 College Physics for AP® Courses

# 33.2The Four Basic Forces

College Physics for AP® Courses33.2 The Four Basic Forces

### Learning Objectives

By the end of this section, you will be able to:

• State the four basic forces.
• Explain the Feynman diagram for the exchange of a virtual photon between two positive charges.
• Define QED.
• Describe the Feynman diagram for the exchange of a photon between a proton and a neutron.

The information presented in this section supports the following AP® learning objectives and science practices:

• 3.G.1.1 The student is able to articulate situations when the gravitational force is the dominant force and when the electromagnetic, weak, and strong forces can be ignored. (S.P. 7.1)
• 3.G.1.2 The student is able to connect the strength of the gravitational force between two objects to the spatial scale of the situation and the masses of the objects involved and compare that strength to other types of forces. (S.P. 7.1)
• 3.G.2.1 The student is able to connect the strength of electromagnetic forces with the spatial scale of the situation, the magnitude of the electric charges, and the motion of the electrically charged objects involved. (S.P. 7.1)
• 3.G.3.1 The student is able to identify the strong force as the force responsible for holding the nucleus together. (S.P. 7.2)

As first discussed in Problem-Solving Strategies and mentioned at various points in the text since then, there are only four distinct basic forces in all of nature. This is a remarkably small number considering the myriad phenomena they explain. Particle physics is intimately tied to these four forces. Certain fundamental particles, called carrier particles, carry these forces, and all particles can be classified according to which of the four forces they feel. The table given below summarizes important characteristics of the four basic forces.

Force Approximate relative strength Range +/−1 Carrier particle
Gravity $10 − 38 10 − 38 size 12{"10" rSup { size 8{ - "38"} } } {}$ $∞ ∞ size 12{ infinity } {}$ + only Graviton (conjectured)
Electromagnetic $10 − 2 10 − 2 size 12{"10" rSup { size 8{ - 2} } } {}$ $∞ ∞ size 12{ infinity } {}$ $+ / − + / − size 12{+/ - {}} {}$ Photon (observed)
Weak force $10 − 13 10 − 13 size 12{"10" rSup { size 8{ - "13"} } } {}$ $+ / − + / − size 12{+/ - {}} {}$ $W+,W−,Z0W+,W−,Z0 size 12{W rSup { size 8{+{}} } ,W rSup { size 8{ - {}} } ,Z rSup { size 8{0} } } {}$ (observed2)
Strong force $11$ $+ / − + / − size 12{+/ - {}} {}$ Gluons (conjectured3)
Table 33.1 Properties of the Four Basic Forces
Figure 33.4 The first image shows the exchange of a virtual photon transmitting the electromagnetic force between charges, just as virtual pion exchange carries the strong nuclear force between nucleons. The second image shows that the photon cannot be directly observed in its passage, because this would disrupt it and alter the force. In this case it does not get to the other charge.
Figure 33.5 The Feynman diagram for the exchange of a virtual photon between two positive charges illustrates how the electromagnetic force is transmitted on a quantum mechanical scale. Time is graphed vertically while the distance is graphed horizontally. The two positive charges are seen to be repelled by the photon exchange.

Although these four forces are distinct and differ greatly from one another under all but the most extreme circumstances, we can see similarities among them. (In GUTs: the Unification of Forces, we will discuss how the four forces may be different manifestations of a single unified force.) Perhaps the most important characteristic among the forces is that they are all transmitted by the exchange of a carrier particle, exactly like what Yukawa had in mind for the strong nuclear force. Each carrier particle is a virtual particle—it cannot be directly observed while transmitting the force. Figure 33.4 shows the exchange of a virtual photon between two positive charges. The photon cannot be directly observed in its passage, because this would disrupt it and alter the force.

Figure 33.5 shows a way of graphing the exchange of a virtual photon between two positive charges. This graph of time versus position is called a Feynman diagram, after the brilliant American physicist Richard Feynman (1918–1988) who developed it.

