to describe, for instance, the motion of planets, Descartes postulated an invisible space-filling “plenum” of invisible matter. He envisaged a complex sea of whirlpools and eddies, upon which the planets surf.
Isaac Newton cut through all those potential complexities by formulating precise, successful mathematical equations for the motion of planets, using his laws of motion and of gravity. Newton’s law of gravity doesn’t fit into Descartes’ framework. It postulates action at a distance, rather than influence by contact. For example, the Sun exerts a gravitational force on Earth, according to Newton’s law, even though it is not in contact with Earth. Despite the success of his equations in providing an excellent, detailed account of planetary motion, Newton was not happy with action at a distance. He wrote:
That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it.
Nevertheless, he left his equations to speak for themselves:
I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called a hypothesis, and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.
Mathematicians and physicists, through familiarity and spectacular success, became comfortable with the idea of action at a distance through empty space. So things stood, in essence, for more than 150 years.
Over the course of the nineteenth century the plenum struck back. The great experimental physicist Michael Faraday, self-educated and more comfortable with his intuition than with the imposing mathematical machinery of Newtonian physics, envisaged electric and magnetic forces as being transmitted by tubes and lines of force, rather than directly through action at a distance. His highly original viewpoint directed him to experiments that probed these invisible structures—what today we’d call electric and magnetic fields. He thereby discovered simple regularities that would be awkward even to formulate without the fields. The most famous one, which we teach our freshmen, is his law of induction, which says that magnetic fields that change in time create electric fields. (Of course, the actual law is more precise and specific.)
James Clerk Maxwell put Faraday’s intuition into precise mathematical form. He introduced electric and magnetic fields that are functions of space and time as the primary ingredients of his theory. He summarized the discoveries of Faraday and others in a system of equations—and found that they were inconsistent! Fortunately, Maxwell realized that he could repair the equations, by adding a new
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