Inexplicably, Einstein did make one surprising mistake in thinking that the cosmological constant would produce a static universe. While the modification did formally allow for a static solution of the equations, that solution described a state of an unstable equilibrium—a bit like a pencil standing on its tip or a ball on the top of a hill—the slightest departure from rest resulting in forces moving the system even further away from equilibrium. One can understand this point even without the aid of sophisticated mathematics. The repulsive force increases with distance, while the ordinary attractive force of gravity decreases with distance. Consequently, while one can find a mass density at which the two forces balance each other precisely, any slight perturbation in the form of, say, a small expansion would increase the repulsive force and decrease the attractive one, resulting in accelerating expansion. Similarly, the slightest contraction would result in total collapse. Eddington was the first to point out this mistake in 1930, and he credited Lemaître with the original perspicacity. However, by then, the fact that the universe was expanding had become widely known, so this particular shortcoming of Einstein’s static universe was no longer of any interest. I should also add that in his original paper, Einstein specified neither the physical origin of the cosmological constant nor its precise characteristics. We shall return to these intriguing questions—and, indeed, to the subject of how gravity can exert a repulsive push at all—in the next chapter.

Despite these unresolved issues, Einstein was generally pleased with having succeeded (or so he thought) in constructing a model for a static universe—a cosmos that he regarded as compatible with the prevailing astronomical thinking. Initially, he was also satisfied with the cosmological constant for another reason. The new modification to the original gravitational field equations seemed to attune the theory with some philosophical principles that Einstein had used previously in conceiving general relativity. In particular, the original equations (without the cosmological constant) appeared to require what physicists call “boundary conditions,” or specifying a set of values of physical quantities at infinite distances. This was at odds with “the spirit of relativity,” in Einstein’s words. Unlike Newton’s concepts of absolute space and time, one of general relativity’s basic premises had been that there is no absolute system of reference. In addition, Einstein insisted that the distribution of matter and energy should determine the structure of space-time. For instance, a universe in which the distribution of matter is trailing off into nothingness would not have been satisfactory, since space-time could not be defined properly without the presence of mass or energy. Yet to Einstein’s chagrin, the original equations admitted an empty space-time as a solution. He was therefore happy to discover that the static universe turned out not to need any boundary conditions at all, since it was finite and curved on itself like the surface of a sphere, with no boundaries whatsoever. A light ray in this universe came back to its point of origin before starting a new circuit. In this philosophical sense, Einstein, like Plato long before him, always recoiled from the open ended—that which philosopher Georg Wilhelm Hegel referred to as “bad infinity.”

I realize that readers who may be a bit rusty on their general relativity would welcome a refresher course, so here is a very brief review of the core principles involved.

In his theory of special relativity, which preceded his articulation of general relativity, Einstein disposed of Newton’s notion of an absolute or universal time, one that all clocks would supposedly measure. Newton’s goal was to present absolute time and absolute space symmetrically. In that spirit, he stated, “Absolute, true and mathematical time, of itself, and from its own nature, flows equally without relation to anything external.” By making the central theme of special relativity the postulate that all observers should measure the same speed for light, no matter how fast or in which direction they are moving, Einstein had to pay the price of forever linking space and time together into one interwoven entity called space-time. Numerous experiments have since confirmed the fact that the time intervals measured by two observers moving relative to each other do not agree. Most recently, by comparing two optical atomic clocks connected through an optical fiber, researchers at the National Institute of Standards and Technology managed in 2010 to observe this effect of “time dilation” even for relative speeds as low as twenty-two miles per hour!

Given the central role of light (more generally, electromagnetic radiation) in the theory, special relativity was tailored to agree with the laws that describe electricity and magnetism. Indeed, Einstein entitled his 1905 paper that presented the theory “On the Electrodynamics of Moving Bodies.” However, as early as in 1907, he was becoming aware of the fact that special relativity was incompatible with Newton’s gravity. Newton’s gravitational force was supposed to act instantaneously across all space. The implication was that, for instance, when our Milky Way galaxy and the Andromeda galaxy will collide a few billion years from now, the change in the gravitational field due to the redistribution of mass would be felt simultaneously throughout the entire cosmos. This condition would manifestly conflict with special relativity, since it would mean that information can travel faster than light—impermissible in special relativity. Moreover, the mere concept of worldwide simultaneity would require the existence of the very universal time that special relativity carefully invalidated. While Einstein would not have used this particular example in 1907 because he was unaware of it, he fully understood the principle. To overcome these difficulties—and, in particular, to also allow his theory to apply to accelerated motion—Einstein embarked on a rather winding path that involved many missteps, but one that eventually led him to general relativity.