Einstein’s Theory of Relativity Gets New Confirmation Thanks to the Moon

Scientists have confirmed with unprecedented accuracy that all properties of mass are equivalent. This greatly strengthens Einstein’s principle of equivalence, which is the basis of the theory of relativity.

One of the most basic assumptions of fundamental physics is that the different properties of mass—weight, inertia, and gravity—always remain the same relative to each other. Without this equivalent, Einstein’s theory of relativity would be disproved and our modern physics textbooks would have to be rewritten. Although all measurements so far confirm the principle of equivalence, quantum theory suggests that there must be a violation. This discrepancy between Einstein’s gravitational theory and modern quantum theory is the reason why increasingly precise tests of the equivalence principle are especially important.

A team from the Center for Applied Space Technology and Microgravity (ZARM) at the University of Bremen in collaboration with the Institute for Geodesy (IfE) at the Leibniz University Hannover succeeded in proving, with 100 times greater accuracy, that a passive gravitational mass and an active gravitational mass are always equivalent—regardless of the specific composition of the respective masses. The study was conducted within the QuantumFrontiers Higher School Cluster. July 13 team published their results in the form of a paper in the scientific journal Physical Review Letters.

Physical context

The inertial mass resists acceleration. For example, it forces you to lean back into your seat when the car starts moving. Passive gravitational mass reacts to gravity and results in our weight on Earth. Active gravitational mass refers to the force of gravity an object experiences, or more precisely, the size of its gravitational field. The equivalence of these properties is fundamental to the general theory of relativity. Therefore, both the equivalence of the inertial and passive gravitational mass and the equivalence of the passive and active gravitational mass are verified with increasing accuracy.

What was the study about?

If we assume that passive and active gravitational mass are not equal—that their ratio depends on the material—then objects made of different materials with different centers of mass must be accelerating. Since the Moon is made up of an aluminum shell and an iron core, with centers of mass offset from each other, the Moon must be accelerating. Such a hypothetical change in speed could be measured with high accuracy using a “lunar laser rangefinder”. The experiment uses directed lasers from the Earth to reflectors on the Moon, placed there by the Apollo missions and the Soviet Luna program. Since then, the time of the return path of laser beams has been fixed. The research team analyzed “lunar laser rangefinder” data collected over a period of 50 years, from 1970 to 2022, and investigated such mass difference effects. Since no effect has been found, this means that the passive and active gravitational masses are equal to about 14 decimal places. This estimate is a hundred times more accurate than the best previous study dating back to 1986.

The Institute of Geodesy at the Leibniz-University of Hannover – one of only four centers in the world analyzing laser measurements of the distance to the Moon – has a unique expertise in data evaluation, especially for testing general relativity. In the current study, the institute analyzed measurements from the lunar laser rangefinder, including error analysis and interpretation of the results.