Comments on the Culture of the Forceстатья из журнала
Аннотация: One of Frank Wilczek’s main themes in “Whence the Force of F = ma? I: Culture Shock” (Physics Today, October 2004, page 11) appears to be that although the force is, in Wilczek’s words, “vaguely defined,” it “continues to flourish” because the microscopic details it conceals are not really relevant for the scale of the phenomena it serves to describe. Further, it “survives the competition” because “it is much easier to work with.” To this second point one might add that nothing succeeds like success. Let me explain.The concept of force had been under attack much before the comments of Peter Tait and Bertrand Russell. Even some of Isaac Newton’s immediate successors, most notably Joseph-Louis Lagrange and Jean Le Rond d’Alembert, were critical of the concept. d’Alembert regarded it as “useless to mechanics” and said that it “ought therefore to be banished from it.” 1 1. C. Truesdell, in Essays in the History of Mechanics, Springer-Verlag, New York (1968) https://doi.org/10.1007/978-3-642-86647-0. However, the use of Newton’s idea that force is a primary, nonderived concept, which was pursued steadfastly by Leonhard Euler, 1 1. C. Truesdell, in Essays in the History of Mechanics, Springer-Verlag, New York (1968) https://doi.org/10.1007/978-3-642-86647-0. led to the greatest successes in continuum mechanics in the two centuries immediately following publication of Newton’s Principia. That period culminated in the 1820s in Augustin-Louis Cauchy’s stress principle, 1 1. C. Truesdell, in Essays in the History of Mechanics, Springer-Verlag, New York (1968) https://doi.org/10.1007/978-3-642-86647-0. which unified the seemingly disparate fields of fluid mechanics and elasticity. This approach, commonly attributed to Newton rather than to Euler or Cauchy, is chosen over its main competitor, the variational formulation of Lagrange, to be taught in a typical fluid mechanics course. The stress has also been given a microscopic interpretation in kinetic theory and in more general statistical mechanics. Wilczek mentions some assumptions about forces. Newton regarded mechanics as “the science of motions that result from any forces whatever.” 1 1. C. Truesdell, in Essays in the History of Mechanics, Springer-Verlag, New York (1968) https://doi.org/10.1007/978-3-642-86647-0. Thus, he did not exclude contact forces, the dominating concept in continuum mechanics. Nor did he demand that all forces be central, which has particular relevance to the derivation of the angular momentum principle.In 1776, Euler, guided by his research on elasticity, came to regard the balance of angular momentum as an independent, second principle of mechanics, 1 1. C. Truesdell, in Essays in the History of Mechanics, Springer-Verlag, New York (1968) https://doi.org/10.1007/978-3-642-86647-0. the first principle being the balance of linear momentum. When Euler arrived at the rigid-body equations of motion in 1752 using the first principle, he had to invoke hypotheses about internal forces. However, once he saw the balance of the moments as an independent principle, he had no need of such hypotheses. In special cases such as that of a perfect fluid, the second principle follows from the first. In fact, the second principle leads to the symmetry of the stress tensor when all torques may be obtained as moments of forces. 2 2. R. Aris, Vectors, Tensors and the Equations of Fluid Mechanics, Dover, New York (1962). The status of the third law has been clarified by the work of Walter Noll, who gives a precise mathematical interpretation of Newton’s verbal statement of the law. 3 3. W. Noll, in The Axiomatic Method with Special Reference to Geometry and Physics, North-Holland, Amsterdam (1959), p. 266. Even in applications of quantum mechanics, Richard Feynman emphasized the importance of forces. 4 4. R. P. Feynman, Phys. Rev. 56, 340 (1939) https://doi.org/10.1103/PhysRev.56.340. He commented that “many of the problems of molecular structure are concerned essentially with forces,” that “forces are almost as easy to calculate as energies are,” and that “the quantities are quite as easy to interpret.” Another application of the concept of force is found in nonequilibrium statistical mechanics. Just as the contact force had to be found as the appropriate force to describe the dynamics of the continuum, the physically realistic short-time force derived from the mean instantaneous potential had to be discovered as the force that describes typical chemical dynamics in liquids, 5 5. S. Adelman, R. Ravi, Adv. Chem. Phys. 115, 181 (2000) https://doi.org/10.1002/9780470141748.ch3. in contrast to the traditional concept of the potential of mean force, which is more appropriate for slow or diffusion processes.REFERENCESSection:ChooseTop of pageREFERENCES <
Год издания: 2005
Авторы: Ramamurthy Ravi
Издательство: AIP Publishing
Источник: Physics Today
Ключевые слова: Advanced Thermodynamics and Statistical Mechanics, stochastic dynamics and bifurcation, Ecosystem dynamics and resilience
Открытый доступ: bronze
Том: 58
Выпуск: 8
Страницы: 15–16