From τὰ φυσικά (ta physika) to physics – LXIV

1023 days ago, I posted the first episode of this series tracking the development of physics from Aristotle’s τὰ φυσικά to the point where the term physics began to be used. Now in the sixty-fourth episode we have finally reached our destination. In that first episode I took a look at the term physics its origins in Aristotle’s Greek and how it changed down the centuries until it first emerged with its modern meaning in 1715. 

Although there is no link, the emergence of the term physics in its modern meaning is with certainty related to the publication of Newton’s Principia. Of course, Newton’s tome proudly contains the term Philosophiæ Naturalis (Natural Philosphy) in its title but it’s the other half of the title that is new Principia Mathematica  (Mathematical Principals). For Aristotle ta physika, the description of nature, could never be mathematical. Numbers are not natural object so, cannot be used to describe nature. Mathematics was confined to the so called mixed or subordinate sciences–astronomy, optics, statics–these are not natural philosophy. Newton’s description of nature is purely mathematical and this was one of the main points of criticism made by both Huygens and Leibniz. Newton’s gravity had no physical explanation. 

Despite these apparent failings Newton’s mechanics slowly but surely became dominant, the accepted norm. When we today refer to everyday physics, non-relativistic mechanics, the sort that’s taught in school we refer to it as classical of Newtonian mechanics or physics. However, the modern physics referred to as Newtonian physics is not Newton’s physics. 

The first thing that changed was that mathematicians on the continent replaced Newton’s extra created analytical Euclidian geometry with Leibniz’s calculus and then later the more modern F’(x) = f(x) notation of the French mathematician, Lagrange (1736–1813). Unfortunately, in England out of a sense of national pride, although the mathematicians replaced the analytical Euclidian geometry they did so with the much more unwieldly Newtonian analysis with its dot notation. This led to the infamous Analytical Society campaign in Cambridge, Newton’s own university, to promote “the principles of d-ism as opposed to the dot-age of the university” in Charles Babbage’s wonderful pun. 

Turning to the physics, Newton had woven together the astronomy concepts of Johannes Kepler (1571–1630) and Giovanni Alfonso Borelli (1608–1679), with the advances in mechanics made by Simon Stevin (1548–1620), Isaac Beeckman !588–1637), Galileo Galilei (1564–1642), Giovanni Alfonso Borelli, René Descartes (1596–1650), Christiaan Huygens (1629–1695) and others to create a unified terrestrial-celestial mechanics that explained mathematically all movement on the earth and in the heavens. However, despite the fact that he had modified and improved his masterpiece in the second (1713) and third (1726) editions, it was still by no means perfect. There were still grey areas that needed improvement. One was the theory of comets that as we have seen was significantly improved by the work Edmond Halley (1656–1742) in his 1706 publication.

Throughout the eighteenth century, people worked on improving, correcting, expanding the foundations that Newton had laid down in his Principia. Unfortunately, very little of that work took place in Britain, which became moribund in its reverence for Newton’s great achievement. In Switzerland, the Bernoullis and Leonard Euler (1707–1783) made significant progress, whilst in France the native-born Italian Joseph-Louis Lagrange (1736–1813) and the Frenchmen Pierre Simon Laplace (1749–1827), Adrien-Marie Legendre (1752–1833), Jean le Rond d’Alembert (1717–1783), Pierre Louis Maupertuis (1698–1759), and Émilie du Châtelet (1706–1749). What follows are very brief sketches of some of the major developments.

Daniel Bernoulli (1700–1782) incorporated the beginnings of the kinetic theory of gasses and hydrostatics into the more general mechanics. Perhaps most spectacular in celestial mechanics was Pierre Simon Laplace’s solution of the problem of the orbit of the Moon (one that Newton had failed to bring convincingly into his general theory of gravity) in his Exposition du système du monde (1796) without details, and more fully in his monumental five volume Traité de mécanique céleste (1798–1825), a work that can be regarded as the crowning glory of Newton’s celestial mechanics.

Two aspects of mechanics which were only beginning to emerge in the late seventeenth and early eighteenth centuries were energy and work. Newton had argued that kinetic energy, the energy released by a moving object on impact, was mv, where m was the mass and v the velocity of a moving object. Johann Bernoulli (1667–1748) and Leibniz had hypothesised that it was mv² but without any real foundation for their claim. Willem s’ Gravesande (1688–1742) carried out a series of experiments in which he dropped steel balls into clay and measured the impact craters. Émilie du Châtelet took the results of his experiments and deduced theoretically that Leibniz was in fact right and E ≈ mv². Work on the concept of energy continued throughout the eighteen and nineteenth centuries.

Work according to the modern definition is the energy transferred to or from an object via the application of force along a displacement. The term work was first used in 1826 but already in a letter to Huygens in 1637 Descartes wrote:

Lifting 100 lb one foot twice over is the same as lifting 200 lb one foot, or 100 lb two feet. (Wikipedia)

In 1686 Leibniz wrote in his Brevis demonstratio:

The same force [“work” in modern terms] is necessary to raise body A of 1 pound (libra) to a height of 4 yards (ulnae), as is necessary to raise body B of 4 pounds to a height of 1 yard. (Wikipedia)

The English civil engineer John Smeaton (1724–1792), famous for building the third Eddystone Lighthouse (1755–59) did experiments relating power (his term for work) and kinetic energy, and supporting the conservation of energy, which he published in 1776 in the Philosophical Transactions of the Royal Society, of which he was a member. He supported Leibniz’s mv², which made him unpopular with the other Royal Society members. His definition of power was  “the weight raised is multiplied by the height to which it can be raised in a given time,” which was very close to the definition for work introduced in the late 1820s by the French mathematician Gaspard-Gustave de Coriolis (1792–1843), who first used the term travail, the French for work in his Calcul de l’Effet des Machines (“Calculation of the Effect of Machines”)in 1829. He established the correct expression for kinetic energy, ⁠1/2⁠mv², and its relation to mechanical work. The French engineer Jean-Victor Poncelet (1788–1867) independently introduced the term mechanical work and its relation to kinetic energy at around the same time. 

In 1773, the French chemist Antoine Lavoisier (1743–1794) stated the law of the conservation of mass based on his own experiment. By the beginning of the nineteenth century a large part of the body of classical physics erected on Newton’s foundations was in place. However, although Newton had written one of the most important books on optics, had discussed magnetism as another example of action at a distance and a series of electrical experiments were carried out at the Royal Society during his period as president, these three areas didn’t become integrated into the main body of physics until the discovery of the electromagnetic spectrum by Michael Faraday (1791–1867) and James Clerk Maxwell (1831–1879) in the middle of the nineteenth century. James Clerk Maxwell’s work developed by Oliver Heaviside into the famous four Maxwell’s Equations announced the beginnings of the fall of Newtonian physics and would lead the way to Einstein’s relativistic physics.