the case of the balloon, the air pressure from inside is the force that counteracts the tension in the rubber. But the real universe doesn’t have an inside with air in it. There is only the surface. So Einstein reasoned that there must be some kind of repulsive force to counteract the gravitational pull. Could there be a hidden possibility of a repulsive force in the General Theory of Relativity?
Examining his equations, Einstein discovered an ambiguity. The equations could be modified without destroying their mathematical consistency by adding one more term. The meaning of the additional term was surprising: it represented an addition to the usual laws of gravity—a gravitational force that became increasingly strong with distance. The strength of this new force was proportional to a new constant of nature that Einstein denoted by the Greek letter λ (lambda). Ever since, the new constant has been called the cosmological constant, and it continues to be denoted by λ.
What had especially caught Einstein’s attention was that if λ were chosen to be a positive number, then the new term corresponded to a universal repulsion that increased in proportion to the distance. Einstein realized he could play off the new repulsive force against the usual gravitational attraction. The galaxies could be kept in equilibrium at a separation that could be controlled by choosing the magnitude of the new constant, λ. The way that it worked was simple. If the galaxies were closely spaced, their attraction would be strong and an equally strong repulsion would be needed to keep them in equilibrium. On the other hand, if the distance between galaxies were so large that they barely felt each other’s gravitational fields, then only a weak repulsion would be needed. Thus Einstein argued that the size of the cosmological constant should be closely connected to the average distance between the galaxies. Although from a mathematical perspective the cosmological constant could be anything, it could be easily determined if one knew the average distance separating galaxies. In fact at that time, Hubble was busy measuring the distance between galaxies. Einstein believed that he had the secret of the universe. It was a world kept in balance by competing attractive and repulsive forces.
Many things are wrong with this theory. From the theoretical point of view, the universe that Einstein had built was unstable. It was in equilibrium but
unstable equilibrium.
The difference between stable and unstable equilibrium is not hard to understand. Think of a pendulum. When the pendulum is vertical and the bob is at its low point, the pendulum is in stable equilibrium. This means that if you disturb it a little, for example, by giving it a slight push, it will return to its original position.
Now imagine turning the pendulum upside down so that the bob is delicately balanced in the straight-up position. If it is disturbed ever so slightly, perhaps by nothing more than the breeze from a butterfly’s wing, the disturbance will build up, and the pendulum will fall over. Moreover, the direction in which it falls is very unpredictable. Einstein’s static universe was like the unstable upside-down pendulum. The slightest perturbation would either cause it to explosively grow or implode it like a popped balloon. I don’t know whether Einstein missed this elementary point or if he just decided to ignore it.
But the worst thing about the theory was that it was trying to explain something that was just not true. Ironically, there was no need for the new term. Hubble, working with the hundred-inch telescope on Mount Wilson in Southern California, discovered that the universe was not standing still. 2 The galaxies were flying apart from one another, and the universe was expanding like an inflating balloon. The forces did not need to cancel, and the cosmological term, which added nothing to the beauty of the equations, could be discarded by setting it to zero.
But
Examining his equations, Einstein discovered an ambiguity. The equations could be modified without destroying their mathematical consistency by adding one more term. The meaning of the additional term was surprising: it represented an addition to the usual laws of gravity—a gravitational force that became increasingly strong with distance. The strength of this new force was proportional to a new constant of nature that Einstein denoted by the Greek letter λ (lambda). Ever since, the new constant has been called the cosmological constant, and it continues to be denoted by λ.
What had especially caught Einstein’s attention was that if λ were chosen to be a positive number, then the new term corresponded to a universal repulsion that increased in proportion to the distance. Einstein realized he could play off the new repulsive force against the usual gravitational attraction. The galaxies could be kept in equilibrium at a separation that could be controlled by choosing the magnitude of the new constant, λ. The way that it worked was simple. If the galaxies were closely spaced, their attraction would be strong and an equally strong repulsion would be needed to keep them in equilibrium. On the other hand, if the distance between galaxies were so large that they barely felt each other’s gravitational fields, then only a weak repulsion would be needed. Thus Einstein argued that the size of the cosmological constant should be closely connected to the average distance between the galaxies. Although from a mathematical perspective the cosmological constant could be anything, it could be easily determined if one knew the average distance separating galaxies. In fact at that time, Hubble was busy measuring the distance between galaxies. Einstein believed that he had the secret of the universe. It was a world kept in balance by competing attractive and repulsive forces.
Many things are wrong with this theory. From the theoretical point of view, the universe that Einstein had built was unstable. It was in equilibrium but
unstable equilibrium.
The difference between stable and unstable equilibrium is not hard to understand. Think of a pendulum. When the pendulum is vertical and the bob is at its low point, the pendulum is in stable equilibrium. This means that if you disturb it a little, for example, by giving it a slight push, it will return to its original position.
Now imagine turning the pendulum upside down so that the bob is delicately balanced in the straight-up position. If it is disturbed ever so slightly, perhaps by nothing more than the breeze from a butterfly’s wing, the disturbance will build up, and the pendulum will fall over. Moreover, the direction in which it falls is very unpredictable. Einstein’s static universe was like the unstable upside-down pendulum. The slightest perturbation would either cause it to explosively grow or implode it like a popped balloon. I don’t know whether Einstein missed this elementary point or if he just decided to ignore it.
But the worst thing about the theory was that it was trying to explain something that was just not true. Ironically, there was no need for the new term. Hubble, working with the hundred-inch telescope on Mount Wilson in Southern California, discovered that the universe was not standing still. 2 The galaxies were flying apart from one another, and the universe was expanding like an inflating balloon. The forces did not need to cancel, and the cosmological term, which added nothing to the beauty of the equations, could be discarded by setting it to zero.
But
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