# physics4me

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## Drop-testing general relativity, Galileo’s way

About 425 years ago, legend has it, Galileo Galilei climbed the Leaning Tower of Pisa. Before a throng of scholars and students, the savant dropped pairs of balls of different weights and materials—say, wood and lead—to show that regardless of their weight or composition, all objects accelerate at the same rate under gravity’s pull. About a year from now, a satellite will blast into orbit to perform the legendary test more precisely than Galileo could have imagined.

Rather than dropping things to the ground, the Drag-Compensated Micro-Satellite for the Observation of the Equivalence Principle (MicroSCOPE) will contain two free-floating weights of different materials and will monitor whether one feels a stronger tug from Earth’s gravity than the other. If so, the result would sink general relativity, Albert Einstein’s theory of gravity. After more than 15 years of development, “the instrument is done, definitely done,” says Pierre Touboul, a physicist at the French aerospace laboratory, ONERA, in Chatillon. “Now we cross our fingers.”

Funded primarily by the French National Center for Space Studies, MicroSCOPE will test a key assumption of general relativity called the equivalence principle, which marries two conceptions of mass. Inertial mass determines how much an object resists moving when pushed by a force—as when you shove a car. Gravitational mass determines how strongly gravity pulls on the object. According to the equivalence principle, the two masses are one and the same, regardless of how heavy a thing is or what it’s made of. That explains Galileo’s experiment: If the two types of mass are identical, then for all objects the pull of gravity varies in strict proportion to the resistance to motion, ensuring that all things fall at the same rate. MicroSCOPE aims to test whether the two masses are the same with a precision 100 times better than any previous experiment, and other efforts could go even further.

Three ways to test the equivalence principle

To tell whether inertial and gravitational mass are the same, scientists can check whether objects made of different materials fall at different rates, orbit at different distances above Earth, or cause a twist in a torsional oscillator. The twist would come about if the net force produced by gravity’s pull toward the center of Earth and the centrifugal force produced by Earth’s rotation pointed in a different direction for each weight.

According to general relativity, the equivalence principle must hold exactly, as acceleration and gravity are essentially the same thing. But general relativity may not be the last word on gravity, because so far it cannot be reconciled with quantum mechanics, which governs physics on the smallest scales. Efforts to bridge that gap often violate the equivalence principle, says Clifford Will, a theorist at the University of Florida in Gainesville. Spotting a violation “would definitely mean that there is some sort of physics beyond Einstein’s theory,” he says.

IRONICALLY, THE MOST FAMOUS TEST of the principle, Galileo’s demonstration at Pisa, probably never happened. “It’s a fiction,” says Alberto Martínez, a historian at the University of Texas, Austin. The first account of the event was penned long after Galileo died by his assistant Vincenzo Viviani, who said the great man wanted to show that Aristotle was wrong when he contended that heavier objects fall faster than lighter ones do.

Galileo did write about such tests in 1638 in his Dialogues Concerning Two New Sciences: “[T]he variation of speed in air between balls of gold, lead, copper, porphyry, and other heavy materials is so slight that … I came to the conclusion that in a medium totally devoid of resistance all bodies would fall with the same speed.” But Galileo likely inferred the result by timing balls rolling down ramps, says John Heilbron, a historian emeritus at the University of California (UC), Berkeley. “He had a clear idea that it didn’t matter what he made the ball out of,” Heilbron says. “I think he was too lazy” to actually drag weights up a tower.

Although Galileo’s analysis jibes with the equivalence principle, he wouldn’t have understood it that way, says Domenico Bertoloni Meli, a historian of science at Indiana University, Bloomington. The concepts of inertial and gravitational mass were invented later by Isaac Newton. Newton proved that the two types of mass were equal by showing that pendulums of equal lengths but different materials swing at the same rate, as he described in Philosophiæ Naturalis Principia Mathematica in 1687.

The equivalence principle proved key to Einstein’s invention of general relativity. Einstein deduced that gravity arises when energy and mass bend spacetime. In that warped spacetime, freefalling objects follow the straightest possible paths, or geodesics, which to us appear as the parabolic arc of a thrown ball and the elliptical orbit of a planet. The change of the object’s speed and direction is its acceleration, which depends on the amount of warping of spacetime. If such warping is all there is to gravity, then in a given situation all things must accelerate at the same rate as they fall. That’s because for any starting position and velocity, there is only one straightest path in spacetime.

But gravity could be more complicated, says Thibault Damour, a theorist at the Institute of Advanced Scientific Studies (IHES) in Bures-sur-Yvette, France. According to Einstein’s famous equation E = mc2, an object’s inertial mass measures the energy trapped inside it. So a sliver of an atom’s mass comes from the electromagnetic force that binds the electrons to the nucleus. Much more comes from the energy of the strong force that binds particles called quarks inside the nucleus’s protons and neutrons. In general relativity, all energy has the same effect regardless of its source, Damour says.

However, in some theories that aim to unify gravity and quantum mechanics, it matters how such energy arises. For example, string theory posits that every fundamental particle is an infinitesimal string rippling through a complex 10-dimensional space. In string theory a “dilaton field” acts like an additional form of gravity but pulls on different types of particles with different strengths. So, two objects with the same internal energy and inertial mass may have different gravitational masses, violating the equivalence principle. The ratio of a nucleus’s inertial and gravitational masses could depend on the tally of protons and neutrons in it or the difference in the numbers of protons and neutrons, Damour says….