An Interlude with Dirac

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

Astronomy Mathematics

Current Issue

This Article From Issue

November-December 2012

Volume 100, Number 6
Page 438

DOI: 10.1511/2012.99.438

In 1975 I was a relatively new research associate at the University of Hawaii Institute for Astronomy. One August morning I was working at my desk at the institute’s Waiakoa office, which sits about 2,500 feet above sea level, in the Kula district on the north slope of Mount Haleakala, Maui. My phone rang. The speaker informed me that she was calling on behalf of P. A. M. Dirac, professor of physics at Florida State University in Tallahassee. Professor Dirac and his wife, Margit, were going to be passing through Hawaii on a trip to Australia. Dirac had read a recent article about our lunar laser ranging (LLR) observatory, part of the NASA Lunar Ranging Experiment (LURE), and would like to visit us. It never crossed my mind that the caller was talking about the renowned British physicist who had shared the Nobel Prize in Physics with Erwin Schrödinger in 1933, years before my birth , “for the discovery of new productive forms of atomic theory.”

(Photograph courtesy of

Ad Right

Later that morning I mentioned the call to Don Landman, the senior solar physicist on the Maui staff, and was surprised by his immediate excitement at the prospect of meeting Dirac. I quickly got to a phone and relayed the news to John Jefferies, our director. John was obviously pleased, and instructed me to spare no effort to make the Diracs’ visit to Maui as pleasant as possible.

On the day the Diracs were scheduled to arrive, my wife, Marilyn, accompanied me to the airport to meet them. Despite never having seen pictures of them, we had no difficulty in recognizing the two among the throngs of Canadian and American tourists. He was wearing a wool tweed jacket, wool sweater vest, long- sleeve dress shirt and tie, carrying a well-worn briefcase, and had a rather battered raincoat thrown over one shoulder. Margit Dirac also defied the category of tourist in paradise; she wore her raincoat buttoned up the front and belted tightly about her waist. Marilyn and I introduced ourselves, picked up their baggage at the outdoor drop, loaded everything into our Volkswagen square-back station wagon and headed for Kula. After a quick stop to check the Diracs into the Silversword Inn on Upper Kula Road, just a half mile or so from our house, we started our drive up to the observatory.

The road up Mount Haleakala winds through forests of mostly eucalyptus trees before climbing into zones of grasslands, cacti and, finally, nearly barren lava. As we ascended through the grasslands, above the Park Service headquarters, Dirac asked, “How long has your lunar laser ranging observatory been operational?”

“The observatory is not yet even complete,” I said. “We are waiting for the receive telescope, which is being built at the University of Colorado. It’s a fly’s eye design, composed of some 70 8-inch refractor telescopes bundled together, each with optics to route the light collected to a common focus on the photomultiplier tube.”

“Then how are you ranging to the Moon?” he asked.

“We have been working with a temporary receiving system, using a telescope at the nearby DARPA observatory.” The Maui scientific community was small, and our friends at the Avco Everett Laboratory operated an observatory to image and study satellites for the U.S. military’s Defense Advanced Research Projects Agency. When they learned that delivery of our receive telescope had been delayed, they offered us time on their telescope.

“How many quanta do you receive back per laser shot?”

“It varies quite a bit, depending on atmospheric conditions, and judging from the temporal clumping of the returns there are probably errors in pointing at the reflector packages, but typically we get between a twentieth and perhaps a tenth of a photoelectron per shot.”

After several seconds of silence: “Perhaps I did not state my question clearly. A fractional quantum of light is not permissible, as it is the smallest unit of light.”

Dirac was, of course, correct. I had used the jargon that our team members used among ourselves. I quickly clarified. “Sorry. It appears as though virtually all of the returns we record are single photo-electron events, and we get about one return for each ten to twenty shots that we fire.”

Another pause, then: “And you are able to detect such a faint signal against the background light from the Moon?”

“Yes. Well, we know the range to within a few meters, so we use a range gate of about ten nanoseconds, or fewer. Combined with a field stop of about five seconds of arc, and a spectral filter of about two Angstroms, we are able to cut out most of the background light. We also cool the photomultiplier tube to reduce its dark noise.”

Once more a few seconds’ delay, then: “Quite remarkable!”

