Warped Passages - Lisa Randall [48]
Gravitational mass, on the other hand, is the mass that enters the gravitational force law and determines the strength of gravitational attraction. As we saw, the strength of the Newtonian gravitational force is proportional to the two masses that get attracted to each other. These masses are gravitational mass. Gravitational mass and the inertial mass that enters Newton’s second force law turn out to be the same, and that’s why we can safely give them the same name: mass. But in principle they could have been different, and we would have had to call one “mass” and the other “ssam.” Fortunately, we don’t need to do that.
The mysterious fact that the two masses are the same has deep implications, which it took an Einstein to recognize and develop. The gravitational force law states that the strength of gravity is proportional to mass, and Newton’s law tells us how much acceleration would be generated by that (or any other) force. Because the strength of gravity is proportional to the same mass that determines the amount of acceleration, the two laws together tell us that even though the force depends on mass through F = ma, the acceleration induced by gravity is entirely independent of the mass that gets accelerated.
The acceleration of gravity that any object experiences must be the same for anyone or anything separated by the same distance from another object. This is the claim that Galileo allegedly verified by dropping objects off the Tower of Pisa,* demonstrating that the Earth induces the same acceleration for all objects, independent of their mass. This fact—that acceleration is independent of the mass of the accelerated object—is unique to the gravitational force, because the strength of no force other than gravity depends on mass. And because the gravitational force law and Newton’s law of motion depend on mass in the same way, the mass cancels out when you calculate acceleration. Acceleration therefore doesn’t depend on mass.
This relatively straightforward deduction has profound implications. Since all objects have the same acceleration in a uniform gravitational field, if this single acceleration could be canceled, the evidence of gravity would be canceled as well. And that is exactly what happens to a freely falling body: it is accelerated precisely so as to cancel the evidence of gravity.
The equivalence principle says that if you and everything around you were freely falling, you would not be aware of a gravitational field. Your acceleration would cancel the acceleration that the gravitational field would otherwise have produced. This state of weightlessness is now familiar from pictures from orbiting spacecraft, where the astronauts and the objects that surround them don’t experience any gravity.
Textbooks often illustrate the absence of gravity’s effects (from the vantage point of the freely falling observer) with a picture of someone dropping a ball in a free-falling elevator. You see the person and the ball falling together in the picture. The person in the elevator would always see the ball at the same height above the elevator’s floor. He wouldn’t see the ball drop (see Figure 36).
Physics texts always present the freely falling elevator as if it were the most natural thing in the world that the observer inside would calmly watch a ball not drop with complete equanimity, with no concern at all for his personal well-being. This is in sharp contrast to the terrified faces in movies in which the cables of an elevator are cut and the actors hurtle towards the ground. Why such different responses? If everything were freely falling, there would be no cause for alarm. The situation would be indistinguishable from everything being at rest, albeit in a zero-gravity environment. But if, as in the movies, someone is falling but the ground