The Four Fundamental Forces

Spec mapping: OCR H556 Module 6.4 — The four fundamental forces and conservation laws. Strong (mediated by gluons; binds quarks into hadrons and nucleons into nuclei; range $\sim 10^{-15}$ m); Electromagnetic (mediated by photons; acts on all charged particles; infinite range); Weak (mediated by $W^\pm$ and $Z^0$ bosons; responsible for beta decay and quark-flavour change; range $\sim 10^{-18}$ m); Gravitational (mediated by the hypothetical graviton; acts on all mass-energy; infinite range; not part of the Standard Model). Conservation of energy, momentum, charge, baryon number and lepton number in all interactions; strangeness conserved by strong and EM but not by weak. Refer to the official OCR H556 specification document for exact wording.

By the time the twentieth century was well underway, physicists had realised that the huge diversity of forces encountered in everyday life — friction, tension, drag, the push of a spring, the pull of gravity, the shocks of chemical reactions, the binding of a nucleus — could all be reduced to just four fundamental forces: the gravitational, electromagnetic, strong nuclear and weak nuclear interactions. Every observed physical process is mediated by one (or a combination) of these four. The Standard Model of particle physics accounts for three of them (all except gravity), and describes them in a unified framework in which every force is mediated by the exchange of a characteristic "gauge boson".

This lesson surveys the four fundamental forces, their relative strengths, their ranges, and which particles they act on. It also gathers together the conservation laws that govern every particle interaction — rules you have already seen individually in earlier lessons, but which deserve their own summary treatment. It covers the closing parts of Module 6.4 of the OCR A-Level Physics A specification (H556).

The Four Fundamental Forces

Gravitational

Gravity is the force between masses. You are familiar with its effects from GCSE onwards: falling apples, planetary orbits, the bending of light by the Sun. It is described classically by Newton's law of universal gravitation (F = GMm/r^2) and more completely by Einstein's general theory of relativity (1915).

Key features:

Acts on everything with mass or energy. No known particle is unaffected by gravity.
Infinite range (F \propto 1/r^2, never reaches zero).
Always attractive. Unlike the electromagnetic force, there is no "negative mass" to produce repulsion.
Extraordinarily weak. About 10^{-36} times the strength of the electromagnetic force between two protons.
Carrier: the graviton (hypothetical — never observed). The quantum theory of gravity is not yet part of the Standard Model.

Because gravity is so weak, it is utterly negligible at the scale of individual particles. Two protons in a nucleus attract each other gravitationally with a force so small that it is swamped by the other three forces by many orders of magnitude. Gravity dominates at astronomical scales only because masses at that scale are enormous and because (unlike electric charges) there is no cancellation.

Electromagnetic

Electromagnetism is the force between electric charges, unified with magnetism by Maxwell in the 1860s and described quantum-mechanically by quantum electrodynamics (QED) — the most precisely tested theory in all of science.

Key features:

Acts on charged particles (quarks, charged leptons, W bosons). Uncharged particles like neutrinos and photons are unaffected.
Infinite range (F \propto 1/r^2).
Both attractive and repulsive (like charges repel, unlike attract).
Strong at atomic and molecular scales. The stability of atoms, the structure of molecules, the rigidity of solids, and the entirety of chemistry are all electromagnetic.
Carrier: the photon (γ), massless and chargeless.

Because charges come in opposite signs that cancel out at macroscopic scales (matter is almost exactly electrically neutral), electromagnetism does not dominate bulk behaviour the way gravity does. But at the atomic scale, where individual charges cannot be shielded, it is the principal architect of the material world.

Strong Nuclear Force

The strong nuclear force — sometimes just "the strong force" — is the interaction that holds quarks together inside hadrons, and that glues nucleons into nuclei. It was postulated in the 1930s to explain why nuclei do not fly apart despite the electrostatic repulsion between protons, and its modern description (quantum chromodynamics, QCD) dates from the 1970s.

Key features:

Acts only on quarks (and gluons). Leptons are immune. When the strong force acts between nucleons, it is a residual effect of the more fundamental colour interaction between their constituent quarks.
Extremely short range (\sim 10^{-15} m, i.e. about the size of a nucleon). Beyond a few femtometres, it switches off sharply.
Strongest of the four forces. About 100 times stronger than electromagnetism at distances of order 1 fm.
Always attractive between colour-charged particles (at the interaction range).
Carrier: 8 massless gluons (g).

The short range is why the strong force does not extend beyond the nucleus: once you get more than a few fm away, its influence vanishes. This is why atoms can exist at all — outside the nucleus, the strong force plays no role, leaving electromagnetism in charge.

