Brilliant Blunders: From Darwin to Einstein - Colossal Mistakes by Great Scientists That Changed Our Understanding of Life and the Universe (33 page)

My subject disperses the galaxies, but it unites the earth.

May no “cosmical repulsion” intervene to sunder us!

—SIR ARTHUR EDDINGTON

W
hen I throw my keys up in the air, they reach some maximum height, and then they fall back into my hand. Only for an instant do the keys stay still, as they reach the highest point. Obviously, the gravitational pull of the Earth is responsible for this behavior. If somehow I could propel the keys to a speed exceeding about seven miles per second, they would escape the Earth altogether, as did, for instance, the Pioneer 10 spacecraft, with which communication was lost in 2003, when the probe was at a distance of more than seven billion miles from Earth. However, in the absence of an opposing force, the Earth’s gravity alone does not allow for the keys to float suspended in midair.

Two scientists showed independently in the 1920s that the behavior of the cosmic space-time is expected to be very similar. Those two researchers, Russian mathematician and meteorologist Aleksandr Friedmann and Belgian priest and cosmologist Georges Lemaître, applied Einstein’s theory of general relativity to the universe as a whole. They soon realized that the gravitational attraction of all the matter and radiation in the universe implies that space-time, Einstein’s combination of space and time, can either stretch or contract,
but it cannot stably stand still at a fixed extent. These important findings eventually provided the theoretical background for the discovery by Lemaître and Hubble that our universe is expanding. But let’s start from the beginning.

In 1917
Einstein himself first attempted to understand the evolution of the entire universe in light of his general relativity equations. This effort initiated the transformation of cosmological problems from speculative philosophy into physics. The expansion of the universe had not been discovered yet. Moreover, not only was Einstein unaware of any observed large-scale motions, but until that time, most astronomers still believed that the universe consisted exclusively of our Milky Way galaxy, with nothing beyond. Astronomer Vesto Slipher’s observations of the
redshifts
(the stretchings of light, which were later interpreted as recession velocities of galaxies) of “nebulae” were neither widely known nor understood at the time. Astronomer Heber Curtis did present some preliminary evidence that the Andromeda galaxy, M31, might be outside the Milky Way, but
Edwin Hubble confirmed unambiguously this profound fact—that our galaxy is not the entire universe—only in 1924.

Convinced in 1917 that the cosmos was unchanging and static on its largest scales, Einstein had to find a way to keep the universe described by his equations from collapsing under its own weight. To achieve a static configuration with a uniform distribution of matter, Einstein guessed that there had to be some repulsive force that could balance gravity precisely. Consequently, just a little over a year after he had published his theory of general relativity, Einstein came up with what appeared, at least at first glance, to be a brilliant solution. In a seminal paper entitled “Cosmological Considerations on the General Theory of Relativity,” he introduced a new term into his equations. This term gave rise to a surprising effect: a repulsive gravitational force! The cosmic repulsion was supposed to act throughout the universe, causing every part of space to be pushing on every other part—just the opposite of what matter and energy do. As we shall soon discover, mass and energy warp space-time in such a way that matter falls together. The fresh cosmological term effectively
warped space-time in the opposite sense, causing matter to move apart. The value of a new constant that Einstein introduced (on top of the familiar strength of gravity) determined the strength of the repulsion. The Greek letter lambda, Λ, denoted the new constant, now known as the
cosmological constant.
Einstein demonstrated that he could choose the value of the cosmological constant to precisely balance gravity’s attractive and repulsive forces, resulting in a static, eternal, homogeneous, and unchanging universe of a fixed size. This model later became known as “Einstein’s universe.” Einstein concluded his paper with what turned out to be a pregnant comment:
“That term is necessary
only
[
my emphasis
] for the purpose of making possible a quasi-static distribution of matter, as required by the fact of the small velocities of the stars.” You’ll notice that Einstein talks here about “velocities of stars” and not of galaxies, since the existence and motions of the latter were still beyond the astronomical horizons at the time.

With few exceptions, hindsight is usually 20/20. Cosmologists tend to emphasize the fact that by introducing the cosmological constant, Einstein missed a golden opportunity for a spectacular prediction. Had he stuck with his original equations, he could have predicted more than a decade before Hubble’s observations that the universe should be either contracting or expanding. This is certainly true. However, as I shall argue in the next chapter, the introduction of the cosmological constant could have constituted an equally significant prediction.

You may wonder how Einstein could add this new repulsive term into his equations without spoiling general relativity’s other successes in explaining several perplexing phenomena. For instance, general relativity elucidated the slight shift in the orbit of the planet Mercury in each successive passage around the Sun. Einstein was, of course, aware that his cosmological constant could undermine agreement with observations, so to avoid undesired consequences,
he modified his equations in such a way that the cosmic repulsion increased proportionally to the spatial separation. That is, the repulsion was imperceptible over the distance scales of the solar system,
but it became increasingly appreciable over vast cosmological distances. As a result, all the experimental verifications of general relativity (which relied on measurements spanning relatively short distances) could be preserved.

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.

General relativity is still considered by many to be the most ingenious physical theory ever articulated. The famous physicist Richard Feynman confessed once, “I still can’t see how he thought of it.”
The theory was based largely on two profound insights: (1) the
equivalence between gravity and acceleration, and (2) the transformation of the role of space-time from that of a passive spectator to that of a major player in the drama of universal dynamics. First, by contemplating the experience of a person who is free-falling in the gravitational field of the Earth, Einstein realized that acceleration and gravity are essentially indistinguishable. A person living inside a closed elevator on Earth, with the elevator accelerating upward continuously, may think that she lives in a place that has a stronger gravity—a bathroom scale will certainly record a weight that is higher than her normal weight. Similarly, astronauts in the space shuttle were experiencing “weightlessness” because both they and the shuttle were undergoing the same acceleration relative to the Earth. In his Kyoto Lecture in 1922, an impromptu speech to students and faculty members, Einstein described how the idea came to him: “I was sitting in a chair in the patent office in Bern when all of a sudden a thought occurred to me:
‘If a person falls freely he will not feel his own weight.’ I was startled. This simple thought made a deep impression on me. It impelled me toward a theory of gravitation.”