Brilliant Blunders: From Darwin to Einstein - Colossal Mistakes by Great Scientists That Changed Our Understanding of Life and the Universe (34 page)

Einstein’s second idea turned Newton’s gravity on its ear. Gravity is not some mysterious force that acts across space, Einstein contended. Rather, mass and energy warp space-time in the same way that a person standing on a trampoline causes it to sag. Einstein defined gravity as the curvature of space-time. That is, planets move along the shortest paths in the curved space-time created by the Sun, just as a golf ball follows the undulation of the green, or a Jeep negotiates the dunes of the Sahara Desert. Light does not travel in straight lines, either, but curves in the warped neighborhood of large masses.
Figure 32
shows a letter written by Einstein in 1913, as he was developing the theory. In the letter, addressed to the American astronomer George Ellery Hale, Einstein explained the bending of light in a gravitational field and the Sun’s deflection of light from a distant star. This crucial prediction was first tested in 1919 during an eclipse of the Sun. The person who organized the observations (in Brazil and on Principe Island in the Gulf of Guinea) was Arthur Eddington, and
the deviations recorded by his team and by the expedition
headed by the Irish astronomer Andrew Crommelin (of about 1.98 and 1.61 seconds of arc) were consistent, within the estimated observational errors, with Einstein’s prediction of 1.74 seconds of arc. (Newtonian gravity predicted half that.) Time is “curved” as well in general relativity: Clocks that are near massive bodies tick more slowly than clocks that are far away from them.
Experiments have confirmed this effect, which is also taken into account routinely by GPS satellites.

Einstein’s pivotal premise in general relativity was a truly revolutionary idea: What we perceive as the force of gravity is merely a manifestation of the fact that mass and energy cause space-time to warp. In this sense, Einstein was closer, at least in spirit, to the geometrical (rather than dynamical) views of the astronomers of ancient Greece than to Newton and his emphasis on forces. Instead of being a rigid and fixed background, space-time can flex, curve, and stretch in response to the presence of matter and energy, and those warps, in turn, cause matter to move the way it does. As the influential physicist John Archibald Wheeler once put it, “Matter tells space-time how to curve, and space-time tells matter how to move.” Matter and energy become eternal partners to space and time.

By introducing general relativity, Einstein dazzlingly solved the problem of the faster-than-light propagation of the force of gravity—the predicament that bedeviled Newton’s theory. In general relativity, the speed of transmission boils down to how fast ripples in the fabric of space-time can travel from one point to another. Einstein showed that such warps and swells—the geometrical manifestation of gravity—travel precisely at the speed of light. In other words, changes in the gravitation field cannot be transmitted instantaneously.

As happy as Einstein might have been with the cosmological constant and his static universe, this satisfaction was soon to evaporate, since new scientific discoveries rendered the concept of a static universe untenable. First,
there were a few theoretical disappointments, the earliest of which hit almost immediately. Just one month after the publication of Einstein’s cosmological paper, his colleague and friend
Willem de Sitter found a solution to Einstein’s equations with no matter at all. A cosmos devoid of matter was clearly in contradiction to Einstein’s aspiration to connect the geometry of the universe
to its mass and energy content. On the other hand, de Sitter himself was quite pleased, since he objected to the introduction of the cosmological constant from day one. In a letter to Einstein dated March 20, 1917, he argued that lambda may have been desirable philosophically but not physically. He was troubled in particular by the fact that he thought that the value of the cosmological constant could not be determined empirically. At that instant, Einstein himself was still keeping an open mind to all options. In his reply to de Sitter, on April 14, 1917, he prophetically wrote a beautiful paragraph, very reminiscent of Darwin’s famous “In the distant future . . . light will be thrown on the origin of man” (see chapter 2):

In any case, one thing stands. The general theory of relativity
allows
the inclusion of Λg
μv
[the cosmological term] in the field equations. One day, our actual knowledge of the composition of the fixed star sky, the apparent motions of fixed stars, and the position of spectral lines as a function of distance, will probably have come far enough for us to be able to decide empirically the question of whether or not Λ vanishes. Conviction is a good motive, but a bad judge!

As we shall see in the next chapter, Einstein predicted precisely what astronomers would achieve eighty-one years later. But in 1917, the setbacks just kept coming. Even though de Sitter’s model appeared at first blush to be static, that proved to be an illusion. Later work by physicists Felix Klein and Hermann Weyl showed that when test bodies were inserted into it, they were not at rest—rather, they flew away from one another.

The second theoretical blow came from Aleksandr Friedmann. As I noted earlier, Friedmann showed in 1922 that Einstein’s equations (with or without the cosmological term) allowed for nonstatic solutions, in which the universe either expanded or contracted. This prompted the disappointed Einstein to write in 1923 to his friend Weyl,
“If there is no quasi-static world, then away with
the cosmological term.” But the most serious challenge was observational. As we have seen in chapter 9, Lemaître (tentatively) and Hubble (unequivocally) showed in the late 1920s that the universe is, in fact, not static—it is expanding. Einstein realized the implications immediately. In an expanding universe, the attractive force of gravity merely slows the expansion. Following Hubble’s discovery, therefore, he had to admit that there was no longer a need for an intricate balancing act between attraction and repulsion; consequently, the cosmological constant could be removed from the equations.
In a paper published in 1931, he formally abandoned the term, since “the theory of relativity seems to satisfy Hubble’s new results more naturally . . . without the Λ term.” Then, in 1932,
in a paper Einstein published together with de Sitter, the authors concluded: “Historically the term containing the ‘cosmological constant’ Λ was introduced into the field equations in order to enable us to account theoretically for the existence of a finite mean density in a static universe. It now appears that in the dynamical case this end can be reached without the introduction of Λ.”