Figure 33.6 is a Feynman diagram for the exchange of a virtual pion between a proton and a neutron representing the same interaction as in Figure 33.3. Feynman diagrams are not only a useful tool for visualizing interactions at the quantum mechanical level, they are also used to calculate details of interactions, such as their strengths and probability of occurring. Feynman was one of the theorists who developed the field of quantum electrodynamics (QED), which is the quantum mechanics of electromagnetism. QED has been spectacularly successful in describing electromagnetic interactions on the submicroscopic scale. Feynman was an inspiring teacher, had a colorful personality, and made a profound impact on generations of physicists. He shared the 1965 Nobel Prize with Julian Schwinger and S. I. Tomonaga for work in QED with its deep implications for particle physics.

Why is it that particles called gluons are listed as the carrier particles for the strong nuclear force when, in The Yukawa Particle and the Heisenberg Uncertainty Principle Revisited, we saw that pions apparently carry that force? The answer is that pions are exchanged but they have a substructure and, as we explore it, we find that the strong force is actually related to the indirectly observed but more fundamental gluons. In fact, all the carrier particles are thought to be fundamental in the sense that they have no substructure. Another similarity among carrier particles is that they are all bosons (first mentioned in Patterns in Spectra Reveal More Quantization), having integral intrinsic spins.

There is a relationship between the mass of the carrier particle and the range of the force. The photon is massless and has energy. So, the existence of (virtual) photons is possible only by virtue of the Heisenberg uncertainty principle and can travel an unlimited distance. Thus, the range of the electromagnetic force is infinite. This is also true for gravity. It is infinite in range because its carrier particle, the graviton, has zero rest mass. (Gravity is the most difficult of the four forces to understand on a quantum scale because it affects the space and time in which the others act. But gravity is so weak that its effects are extremely difficult to observe quantum mechanically. We shall explore it further in General Relativity and Quantum Gravity). The $W+,W−W+,W− size 12{W rSup { size 8{+{}} } ,`W rSup { size 8{ - {}} } } {}$, and $Z0Z0 size 12{Z rSup { size 8{0} } } {}$ particles that carry the weak nuclear force have mass, accounting for the very short range of this force. In fact, the $W+,W−W+,W−$, and $Z0Z0 size 12{Z rSup { size 8{0} } } {}$ are about 1000 times more massive than pions, consistent with the fact that the range of the weak nuclear force is about 1/1000 that of the strong nuclear force. Gluons are actually massless, but since they act inside massive carrier particles like pions, the strong nuclear force is also short ranged.

Figure 33.6 The image shows a Feynman diagram for the exchange of a $π+π+ size 12{π rSup { size 8{+{}} } } {}$ between a proton and a neutron, carrying the strong nuclear force between them. This diagram represents the situation shown more pictorially in Figure 33.4.

The relative strengths of the forces given in the Table 33.1 are those for the most common situations. When particles are brought very close together, the relative strengths change, and they may become identical at extremely close range. As we shall see in GUTs: the Unification of Forces, carrier particles may be altered by the energy required to bring particles very close together—in such a manner that they become identical.

### Making Connections: Why You Stay on the Earth, but Do Not Fall Through

You are familiar with gravity pulling you towards the Earth. It's why when you jump, you come back down. In this action, and at distances and speeds that we experience in our everyday lives, gravity is the only one of the four fundamental forces that has such an obvious effect on us.

Electromagnetism is vital for our society to run, but due to your body having the same (or very nearly the same) number of positive and negative charges, it doesn't usually have as much of an effect on us. Except for one very important feature: the electrons in the bottom of your feet experience a mutually repulsive force with the electrons in the material you stand on. This is what keeps us from falling into the planet, and also allows us to push on other objects and generally interact with them.

These electromagnetic forces are dominant in the electron shells of an atom, and also the interaction of the electrons with the nucleus. However, within the nucleus, the electrostatic repulsion of the protons would break the nucleus apart if it were not for the strong force, which holds the nucleus together. At even smaller scales, within nucleons such as protons and neutrons, the weak force is responsible for nuclear decays.

The relative strengths of the forces given in the Table 33.1 are those for the most common situations. When particles are brought very close together, the relative strengths change, and they may become identical at extremely close range. As we shall see in GUTs: the Unification of Forces, carrier particles may be altered by the energy required to bring particles very close together—in such a manner that they become identical.

### Footnotes

• 1 + attractive; ‑ repulsive; $+/−+/− size 12{+/ - {}} {}$ both.
• 2Predicted by theory and first observed in 1983.
• 3Eight proposed—indirect evidence of existence. Underlie meson exchange.
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