Einstein's Unfinished Dream by Lincoln Don;

Author:Lincoln, Don;
Language: eng
Format: epub
Publisher: Oxford University Press, Incorporated
Published: 2023-05-15T00:00:00+00:00

Alternatives to Dark Matter

Given the long and unsuccessful history in searching for dark matter, we should consider some of the other alternatives. As I described in the section discussing Vera Rubin, it is possible that dark matter doesn’t actually exist. Instead, the other big possibility is that we don’t fully understand the laws of motion or how gravity works.

In this section, I’ll talk about those two possibilities. While they seem to be different, they are more intertwined than appears at first blush. Hopefully it will all be clear.

The first attempt to come up with a non–dark matter explanation for the glut of astronomical mysteries that became apparent in the 1970s was made by Israeli physicist Mordehai Milgrom in 1982. He came up with an explanation that approached the problem by assuming that Newton’s second law of motion was incomplete.

Newton’s second law states that the acceleration an object experiences is directly proportional to the force applied to it. (If you ever took a physics class and remember any of it, this is the equation F = ma.) Increase a force by 50%, and the acceleration will go up by the same amount.

Milgrom decided to use Rubin’s measurements of the rotation rates of galaxies to motivate his thinking. As a reminder, she showed that at large distances from the galactic center that stars orbited at roughly constant speed, while Newton’s equations predicted that the orbital speed would get slower and slower as one looks at stars far from the center. What Milgrom wanted to do was to generate equations that would predict a stellar speed that was constant, independent of radius (at large orbital radii), while keeping the behavior predicted by Newton at small orbital radii.

In the case of galactic rotation, the force (and consequently acceleration) is larger near the center and weaker at the periphery. So he proposed that for large accelerations, Newton’s law still held. However, for smaller accelerations, he suggested a new equation.

The acceleration due to gravity depends on one over the radius squared (1/r2), while the acceleration required to move in a circle depends on one over the radius (1/r). Since the two accelerations are on opposite sides of the equal sign (of the motion equals gravity equation), and he wanted to get rid of any radial dependence, he simply modified Newton’s second law from being the familiar version, which says force is proportional to acceleration (F ∝ a), to a new equation that says that force is proportional to acceleration squared (F ∝ a2).

This choice put a one over radius squared on both sides of the equation, which then cancelled out. The result was that he got the result he wanted: At large distances from the center of galaxies, stars moved with constant velocity.

Of course, he got that result because he engineered the equations to get the desired outcome. That’s not necessarily a bad thing; after all, looking at data and devising equations that agree with it is a time-honored technique for trying to understand the natural world.

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