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An Interlude with Dirac

A geodesist remembers Paul Dirac’s visit to the University of Hawaii Lunar Laser Ranging Observatory

William E. Carter

The next day we had planned a lunch for the Diracs and the entire Waiakoa staff at the Kula Lodge, which was only a few hundred yards down Upper Kula Road from the inn. Dirac was seated at one end of a long table, with Don Landman at his left and me at his right. Margit Dirac was seated at the far end of the table with Marilyn, our secretary and a few other wives (all of the scientists and technicians on the Maui staff were men at that time). Landman and Don Mickey, another solar astronomer, brought copies of one of Dirac’s books and asked him to sign them, which he did with a smile.

2012-11MacroCarterFB.jpgClick to Enlarge ImageAfter everyone had eaten enough to take the edge off of their hunger, Landman turned his attention to physics. He and Dirac embarked on a wide-ranging discussion, including solar physics and the current focus of research at the University of Hawaii’s Mees Solar observatory. These topics were outside my area of knowledge, so I listened and tried to follow the gist of things but had nothing to add to the conversation. Then Landman changed his focus to Dirac’s work on cosmology.

From the little that I had read on the subject, I remembered that Dirac’s study of such fundamental constants as Newton’s gravitational constant, Planck’s constant, the speed of light and the charge and masses of the electron and proton had led him to assign cosmological significance to a set of very large dimensionless numbers formed as the ratios of pairs of the constants. Years later I happened to read a 1993 Scientific American article about Dirac, written by R. Coby Hovis and Hedge Kragh, elaborating on these concepts further. The authors wrote:

The ratio of the electric force between a proton and electron to the gravitational force between the same two particles is a very large number, about 1039. Curiously, Dirac noted, this number approximates the age of the universe (as then estimated) when that age is expressed in terms of an appropriate unit of time, such as the time needed for light to cross the diameter of a classical electron.

From this and other correlations he found between large pure numbers, Dirac postulated a new cosmological principle, the Large Number Hypothesis. It has not been supported by recent work, but Dirac was devoted to it.

After discussing this subject with Landman for several minutes, Dirac turned to me and said, “You have been very quiet, Bill. What do you think of the Large Number Hypothesis?”

“Sorry, I’ve been trying to follow your discussion, but I really don’t know enough about cosmology to have anything useful to contribute.”

“But part of the beauty of the hypothesis is its very simplicity. You surely must have some initial reaction, and I would be pleased if you would share it with us.”

After taking a couple of seconds to consider how candid I should be, I blurted out, “To be perfectly honest, it sounds more like astrology than astrophysics to me.”

Landman cringed. “Bill, that was rude. I think you owe Professor Dirac an apology.”

“Sorry, I did not mean to be impolite, but Professor Dirac asked for my initial reaction, and that is in fact my initial reaction.”

“Quite right,” Dirac said. “I did ask for your initial reaction, and I must say, I fully understand your thoughts. I admit to having had similar thoughts from time to time. But do you not agree that the existence in nature of these very large dimensionless numbers, all of nearly the same order of magnitude, must be more than pure coincidence?”

“Sorry, but I’m a geodesist, and I have all that I can handle trying to get enough photons to and from the Moon to measure its distance from Earth at any given time. I must confess that I don’t even fully understand the differences between Albert Einstein’s and Bob Dicke’s versions of the physics that some of my colleagues on the LURE team hope to settle based on the rate of lunar recession derived from our observations.”

“Ah, yes. Well, that is a subject that I hoped to discuss with you during my visit….”

Later that afternoon, Marilyn and I took the Diracs to the airport to catch a flight back to Honolulu. As Father Dirac checked their baggage and obtained their boarding passes, Margit very graciously thanked Marilyn and me for our hospitality, and particularly for the high point of their visit, the evening they spent with our family. She said that it had been simply wonderful to see Father so enthralled with our children, reading books with Pamela at his side. She only wished that she had a picture of the pair of them.

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