When confronting such a paradox, scientists have only a few options: Question the data, question the theory, or invent something new, maybe even something invisible, to explain the effect. In the late 1970s, astronomers were beginning to line up behind the last alternative. Faced with flat rotation curves that seemed to flout Newton's laws, astronomers assumed the existence of a halo of dark matter around every spiral galaxy. Whatever the stuff was, it did not emit light, but it did exert a gravitational pull. The dark matter tugged on the stars, cranking up their speeds and creating the flat rotation curves.
The choice was reasonable, but it was still a choice. "Science does not emerge in some perfect, complete crystalline form," says Princeton University cosmologist James Peebles. "Sometimes one must make extended conclusions from limited data. Why should all matter be in the visible sector? Dark matter was a simple solution to the problem." It was a solution, however, that Milgrom could not accept. He took a shot at the second alternative. Milgrom decided to retrofit Newton.
He set out to modify aspects of Newton's laws of motion so that they could naturally yield the flat rotation curves for galaxies. "I was systematic," he says. "I knew Newton's laws worked for the solar system, but they didn't seem to work for galaxies. So I made a table of solar system properties and galaxies' properties to see which one might present the best road to modifying the equations."
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| The gravitational pull of a galaxy cluster has bent and split light to create multiple images of a quasar and multiple images of a galaxy. |
Milgrom's systematic method was critical. Spiral galaxies can be a hundred million times larger than the solar system. A naive approach would simply change Newton's gravitational force law at large distances, but this attack fails to describe accurately other properties of large systems like galaxies. Milgrom then tried modifying the gravitational force based on the spin of the galaxy. No dice. "The last property on my table was acceleration," Milgrom says, "and that one worked."
If you took high school physics, you may remember having Newton's most important equation pounded into your head:
F = ma. With this simple formula, known as Newton's second law, Newton forever linked forces (F) to their action on mass (m) in the form of acceleration (a). We all experience the relation between force and acceleration whenever we're in a car. As the car accelerates, we're forced back in our seats; when it decelerates, we're forced forward. Milgrom found that the best way to resolve the problem of the flat rotation curves was to modify this hallowed equation.
"I assumed that when the accelerations due to gravitational forces became very small, the formula changes to F = ma²/a0," Milgrom says. According to Milgrom, this change holds only when accelerations fall below one 10-billionth of a meter per second every second. Not only does this modification work best with the data, he adds, but the new constant, a0, may be of cosmological significance: Accelerating at this rate will take you from a resting state to the speed of light in the lifetime of the universe. Otherwise Newton's law operates as usual. So with MOND, stars in the outer reaches of galaxies move faster than expected, not because of the influence of some invisible matter but because Milgrom's amended version of Newton's second law increases the force acting on them.
When he used this modified equation to plot the rotation curves, the flatness at the outer distances was predictable, not puzzling. Nothing else was needed to explain it. To a layperson, Milgrom's innovation might seem like a negligible tweak, but to his colleagues, it was bold to the point of foolhardiness. He was changing a cornerstone of physics. Opposition was a given.
