# Life in a Freely Falling Elevator

Einstein’s ‘happiest thought’ led to the Equivalence Principle 108 years ago.

Travel into deepest space — the emptiest region imaginable — toss a stone into the void and it will keep moving at a constant speed in a straight line. That’s inertia, a state broken only by the application of an external force such as gravity. But inertia itself isn’t a force; rather it is the absence of force.

Another way of stating this is that no force is needed for an object to maintain constant velocity. Otherwise, in the game of bowling, as soon as the bowler released the ball, it would stop. He would need to keep pushing it if he wanted it to travel down the alley and strike the pins. But that’s not what happens. It is precisely when the bowler removes the force of his hand that the ball follows a uniform trajectory of constant speed (aside from the effects of spin or friction), traveling in a straight line.

Being at rest is another form of inertia. The state of rest is relative, however. Sit on your porch and watch a biker fly past at constant speed, and she could envision herself as still and you as moving backward. Only context makes her realize that she is the one who is moving, not the porch.

When we conduct physics experiments, we generally don’t want them to be shaky. We don’t want the apparatus to be rocked by forces. That is why a still place, such as a porch, steady room, or solid, unwavering laboratory, is ideal. But a lab space moving at constant velocity would do just as well, since such motion is relative. We call anything moving at constant velocity relative to the state of rest an inertial framework. An inertial framework, according to Newton’s first law of motion, has no net force and is thereby in a state of equilibrium.

Now you may be thinking that, because the Earth is turning, a “fixed” laboratory really isn’t at rest. We call it “rest” just to keep things simple, but really there is an unbalanced force on it, causing it to rotate with the Earth’s surface. Where, then, is the genuine state of rest, by which we might define inertial frameworks?

As Newton realized, all celestial bodies are moving. Therefore he defined an imaginary framework called “absolute space” against which to measure inertia. The need in classical, Newtonian physics for absolute space can be seen through a simple thought experiment. Imagine being on a spinning merry-go-round and watching the scenery go by. You shout to your friends that the amusement park you’re in is whirling around you. Your friends standing on the ground shout back that it is in fact you who are rotating. How can you settle the argument? To prove that the steady ground and not the merry-go-round is the more suitable inertial frame, you need to match it against a definitive measure of rest. Newton saw that gold standard as absolute space.

The great Austrian philosopher Ernst Mach criticized Newton’s definition, asserting that it lacked a physical basis and wasn’t measurable. He preferred to believe that some kind of unknown influence from the stars caused inertia, and that there ought to be a definition of inertia that wasn’t reliant on a reference frame.

In 1907, two years after developing the special theory of relativity, Einstein began crafting the rudiments of a theory of gravitation. The special relativistic notion that information travels at the speed of light or slower had rendered insufficient the Newtonian concept that gravitation is an “invisible thread” or “action-at-a-distance” connecting two masses. If the Sun was blotted out, how could Earth instantly “know” to start traveling in a straight line? Rather, Einstein realized, gravity must have a local explanation — what physicists call a “field” — something that maps out the potential action of a force at each point. Electricity is conveyed by the electric field. What then, he wondered, comprises the gravitational field?

While pondering the nature of gravity, Einstein had a sudden revelation, which he would later dub his “happiest thought.”

Imagine a workman standing on the roof of a house and losing his footing. As he plummeted in free fall, everything within his grasp (a toolbox, for example) would plunge with him. Therefore, from his local perspective gravity wouldn’t seem to exist.

A freely falling elevator, therefore, could serve as a miniature laboratory. Perform any physics experiment within it, and there would be no effect due to external forces. Because everything within it would be plunging at the same rate (assuming no air resistance) it would effectively appear as if it were at rest in an empty region of space.

You can try this out by going on a free fall ride at an amusement park. As you plunge, let go of a balled-up piece of paper (or something equally safe) and watch it seem to hover in front of you (once again, unless air resistance disrupts the effect). Because you and the ball match each other’s acceleration, you would effectively be sharing a rest frame.

Einstein brilliantly realized that he could redefine inertia locally by use of freely falling elevators. Each elevator interior would constitute an inertial framework. Pick any point in space, and the state of inertia would be measured with respect to a freely falling framework at that location, rather than in comparison to a hypothetical absolute space. In that manner, Einstein felt that he had moved closer to realizing Mach’s dream of a more tangible definition of inertia. He called this idea the “equivalence principle.”

The fact that all objects in a freely falling framework accelerate at the same rate can be chalked up to a cosmic coincidence: the fact that gravitational mass and inertial mass always have identical values. These aren’t different things, as it turns out, but rather different roles played by mass. Their identity produces a kind of mathematical cancellation that ensures that acceleration under gravity is independent of mass.

Gravitational mass is a measure of the ability of matter to influence other matter through the gravitational force. All other factors being equal, the more gravitational mass an object has the greater its gravitational attraction to other bodies. Inertial mass pertains to the response of an object to any force: the greater the inertial mass, the lesser the acceleration for the same force.

We can see the difference by imagining an asteroid tumbling toward Earth and a planned interception with a missile designed to veer it away from its doomsday path. The asteroid’s gravitational mass sets the strength of its gravitational pull on and by Earth. Its inertial mass, in contrast, determines to what extent it would change its motion after being struck by the missile.

One might imagine a hypothetical universe in which the two have different values. However, in our universe all experiments to date indicate that the two are identical. The most famous of these tests were conducted from the 1890s until the 1920s by Hungarian physicist Loránd Eötvös using a device called the torsion balance. A typical torsion balance experiment involves suspending materials of two different masses on a balance beam and measuring the amount of twisting due to the mass imbalance. This angle is highly sensitive to both the inertial and gravitational mass values, indicating any smidgeon of a discrepancy, which Eötvös did not find.

The MICROSCOPE (MICRO-Satellite à traînée Compensée pour l’Observation du Principe d’Equivalence) experiment, expected to be launched in 2016, will test the equivalence principle more directly by measuring the acceleration of two masses of different compositions and amounts. It is anticipated to record any difference between gravitational and inertial masses with an accuracy greater than 10^-15, about a factor of 1,000 greater than the best current limits.

Einstein made the equivalence principle the core concept of his general theory of relativity, completed in late 1915. General relativity relies on the techniques of a mathematical field called differential geometry to sew together the coordinate systems of each freely falling patch into a continuous fabric of spacetime. The beauty of this method is that conventional Newtonian dynamics, as modified by special relativity, can be applied to each local patch—offering a point-by-point way of defining the laws of motion.

With March 14 having just past, as we put not only Pi Day but what would have been Einstein’s 136th birthday behind us, it is instructive to see how some of his simple thought experiments, such as a man falling off the roof of his house or plunging in a freely falling elevator, have led to the most extraordinary of breakthroughs in physics. Einstein greatly valued the power of imagination and of thought-experiments, and certainly put it to good use.

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