As we neared the summit of Mount Haleakala, Dirac asked where the crater was and whether we would be able to see it. Within a few minutes we reached a turnoff that led to an overview of the crater. We all climbed out of the car, and Mrs. Dirac insisted that “Father” put on his raincoat, as the air was chilly and a strong wind was blowing. When we got to the overlook Dirac leaned far out over the railing to see the wall of the crater immediately below. Mrs. Dirac, a.k.a. “Mother,” asked me to take hold of him to make sure that he did not fall. So there we were: Margit Dirac and Marilyn standing well back from the edge of the overlook platform, and me holding the Nobel laureate by the scruff of the neck (actually the collar of his raincoat) to make sure he did not fall into Haleakala crater.

The tour of the LLR observatory went well—both Mother and Father Dirac seemed to enjoy it. Afterward we returned to the Silversword Inn and dropped them off for an hour of rest before supper, for which we had invited them to our house. I returned to the inn to retrieve them, and when we arrived, our three daughters were home from school and were helping Marilyn prepare the table for dinner. The Diracs and I took a brief walk to see the fields of flowers, mostly carnations, that were grown commercially along the slopes of Haleakala, in the moderate temperatures and rainfall typical of that elevation. At dinner, Dirac asked each of the girls about their school work, life on Maui and their favorite pastimes. Dinner ended a bit later than usual, and after helping clear the table, the girls went to their rooms to get ready for bed. Dirac and I sat in the matching overstuffed swivel rockers that Marilyn and I usually sat in, and our wives sat on the couch. The four of us chatted about life on Maui as we finished our iced teas.

Soon our youngest daughter, Pam, returned in her nightgown, smelling of bubble bath, with a book in her hand. She was nine years old at the time, but she could easily have been mistaken for closer to six or seven. She went directly to Dirac, placed the book on his knee, opened it, and began to point to and talk about one of the pictures. After a minute or so, Dirac asked if she would like to sit with him so they could read the book together. She squeezed into the chair beside him, and the two of them spent the next 20 minutes reading the book and looking at the pictures, from cover to cover. When they completed it Marilyn said that it was getting late and that Professor Dirac might be tired from his long day of travel, so it would probably be best if Pam said goodnight. But Dirac said that he was fine and asked if there might be time for just one more book. He seemed to be thoroughly enjoying himself, so Marilyn agreed and Pam ran for another book. The two spent another half hour or so reading together.

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.

Photograph courtesy of William E. Carter.

After 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 10 39 . 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.

We moved back to the mainland in 1976, and the Diracs’ visit to Maui rarely crossed my mind until I read the Scientific American article on Dirac nearly two decades later. I was surprised to learn from it that Dirac had had an unhappy childhood, which was attributed to the tyrannical behavior of his father, whose death he not only did not grieve but wrote off with the statement “I feel much freer now.” The article also contains this quote from Margit Dirac:

It is the irony which only life can produce that Paul suffered severely from his father, who had the same difficulties with his family. Paul, although not a domineering father, kept himself too aloof from his children. That history repeats itself is only too true in the Dirac family.

Photograph from Paul A. M. Dirac Papers, 1788–1999, courtesy of the Florida State University Libraries, Special Collections and Archives.

A year or two ago, I learned of Graham Farmelo’s biography The Strangest Man: The Hidden Life of Paul Dirac , and sent off immediately for a copy. The book offers detailed accounts of both the personal and professional sides of P. A. M. Dirac’s life, and I found it both fascinating and sad. It was difficult for me to reconcile the man that I had so briefly met and immediately liked with the “awkward” and “extremely taciturn” man (in the words of physicist Walter Elsasser) described by those who had known him much longer and more intimately. Marilyn, our three girls and I did not find him strange, but rather an intelligent, warm, grandfatherly man with whom we greatly enjoyed sharing a couple of days on Maui.


  • Dirac, P. A. M. 1978. Directions in Physics. Edited by H. Hora and J. R. Shepanski. New York: John Wiley and Sons, Inc.
  • Farmelo, Graham. 2009. The Strangest Man: The Hidden Life of Paul Dirac. New York: Basic Books.
  • Hovis, R. Corby, and Helge Kragh. 1993. P.A.M. Dirac and the beauty of physics. Scientific American 268:5, pp. 104–109, May.
    • Tuan, San Fu. 2003. Dirac and Heisenberg in Hawaii. Indian Journal of History of Science 38:1, pp. 59-66.
    • Williams, James G., Slava G. Turyshev and Dale H. Boggs. 2004. Progress in lunar laser ranging test of relativistic gravity. Physical Review Letters 93:26, p. 1101.