Test of Newton’s inverse-square law in the Greenland ice cap

Abstract

An Airy-type geophysical experiment was conducted in a 2-km-deep hole in the Greenland ice cap at depths between 213 and 1673 m to test for possible violations of Newton's inverse-square law. An anomalous gravity gradient was observed. We cannot unambiguously attribute it to a breakdown of Newtonian gravity because we have shown that it might be due to unexpected geological features in the rock below the ice.PACS numbers: 04.80,+z, 04.90.+e, 93.30.Kh Some unified field theories 1 raise the possibility that forces exist in nature with ranges on the order of 10 2 -10 5 m and coupling strengths close to that of gravity. If they exist, these new forces would be apparent as violations of Newton's inverse-square law. Recent geophysical measurements in a mine 2 and on a tall television antenna 3 have reported small deviations from the classical law. This paper describes a geophysical experiment to search for possible finite-scale, non-Newtonian gravity over a vertical distance of 213-1673 m in the glacial ice of the Greenland ice cap. The principal reason for the choice of experimental site is that the uniformity of the ice eliminates one of the major sources of uncertainty arising in the first of the earlier studies, 2 namely, the heterogeneity of the rocks through which the mine shaft passes. Our observations were made at Dye 3, Greenland, in a 2033-m-deep borehole, which reached the basement rock. The site is 60 km south of the Arctic Circle, 125 km inland from Greenland's east coast, and at a 2530-m elevation.The Newtonian prediction of the gravity profile in the borehole, based on a density model of the ice and the topographic relief of the bedrock developed from geophysical measurements, was compared with measured values. Differences in gravity g were measured at several depths z and modeled bylaboratory experiments, p, is the ice density, and g r is a correction to the gravity differences based on the attraction of the subice terrain. (The effect of the ice-surface topography is negligible.) Although Eq. (1) is adequate within the uncertainties of our experiment, a more exact expression 4 which accounts for p, ?=^p/(z), /« y(z), and the Earth's ellipticity was used in the calculations. The gravity anomaly Ag is defined as the difference between the modeled gravity g m and the observed gravity in the borehole g obs , Ag=g obs (z)-g m (z) .(2)where / is the theoretical free-air gravity gradient, G is the Newtonian gravitational constant as determined in Now we describe the steps taken to obtain the experimental observations and model calculations given in Table I. The uncertainties in this table include contributions from the measurements themselves and from imperfect knowledge of the ice density and the terrain, with the latter effect dominating. They do not reflect our ignorance of the density inhomogeneities in the underlying rock. This issue, which in the end has the least controlled systematic uncertainty, will be discussed below.Before the measurements were made in Greenland, the borehole gravity meter was...

… and Fall

“…Shortly after the 1989 Moriond workshop the Greenland group ice cap measurement was published (Ander et al 1989). As they had earlier, they reported a 3.87 mGal anomaly between the gravity values at depths of 213 and 1673 m, but their conclusion had changed (p. 985): "We cannot unambiguously attribute it to a breakdown of Newtonian gravity because we have shown it might be due to unexpected geological features below the ice."…”

“…The Greenland group measured gravity in a 2 km deep borehole located in the Greenland ice cap. They found an unexplained difference between the measurements at 213 and 1673 m of 3.87 mGal (this value is taken from their later published report (Ander et al 1989)). The anomaly was both larger and opposite in sign to that reported by Stacey et al Once again this anomaly depended strongly on the model used to calculate the predicted Newtonian result.…”

Testing the inverse-square law of gravity in boreholes at the Nevada Test Site

“…All of the existing borehole experiments suffer from this problem. 21,22 This work was supported in part by grants from the Department of Energy (No. DEAC-0381-ER40050) and by the Lawrence Livermore National Laboratory Individual Research and Development fund.…”

Search for non-Newtonian gravitation-a gravimetric experiment in a hydroelectric lake

“…These 'geophysical' experiments are measurements along vertical profiles through mine shafts and boreholes (Stacey et al 1981;Holding & Tuck 1984;Holding, Stacey & Tuck 1986;Stacey et al 1987;Hsui 1987;Ander et al 1989) and on a high tower (Eckhardt et al 1988a;Romaides et al 1989).…”