In essence the composition of physics resembles a palace. Whose exterior form is apparent to the unceremonious visitor, but whose inner life, it's conventions, traditions and rituals which give a special outlook and kinship to it's occupants, requires time and effort to comprehend. Initiation into this special knowledge is the goal of our endeavor, low and behold the endeavor isn't as simple, since this palace is of an ancient origin. The momentum generated by Newton's discoveries gave physics an impetus which is still prevalent. The eighteenth and nineteenth centuries saw a flowering of science as great minds such as Euler, Lagrange, Laplace, Faraday, and Maxwell extended our knowledge of the physical world. However, their efforts were directed at upward extension of the palace, Newton's account of the fundamental laws of physics was so overwhelming, and so successful, that not until the last quarter of the nineteenth century was there a serious attempt to investigate the foundations.
It was an Austrian mind, who first successfully challenged the Newtonian thought, It was Ernst Mach. Although Mach's work left Newtonian physics more or less intact, his thinking was crucial in the revolution shortly to come. In 1883, Mach published his texts "The Science of Mechanics," which incorporated a critique of Newtonian physics, the first incisive criticism of Newton's theory of dynamics. In addition to presenting a lucid account of Newtonian mechanics the text incorporates several significant contributions to the fundamentals of mechanics. Mach clarified Newtonian dynamics by carefully analyzing Newton's explanation of the dynamical laws, taking care to distinguish between definitions, derived results, and statements of physical law. Mach's approach is now widely accepted.
"The Science of Mechanics" raised the question of the distinction between absolute and relative motion. Mach pointed out Newton's ambivalence on this subject, although he went on to show that the question was irrelevant to the application of Newtonian dynamics. In the process he dwelt on the problem of inertia and enunciated the principle that now bears his name, inertia is not an intrinsic property of matter or space but depends on the existence of all matter in the universe. The problem of inertia was not the crucial difficulty with Newtonian mechanics.
The fundamental weakness in Newtonian dynamics, as Mach pointed out, centers on Newton's conception of space and time. In a preface to his dynamical theory, Newton avowed that he would forgo abstract speculation and deal only with observable facts. Although such a point of view is now commonplace, at the time it represented a tremendous intellectual leap. Before Newton, the business of natural philosophy was to explain the reasons for things, to find a rational account for the workings of nature, rather than to describe natural phenomena quantitatively. Newton essentially reversed the priorities. Against the criticism that his theory of universal gravitation merely described gravity without accounting for it's origin, Newton said "I do not make hypotheses".(from STEVEN WEINBERG's The Revolution That Didn't Happen )
Unfortunately, Newton was not completely faithful to his resolve to avoid abstract speculation and to deal only with demonstrable facts. In particular, consider the following description of time. that appears in the Principia.
"Absolute, true and mathematical time, of itself and by its own true nature, flows uniformly on, without regard to anything external.
Relative, apparent and common time is some sensible and external measure of absolute time estimated by the motions of bodies, whether. accurate or in-equable, and is commonly employed in place of true time; as an hour, a day, a month, a year.."
Mach comments,
"it would appear as though Newton in the remarks cited here still stood under the influence of medieval philosophy, as though he had grown unfaithful to his resolve to investigate only actual facts."
Mach goes on to point out that since time is necessarily measured by the repetitive motion of some physical system, for instance the pendulum of a clock or the revolution of the earth about the sun, then the properties of time must be connected with the laws which describe the motions of physical systems. Simply put, Newton's idea of time without clocks is metaphysical. To understand the properties of time we must observe the properties of clocks. A simple idea? Yes, indeed, were it not for the fact that the idea of absolute time is so natural that the eventual consequences of Mach's position, the relativistic description of time, still come as something of a surprise.
There are similar weaknesses in the Newtonian view of space. Mach argued that since position in space is determined with measuring rods, the properties of space can be understood only by investigating the properties of meter sticks. We must look to nature to understand space, not to platonic ideals. Mach's special contribution was to examine the most elemental aspects of Newtonian thought, to look critically at matters which seem too simple to discuss, and to insist that we turn to experience to understand the properties of nature rather than to rely on abstractions of the mind. From this point of view, Newton's assumptions about space and time must be regarded merely as postulates.
Mach's review had little immediate effect, but its influence was eventually profound. In particular, the youthful Einstein, while a student at the Polytechnic Institute in Zurich in the period 1897-1900, was much attracted by Mach's ideas on the foundations of Newtonian physics and by Mach's insistence that physical concepts be defined in terms of observations. However, the immediate cause for the overthrow of Newtonian physics was not Mach's criticisms of Newtonian thought. The difficulties lay with Maxwell's electromagnetic theory, the utmost achievement of classical physics, which could be an intriguing topic for discussion in a future post!
In hindsight, Ernst Mach's contribution through his Science of mechanics, unclogged unaware minds, and gave rise to tremendous achievements with regards to understanding space, time and motion.
Further reading:
https://plato.stanford.edu/entries/ernst-mach/