Einstein's theory of relativity was supported, despite the doubts of the quantum scientists.

The idea that the various characteristics of mass—weight, inertia, and gravitation—always remain constant in respect to one another is one of the core tenets of fundamental physics. 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 to far, although according to quantum theory, there should be a violation.

It is because of this contradiction between Einstein's gravitational theory and contemporary quantum theory that ever-more accurate testing of the equivalence principle is so crucial. In order to demonstrate that passive gravitational mass and active gravitational mass are always equal—regardless of the specific composition of the respective masses—a team from the Center of Applied Space Technology and Microgravity (ZARM) at the University of Bremen worked with the Institute of Geodesy (IfE) at the Leibniz University Hannover.


The study was carried out under the auspices of the Excellence Cluster "QuantumFrontiers." The team's research was recently highlighted in a Physical Review Letters article.

Physical Context

Acceleration is resisted by inertial mass. For instance, when the automobile begins, it pushes you backward into your seat. Our weight on Earth is a result of the gravitational reaction 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.


General relativity is predicated on these qualities' equality. As a result, it is becoming increasingly accurate to evaluate the equivalence of inertial and passive gravitational mass as well as passive and active gravitational mass.

What was the study about?

If we suppose that the ratio of passive to active gravitational mass depends on the material and that it is not equal, then objects composed of various materials with various centers of mass would accelerate. The iron core and aluminum shell that make up the moon have mass centers that are offset from one another, hence the moon should move faster. By using "Lunar Laser Ranging," it would be possible to measure this fictitious change in speed with extreme accuracy.

This entails using lasers to illuminate reflectors that the Apollo missions and the Soviet Luna program had positioned on the moon. Since then, laser beam round-trip times have been noted. The research team analyzed "Lunar Laser Ranging" data collected over a period of 50 years, from 1970 to 2022, and investigated such mass difference effects.

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.


The Institute of Geodesy at LUH has specialized knowledge in evaluating the data, notably for proving general relativity. It is one of only four facilities worldwide that analyzes laser distance measurements to the moon. The institute examined the Lunar Laser Ranging measurements in the current study, including error analysis and result interpretation.