The first difficulty arose in the discussion of the electromagnetic fi — Classical mechanics

"... Inertia resists acceleration, but acceleration relative to what? Within the frame of classical mechanics the only answer is: Inertia resists acceleration relative to space. This is a physical prop­erty of space—space acts on objects, but objects do not act on space. Such is prob­ably the deeper meaning of Newtons assertion spatium est absolutum (space is absolute). But the idea disturbed some, in particular Leibnitz, who did not ascribe an independent existence to space but considered it merely a proper­ty of "things" (contiguity of physical objects)."

"Newtonian mechanics does not apply to all situations. If the speeds of the interacting bodies are very large —an appreciable fraction of the speed of light —we must replace Newtonian mechanics with Einstein’s special theory of relativity, which holds at any speed, including those near the speed of light. If the interacting bodies are on the scale of atomic structure (for example, they might be electrons in an atom), we must replace Newtonian mechanics with quantum mechanics. Physicists now view Newtonian mechanics as a special case of these two more comprehensive theories. Still, it is a very important special case because it applies to the motion of objects ranging in size from the very small (almost on the scale of atomic structure) to astronomical (galaxies and clusters of galaxies)."

"Wave functions, probabilities, quantum tunneling, the ceaseless roiling energy fluctuations of the vacuum, the smearing together of space and time, the relative nature of simultaneity, the warping of the spacetime fabric, black holes, the big bang. Who could have guessed that the intuitive, mechanical, clockwork Newtonian perspective would turn out to be so thoroughly parachial—that there would be a whole new mind-boggling world lying just beneath the surface of things as they are ordinarily experienced?"

"The foundational achievement of classical mechanics is to establish that the first point is faulty. It is fruitful, in that framework, to allow a broader concept of the character of physical reality. To know the state of a system of particles, one must know not only their positions, but also their velocities and their masses. Armed with that information, classical mechanics predicts the system’s future evolution completely. Classical mechanics, given its broader concept of physical reality, is the very model of Einstein Sanity."

"Newtons system was for a long time considered as final and the task... seemed simply to be an expansion.... From the theory of the motion of mass points one could go over to the mechanics of solid bodies, to rotatory motions, and one could treat the continuous motion of fluid or the vibrating motion of an elastic body. All these... were gradually developed... with the evolution of mathematics, especially of the differential calculus... checked by experiments. and hydrodynamics became a part of mechanics. Another science... was astronomy. Improvements... led to... more accurate determinations of the motions of the planets... When the phenomena of electricity and magnetism were discovered, the... forces were compared to the gravitational forces... Finally, in the nineteenth century, even the theory of heat could be reduced..."

"Newton then elevates this approximate empirical discovery to the position of a rigorous principle, the principle of inertia, and states that absolutely free bodies hence will cover equal distances in equal times. ...It is the principle of inertia coupled with an understanding of spatial congruence that yields us a definition of congruent stretches of absolute time. ...The principle of inertia, together with the other fundamental principles of mechanics, enables us... to place mechanics on a rigorous mathematical basis, and rational mechanics is the result. ...science, in the case of mechanics, has followed the same course as in geometry. Initially our information is empirical and suffers from all the inaccuracies ...But this empirical information is idealised, then crystallised into axioms, postulates or principles susceptible of direct mathematical treatment. ...If peradventure further experiment were to prove that our mathematical deductions ...were not born out in the world of reality, we should have to modify our initial principles and postulates or else agree that nature is irrational. With mechanics, the necessity of modifying the fundamental principles became imperative when it was recognized that the mass of a body was not the constant magnitude we thought it to be; hence it was experiment that brought about the revolution. On the other hand, in the case of geometry, it was the mathematicians themselves who forsaw the possibility of various non-Euclidean doctrines, prior to any suggestion of this sort being demanded by experiment."