisting of molecules whose positions and velocities at a given time are rigorously determined, is pure abstract fiction; it cannot be closer to reality than imagining a stack of models, that is to say, by assigning to the initial data some uncertainty. So weak as this uncertainty, however small one supposes the uncertainty of external forces, the effect of collisions quickly disperses the beams trajectories assumed infinitely thin strokes and the problem of subsequent movement of molecules is in a very short of seconds, very indeterminate, in that a huge number of different possibilities are a priori equally probable.