The weakest, and yet the most pervasive, of the four basic forces is gravity. It acts on all forms of mass and energy and thus acts on all subatomic particles, including the gauge bosons that carry the forces. The 17th-century English scientist Isaac Newton was the first to develop a quantitative description of the force of gravity. He argued that the force that binds the Moon in orbit around Earth is the same force that makes apples and other objects fall to the ground, and he proposed a universal law of gravitation.

According to Newton’s law, all bodies are attracted to each other by a force that depends directly on the mass of each body and inversely on the square of the distance between them. For a pair of masses, m₁ and m₂, a distance r apart, the strength of the force F is given by F = Gm₁m₂/r². G is called the constant of gravitation and is equal to 6.67 × 10⁻¹¹ newton-metre²-kilogram⁻².

The constant G gives a measure of the strength of the gravitational force, and its smallness indicates that gravity is weak. Indeed, on the scale of atoms the effects of gravity are negligible compared with the other forces at work. Although the gravitational force is weak, its effects can be extremely long-ranging. Newton’s law shows that at some distance the gravitational force between two bodies becomes negligible but that this distance depends on the masses involved. Thus, the gravitational effects of large, massive objects can be considerable, even at distances far outside the range of the other forces. The gravitational force of Earth, for example, keeps the Moon in orbit some 384,400 km (238,900 miles) distant.

Newton’s theory of gravity proves adequate for many applications. In 1915, however, the German-born physicist Albert Einstein developed the theory of general relativity, which incorporates the concept of gauge symmetry and yields subtle corrections to Newtonian gravity. Despite its importance, Einstein’s general relativity remains a classical theory in the sense that it does not incorporate the ideas of quantum mechanics. In a quantum theory of gravity, the gravitational force must be carried by a suitable messenger particle, or gauge boson. No workable quantum theory of gravity has yet been developed, but general relativity determines some of the properties of the hypothesized “force” particle of gravity, the so-called graviton. In particular, the graviton must have a spin quantum number of 2 and no mass, only energy.

Electromagnetism

The first proper understanding of the electromagnetic force dates to the 18th century, when a French physicist, Charles Coulomb, showed that the electrostatic force between electrically charged objects follows a law similar to Newton’s law of gravitation. According to Coulomb’s law, the force F between one charge, q₁, and a second charge, q₂, is proportional to the product of the charges divided by the square of the distance r between them, or F = kq₁q₂/r². Here k is the proportionality constant, equal to 1/4πε₀ (ε₀ being the permittivity of free space). An electrostatic force can be either attractive or repulsive, because the source of the force, electric charge, exists in opposite forms: positive and negative. The force between opposite charges is attractive, whereas bodies with the same kind of charge experience a repulsive force. Coulomb also showed that the force between magnetized bodies varies inversely as the square of the distance between them. Again, the force can be attractive (opposite poles) or repulsive (like poles).

Magnetism and electricity are not separate phenomena; they are the related manifestations of an underlying electromagnetic force. Experiments in the early 19th century by, among others, Hans Ørsted (in Denmark), André-Marie Ampère (in France), and Michael Faraday (in England) revealed the intimate connection between electricity and magnetism and the way the one can give rise to the other. The results of these experiments were synthesized in the 1850s by the Scottish physicist James Clerk Maxwell in his electromagnetic theory. Maxwell’s theory predicted the existence of electromagnetic waves—undulations in intertwined electric and magnetic fields, traveling with the velocity of light.

Max Planck’s work in Germany at the turn of the 20th century, in which he explained the spectrum of radiation from a perfect emitter (blackbody radiation), led to the concept of quantization and photons. In the quantum picture, electromagnetic radiation has a dual nature, existing both as Maxwell’s waves and as streams of particles called photons. The quantum nature of electromagnetic radiation is encapsulated in quantum electrodynamics, the quantum field theory of the electromagnetic force. Both Maxwell’s classical theory and the quantized version contain gauge symmetry, which now appears to be a basic feature of the fundamental forces.

The electromagnetic force is intrinsically much stronger than the gravitational force. If the relative strength of the electromagnetic force between two protons separated by the distance within the nucleus was set equal to one, the strength of the gravitational force would be only 10⁻³⁶. At an atomic level the electromagnetic force is almost completely in control; gravity dominates on a large scale only because matter as a whole is electrically neutral.

The gauge boson of electromagnetism is the photon, which has zero mass and a spin quantum number of 1. Photons are exchanged whenever electrically charged subatomic particles interact. The photon has no electric charge, so it does not experience the electromagnetic force itself; in other words, photons cannot interact directly with one another. Photons do carry energy and momentum, however, and, in transmitting these properties between particles, they produce the effects known as electromagnetism.

In these processes energy and momentum are conserved overall (that is, the totals remain the same, in accordance with the basic laws of physics), but, at the instant one particle emits a photon and another particle absorbs it, energy is not conserved. Quantum mechanics allows this imbalance, provided that the photon fulfills the conditions of Heisenberg’s uncertainty principle. This rule, described in 1927 by the German scientist Werner Heisenberg, states that it is impossible, even in principle, to know all the details about a particular quantum system. For example, if the exact position of an electron is identified, it is impossible to be certain of the electron’s momentum. This fundamental uncertainty allows a discrepancy in energy, ΔE, to exist for a time, Δt, provided that the product of ΔE and Δt is very small—equal to the value of Planck’s constant divided by 2π, or 1.05 × 10⁻³⁴ joule seconds. The energy of the exchanged photon can thus be thought of as “borrowed,” within the limits of the uncertainty principle (i.e., the more energy borrowed, the shorter the time of the loan). Such borrowed photons are called “virtual” photons to distinguish them from real photons, which constitute electromagnetic radiation and can, in principle, exist forever. This concept of virtual particles in processes that fulfill the conditions of the uncertainty principle applies to the exchange of other gauge bosons as well.