Physicists: Stop saying “gravitational force” or that a body is”accelerated under/by gravity.”

This objection is only true within the frame of general relativity – when using classical mechanics (to mean Newtonian or non-relativistic quantum mechanics), you can say “gravitational force” or “Newtonian force” as much as you would like to refer to gravity, but within general relativity, it is not a meaningful term.

To really appeal to the English language (instead of just mathematical definitions for this one), the word “force” in physics, according to 2009 Random House Dictionary means:

[A]n influence on a body or system, producing or tending to produce a change in movement or in shape or other effects.

More specifically, the 2009 American Heritage Dictionary gives the definition of a force in physics as:

A vector quantity that tends to produce an acceleration of a body in the direction of its application.

For those familiar with the description of gravity due to general relativity, it should be clear then, that gravity is not a force, in either of the above two senses.  The motivation behind general relativity is to no longer describe gravity as a force: gravity is a consequence of the geometry (specifically meaning the curvature) of spacetime. Particles travel along geodesics (locally straight paths) through the curved spacetime. As far as they are concerned, they aren’t being accelerated (ie. being acted on by a force); they are just travelling along inertial paths (the same as a book sliding across a frictionless table).

For a satellite falling into a planet, one shouldn’t say that it is “being accelerated around the planet by the force of gravity due to the planet” but we should say that it is “travelling along a locally straight path that, to an observer in a non-inertial frame, appears to be curved because of the curvature in spacetime due to the matter of the planet” (although one could probably word it a bit more nicely).

If the satellite turned on a rocket and left its geodesic, then it would be acted on by a force, but that force would be due to the rocket. In the same way, in the Newtonian definition, you wouldn’t say that cart moving with constant velocity (on a frictionless track) was being acted on by a force; you shouldn’t say that an inertial body moving along a geodesic through spacetime is being acted on by a force, whether it’s a satellite in orbit around a planet or a particle falling into a black hole (to them, they’re just going straight).  When you throw a ball and it falls in a parabolic arc, remember it’s spacetime that is curved, not the particle’s trajectory (unless it really is being acted on by another force). It just looks curved to us, because we are in a non-inertial frame (when we’re standing watching the ball, the Earth is exherting a force on us, so we aren’t following a geodesic relative to the Earth, unlike the ball).

Despite the relative simplicity of this concept, many people continue to refer to gravity as a force, within the scope of general relativity, when, by definition of English or of relativist, it is not. In quantum gravity, it may be the case to again treat gravity as a force, but in terms of general relativity, it is an inappropriate use of language, and really goes against the basic “equivalence” motivation behind general relativity.

One example in the literature:

“Hawking Radiation As Tunneling” by Maulik K. Parikh and Frank Wilczek (Phys. Rev. Lett. 85, 5042 (2000). Cited 215 times ).

When considered at the very broadest level, radiation of mass from a black hole resembles tunneling of electric charge off a charged conducting sphere…For while the electric force between like charges is repulsive, the gravitational force is always attractive.

Despite an otherwise very formal (and brilliant) paper, gravity is still paired, analogously, with the electromagnetic force. Within general relativity, this is simply not a valid analogy. Although it sometimes helps to give physical motivation to problems by considering them in terms of our classical pictures, it shouldn’t be the basis for anything (especially when the actual explicit work of the paper is done within proper general relativity). While tunneling may in fact be the mechanism for Hawking radiation, its motivation comes from a faulty analogy.

If it wasn’t for our familarity with Newtownian forces, removing that usage of force from the relativist vocabulary wouldn’t be so difficult. Why use an expression that is actually not meaningful within a field (and is in fact contradictory to the basic principles behind it)?

-S.C. Kavassalis