Einstein’s Experimental Elevator

In 1907, physicist Albert Einstein devised what we now call the “elevator” thought experiment, in which he dreamed up the idea of having an entire physics laboratory inside a falling elevator. The result of that thought experiment was nothing less than the principles underlying the General Theory of Relativity.

Illustration of elevators in the sky

Shortly after introducing the special theory of relativity in 1905, Einstein began to worry about the fact that its scope was limited to transformations among inertial frames—frames moving relative to one another with constant velocity in a straight line. He asked if a more general theory could be formulated, one valid for transformations among frames moving arbitrarily with respect to one another.

photograph of Albert Einstein, the German physicist
Albert Einstein, the German physicist

Einstein took a first, important step toward a general theory of relativity in 1907 with what we now call the “elevator” thought experiment, by means of which Einstein uncovered a deep connection between accelerated frames of reference and gravitation. One legend has it that the idea first occurred to Einstein when he looked out a window at the patent office and saw some construction workers on a nearby building, realizing that if one were to fall through a great distance, one would not feel the force of gravity while one was falling. Einstein realized that the acceleration one experienced while falling would cancel out (or negate) the feeling of gravity’s pull upon oneself. By the way, skydiving doesn’t quite work as an example, because one feels resistance from the comparatively dense atmosphere through which one is falling—that’s the wind one feels while falling.

A Complete Physics Lab in an Elevator

photo of a hand throwing a tennis ball up into the air
Part of Einstein’s elevator experiment imagined throwing a ball across the elevator lab in a simple demonstration of physics.

But the elevator thought experiment comes to us in a slightly different form. Einstein imagined an observer inside a closed space, like an elevator, that is equipped with a complete physics lab. Inside the closed lab one can perform any physics experiment, but one cannot communicate directly with observers or the world outside the closed laboratory. Think about doing experiments, like throwing a ball from one side of the laboratory to the other, when the laboratory is in empty space and is stationary or otherwise moving inertially—which is to say, again, with constant speed and direction. And let’s assume that it’s moving in an upward direction. The ball will appear to travel straight across the lab. This is just the old Galilean principle of relativity.

But imagine now that the lab is stationary on the surface of the Earth, and repeat the experiment. Thanks to the Earth’s gravitation, the ball will be observed to follow a downward parabolic trajectory. Imagine next that the lab is again in empty space but now is accelerated upward with a constant acceleration. Not moving upward with a constant velocity or speed, but accelerated upward with a constant acceleration, as when an elevator ascends or a rocket carries the space shuttle aloft. One will see exactly the same thing that one saw in the lab at rest in the Earth’s gravitational field.

Einstein realized that no experiment performed inside the closed lab could distinguish between the lab’s being in a strong gravitational field and its being accelerated rapidly upward.

Einstein realized that no experiment performed inside the closed lab could distinguish between the lab’s being in a strong gravitational field and its being accelerated rapidly upward. He concluded that a general theory of relativity, one valid for transformations between mutually accelerated frames of reference, would therefore also have to be a theory of gravity. He formulated this insight in what is known as the “equivalence principle,” which asserts that uniform acceleration is equivalent to the presence of a homogenous, or uniform, gravitational field. Now, of course, since the Earth is spherical, its gravitational field is not, strictly speaking, homogenous or uniform, because its lines of gravitational force diverge. But the equivalence principle still holds for reasonably small regions of space where the divergence is negligible.

The Problem of Universal Gravitation

The equivalence principle cleared up an old and vexing puzzle about Newtonian physics, which is why the term for mass in Newton’s second law of motion, the force law, always takes the same value as the term for mass in the law of universal gravitation.

The equivalence principle cleared up an old and vexing puzzle about Newtonian physics, which is why the term for mass in Newton’s second law of motion, the force law, always takes the same value as the term for mass in the law of universal gravitation. In Newton’s second law, or force law, F = ma says that force is equal to mass times acceleration. The mass might be that of our ball thrown across the lab.

Newton’s law of universal gravitation asserts that the gravitational force that two bodies exert on one another, say the Earth and a ball falling downward toward the Earth, is proportional to the product of the two masses divided by the square of the distance between them. There’s also a constant of proportionality, G, called the “gravitational constant.” Mass in the second law of motion, which is called “inertial mass,” is a measure of a body’s inertia, its resistance to changes in its state of motion. Mass in the law of universal gravitation, which is called “gravitational mass,” is a measure of a body’s ability to feel and exert gravitational attraction.

The old question that arose already in Newton’s day was this: Why should one and the same property of a body be responsible for both its resistance to changes in motion and its ability to feel and exert gravitational force? That’s clearly not the case with electrical forces, for example, where inertial mass measures resistance to a change in motion but electrical charge measures the body’s ability to feel and exert electrical attractions or repulsions. Einstein’s radical new answer to this old question is that inertial and gravitational mass are equal because they are, literally, one and the same property of a body. This is a consequence of the equivalence principle’s assertion of the indistinguishability of gravitation and uniform acceleration.

Experiencing the Equivalence Principle

image of the launch of a Saturn roket
Astronauts being accelerated by a giant rocket are well-familiar with the equivalence principle.

There is a sense in which all of us are perfectly familiar with the equivalence principle. Think about the fact that when we talk about astronauts experiencing the strong acceleration of a rocket at launch, we say that they are experiencing perhaps 2.5 g’s. The symbol g in such an expression stands for the acceleration due to the force of gravity at the Earth’s surface, which is 9.8 meters per second squared. In fact, the astronaut is being accelerated upward on a powerful rocket, but it feels to the astronaut exactly the same as it would if the Earth’s gravitational field had suddenly been intensified by a factor of 2.5. We all have a similar experience to a lesser degree when we step on the accelerator in a car and feel ourselves being pushed back into the seat.

How to Bend Light

Another important consequence of the elevator thought experiment is that since electromagnetic phenomena are no more capable of distinguishing acceleration and gravitation than are mechanical phenomena, therefore the paths of light rays should be curved in the presence of a gravitational field. If an observer in an upwardly accelerated elevator shines a light beam perpendicularly across the elevator, then because of the upward acceleration of the elevator during the time it takes the light to travel from one side to the other, the beam will strike the opposite wall a little below where it was emitted. The observer inside the elevator will see the light beam curve downward in a parabolic trajectory similar to, but less pronounced than, the parabolic trajectory of a ball thrown across the elevator.

false color image of the sun
The Sun, shown here in false color image, produces a strong enough gravitational pull that light from distant stars can be seen to bend as it passes through the Sun’s gravitational field.

But acceleration and gravitation are equivalent, so a gravitational field should produce the same effect. The bending of light produced by the Earth’s gravitational field, or even by the kinds of accelerations actually achievable with powerful rockets, is so slight as to be unnoticeable, because the speed of light (300 million meters per second) is so much greater than the speed of a baseball thrown across the elevator. But the sun’s gravitational field is strong enough to produce a measurable effect, and the predicted bending of light from distant stars as it passes near the sun became the basis for the most famous confirmation of the general theory of relativity.

From the lecture series Albert Einstein: Physicist, Philosopher, Humanitarian
Taught by Professor Don Howard, University of Notre Dame
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