Gravity accelerates objects equally, despite differences in their mass or composition. This core principle of modern physics was known by the 16th century thanks to observations by Galileo Galilei, which were later confirmed by astronaut Dave Scott during the Apollo 15 moonwalk.
“What do you know! Mr. Galileo was right,” Scott said during a television demonstration broadcast from the Moon, where he dropped a geologic hammer and a feather and watched them fall at the same rate in the airless lunar atmosphere.
Based on such observations, it is widely accepted that the relationship between weight, inertia, and gravitation are three properties of mass that must always remain consistent in relation to one another. These phenomena are at the core of the equivalence principle, a cornerstone of Einstein’s theory of gravity.
Past measurements have always confirmed the equivalence principle, although the potential that inconsistencies could yet be found in the theory has haunted physicists. As Washington University physicist Clifford Will once said, “Discovering even the slightest difference in how gravity acts on objects of different materials would have enormous implications.”
One of the things that keeps physicists preoccupied with this possibility involves a potential violation that arises from observations in quantum theory, prompting ongoing experimentation to test for anything that appears to be inconsistent with Einstein’s theory of gravity. If ever found, it would be a discovery that could potentially cause us to have to rewrite our textbooks.
For now, our understanding of the equivalence principle remains intact, thanks to a team of scientists who employed close to half a century of Lunar Laser Ranging data collected about the Moon, which allowed them to confirm the equivalence of all properties of mass with far greater precision than ever before.
According to a team of researchers with the University of Bremen’s Center of Applied Space Technology and Microgravity, working in cooperation with the Institute of Geodesy at Leibniz University Hannover, measurements derived from lunar laser ranging data collected over the last half-century demonstrated the equivalence of passive gravitational mass and active gravitational mass with greater than 100 times the accuracy of past measurements.
Fundamental to the team’s measurements is the fact that inertial mass will resist acceleration, a phenomenon we experience if we apply pressure to the gas pedal too quickly when a car begins to move, causing us to be pushed against our seat. On the other hand, passive gravitational mass reacts on gravity, the same phenomenon that gives rise to our weight on Earth. When we talk about active gravitational mass, it relates to the force of gravitation that any object exerts and the proportional size of its gravitational field.
Since 1969, Lunar Laser Ranging (LLR) has been used to measure the Moon’s distance from Earth-based observatories using retroreflectors placed there by the Apollo missions, as well as the Soviet Luna program. Based on LLR data, the research team was able to examine potential violations of the equivalence of both passive and active gravitational mass for two elements, aluminum, which is abundant in the Moon’s outer layers, and iron, of which the Moon’s core is composed.
Based on the assumption that active and passive gravitational mass are not equal, but that their ratios are dependent on material composition, it stands to reason objects made of different materials and with different centers of mass—like the Moon’s aluminum shell and its iron core—would accelerate themselves. Based on this, the Moon would also accelerate, a reality that more than 50 years of LLR data would easily be capable of conveying.
However, based on LLR data collected between 1970 and 2022, no such difference in mass effects was found, confirming the equality of active and passive gravitational masses to 14 decimal places, a figure 100 times more accurate than past measurements carried out in 1986 that represented the previous most accurate measurements of this kind.
Thanks to the team’s findings, the equivalence principle does indeed remain intact, and thereby offers further confirmation of Einstein’s theory of gravity, despite any doubts that arise from quantum physics.
The team’s paper, “Equivalence of Active and Passive Gravitational Mass Tested with Lunar Laser Ranging,” appeared in Physical Review Letters on July 13, 2023.