Diracs Bold Idea

Oxford mathematician loan James has detected a curious pattern among members of his own profession. Surveying their personalities and achievements, he has arrived at the conclusion that particular kinds of social deficits, possibly neurological in origin, often correlate with the focus needed for monumental discoveries. Perhaps certain personal, physical, or psychological limitations help concentrate the mind. Or, alternatively, perhaps development in some areas of the brain comes at the sacrifice of other areas. Thus, for instance, mathematical geniuses may not always make the best conversationalists.

The physicist Paul Adrien Maurice Dirac, one of the subjects of James's study, was a notoriously inscrutable 20th century thinker. He was a mystery even to many of his closest friends. "Nobody knew him very well," recalled physicist Engelbert Schucking, who encountered Dirac at various conferences. His colleagues joked that he rarely said anything more than "Yes," "No," or "I don't know." Legends swirled around him like tales spun about uncharted islands. They typically focused on his economy of words and his solemn dedication to pure science. In one such story, Dirac had just finished reading Dostoevsky's Crime and Punishment. Asked about his impressions of the classic Russian novel, he had only one comment: "It is nice, but in one of the chapters the author made a mistake. He describes the Sun rising twice on the same day."

Another time Dirac was delivering a lecture in his usual crisp and precise style. He never minced words and always planned each sentence meticulously. After the talk, there was a question-and-answer session. Someone raised his hand and said, "Professor Dirac, I do not understand how you derived the formula on the top left side of the blackboard."

"This is not a question," Dirac curtly responded. "It is a statement. Next question, please."

Dirac's rigidity in conversation contrasted with his extraordinary brilliance and creativity in discerning the properties of the universe. In the early days of quantum mechanics, his agile mathematical mind rapidly encompassed radical new ways of interpreting physics. He developed theories and ideas so fantastic, such as a negative energy sea that fills all of space, that they knocked the breath out of his colleagues. This concept relates to arguably his most important contribution to physics, the Dirac equation, proposed in 1928. The Dirac equation offered a quantum, relativistic description of an electron, encompassing properties such as its mass, charge, and spin. It predicted the existence of positively charged counterparts to electrons. Known as positrons, they were first experimentally detected in 1932. For his pivotal scientific contributions, Dirac was awarded a Nobel Prize the following year.

In 1937, Dirac applied his prodigious talents in an attempt to explain an astonishing physical coincidence in cosmology. Comparing the strength of the electrical and gravitational forces acting between the proton and electron in a hydrogen atom, he noticed that the ratio is an immense number, approximately 1040 (one followed by 40 zeros). The fact that this value is so large is related to what is now known as the "hierarchy problem." Curiously, Dirac found that the present age of the universe as expressed in atomic units (the time for a light particle to trek across a hydrogen atom) is roughly the same size. In what is known as the Large Numbers Hypothesis (LNH), Dirac suggested that the two numbers are in fact equal.

Sometimes apparent coincidences mask fundamental truths. For example, when physicist Murray Gell-Mann discovered that he could arrange the properties of elementary particles into curious arrays, he speculated that these patterns stemmed from groupings of yet more fundamental objects called quarks. If he had turned out to be wrong, his methods would have been deemed numerological hokum. But he was right, and his insight led to the modern field of quantum chromodynamics—the theory of the strong nuclear interaction that binds protons and neutrons together.

Following a similar hunch, Dirac bet that the coincidence he discovered between various large numbers in the universe stemmed from a fundamental principle of nature. He proposed that the ratio of the strengths of the gravitational and electromagnetic forces was equal in the cosmic beginning but diminished proportionally with each atomic interaction. That is, each time the "clock" of a hydrogen atom ticked, gravity would become slightly weaker. Consequently, by 1040 ticks, gravity would be that much scrawnier than still-brawny electromagnetism—the unequal match we witness today. In general form the LNH states that large dimensionless numbers should vary with the epoch of the Universe.

Is Dirac's result profound or simply prestidigitation? In purest numerical form it is almost certainly not correct, since it does not match up with any known gravitational theory. However, there are compelling ways of altering general relativity to produce a changing gravitational strength that have attracted their share of supporters over the decades.

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