The idea that inertial and gravitational mass are the same is known as the weak equivalence principle. It became a crucial issue when Einstein formulated his theory of general relativity around 1912-16, which rested on the central idea that the acceleration caused by gravity is the same as the acceleration of an object subject to the same force in free space. If that’s not true, general relativity won’t work.“
The equivalence principle is one of the basic assumptions of general relativity,” says Stephan Schlamminger, who works at the Mecca of high-precision measurement, the National Institute of Standards and Technology in Gaithersburg, Maryland. “As such, it should be thoroughly tested. Tests of the equivalence principle are relatively cheap and simple, but could have a huge impact if a violation was found. It would be careless not to perform these experiments.
”If the weak equivalence principle fails, then there are two possibilities. Either Newton’s expression for the force of gravity between two masses (which is also what general relativity predicts if gravity and speeds are not extreme) is slightly inaccurate and needs tweaking. Or gravity might be fine as it stands—but there might be a new, fifth force that makes it look different. That fifth force would add to the four we already know to exist: gravity, electromagnetism, and the strong and weak nuclear forces that govern the interactions of subatomic particles inside atomic nuclei.
Whether we think about “modified gravity” or a fifth force is, says Fischbach, in the end just a semantic distinction. Either way, says Feng, there is “no reason at all that there can’t be a fifth force that we have not noticed until now.”