Letters

Probing Pyramids to Identify Internal Structure

The news that Mexican physicist Arturo Menchaca and archaeologist Linda Manzanilla have launched a cosmic muon search for hidden chambers in the Pyramid of the Sun in Mexico (Physics Today, February 2004, page 31) opens a new and exciting chapter in cross−disciplinary research. The two researchers have chosen the technique of pyramid probing with vertical muons—that is, those making an angle less than 45° to zenith. Vertical muons were first used in 1955 in Australia (ref. 5 of ref. 1). Luis Alvarez and coworkers used the method in their 1967−68 probing of Chephren's pyramid, the second of the great pyramids of Egypt. The Alvarez team searched for equivalents of the king's and queen's chambers that had been found in the first pyramid, that of Chephren's father, Cheops.

The vertical muon probing method consists of measuring, from beneath the pyramid, the absorption pattern of the muons as a function of their angle to zenith after they pass through the pyramid. The detector was placed in the only known chamber beneath Chephren's pyramid. As a result of the probing, Alvarez concluded that no other chamber existed.¹ "It's not that we did not find the chamber," said Alvarez. "We found that there wasn't any chamber."²

Menchaca and Manzanilla appear to be unaware of an article by two French architects³ that was published two decades after Alvarez's investigation. In describing their search for cavities in the Cheops pyramid, the architects pointed out an important construction feature, unknown to Alvarez at the time of his search, that brings into question the feasibility of observing hidden chambers from beneath the pyramids.

Alvarez assumed that the pyramids were filled with only one kind of stone—limestone—so that their interior density is uniform. The architects reported that the Cheops pyramid was built of two kinds of stone with different densities: limestone, at 1.8 g/cm², and granite, at 2.7 g/cm². While most of the first pyramid's interior consists of limestone, the roofs and walls of all chambers and galleries are made of granite. The mass of the granite roof above the king's chamber is equal, within 5%, to the sum of the missing mass of the chamber plus the mass of the roof if it were made of limestone;⁴ the apparent area density of the king's chamber, as detected by the vertical muons, approximately equals that of limestone. By accident or by design, the excess density of granite over that of the limestone nearly exactly masks the void. Had Alvarez first tested his system in the Cheops pyramid, from beneath, he could not have detected the king's chamber with vertical muons.

Are these considerations, based solely on our knowledge of the Cheops pyramid, valid for Chephren's as well? They would be invalid if Chephren's pyramid was built without granite. However, the lower chamber's granite roof suggests that no such radical departure in architecture took place between the father's pyramid and the son's.

I first saw the French architects' article³ in January 1987 while in Cairo filming a documentary about the pyramids.² I immediately informed Alvarez of the French group's findings. He confirmed that he was unaware of the use of granite in the pyramids.

I suggested to Alvarez that to unambiguously state that there are no other chambers in Chephren's pyramid, one would have to repeat the measurement using horizontal muons—those that make an angle greater than 45° to zenith—and that the detector should be on the ground outside the pyramid.⁵ The intensity of the horizontal muons is much lower than that of the vertical ones, but the horizontal muons have the advantage of being "hardened" by their longer passage through the atmosphere. In fact, Alvarez's experiment¹ had confirmed the feasibility of using horizontal muons: The muon absorption pattern had clearly shown the ridges of the peak of the Cheops pyramid viewed from the Chephren pyramid's lower chamber.

In a letter written to me less than a year before his death, Alvarez stood by his conclusion that no king's or queen's chambers exist in Chephren's pyramid. He argued that if a hypothetical king's chamber had included a granite roof, his detector would have observed it as a density bump. Because no such bump was observed, Chephren's pyramid must have been constructed differently from Cheops's. Alvarez did tacitly imply, however, that the issue was not closed; he said another measurement, using horizontal muons, would confirm his conclusion.

Actually, the issue is wide open, because the only chamber found in the Chephren pyramid was built like all chambers in the Cheops pyramid—with a granite roof. To exclude the existence of chambers in the Chephren pyramid, an experiment with horizontal muons is called for.

How is this story relevant to the Pyramid of the Sun? If the Mexican pyramid's interior density is homogeneous, it will be irrelevant. If the density is not homogeneous, the story may be quite relevant. According to the Physics Today story, Menchaca says the Pyramid of the Sun has a more irregular shape, is less dense, and is also less homogeneous.

Menchaca comments: The account by Bogdan C. Maglich on unpublished details of the Chephren pyramid experiment by Luis Alvarez and coworkers¹ provides fascinating insight into this pioneering application of high−energy physics to archaeology. The method used by Alvarez involves finding statistically significant differences between measured and simulated muon flows in a given direction. The necessary ignorance of a detailed density distribution inside the investigated volume requires an approximation. As Maglich implies, both we and the Alvarez group assumed that the internal pyramid density is constant. Also, we are aware² of the limitations introduced, not only by uncertainties related to the internal density distribution, but also by uncertainties about the external shape description, among other factors.

In Teotihuacan we assume that the mean composition and density distribution are similar to those found inside a 200−meter−long horizontal tunnel excavated near the base of the Pyramid of the Sun last century. We sampled the pyramid filling along that tunnel. The study reveals that the Mexican monument, although fairly uniform, is more heterogeneous than the Egyptian pyramid seems to be as judged by the limestone walls of the tunnel leading to the Belzoni chamber, where the Alvarez team located its muon detector. The measured mean density in Teotihuacan turns out to be appreciably smaller than the density of rock. As Maglich correctly suggests, we do consider the conditions in which stony walls of a hypothetical hidden cavity would result in a compensated mean density that would cancel the sought−for signal. This and other considerations helped determine the limitations of our experiment.²

In contrast with the Chephren case, archaeological excavations in the Pyramid of the Sun provide excellent calibration references. Finally, in the Egyptian case, we tend to agree with the private response Maglich says he received from Alvarez concerning the unlikely possibility that a cavity having a granite ceiling would result in mean density compensation in all directions. That would be particularly unlikely with internal structures as large and intricate as those found in the Cheops pyramid.

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