Forces are more mysterious than you might think
By Steve Humphrey
Force is a term ubiquitous in Physics and in ordinary life. We talk about the force acting on some object or person which causes some change in that object or person. But forces can be mysterious and invisible, and sometimes even nonexistent. Examples of the latter are the centrifugal force and the Coriolis Force. These are known as “fictitious forces”, whose apparent existence results from an infelicitous choice of reference frame. It turns out that the force of gravity might be of just this sort.
For Aristotle (and all things begin with Aristotle), everything in the world is composed of some combination of five basic elements: Earth, Air, Fire, Water and Quintessence (“Fifth Element”. Great movie, by the way, starring Bruce Willis and Mila Jovovich.) In those days it was widely believed that the Earth was flat, and up and down were much different that left and right, or forward and back, in that while it is just as easy to move left or right, no such symmetry exists for up and down. Each of the elements has a “Natural Place”. Earth’s place is lowest, then Water’s, then Air’s and then Fire’s. The Natural Motion of an object is toward its natural place. So, objects made of Earth tend to fall, as do objects made of water (think of rain). Air tends to rise, and Fire rises more rapidly. In Aristotle’s day, it was believed that the Earth was at rest while the heavens revolved around it, in perfect circles. The Natural Motion of Quintessence is to go in a circle, which explains the motion of the extra-lunar planets and stars without requiring the introduction of a force.
Now, a force is defined as anything that changes a body’s motion away from its natural state. This presents puzzles. Consider an archer shooting an arrow into the air. The arrow is composed primarily of Earth, so its natural motion would be to fall straight to the ground after leaving the bow. But it doesn’t. Why not? There must be a force preventing it from falling. It was proposed that a force was impressed upon the arrow by the string of the bow which pushes the arrow along. This force gradually leaks away, so the arrow follows an arced path and eventually comes to rest on the ground.
But then along came Galileo, who I have mentioned before in discussing his experiments with inclined planes. Quite amazingly, he came to believe that the natural motion of all bodies, regardless of composition, was to proceed in a straight line at a constant rate forever. “Amazingly”, because his observations were confined to small balls rolling down inclined planes in a limited area, and he never saw anything go in a straight line forever. Even the planets go in circles. So, this was pure conjecture. Newton picked up on this, and it became his First Law of Motion. “A body at rest remains at rest unless acted on by an outside force, and an object in motion remains in motion in a straight line at a constant speed unless acted on by an outside force.” Let’s go back to the archer.
Now we have a different puzzle. If the natural motion of the arrow would be to fly straight at a constant speed forever, leaving the Earth, and going out into space, we have to explain why it doesn’t, that is, why it slows and falls to Earth. So, we need to posit a force to explain its deviation from uniform straight-line motion. The slowing is caused by the resistance of the air, and, for Newton, the falling is caused by, of course, gravity. Gravitation became one of the fundamental forces in nature.
But we’re not done, for in 1916, Einstein published his theory of gravity, which again redefines Natural Motion. Remember in an earlier column I discussed non-Euclidean geometries. These had been developed by mathematicians in the 18th and 19th centuries and introduced the notion of a “geodesic”, which is the straightest line possible in a particular geometry. For example, the geodesics on the surface of a sphere, such as the Earth, are the great circles, going around the Earth like the lines of longitude. The shortest distance between two points on the Earth’s surface is along a great circle, which is why a plane flying from Los Angeles to London goes over the North Pole, and not over New York.
According to Einstein’s theory, the natural motion of an object is along a geodesic of the local four dimensional space-time geometry, which is determined by the presence of mass-energy. The Sun, for example, warps the space-time geometry around it so that geodesic motion is no longer along a straight line. Back to the archer. Now the arrow is in what is called “inertial motion”, following a geodesic, i.e., moving naturally, and so no force is needed to explain its behavior. Einstein is said to have “geometrized away gravitation”. For Einstein, gravity, as a force acting on objects causing them to fall, is a fictitious force. On the other hand, mass-energy does cause the local geometry to distort and geodesics to become non-straight. But as far as a massive object exerting a gravitational force on some object, causing it to fall, that is no longer the correct way to describe the situation.
So we went from Aristotle’s teleological explanations (objects want to go home), to Newton’s (a force drags things down) to Einstein’s (it’s all about geometry), and only Newton’s requires the existence of an external force. What I find most interesting is that the definition of “natural motion” is key to postulating the existence of a force.
Steve Humphrey has a Ph.D. in the history and philosophy of science, with a specialty in the philosophy of physics.
Questions? Comments? Suggestions? Email him at Steve@thevoicelouisville.com