The residual strong force between nucleons is the nuclear force you met in Lesson 4. The original Yukawa theory (1935) described it as a pion exchange between nucleons; the modern QCD picture sees pion exchange as just one of many ways that the underlying quark-gluon interaction "leaks" out of individual nucleons. Either way, the range and strength are consistent with what we measure.

Weak Nuclear Force

The weak nuclear force is responsible for radioactive beta decay and related processes, including neutrino interactions and the decay of heavier quarks and leptons into lighter ones. It is the only force capable of changing the flavour of a quark (e.g. d \to u in beta-minus decay).

Key features:

Acts on all fermions — quarks, leptons and their neutrinos.
Short range (\sim 10^{-18} m, even shorter than the strong force). The range reflects the mass of the force carriers.
Weak in the sense that interaction probabilities are low. A neutrino can pass through the whole Earth without interacting. But per interaction, the coupling is not as small as gravity.
Carriers: W⁺, W⁻ and Z bosons — all massive (M_W \approx 80 GeV/c², M_Z \approx 91 GeV/c²).

The weak force is the only one that can change a quark from one flavour to another, or a lepton from one flavour to another. Without it, beta decay, muon decay, and neutrino interactions would all be impossible. Stars, pulsars and supernovae are all partly powered by weak processes; in particular, the proton-proton chain in the Sun involves weak interactions that turn protons into neutrons.

The weak and electromagnetic forces are unified at high energies into a single electroweak force (Glashow, Weinberg and Salam, Nobel 1979). They appear separate at low energies because the W and Z are heavy while the photon is massless.

Comparison Table

Force	Relative strength	Range	Acts on	Carrier(s)
Strong nuclear	`1`	`\sim 10^{-15}` m	quarks, hadrons	gluons
Electromagnetic	`10^{-2}`	infinite	charged particles	photon (`γ`)
Weak nuclear	`10^{-6}`	`\sim 10^{-18}` m	all fermions	`W^\pm`, `Z^0`
Gravitational	`10^{-38}`	infinite	everything with mass	graviton (?)

Note how the "strengths" span 38 orders of magnitude. Relative strengths depend on the distance scale and the process in question; this table gives rough values at nuclear distances.

Conservation Laws in Particle Interactions

Every interaction and decay obeys a set of strict conservation laws. In an OCR exam you will be asked to check candidate reactions against these laws to see if they are allowed.

Always Conserved (in every interaction)

Energy (including rest energy).
Linear momentum.
Angular momentum (including spin).
Electric charge.
Baryon number (B): protons and neutrons have B = 1; antibaryons have B = -1; mesons and leptons have B = 0.
Lepton number (L): electrons and neutrinos have L = +1; their antiparticles have L = -1; quarks and hadrons have L = 0.

These six are absolute conservation laws. They hold for every force: strong, electromagnetic and weak.

Conserved in Strong and EM, Not in Weak

Flavour (including strangeness, charm, bottomness). Strong and EM interactions preserve the number of each type of quark; weak interactions can change one quark flavour into another.

For A-Level purposes, strangeness is the example OCR will focus on. Strangeness is conserved in strong and electromagnetic interactions but can change by 0 or \pm 1 in weak interactions. This is why strange-containing particles (such as the \Lambda, \Sigma, kaons) are produced in pairs via the strong interaction but decay slowly via the weak interaction: the decay changes a strange quark into a lighter quark and so takes \sim 10^{-10} s, much longer than strong decays (\sim 10^{-23} s).

Worked Example 1: Is this reaction allowed?

Check whether the reaction p + p \to p + n + \pi^+ is allowed.

Solution.

Charge: (+1) + (+1) = (+1) + (0) + (+1) = +2 ✓
Baryon number: 1 + 1 = 1 + 1 + 0 = 2 ✓
Lepton number: 0 + 0 = 0 + 0 + 0 ✓

All checks pass. (Energy and momentum also need to be conserved, which requires the initial protons to have enough kinetic energy to produce the pion rest mass of 140 MeV/c².) The reaction is allowed and is in fact observed in proton-proton collisions above threshold.

Worked Example 2: Is this reaction allowed?

Check whether the decay n \to p + e^- (without an antineutrino) is allowed.

Solution.

Charge: 0 = (+1) + (-1) ✓
Baryon number: 1 = 1 + 0 ✓
Lepton number: 0 \ne (0) + (+1) = +1 ✗

Lepton number is not conserved — so the decay is forbidden. This is why the antineutrino must appear in beta-minus decay: to carry away one unit of negative lepton number. The correct decay is n \to p + e^- + \bar\nu_e.

Worked Example 3: Classifying an interaction by force

A \Lambda^0 baryon decays via \Lambda^0 \to p + \pi^- with a lifetime of about 2.6 \times 10^{-10} s. By which force does this decay proceed?

Solution. The lifetime is characteristic of the weak interaction (10^{-10} to 10^{-8} s). Strong decays are much faster (10^{-23} s), electromagnetic decays intermediate (10^{-16} s). Moreover, the initial state contains one strange quark (\Lambda^0 = uds) and the final state contains none (p = uud, \pi^- = \bar{u}d), so strangeness changes by 1. Only the weak interaction can change quark flavour. Hence the decay is weak.

Exchange of Bosons: Feynman Diagrams

Every force in the Standard Model is understood as an exchange of virtual gauge bosons between the interacting particles. The simplest example is electromagnetic scattering of two electrons, in which one electron emits a photon which is absorbed by the other:

flowchart LR
    e1["e⁻"]
    e2["e⁻"]
    e1f["e⁻ (final)"]
    e2f["e⁻ (final)"]
    g["γ (virtual)"]
    e1 --> g
    e2 --> g
    g --> e1f
    g --> e2f

In beta-minus decay, the relevant exchange is a W^- boson:

d → u + W⁻   (at one vertex)
W⁻ → e⁻ + ν̄_e   (at the other vertex)

The W is virtual: it exists for only about 10^{-25} s before decaying, borrowing its mass-energy briefly via the Heisenberg uncertainty principle. Its short-lived existence is what gives the weak force its ultra-short range.

Feynman diagrams are not part of the OCR specification in detail, but you should be aware of the general picture: forces are exchange of bosons, and the mass of the boson determines the range of the force.

Why Matter Is Stable

The conservation laws have a profound implication for the stability of matter. Because baryon number is conserved, the lightest baryon (the proton) has nothing to decay into — any decay would produce particles with baryon number 0, violating conservation. Hence the proton is stable, as observed (lifetime > 10^{34} years).

Similarly, the lightest charged lepton (the electron) has nothing lighter to decay into — it cannot become a neutrino because that would violate charge conservation. Hence the electron is stable.

The stability of ordinary matter thus rests on two conservation laws: baryon number (protecting the proton) and charge conservation (protecting the electron). Remove either of these and the universe we know would collapse in a burst of radiation.

Synoptic Links

Standard Model and quark/lepton content (last three lessons): This lesson supplies the force half of the Standard Model to complement the matter half built up over the preceding lessons. Each gauge boson identified in the Standard Model chart corresponds to one of the three non-gravitational forces surveyed here. The conservation laws checked in beta decay, annihilation and pair production all derive from gauge symmetries of these forces.
Beta decay (Module 6.4 — earlier): The weak interaction's signature process — $d \to u + e^- + \bar{\nu}_e$ via a virtual $W^-$ boson — is the canonical example of a quark-flavour change. Without the weak force, beta decay would not exist; the existence of long-lived radionuclides (and thus radioactive dating, nuclear medicine, and the Sun's proton-proton fusion chain) depends on it.
Newton's law of gravitation (Module 5.4): Gravity at the macroscopic scale is governed by Newton's $F = GMm/r^2$ (or by general relativity at high mass densities). At the particle scale gravity is utterly negligible — about $10^{-36}$ times weaker than electromagnetism between two protons — but it is included here as the fourth fundamental force for completeness.
Capacitors and electric fields (Module 5.2): The electromagnetic force, which dominates at atomic and molecular scales, is the same force that drives charging and discharging of capacitors, electron motion in conductors, and the photoelectric effect. The gauge-boson picture in this lesson reframes the EM force as photon exchange — the same photon you met as a quantum of light.
Mass-energy equivalence and nuclear binding (Module 6.4 — earlier): The nuclear "strong force" you met in the binding-energy lesson is the residual effect of the underlying QCD interaction between quarks. The deeper picture — gluons binding quarks, then the residual leakage binding nucleons — is sketched in this lesson.

Specimen question modelled on the OCR H556 paper format

Question (10 marks): Particle physicists classify all known fundamental interactions into four forces: gravitational, electromagnetic, strong nuclear and weak nuclear.

(a) Complete the following comparison table by naming the gauge boson(s) that mediate each force and stating the approximate range of each force (use "infinite" where appropriate). [4]

Force	Gauge boson(s)	Range
Strong
Electromagnetic
Weak
Gravitational

(b) State, with reasoning, whether each of the following reactions is allowed or forbidden by the conservation laws. For each forbidden reaction, name the law (or laws) it violates.

The Four Fundamental Forces

The Four Fundamental Forces