In 1887 Helmholtz discussed the foundations of measurement in science as a last contribution to his philosophy of knowledge. This essay borrowed from earlier debates on the foundations of mathematics, on the possibility of quantitative psychology, and on the meaning of temperature measurement. Late nineteenth-century scrutinisers of the foundations of mathematics made little of Helmholtz’s essay. Yet it inspired two mathematicians with an eye on physics, and a few philosopher-physicists. The aim of the present paper is to situate Helmholtz’s contribution (...) in this complex array of nineteenth-century philosophies of number, quantity, and measurement.Author Keywords: Helmholtz; Measurement; Arithmetic; P. Du Bois-Reymond; H. and R. Grassmann; J. von Kries. (shrink)
This book is a long-term history of optics, from early Greek theories of vision to the nineteenth-century victory of the wave theory of light. It is a clear and richly illustrated synthesis of a large amount of literature, and a reliable and efficient guide for anyone who wishes to enter this domain.
This book recounts a few ingenious attempts to derive physical theories by reason only, beginning with Descartes' geometric construction of the world, and finishing with recent derivations of quantum mechanics from natural axioms.
Any advanced theory of physics contains modules defined as essential components that are themselves theories with different domains of application. Different kinds of modules can be distinguished according to the way in which they fit in the symbolic and interpretive apparatus of a theory. The number and kind of the modules of a given theory vary as the theory evolves in time. The relative stability of modules and the variability of their insertion in other theories play a vital role in (...) the application, comparison, construction, and communication of theories. Modularity conveys some global unity to physics through the sharing of modules by diverse theories. This alternative to rigid hierarchies and holistic totalities permits a dynamical, plastic, and symbiotic approach to physical theory. (shrink)
In French mechanical treatises of the nineteenth century, Newton’s second law of motion was frequently derived from a relativity principle. The origin of this trend is found in ingenious arguments by Huygens and Laplace, with intermediate contributions by Euler and d’Alembert. The derivations initially relied on Galilean relativity and impulsive forces. After Bélanger’s Cours de mécanique of 1847, they employed continuous forces and a stronger relativity with respect to any commonly impressed motion. The name “principle of relative motions” and the (...) very idea of using this principle as a constructive tool were born in this context. The consequences of Poincaré’s and Einstein’s awareness of this approach are analyzed. Lastly, the legitimacy and significance of a relativity-based derivation of Newton’s second law are briefly discussed in a more philosophical vein. (shrink)
The relativistic revolution led to varieties of neo-Kantianism in which constitutive principles define the object of scientific knowledge in a domain-dependent and historically mutable manner. These principles are a priori insofar as they are necessary premises for the formulation of empirical laws in a given domain, but they lack the self-evidence of Kant’s a priori and they cannot be identified without prior knowledge of the theory they purport to frame. In contrast, the rationalist endeavors of a few masters of theoretical (...) physics have led to comprehensibility conditions that are easily admitted in a given domain and yet suffice to generate the theory of this domain. The purpose of this essay is to compare these two kinds of relativized a priori, to discuss the nature of the comprehensibility conditions, and to demonstrate their effectiveness in a modular conception of physical theories. (shrink)
A slight modification of Helmholtz’s metrical approach to the foundations of geometry leads to the locally Euclidian character of space without restriction of the curvature. A bolder generalization involving time measurement leads to the locally Minkowskian character of spacetime. Some philosophical consequences of these results are drawn.Keywords: Hermann Helmholtz; Space; Time; Spacetime.
Faraday's field concept presupposes that field stresses should share the axial symmetry of the lines of force. In the present article, the field dynamics is similarly required to depend only on field properties that can be tested through the motion of test-particles. Precise expressions of this 'Faradayan' principle in field-theoretical language are shown to severely restrict the form of classical field theories. In particular, static forces must obey the inverse square law in a linear approximation. Within a Minkowskian and Lagrangian (...) framework, the Faradayan principle automatically leads to Maxwell's theory of electromagnetism and to Einstein's theory of gravitation, without appeal to the equivalence principle. A comparison is drawn between this, Feynman's, and Einstein's way to arrive at general relativity. (shrink)
The first of its kind, this book is an in-depth history of hydrodynamics from its eighteenth-century foundations to its first major successes in twentieth-century hydraulics and aeronautics. It documents the foundational role of fluid mechanics in developing a new mathematical physics. It gives full and clear accounts of the conceptual breakthroughs of physicists and engineers who tried to meet challenges in the practical worlds of hydraulics, navigation, blood circulation, meteorology, and aeronautics, and it shows how hydrodynamics at last began to (...) fulfill its early promise to unify the different worlds of flow. Richly illustrated, technically thorough, and sensitive to cross-cultural effects, this history should attract a broad range of historians, scientists, engineers, and philosophers and be a standard reference for anyone interested in fluid mechanics. (shrink)