Basic Concepts: Force

This is the first post I’m doing for the “Basic Concepts” series. When I asked for suggestions, I got a good long list of stuff, and it’s hard to know quite where to start. I’m going to start with “Force,” because physics as we know it more or less started with Isaac Newton, and Newton is best known for his work on forces. In fact, as-you-know-Bob, the SI unit of force is the “Newton,” in ol’ Isaac’s honor.

(I should note that this particular discussion is adapted from a lecture that I give in the introductory mechanics class, so there’s also a “path of least resistance” argument for starting with “Force.”)

“Force” is one of those words that gets used both in everyday speech and in physics, but in this case, the technical meaning isn’t all that far removed from the everyday meaning. When you think of forces in an everyday sense, you think of things that you do to try to change the behavior of objects (or people)– pushing them, pulling them, hitting them, threatening to hit them, etc. The basic idea carries over– forces are things that change the motion of objects.

To put it a little more formally, and give the broadest possible definition (I’ll get more specific below):

Force is the quantification of an interaction between two objects.

If you have two objects that interact with one another in some way, you describe the size and effect of that interaction in terms of a force. Force, in turn, is related to the motion of the object via Newton’s Laws of Motion, of which there are three, because three is the magic number:

1. An object at rest tends to remain at rest, and an object in motion tends to remain in motion in a straight line at constant speed, unless acted on by a force.
2. The net force on an object is equal to the time rate of change of the momentum, or Fnet = dp/dt (which is equal to mass times acceleration for reasonable-size objects at speeds much lower than the speed of light).
3. If one object exerts a force on a second object, the second object exerts a force on the first that is equal in magnitude to the first force, and in the opposite direction.

These can be summarized as “1) Inertia, 2) F = ma, 3) Action-Reaction,” and anybody who has ever taken physics has seen them. They can be understood a little better by thinking in terms of force as the quantification of interaction. The first law is just the codification of common sense: objects don’t change their motion unless some interaction causes them to do so. If you see a change in the motion of some object, you can deduce that there must’ve been an interaction to cause that change, and indeed that’s how we detected all the forces we know (about which more later).

The second law is just the quantification of the first law: it tells you how big a force you need to get a given change in motion. The units of force are defined in terms of the second law: a one-newton force is the result of an interaction that causes a one-kilogram object to accelerate at one meter per second.

The third law tells you that interactions always go both ways. If particle A interacts with particle B, particle A is also affected by that interaction. This is why I specify that force is the interaction between two objects– there may be more than two objects in a system (nine eight planets orbiting the Sun, say), but in terms of forces, you think about them two at a time. The interaction between the Earth and the Sun produces a force on the Earth and a force on the Sun. The interaction between the Earth and Jupiter produces a force on Jupiter, and a second force on the Earth, and so on. You determine the motion by adding up the forces due to all possible pairs, and then applying the second law.

So, if forces are interactions, what sort of interactions are allowed? Modern physics says that there are only four types of interactions possible between fundamental particles (though there’s a sort of cottage industry in looking for a fifth). Every particle interaction you see is due to one of these four fundamental forces: gravity, electromagnetism, the strong nuclear force, and the weak nuclear force.

The most obvious and inescapable of the forces we see in daily life is gravity. The graviational interaction says that all objects with mass experience a force that pulls them toward every other object with mass. The gravitational force in incredibly weak, on the scale of fundamental forces, but is really obvious in everyday life because the mass of the Earth is gigantic. Every person reading this is being pulled toward the center of the Earth with a force that is rather substantial– 9.8 newtons per kilogram of your mass (assuming you’re near the surface of the Earth, anyway– if you’re reading this from orbit, the force will be somewhat smaller). You’re also attracted to the monitor of your computer, with a force that’s smaller by something like ten orders of magnitude, by virtue of the fact that both you and it are objects with mass. This force is totally insignificant compared to the other forces you experience, but it’s there all the same.

