One of the essential tenets of fundamental physics is that the various characteristics of massâ€”weight, inertia, and gravitationâ€”always remain constant in proportion to one another. Without this equivalence, Einstein’s theory of relativity would be in conflict, necessitating the revision of our current physics textbooks.

The equivalence principle has been verified by all measurements so far, although according to quantum theory, there should be a violation. Because of this contradiction between Einstein’s gravitational theory and contemporary quantum theory, ever-more accurate testing of the equivalence principle is so crucial.

A new study by the research teams from Leibniz University Hannover and the University of Bremen confirms another equivalence principle with 100 times greater accuracy, suggesting that passive gravitational mass and active gravitational mass are always equivalent. This equivalence principle exists regardless of the particular composition of the respective masses.

Our weight on Earth results from the gravitational response caused by passive gravitational mass. A body’s gravitational pull or, more accurately, the extent of its gravitational field is measured by its active gravitational mass. The equivalence of these properties is fundamental to general relativity. As a result, the equivalence of inertial and passive gravitational mass and the equivalence of passive and active gravitational mass are being examined more precisely.

If passive and active gravitational mass are not equal and their ratio varies depending on the material, then objects constructed of various materials with various centers of mass would accelerate. The Moon should accelerate because it comprises an iron core and an aluminum shell, with their centers of mass offset from one another.

Scientists noted,Â *“This hypothetical change in speed could be measured with high precision, via “Lunar Laser Ranging.” This involves pointing lasers from Earth at reflectors on the Moon placed there by the Apollo missions and the Soviet Luna program. Since then, round trip travel times of laser beams are recorded.”*

The research team examined such mass difference effects by analyzing *“Lunar Laser Ranging” data gathered over 50 years from 1970 to 2022. This means that the passive and active gravitational masses are equal to roughly 14 decimal places because no effect was discovered. The best prior study, from 1986, was one hundred times less precise than this estimate.”*

LUH’s Institute of Geodesy, in this study, analyzed the Lunar Laser Ranging measurements, including error analysis and interpretation of the results.

**Journal Reference:**

- Vishwa Vijay Singh, JÃ¼rgen MÃ¼ller, Liliane Biskupek, Eva Hackmann, and Claus LÃ¤mmerzahl Equivalence of active and passive gravitational mass tested with lunar laser ranging. Phys. Rev. Lett. 131, 021401 (2023). DOI: 10.1103/PhysRevLett.131.021401