Einstein was aware of the fact that without the cosmological constant, Hubble’s measured rate of expansion produced an age for the universe that was uncomfortably short compared with estimated stellar ages, but he was initially of the opinion that the problem might be with the latter. The largest contribution to the error in the observationally determined cosmic expansion rate was corrected only in the 1960s, but uncertainties of a factor of about two in the rate continued to linger until the advent of the Hubble Space Telescope. Surprisingly, however, the banished cosmological constant did return with a bang in 1998.

You’ll notice that the language used by Einstein and de Sitter regarding the cosmological constant is benign; they note merely that in an expanding universe, it is not needed. Yet, if you read almost any account of the history of the cosmological constant, you will invariably find the story that Einstein denounced the introduction of this constant into his equations as his “biggest blunder.” Did Einstein actually say this, and if so, why?

After scrutinizing all the available documents, I first confirmed something that a few historians of science have already suspected: The tale of Einstein calling the cosmological constant his biggest blunder originated from a single source: the colorful George Gamow. Recall that Gamow was responsible for the idea of big bang nucleosynthesis, as well as for some of the early thinking about the genetic code. James Watson, the codiscoverer of the structure of DNA, once said about Gamow that he was “so very often a step ahead of everybody.” Gamow told the “biggest blunder” story in two places.
In an article entitled “The Evolutionary Universe,” published in the September 1956 issue of
Scientific American,
Gamow wrote, “Einstein remarked to me many years ago that the cosmic repulsion idea was the biggest blunder he had made in his entire life.” He repeated the same story [and for some reason, most accounts of the history of the cosmological constant are aware only of this source]
in his autobiographical book
My World Line,
which was published posthumously in 1970: “Thus, Einstein’s original gravity equation was correct, and changing it [to introduce the cosmological constant] was a mistake. Much later, when I was discussing cosmological problems with Einstein, he remarked that the introduction of the cosmological term was the biggest blunder he ever made in his life.”

Since Gamow was known, however, to embellish many of his anecdotes (his first wife said once, “In more than twenty years together, Geo has never been happier than when perpetuating a practical joke”), I decided to dig a bit deeper in an attempt to establish the authenticity of this account. My motivation to investigate this particular quote was enhanced by the fact that the recent resurrection of the cosmological constant has turned “biggest blunder” into one of Einstein’s most cited phrases. The last time I checked, there were more than a half million Google pages containing “Einstein” and “biggest blunder”!

I started by trying to ascertain whether Gamow was purporting to actually quote Einstein directly. Unfortunately, each of the two citations presented above appears insufficient, as it stands, to determine whether Gamow was claiming that Einstein himself had
used the words “biggest blunder” that he ever made in his life, or whether Gamow was merely reporting the spirit of the conversation. However, in
My World Line,
Gamow continued to say, “But this ‘blunder,’ rejected by Einstein, is still sometimes used by cosmologists even today, and the cosmological constant denoted by the Greek letter ‘Λ’ rears its ugly head again and again.” The use of quotation marks around the word “blunder” seems at least to suggest that Gamow meant to imply an authentic quote. The fact that Gamow used precisely the same language twice also indicates that he was trying to give the impression, at least, that he was quoting Einstein directly. Note also that Gamow reveals here his own prejudice concerning the cosmological constant, through the phrase “its ugly head.”

Intriguingly, I discovered that Einstein did actually use the expression “I made one great mistake in my life,” but in an entirely different context. Linus Pauling spoke with Einstein (as one leading scientist and pacifist to another) at Princeton, on November 16, 1954. Immediately following the conversation, Pauling wrote in his diary that Einstein told him the following (
figure 33
shows Pauling’s diary entry): “He had made one great mistake—when he signed the letter to President Roosevelt recommending that atom bombs be made; but that there was some justification—the danger that the Germans would make them.” Clearly, this fact in itself does not necessarily preclude the possibility that Einstein might have used “biggest blunder” also in a scientific context, although the language employed in the conversation with Pauling (“
one
great mistake”) does make you wonder.

The second question I wanted to try to settle was that of the circumstances;
when
might Einstein have used this expression with Gamow? In
My World Line
Gamow gives the impression that he and Einstein were very close friends. He describes how during World War II, the two of them served at the same time as consultants in the Division of High Explosives of the US Navy’s Bureau of Ordnance. Since Einstein was unable at the time to travel from Princeton to Washington, DC, Gamow recounts, Gamow was “selected,” in his words, by the navy to bring documents to
Einstein “every other Friday,” since he “happened to have known Einstein earlier, on nonmilitary grounds.” Gamow goes on to depict a very warm and intimate bond between him and Einstein: