The Four Fundamental Forces and Gauge Bosons
There are four fundamental interactions: the strong interaction (binds quarks into hadrons and nucleons into nuclei; carried by gluons), the electromagnetic interaction (acts between charged particles; carried by the photon), the weak interaction (causes beta decay and neutrino interactions; carried by the W+, W− and Z0 bosons) and gravity (acts between all masses; the carrier, the graviton, is hypothetical). In brief: in quantum field theory, forces arise from the exchange of virtual gauge bosons between particles. The range of a force is related to the mass of the exchanged particle: R ≈ ħc ÷ mc2. Massless carriers (photon, gluon, graviton) give infinite range (but the strong force is confined to about 1 fm), while the heavy W and Z give a range of about 10−18 m. The relative strengths for two protons just touching are approximately: strong 1, electromagnetic 10−2, weak 10−6, gravity 10−38.
All the phenomena of the universe, from the structure of atoms to the motion of galaxies, are governed by four basic interactions. This guide describes each of them and its carrier particle, explains the exchange picture and Feynman diagrams, the electroweak unification and the Higgs mechanism, compares the forces in a table, works through numerical examples and corrects common mistakes.
What are the fundamental interactions?
All other forces, such as friction, tension, contact forces and chemical bonds, are manifestations of the four fundamental ones, mainly electromagnetism. Gravity governs the large-scale structure of the universe (planets, stars, galaxies) because it is always attractive and cumulative. The electromagnetic force governs atoms, molecules, chemistry and most of everyday life. The strong force binds quarks inside nucleons and nucleons inside nuclei, and the weak force is responsible for radioactive beta decay, the fusion reactions of the Sun, and the interactions of neutrinos.
How do exchange particles work?
In quantum field theory, interacting particles exchange gauge bosons, force carriers. Two electrons repel each other by exchanging virtual photons: each photon carries momentum from one electron to the other. The picture is drawn with Feynman diagrams, in which lines represent particles and vertices the interactions (for example, an electron emitting a photon). The exchanged particle is “virtual”: it may violate energy conservation for a short time Δt ≈ ħ ÷ ΔE (the uncertainty principle), so a boson of mass m can exist for about ħ ÷ mc2, and travel at most a distance R ≈ cΔt = ħc ÷ mc2, the range of the force. Using ħc = 197.3 MeV·fm: for pions (139.6 MeV), the range is 1.4 fm (Yukawa’s argument, 1935, for the nuclear force); for W (80.4 GeV), 2.5 × 10−3 fm = 2.5 × 10−18 m. Massless carriers give an infinite range. The potential of the electromagnetic and gravitational forces varies as 1/r.
What does each force do?
- Strong interaction: acts on quarks (and gluons) through color charge. The fundamental carrier is the gluon (8 types, massless, and carrying color charge itself, so gluons interact with each other). The force between quarks does not decrease with distance, but stays roughly constant at about 1 GeV/fm (about 160,000 N, the weight of 16 tonnes), so the energy needed to separate quarks keeps growing, which results in confinement. The force between nucleons (the residual strong force) is the short-range force that binds nuclei, with a range of about 1 to 3 fm.
- Electromagnetic interaction: acts on particles with electric charge. The carrier is the photon (massless, spin 1, neutral). The strength is measured by the fine-structure constant α = e2 ÷ (4πε0ħc) ≈ 1/137. The theory is quantum electrodynamics (QED), the most precisely tested theory in physics (the magnetic moment of the electron is predicted to better than 1 part in 1012).
- Weak interaction: acts on all quarks and leptons (including neutrinos). The carriers are the charged W+ and W− and the neutral Z0. It changes the flavor of quarks and leptons (a down quark into an up quark in beta decay: d → u + W−, W− → e− + ν̄e). It violates parity (Wu’s experiment, 1956). It is weak at low energies because the carriers are heavy; at energies of about 100 GeV, it is as strong as the electromagnetic force, and the two merge into the electroweak interaction.
- Gravity: acts on all mass-energy. It is by far the weakest force: the gravitational attraction between two protons is about 10−36 times the electric repulsion. It is described by general relativity (curved spacetime); no quantum theory of gravity has yet been verified.
What is the role of the Higgs boson?
In the electroweak theory (Glashow, Salam and Weinberg), the W, Z and photon would all be massless if the symmetry were exact. The Higgs mechanism (1964) breaks the symmetry: a field that fills all space, with a nonzero value everywhere, interacts with the W and Z, giving them mass, while leaving the photon massless. The Higgs boson is the excitation of this field. Its discovery at the LHC in 2012 (mass about 125 GeV/c2) completed the Standard Model. Fermions also get their masses through their coupling to the Higgs field. The Higgs boson is not a force carrier, and the Higgs mechanism does not explain the origin of gravity or most of the mass of ordinary matter, which comes from the strong interaction.
The four forces compared
| Interaction | Acts on | Carrier | Relative strength | Range |
|---|---|---|---|---|
| Strong | Quarks, gluons | Gluons (8) | 1 | About 1 fm (confined) |
| Electromagnetic | Charged particles | Photon | About 10−2 | Infinite |
| Weak | Quarks and leptons | W+, W−, Z0 | About 10−6 | About 10−18 m |
| Gravity | All mass-energy | Graviton (hypothetical) | About 10−38 | Infinite |
Worked example: ranges and strengths
- Range of the nuclear force. Pion exchange: R = ħc ÷ mc2 = 197.3 MeV·fm ÷ 139.6 MeV = 1.41 fm.
- Range of the weak force. W boson: R = 197.3 MeV·fm ÷ 80,379 MeV = 2.45 × 10−3 fm = 2.5 × 10−18 m. Z boson (91.19 GeV): 2.16 × 10−18 m.
- Electric to gravitational force between two protons: Fe ÷ Fg = ke2 ÷ (Gmp2) = (8.99 × 109 × (1.602 × 10−19)2) ÷ (6.674 × 10−11 × (1.673 × 10−27)2) = 2.31 × 10−28 ÷ 1.87 × 10−64 = 1.2 × 1036, independent of the separation (both vary as 1/r2).
- Fine-structure constant: α = 1 ÷ 137.04 = 0.0073. The ratio of the strengths of the strong to the electromagnetic force at the scale of nucleons is of the order of 100 (the strong coupling αs ≈ 1 at 1 GeV, falling to about 0.12 at 91 GeV: asymptotic freedom).
- Beta decay as a weak interaction: n → p + e− + ν̄e (quark level: d → u + e− + ν̄e through a virtual W−). The decay is slow (neutron lifetime 880 s) compared with strong or electromagnetic processes (10−23 s and 10−16 s), because of the heavy W.
- Virtual photon exchange. Two electrons 1.0 nm apart repel with a force F = 8.99 × 109 × (1.602 × 10−19)2 ÷ (10−9)2 = 2.3 × 10−10 N, described in QED by the exchange of virtual photons.
How were the forces unified?
Newton unified terrestrial and celestial gravity (1687), and Maxwell unified electricity, magnetism and light (1865). Enrico Fermi gave a theory of the weak interaction in 1934; Yukawa proposed the meson exchange for the nuclear force in 1935. Quantum electrodynamics was developed by Feynman, Schwinger and Tomonaga in the 1940s (Nobel Prize 1965). Glashow, Salam and Weinberg unified the electromagnetic and weak forces in 1967 to 1968; the neutral currents were found in 1973, and the W and Z at CERN in 1983 (Nobel Prize to Rubbia and van der Meer, 1984). Quantum chromodynamics (QCD) for the strong force was developed in the 1970s (Gross, Politzer and Wilczek, Nobel Prize 2004). Grand unified theories and string theory are attempts to include the strong force and gravity, with no experimental confirmation so far.
Which mistakes are common?
Mistake 1: Thinking that gravity is a strong force because it holds planets and stars
It is the weakest force. It dominates on large scales because there are no negative masses to cancel it, and electric charges are almost neutral overall.
Mistake 2: Confusing the strong force between quarks with that between nucleons
The nuclear force between protons and neutrons is a residual effect of the color force between quarks, like the weak van der Waals forces between neutral molecules.
Mistake 3: Believing that the exchanged particles are real objects
Virtual particles are a way of describing the interactions in quantum field theory. They do not satisfy the usual energy-momentum relation, and are not directly observed.
Mistake 4: Saying that the weak force is weak because it is short-ranged only
The apparent weakness at low energy comes from the large mass of the W and Z. At high energy, the weak and electromagnetic interactions are comparable in strength.