# Fundamental Forces

The known fundamental forces of nature are:
The electromagnetic force
The strong nuclear force
The weak nuclear force
The force of gravity

See the main pages on Gravity and General Relativity for more information on the force of gravity.

## The Electromagnetic Force

As the name suggests, the electromagnetic force is responsible for electrical and magnetic interactions, which occur between charged particles – for example, the proton, which is considered by convention to have a positive charge of +1, and the electron, which has an opposite negative charge of -1.

A charged particle is considered to generate an electrical field that fills the space surrounding it. This field exerts a force on other electrically charged particles in its vicinity.

Through this force, particles of negative charge will attract particles with a positive charge towards themselves and repel other negatively charged particles. Whereas positively charged particles will repel other positively charged particles and attract those with a negative charge. This is why electrons, with their negative charge, orbit the positively charged nuclei of atoms, which are made up of protons.

The strength of this force between particles depends on how much positive or negative charge the particles possess as well as the distance between them.

For example, a particle such as a helium nucleus contains two protons, and therefore has a charge of +2, meaning it will attract an electron with twice as much force (at a given distance) as a hydrogen nucleus, which only contains one proton and therefore has a charge of +1. The strength of this force weakens in relation to the square of the distance between the particles as it spreads out though space.

Electrically neutral particles, such as the neutron, which are also present within the nuclei of atoms, do not have an electrical charge.

Balanced combinations of negative and positive charges will also be electrically neutral, for example an atom (that is not ionised) will have the same number of electrons surrounding it as there are protons in its nucleus. The electrical charges of these electrons and protons exactly cancel each other out so that the atom will be electrically neutral overall and not give off an electrical field.

Magnetism is considered to be a different manifestations of the same phenomenon as electricity, since a moving electrically charged particle will generate a magnetic field that can deflect a magnet.

This is why electrical and magnetic forces are considered to be the result of just one type of fundamental force, known as the electromagnetic force. The quantum theory of how electromagnetic fields interact is known as quantum electrodynamics.

The magnetic field of a magnetised piece of iron is actually generated by the movement of electrons spinning as they orbit their atomic nuclei. Each atom therefore generates a tiny magnetic field. In non-magnetic materials the electrons spin in random directions and their magnetic fields cancel each other out. However, in a magnetised piece of iron, the spin of the electrons can be aligned meaning that their magnetic fields combine to give the piece of iron an overall magnetic field.

Magnets are said to have north and south poles, in analogy to the north and south magnetic poles of the Earth, to which a magnetic compass needle is attracted. Like electrical charges, opposite poles are attracted to each other, while the same poles repel each other.

Light is a form of electromagnetic radiation, which is a result of the electromagnetic force. In classical mechanics, light can be considered to be a combination of an electric field and a magnetic field oscillating alongside each other such that they self perpetuate without the loss of energy as they travel through space. In quantum mechanics, light can be considered to be made up of many individual particles known as photons. However, through the concept of wave-particle duality, individual photons can also be thought of as ‘wavepackets’ of energy that behave more like particles or more like waves depending on the circumstances. (See Quantum Mechanics)

## The Strong Nuclear Force

The strong nuclear force is responsible for binding together quarks inside of protons and neutrons, as well as other more exotic particles that are also composed of quarks.

Each proton is made up of three quarks – two up quarks, with an electrical charge of +2/3, and a down quark, with an electrical charge of -1/3. This gives the proton its overall electrical charge of +1.

Each neutron is also made up of three quarks – two down quarks, and an up quark. This gives the neutron its overall electrical charge of 0.

Such combinations of charged quarks wouldn’t form stable particles on their own, since like charges repel each other. However, the quarks also possess a property known as colour, or colour charge, due to the strong nuclear force.

This doesn’t mean that the quarks have a colour in the traditional sense. The term is simply an analogy to the three primary colours of light. The ‘colour’ of a quark corresponds instead to a quantum property it possesses that can take one of six value, designated by the names red, green and blue, as well as anti-red, anti-green and anti-blue.

