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When he invented what we now call classical mechanics, Isaac Newton discovered a variety of concepts that are fundamental to our understanding of how forces work to move objects. If anybody actually remembers anything about Newton’s contributions to classical physics, it’s his formulation of the three laws of motion (the most important to this discussion being F = ma, that is the magnitude of a force moving an object is equal to the product of the mass of the object and its acceleration), and his universal law of gravitation (expressed by the equation F = (Gxm_{1}xm_{2})/r^{2}where m_{1} and m_{2} are the masses of the objects attracted to each other, r is the separation between the two masses, and G is the universal gravitational constant). Mass enters into both of these equations, but since Newton formulated these two laws separately, there was no reason to think that the mass of an object in the context of F = ma was the same as the mass of the same object in its gravitational attraction to another object. In Newtonian physics, the first mass is called inertial mass, and the second mass is called gravitational mass. Since the formulation of these two laws, as far as anybody can tell, for any object, the two values, inertial mass and gravitational mass, are equal, but in Newton’s formulation, there’s no reason that they have to be.

Centuries later, along comes Einstein. After developing the theory of special relativity for objects moving at constant speeds relative to each other, he starts thinking about objects that are accelerating relative to each other. He considers a thought experiment where a person is on an elevator in interstellar space, where there is no gravity, and the elevator is accelerating at a rate of 9.8 m/s^{2} (which is equal to gravitational acceleration at the surface of the Earth). Can the person in the elevator tell whether he or she is in an elevator accelerating in interstellar space, or in an unmoving elevator at the surface of the Earth? The answer is no. Einstein was the first to understand that the nature of inertial acceleration and gravitational acceleration are the same, and therefore, the inertial mass and gravitational mass of any object must be one in the same. This idea is called the equivalence principle, and it is at the heart of general relativity, which is the theory that explains how massive objects curve spacetime, thus bending the trajectories of objects moving near massive bodies.

One way that physicists stay out of trouble is to, on occasion, put the equivalence principle to the test to see if indeed the inertial mass of an object is the same as its gravitational mass. The results of the most stringent experiment of this sort have just recently been published.

The experiment was called MICROSCOPE, and it took place in a satellite (see above).

[T]he MICROSCOPE experiment tracked the motion of nested metal cylinders — a 300-gram titanium outer cylinder and a 402-gram platinum inner one — as they orbited the Earth in near-perfect free fall. Any difference in the effect of gravity on the respective cylinders would cause them to move relative to each other. Small electrical forces applied to bring the cylinders back into alignment would have revealed a potential violation of the equivalence principle.

From April 2016 to October 2018, the cylinders were shielded inside a satellite that protected them from the buffeting of solar winds, the minuscule pressure that sunlight exerts and the residual atmosphere at an orbital altitude of a little over 700 kilometers high.

By performing the experiment in orbit, the researchers could compare the free fall of two different materials for extended periods without the confounding effects of vibrations or of nearby objects that could exert gravitational forces, says Manuel Rodrigues, a MICROSCOPE team member and physicist with the French aerospace lab ONERA in Palaiseau. “One of the lessons learned by MICROSCOPE is … that space is the best way to get an important improvement in the accuracy for this kind of test.”

The conclusion of the experiment was tha the equivalence principle holds to “about one part in a thousand trillion,” which is a stunning level of precision.

So Einstein is still right!

Comments are below the fold.