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Celebrating Newton, 325 years after Principia

By Robyn Arianrhod


This year, 2012, marks the 325th anniversary of the first publication of the legendary Principia (Mathematical Principles of Natural Philosophy), the 500-page book in which Sir Isaac Newton presented the world with his theory of gravity. It was the first comprehensive scientific theory in history, and it’s withstood the test of time over the past three centuries.

Unfortunately, this superb legacy is often overshadowed, not just by Einstein’s achievement but also by Newton’s own secret obsession with Biblical prophecies and alchemy. Given these preoccupations, it’s reasonable to wonder if he was quite the modern scientific guru his legend suggests, but personally I’m all for celebrating him as one of the greatest geniuses ever. Although his private obsessions were excessive even for the seventeenth century, he was well aware that in eschewing metaphysical, alchemical, and mystical speculation in his Principia, he was creating a new way of thinking about the fundamental principles underlying the natural world. To paraphrase Newton himself, he changed the emphasis from metaphysics and mechanism to experiment and mathematical analogy. His method has proved astonishingly fruitful, but initially it was quite controversial.

He had developed his theory of gravity to explain the cause of the mysterious motion of the planets through the sky: in a nutshell, he derived a formula for the force needed to keep a planet moving in its observed elliptical orbit, and he connected this force with everyday gravity through the experimentally derived mathematics of falling motion. Ironically (in hindsight), some of his greatest peers, like Leibniz and Huygens, dismissed the theory of gravity as “mystical” because it was “too mathematical.” As far as they were concerned, the law of gravity may have been brilliant, but it didn’t explain how an invisible gravitational force could reach all the way from the sun to the earth without any apparent material mechanism. Consequently, they favoured the mainstream Cartesian “theory”, which held that the universe was filled with an invisible substance called ether, whose material nature was completely unknown, but which somehow formed into great swirling whirlpools that physically dragged the planets in their orbits.

The only evidence for this vortex “theory” was the physical fact of planetary motion, but this fact alone could lead to any number of causal hypotheses. By contrast, Newton explained the mystery of planetary motion in terms of a known physical phenomenon, gravity; he didn’t need to postulate the existence of fanciful ethereal whirlpools. As for the question of how gravity itself worked, Newton recognized this was beyond his scope — a challenge for posterity — but he knew that for the task at hand (explaining why the planets move) “it is enough that gravity really exists and acts according to the laws that we have set forth and is sufficient to explain all the motions of the heavenly bodies…”

What’s more, he found a way of testing his theory by using his formula for gravitational force to make quantitative predictions. For instance, he realized that comets were not random, unpredictable phenomena (which the superstitious had feared as fiery warnings from God), but small celestial bodies following well-defined orbits like the planets. His friend Halley famously used the theory of gravity to predict the date of return of the comet now named after him. As it turned out, Halley’s prediction was fairly good, although Clairaut — working half a century later but just before the predicted return of Halley’s comet — used more sophisticated mathematics to apply Newton’s laws to make an even more accurate prediction.

Clairaut’s calculations illustrate the fact that despite the phenomenal depth and breadth of Principia, it took a further century of effort by scores of mathematicians and physicists to build on Newton’s work and to create modern “Newtonian” physics in the form we know it today. But Newton had created the blueprint for this science, and its novelty can be seen from the fact that some of his most capable peers missed the point. After all, he had begun the radical process of transforming “natural philosophy” into theoretical physics — a transformation from traditional qualitative philosophical speculation about possible causes of physical phenomena, to a quantitative study of experimentally observed physical effects. (From this experimental study, mathematical propositions are deduced and then made general by induction, as he explained in Principia.)

Even the secular nature of Newton’s work was controversial (and under apparent pressure from critics, he did add a brief mention of God in an appendix to later editions of Principia). Although Leibniz was a brilliant philosopher (and he was also the co-inventor, with Newton, of calculus), one of his stated reasons for believing in the ether rather than the Newtonian vacuum was that God would show his omnipotence by creating something, like the ether, rather than leaving vast amounts of nothing. (At the quantum level, perhaps his conclusion, if not his reasoning, was right.) He also invoked God to reject Newton’s inspired (and correct) argument that gravitational interactions between the various planets themselves would eventually cause noticeable distortions in their orbits around the sun; Leibniz claimed God would have had the foresight to give the planets perfect, unchanging perpetual motion. But he was on much firmer ground when he questioned Newton’s (reluctant) assumption of absolute rather than relative motion, although it would take Einstein to come up with a relativistic theory of gravity.

Einstein’s theory is even more accurate than Newton’s, especially on a cosmic scale, but within its own terms — that is, describing the workings of our solar system (including, nowadays, the motion of our own satellites) — Newton’s law of gravity is accurate to within one part in ten million. As for his method of making scientific theories, it was so profound that it underlies all the theoretical physics that has followed over the past three centuries. It’s amazing: one of the most religious, most mystical men of his age put his personal beliefs aside and created the quintessential blueprint for our modern way of doing science in the most objective, detached way possible. Einstein agreed; he wrote a moving tribute in the London Times in 1919, shortly after astronomers had provided the first experimental confirmation of his theory of general relativity:

“Let no-one suppose, however, that the mighty work of Newton can really be superseded by [relativity] or any other theory. His great and lucid ideas will retain their unique significance for all time as the foundation of our modern conceptual structure in the sphere of [theoretical physics].”

Robyn Arianrhod is an Honorary Research Associate in the School of Mathematical Sciences at Monash University. She is the author of Seduced by Logic: Émilie Du Châtelet, Mary Somerville and the Newtonian Revolution and Einstein’s Heroes. Read her previous blog posts.

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