Quarks can only combine with each other if their colours combine to produce ‘white’ overall, following the analogy of the way red, green and blue lights combines to produce white light.

For a particle made up of three quarks, this means that its quarks must be either red, green and blue, or anti-red, anti-green and anti-blue.

Three-quark particles are known as baryons. The proton and neutron are both baryons, although there are many other types that combine other varieties, or flavours, of quark (i.e strange charm, true and beauty quarks – see Particle Physics)

Quarks of a particular colour can also combine in pairs with a quark of the corresponding anti-colour. These two-quark particles are known as mesons. For example, the π+ meson is composed of an up quark and an anti-down quark, which can have any of the colour combinations red / anti-red, blue / anti-blue or green / anti-green.

Baryons and mesons are collectively known as hadrons, although more exotic varieties of hadron can also exist, such a pentaquarks. These are combination of three quarks, with the colours red, green, blue and two antiquarks, for example with colours red and anti-red.

The strong nuclear force mediates the attraction between the different coloured quarks. However, unlike the electromagnetic force, the force of this attraction remains constant if you were to somehow try to pull the quarks apart from each other.

Eventually, if you were to keep pulling, you would find that the energy you are putting in to separate the quarks spontaneous creates new quarks that combine to create independent hadrons. For example, if you tried to separate the blue quark from a proton, you would end up forming a new blue / anti-blue quark pair, leaving you with both a proton and a meson.

Because of this property of the strong nuclear force, it is believed that it would be impossible to observe a unbound quark on its own. This principle is known as colour confinement.

The quantum theory of how particles interact via the strong nuclear force is known as quantum chromodynamics.

The strong nuclear force is also responsible for binding together the protons and neutrons in the nuclei of atoms. This is because the field of the nuclear force extends out beyond the edges of these particles, attracting them together.

If it were not for this effect, the repulsive electromagnetic force between protons would not allow them to combine to form atomic nuclei.

Note, however, that although the strong nuclear force is powerful enough to overcome the electromagnetic repulsion between protons when holding atomic nuclei together, it can only act over very short range, within the nucleus of an atom. Whereas, the electromagnetic force is effectively unlimited in range even though it is weaker that the strong nuclear force over short distances. This is why it is very difficult to overcome the repulsive force between positively charged atomic nuclei in the process of nuclear fusion.

The high binding energies of atomic nuclei, that makes the potential for energy production from nuclear power so attractive, are testement to the strength of the strong nuclear force. As, indeed, is the existence of atomic weapons, and of course the stars themselves, whose energy derives from nuclear fusion reactions due to the strong nuclear force.

## The Weak Nuclear Force

The weak nuclear force is another fundamental force that acts between subatomic particles.

Like the strong nuclear force, it is also involved in nuclear fusion and fission reactions, playing a role in initiating the fusion reactions that power stars like the Sun.

The weak nuclear force is also responsible for the radiative beta decay of atoms as well as the decay of muons into electrons and neutrinos. This is because the weak interaction can change the flavour of quarks and leptons. For example, in electron-emission beta decay the weak force changes a down quark in a neutron into an up quark, converting the neutron into a proton.

The weak force acts over an even shorter range that the strong nuclear force, less than the diameter of a proton. And, as the name suggests, it is much weaker than the strong nuclear force when comparing how frequently its interactions between particles occur, i.e. it’s coupling constant.

The coupling constant of the weak force is between 10−7 and 10-6, compared to the strong interaction’s coupling constant of 1. (For reference, the coupling constant of the electromagnetic force is about 10-2. Note this is 43 orders of magnitude greater than the coupling constant for gravity, when defined using the gravitational force between two electrons).

The weak nuclear force is unique in that it is the only interaction that can violate parity symmetry. As an example of what this means, consider the case of radioactive beta decay.

One of the two forms of beta decay occurs when a down quark in a neutron spontaneous becomes a up quark in the nucleus of an atom – a process driven by the weak nuclear force. This converts the neutron into a proton, by emitting both an antineutrino and an electron (also known as a beta particle in this case).

