Fictitious Forces

Gravity is a myth.

Not because, as bumper stickers tell you, "The Earth sucks." Rather, the "force" we call gravity is an illusion that arises from our own motion through space.

Physicists have known this for almost a century, but for some reason this simple and beautiful reality is withheld from everyone except select graduate students. I'm going to let you in on the secret.

You feel a force when your back presses against the seatback of an accelerating car. But you probably no longer perceive it as a force, knowing that it is really an artifact of the car's motion: your body is just trying to stay put, or at whatever speed it was already moving. The push of the seatback nudges you to a higher speed so you can keep up with the car.

Another fictitious force is the so-called centrifugal force that throws you outward in a turning car. If you looked down on this scene, you'd see that your body is just trying to keep moving in a straight line. The real force is the centripetal force that pulls you back toward the center of rotation, staying with the car.

These forces are fictitious. They only appear because an object's motion is compared with an accelerating reference (the car). The clue is that, if left alone, all objects accelerate the same way, independent of their mass.

Normal forces produce smaller acceleration for "heavier" objects--those with greater mass. The introductory physics equation F=ma captures this relationship between Force, mass, and acceleration.

Because the acceleration from a fictitious force is independent of mass, the apparent force must grow in proportion to the mass. Holding a toddler on your lap during a sharp turn is harder than holding a less massive soda can. This proportionality to mass is a clear signal that a force is fictitious: the objects are really just trying to move at a constant speed. It's the car that's accelerating. The equation for centrifugal "force," for example, includes the mass of the object, as it should.

Perhaps you can see where this is going: according to Newton, gravity is also proportional to mass in precisely this way. Unless this is a coincidence, this means gravity is a fictitious force. Over the years physicists have tested the coincidence idea by comparing the "gravitational" and "inertial" mass. They're always exactly the same.

It was Einstein who took the fictitious nature of gravitation seriously. He developed his theory of general relativity by starting with this equivalence principle: inside a small box, like an elevator car, there's no way to distinguish the force of gravity from acceleration of the car.

In this view, the natural state of all objects around you, as well as your own body, is to constantly accelerate downward. The reason you don't do that is that your chair is constantly pushing up on you, accelerating you upward relative to this natural state of motion.

The idea of "free fall" is easier to accept for an orbiting spacecraft or NASA's "vomit comet" on its parabolic arc. But once you accept the idea that you and everything around you are constantly accelerating upward, it's pretty simple, right?

One reason this isn't common knowledge is that pretending gravity is a force makes it easier to connect the falling of an apple on earth to what keeps the planets in their orbits, which is pretty profound, too.

For orbits, acceleration is in different directions, for example, on opposite sides of the earth. It took Einstein more than a decade to figure out how to stitch together different accelerations at different places, using the sophisticated mathematics of curved spaces that had only been developed in the 19^th century. He also had to figure describe how massive (or energetic, thanks to E=mc²) objects warp space to create the curvature, without screwing up the interconnection between space and time that he had found in his theory of special relativity.

For most purposes, regarding gravity as a force gives the same, correct answer. But not always: small timing corrections from general relativity are critical for global positioning systems (GPS).

And isn't it interesting to imagine your chair accelerating you upwards?