On the use, by Einstein, of the principle of dimensional homogeneity, in three problems of the physics of solids

Abstract

Einstein, in 1911, published an article on the application of the principle of dimensional homogeneity to three problems of the physics of solids: the characteristic frequency of the atomic nets of crystalline solids as a function of their moduli of compressibility or of their melting points, and the thermal conductivity of crystalline insulators. Recognizing that the physical dimensions of temperature are not the same as those of energy and heat, Einstein had recourse to the artifice of replace that physical parameter by its product by the Boltzmann constant, so obtaining correct results. But nowadays, with the new basic quantities "Thermodynamic Temperature θ (unitKelvin)", "Electric Current I (unit Ampère)" and "Amount of Substance MOL (unit-mole)", incorporated to the SI International System of Units, in 1960 and 1971, the same results are obtained in a more direct and coherent way. At the time of Einstein's article only three basic physical quantities were considered -length L, mass M, and time T. He ignored the theorem of dimensional analysis diffused by Buckingham three years later, and obtained the " numbers" by trial and error. In the present paper is presented a revisitation of the article of Einstein, conducted by the modern methodology of dimensional analysis and theory of physical similitude.

Average hydroxyapatite concentration is uniform in the extracollagenous ultrastructure of mineralized tissues: evidence at the 1?10-?m scale

“…3 is that the two quantities involved are defined on different levels: the equatorial diffraction spacing d w is a local distance of 1.2-1.5 nm between collagen molecules in a fibril; while q w is a quantity defined at the level of 1-10 lm. Following dimensional analysis (Buckingham 1914;Barenblatt 1996), it appears that if a physically meaningful relation exists between only these two parameters, it must be of the form (Carneiro 2000):…”