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November 2009 (Volume 18, Number 10)

This Month in Physics History

November 27, 1783: John Michell anticipates black holes

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We think of black holes as a 20th century invention, dating back to 1916, when Albert Einstein first published his theory of general relativity and fellow physicist Karl Schwarzschild used those equations to envision a spherical section of spacetime so badly warped around a concentrated mass that it is invisible to the outside world. But the true “father” of the black hole concept was a humble 18th century English rector named John Michell–a man so far ahead of his scientific contemporaries that his ideas languished in obscurity, until they were re-invented more than a century later.

Born in 1724, Michell attended Cambridge University and wound up teaching there for a time, before becoming rector of Thornhill, near the town of Leeds. He is described somewhat unflatteringly in contemporary accounts as “a little short man, of black complexion, and fat,” who was nonetheless “esteemed a very ingenious Man, and an excellent Philosopher.” For a small-town rector, he had some pretty impressive scientific connections: Benjamin Franklin, Joseph Priestley, and Henry Cavendish all visited him at some point in his career.

Michell’s research interests spanned several areas of science. He started out looking into magnetism, demonstrating that the magnetic force exerted by each pole of a magnet decreases with the square of the distance. After a major Lisbon earthquake in 1755, he proposed that earthquakes propagate as waves through solid earth, thereby helping establish the field of seismology. He won election to the Royal Society for that insight.

In the realm of physics, he conceived and designed the experimental apparatus later used by Cavendish to measure the force of gravity between masses in the laboratory to obtain the first accurate value for the gravitational constant (“G”). And he was the first to apply statistical methods to astronomy. He studied how stars were distributed in the night sky and argued that there were far more “pairs” or groups or stars than would happen with random alignments. His analysis provided the first evidence for binary stars and star clusters.

But it was a paper Michell wrote in November 1783 to Cavendish–later published in the Royal Society’s journal–that proved the most prescient. His intent was not to “invent” exotic objects, but to discover a useful method to determine the mass of a star. Michell adhered to Isaac Newton’s corpuscular theory of light, and since light was made of particles, he reasoned that when they were emitted by a star, that star’s gravitational pull would reduce their speed, producing an observable shift in the starlight. He thought he could measure how much the speed of light was reduced by passing it through a prism; it ought to be deflected differently because of the reduced energy. He could conceivably compare the refracted images of different stars to determine the difference in their surface gravity, and from that, calculate their respective masses.

It was a sensible enough scheme based on what was known at the time: Ole Roemer had measured the speed of light the century before, so Michell had a ballpark figure with which to work. He also understood the concept of “escape velocity,” and that this critical speed would be determined by the mass and size of the star. Specifically, Michell pondered what would happen if a star were so massive, and its gravity so strong, that the escape velocity was equivalent to the speed of light. He concluded:

“If the semi-diameter of a sphere of the same density as the Sun in the proportion of five hundred to one, and by supposing light to be attracted by the same force in proportion to its [mass] with other bodies, all light emitted from such a body would be made to return towards it, by its own proper gravity.”

This would render that star invisible to astronomers. He thought there could be many such objects in the universe, undetectable because they emitted no light. Today, astronomers believe there are black holes at the centers of most galaxies.

Michell did think it might be possible to indirectly detect such “dark stars” if they had a luminous “twin” circling them, making him doubly prescient: such binary star systems are indeed one of several different methods modern astronomers use to infer the existence of black holes. He was only wrong about the speed of light: Einstein proved in 1905 that light travels at a constant speed, regardless of the local strength of gravity. Michell’s original intent of using this to determine the mass of star would not work, although modern spectroscopy uses identifiable notches in a star’s spectrum of light as references for spectral shifts–a similar concept to the scheme Michell proposed.

A few years after Michell’s extraordinary insight, mathematician Pierre-Simon Laplace suggested a similar concept of light being trapped by objects with very high gravity in his book, Exposition du Système du Monde, published in 1796. “It is therefore possible that the greatest luminous bodies in the universe are on this account invisible,” Laplace reasoned.

Newton’s corpuscular theory of light lost favor with the scientific community after Thomas Young’s 1799 experiment demonstrating that light behaves like a wave, and since Michell’s hypothetical “dark star” was based on that assumption, it too was abandoned. Nonetheless, Michell’s unexpected insight about trapped particles of light has withstood the test of time. The revolutionary physics breakthroughs in the 20th century, from Einstein and Schwarzschild to Robert Oppenheimer and Stephen Hawking, made the concept almost mainstream. The term “black hole” was coined by physicist John Wheeler in 1968 in a lecture to the American Astronomical Society.

It might be said that John Michell, that short, fat humble village rector, was born under a dark star. He never achieved sufficient escape velocity for his ideas to break out of Thornhill. He died in quiet obscurity, and his notion of a “dark star” was forgotten until his writings re-surfaced in the 1970s. Finally, his ideas found their way into the light.

Image: Title and excerpt from Michell’s 1783 paper in which he first described the concept of a “dark star.” Source: Philosophical Transactions of the Royal Society of London, Vol. 74, p.35, 1783.

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November 2009 (Volume 18, Number 10)

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