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Section 1: Introduction

The underlying theory of the physical world has two fundamental components: Matter and its interactions. We examined the nature of matter in the previous unit. Now we turn to interactions, or the forces between particles. Just as the forms of matter we encounter on a daily basis can be broken down into their constituent fundamental particles, the forces we experience can be broken down on a microscopic level. We know of four fundamental forces: electromagnetism, gravity, the strong nuclear force, and the weak force.

Electromagnetism causes almost every physical phenomenon we encounter in our everyday life: light, sound, the existence of solid objects, fire, chemistry, all biological phenomena, and color, to name a few. Gravity is, of course, responsible for the attraction of all things on the Earth toward its center, as well as tides—due to the pull of the Moon and the Sun on the oceans—the motions within the solar system, and even the formation of large structures in the universe, such as galaxies. The strong force takes part in all nuclear phenomena, such as fission and fusion, the latter of which occurs at the core of our Sun and all other stars. Finally, the weak force is involved in radioactivity, causing unstable atomic nuclei to decay. The latter two operate only at microscopic distances, while the former two clearly have significant effects on macroscopic scales.

This chart shows the known fundamental particles—those of matter and those of force.

Figure 1: This chart shows the known fundamental particles—those of matter and those of force.

Source: © Wikimedia Commons, Creative Commons Attribution ShareAlike 3.0, Author: Headbomb, 21 January 2009. More info

The primary goal of physics is to write down theories—sets of rules cast into mathematical equations—that describe and predict the properties of the physical world. The eye is always toward simplicity and unification—simple rules that predict the phenomena we experience (e.g., all objects fall to the Earth with the same acceleration), and unifying principles which describe vastly different phenomena (e.g., the force that keeps objects on Earth is the same as the force that predicts the motion of planets in the solar system). The search is for the "Laws of Nature." Often, the approach is to look at the smallest constituents, because that is where the action of the laws is the simplest. We have already seen that the fundamental particles of the Standard Model naturally fall into a periodic table-like order. We now need a microscopic theory of forces to describe how these particles interact and come together to form larger chunks of matter such as protons, atoms, grains of sand, stars, and galaxies.

In this unit, we will discover a number of the astounding unifying principles of particle physics: First, that forces themselves can be described as particles, too—force particles exchanged between matter particles. Then, that particles are not fundamental at all, which is why they can disappear and reappear at particle colliders. Next, that subatomic physics is best described by a new mathematical framework called quantum field theory (QFT), where the distinction between particle and force is no longer clear. And finally, that all four fundamental forces seem to operate under the same basic rules, suggesting a deeper unifying principle of all forces of Nature.

Many forms of force

How do we define a force? And what is special about the fundamental forces? We can start to answer those questions by observing the many kinds of forces at work in daily life—gravity, friction, "normal forces" that appear when a surface presses against another surface, and pressure from a gas, the wind, or the tension in a taut rope. While we normally label and describe these forces differently, many of them are a result of the same forces between atoms, just manifesting in different ways.

An example of conservative (right) and non-conservative (left) forces.

Figure 2: An example of conservative (right) and non-conservative (left) forces.

Source: © Left: Jon Ovington, Creative Commons Attribution-ShareAlike 2.0 Generic License. Right: Benjamin Crowell,, Creative Commons Attribution-ShareAlike 3.0 License. More info

At the macroscopic level, physicists sometimes place forces in one of two categories: conservative forces that exchange potential and kinetic energy, such as a sled sliding down a snowy hill; and non-conservative forces that transform kinetic energy into heat or some other dissipative type of energy. The former is characterized by its reversibility, and the latter by its irreversibility: It is no problem to push the sled back up the snowy hill, but putting heat back into a toaster won't generate an electric current.

But what is force? Better yet, what is the most useful description of a force between two objects? It depends significantly on the size and relative velocity of the two objects. If the objects are at rest or moving much more slowly than the speed of light with respect to each other, we have a perfectly fine description of a static force. For example, the force between the Earth and Sun is given to a very good approximation by Newton's law of universal gravitation, which only depends on their masses and the distance between them. In fact, the formulation of forces by Isaac Newton in the 17th century best describes macroscopic static forces. However, Newton did not characterize the rules of other kinds of forces beyond gravity. In addition, the situation gets more complicated when fundamental particles moving very fast interact with one another.

Forces at the microscopic level

At short distances, forces can often be described as individual particles interacting with one another. These interactions can be characterized by the exchange of energy (and momentum). For example, when a car skids to a stop, the molecules in the tires are crashing into molecules that make up the surface of the road, causing them to vibrate more on the tire (i.e., heat up the tire) or to be ripped from their bonds with the tire (i.e., create skid marks).

A microscopic view of friction.

Figure 3: A microscopic view of friction.

Source: © David Kaplan. More info

When particles interact, they conserve energy and momentum, meaning the total energy and momentum of a set of particles before the interaction occurs is the same as the total energy and momentum afterward. At the particle level, a conservative interaction would be one where two particles come together, interact, and then fly apart after exchanging some amount of energy. After a non-conservative interaction, some of the energy would be carried off by radiation. The radiation, as we shall see, can also be described as particles (such as photons and particles of light).

When conserving energy, however, one must take into account Einstein's relativity—especially if the speeds of the particles are approaching the speed of light. For a particle in the vacuum, one can characterize just two types of energy: The energy of motion and the energy of mass. The latter, summarized in the famous equation E=mc2, suggests that mass itself is a form of energy. However, Einstein's full equation is more complicated. In particular, it involves an object's momentum, which depends on the object's mass and its velocity. This applies to macroscopic objects as well as those at the ultra-small scale. For example, chemical and nuclear energy is energy stored in the mass difference between molecules or nuclei before and after a reaction. When you switch on a flashlight, for example, it loses its mass to the energy of the photons leaving it—and actually becomes lighter! math icon See the math

When describing interactions between fundamental particles at very high energies, it is helpful to use an approximation called the relativistic limit, in which we ignore the mass of the particles. In this situation, the momentum energy is much larger than the mass energy, and the objects are moving at nearly the speed of light. These conditions occur in particle accelerators. But they also existed soon after the Big Bang when the universe was at very high temperatures and the particles that made up the universe had large momenta. As we will explain later in this unit, we expect new fundamental forces of nature to reveal themselves in this regime. So, as in Unit 1, we will focus on high-energy physics as a way to probe the underlying theory of force.


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