One of the fundamental assumptions of fundamental physics is that the various properties of mass—weight, inertia, and gravity—always remain constant with respect to one another. Without this equivalence, it would contradict Einstein’s theory of relativity and our existing physics textbooks would have to be rewritten. Although all measurements to date confirm the equivalence principle, quantum theory assumes that there must be a violation.

This inconsistency between Einstein’s theory of gravity and modern quantum theory is why increasingly sensitive tests of the equivalence principle are particularly important. A group from the Center for Applied Space Technology and Microgravity (ZARM) at the University of Bremen, in collaboration with the Institute of Geodesy (IfE) of the Leibniz University Hannover, has now succeeded in proving that there is passive gravity with 100 times greater precision. mass and active gravitational mass – always equivalent regardless of the specific composition of the mass concerned

The study was conducted within the framework of the QuantumFrontiers Excellence Cluster. Today, the team published their findings in an important paper. Physical Review Letters .

physical context

Inertial mass resists acceleration. For example, it causes you to be pushed back into your seat when the car starts. Passive gravitational mass responds to gravity and results in our weight on Earth. The active gravitational mass belongs to the gravitational force exerted by the object, or more precisely the size of the gravitational field.

The equivalence of these properties is essential to general relativity. Therefore, both the equivalence of inert and passive gravitational mass and the equivalence of passive and active gravitational mass are verified with increasing precision.

What was the study about?

Assuming that the passive and active gravitational masses are not equal – their ratio depends on the material – then objects made of different materials with different centers of mass will accelerate. Since the Moon is composed of an aluminum shell and an iron core whose centers of mass are balanced relative to each other, the Moon must be accelerating. This hypothetical change in velocity can be measured with high precision using the “Lunar Laser Locator”.

This includes aiming lasers from Earth at reflectors placed on the Moon by the Apollo missions and the Soviet Moon program. Since then, the time it takes for laser beams to pass through and come back has been recorded. The research team analyzed Lunar Laser Locator data collected over 50 years from 1970 to 2022 and explored the following effects of mass difference.

Since no effect was found, this means that the passive and active gravitational masses equal approximately 14 decimal places. This estimate is a hundred times more accurate than the previous best study dating back to 1986.

As one of four centers worldwide that analyze laser measurements of the distance to the Moon, the LUH Geodesy Institute has unparalleled expertise in evaluating data specifically to test general relativity. In the current study, the institute analyzed lunar laser position measurements, including error analysis and interpretation of results. Source