The next most obvious force is electromagnetism, which involves forces between charged particles. When your clothes stick to you on a dry winter day, that’s electromagnetism. Odds are, it’s also holding something to your refrigerator right now. But more than that, electromagnetism is resposible for your ability to operate a computer– the atoms making up your body are held together by electromagnetic forces, as are the atoms making up the computer itself. Pretty much any everyday force you can think of (other than gravity) is ultimately due to electromagnetic forces between the component atoms of the interacting objects.

The other two are less obvious, but no less important. The strong nuclear force binds quarks together into protons and neutrons, and hold protons and neutrons together in the nuclei of atoms. It is, as the name implies, an extremely strong force– 137-ish times stronger than electromagnetism, and better than 30 orders of magnitude stronger than gravity. It’s also an extremely short-range force– protons and neutrons separated by more than 10-15 m (the radius of the nucleus of an atom, more or less) don’t feel the strong force at all. So it’s not something that you’re likely to experience directly any time soon.

The final fundamental force is the weak nuclear force, which is somewhere between gravity and electromagnetism in strength. It’s even less obvious than the strong nuclear force, and really only turns up indirectly through certain types of radioactive decay. Which is not to say that it’s not important– the weak force plays a crucial role in determining the abundances of heavy elements (basically anything other than hydrogen), and since you’re mostly made of heavy elements, that’s pretty darn important, whether you realize it or not.

How are these interactions transmitted from one particle to another? All of these forces act between particles that are separated by some distance of empty space. So, how is that possible?

In the classical picture, this is just one of those things. Physicists generally speak of these forces in terms of “fields” which fill all of space, which is pretty much just a way of saying “the interaction extends through empty space, don’t ask me why.” You can deal with most everyday phenomena involving gravity and electromagnetism by working with continuous fields, and not really worrying about the mechanism by which the forces are transmitted from one particle to another. I may try to talk more about “fields” in a later Basic Concepts post.

When you start to think about forces between particles at the level where quantum mechanics becomes important, a couple of weird things happen, which cause this “field” business to break down. In order to make an accurate description of the interaction between quantum particles, it’s necessary to think in more detail about how the forces are transmitted, and the concept of “exchange bosons” or “force carriers” has to be introduced. In this picture, any interaction between fundamental particles– two electrons repelling each other, for example– has to be mediated by the exchange of a particle. At the most fundamental level, we understand the repulsion between two electrons as being due to the exchange of a photon: One electron emits a photon, the other absorbs it, and the recoil due to the emission and absorption is responsible for pushing the two apart.

All of the fundamental forces are, in principle, understood in these terms, and each force has its own exchange bosons. Particles interact through the electromagnetic force by exchaging photons, which are basically little bundles of light. The weak force operates through the emission and absorption of three different particles, the W+, W, and Z– which one is passed between the particles depends on the charge of the particles involved. It may seem extravagent to have three different exchange bosons for the weak force, but that’s nothing compared to the strong force: the strong force operates by the exchange of “gluons,” which come in eight varieties.

Photons, W, and Z particles have all been directly detected (photons in experiments with lasers and atoms, the W and Z bosons in accelerator experiments). Gluons can’t really be seen by themselves, but their existence is strongly implied by a variety of accelerator experiments.

In the exchange picture, gravity would be carried by a particle called a “graviton.” Nobody has yet constructed a successful theory of “quantum gravity” yet, though. That is, nobody has a theory that matches up with reality and describes the gravitational interaction between particles in terms of the exchange of gravitons, let alone detected a graviton (there’s some question about whether it’s even possible to detect a single graviton). Our current working theory of gravity– Einstein’s General Theory of Relativity– describes the force in geometric terms, as resulting from the curvature of space and time, which are continuous. This doesn’t really play nice with the other theories, and that situation makes lots of people unhappy. It’s generally believed that there ought to be a quantum theory of gravity that works like the quantum theory of the other forces, but writing one down turns out to be ridiculously difficult, and attempts to do so have required all sorts of bizarre contortions.

And that’s pretty much everything I can think of to say about the concept of “Force” as it occurs in physics. Any questions?