Particles/molecules versus continuum: The never-ending debate

Abstract

Corpuscular tiny bodies (“particles”) interacting through empty space via at-a-distance forces and a continuum transmitting forces by contact are traditionally presented as two alternate pictures of the physical mechanical world, and this from the early inception of physics by the ancient Greek “philosophers of Nature”. But for more than two millenaries endeavours by the most illustrious physicists and mathematicians have been to reconcile these two visions or, for the least, to deduce the second one from the first thought to be more “physical”. This contribution focuses more precisely on such a move from Newton to the early twentieth century with special attention to mechanicians of fluids and solids such as Poisson, Navier, Cauchy, Piola, Green, and others, who created the modern theory of continuum mechanics, essentially through its special branch known as the theory of elasticity. The latter provides the best illustration of the various strategies applied by great scientists in their harsh competition. The nineteenth century French engineers-scientists take the largest share in this endeavour. The subject matter, however, remains an unsettled one, all the more that recent powerful techniques of computation favour a return to the corpuscular vision.