It was shown experimentally in 1957 that more electrons will be emitted in a particular direction relative to quantum spin of the atomic nucleus. This was a surprising result since it suggests that the weak nuclear force does not have the same symmetry as the other fundamental forces and instead has a preferred chirality.

This means that the mirror image of a process such as beta decay cannot be rotated in any way such that it will appear exactly the same as the original, much like a left-handed glove cannot be simply rotated in any way to covert it into a right-handed glove.

Like a glove, a particle can be chiral, i.e. it can be defined as left or right handed depending on the direction it is moving relative to the direction of its spin. It seems that the weak nuclear force only acts on particles if they are left-handed particles and only acts on antiparticles is they are right-handed, although it is not understood why this should be the case.

The weak nuclear force is also the only interaction that can violates charge congugation–parity symmetry. This was discovered in 1964 using an experiment with neutral kaons – a type of meson. This means that if you take a mirror image of the process and then also swap the particles involved with their antiparticles, the result will still not be equivalent to the original in terms of chirality.

This asymmetry in the weak nuclear force might lead to an explanation for why our universe is dominated by normal matter instead of containing an equivalent amount of antimatter.

## Gauge Field Theory

In quantum gauge field theory, a gauge field corresponding to each of the fundamental forces is considered to exist at every point in space, throughout the Universe, even in the absence of light or a charged particle.

Electromagnetic radiation, for example, is described as a ripple of energy travelling through the electromagnetic gauge field. A two-dimensional analogy would be the surface of a pond, where energy can be introduced by throwing in a pebble, causing a ripple to spread across the surface.

Note, however, that this does not make a gauge field equivalent to the 19th century concept of the aether – a material substance that was proposed to permeate all of space – as an aether would be at rest in only one inertial reference frame (see Relativity Theory).

It might be that a field is locally created by the presence of particles rather than existing across all space in the absence of matter; however, the concepts are mathematically equivalent, and we currently have no way to distinguish between the two possibilities.

A gauge boson is a quantum of energy that can be considered to be a ripple in a gauge field. Through the concept of wave-particle duality, the gauge bosons can also be identified with the fundamental spin 1 particles from the standard model of particle physics.

Each of the fundamental forces (with the possible exception of gravity) can be considered to be mediated by exchanges of virtual gauge bosons between particles.

A virtual gauge boson is a particle that spontaneously emerges from its quantum field (with its equivalent antiparticle if it has one) by effectively borrowing energy from empty space. This is allowed within quantum mechanics, as long as the virtual particles disappear again within the limits of the energy-time uncertainty principle.

Different gauge bosons mediate the different fundamental forces as follows:

• Photons – carrying the electromagnetic interaction
• W and Z bosons – carrying the weak interaction
• Gluons – carrying the strong interaction

It has also been proposed that gauge field theory might be extended to include the graviton – a hypothetical particle that mediates the force of gravity. However the theories of general relativity and quantum mechanics have yet to be successfully combined to form a workable theory of quantum gravitation.

## Quantum Electrodynamics

Quantum Electrodynamics (QED) is the theory describing the electromagnetic interaction through the disturbances in the electromagnetic gauge field.

This theory proposes that a charged particle induces a swarm of virtual photons around itself that can allow it to exchange energy with another charged particle. This is known as vacuum polarisation.

This exchange of energy, via virtual photons, leads to a change in momentum for the two particles, which can be equivalent either to an attractive force if the particles have opposite charges or a repulsive force if they have like charges.

As the virtual photons have zero rest mass, the energy-time uncertainty principle effectively gives them an unlimited time to travel between the two charged particles in order to exchange energy, meaning that that there is no theoretical limit to the distance over which the electromagnetic force can act. However, because the virtual photons spread out in three-dimensional space in accordance with an inverse square law, this means that the force between particles also reduces accordingly with distance.

## Quantum Chromodynamics

Quantum Chromodynamics (QCD) describes the strong nuclear force between quarks and gluons, using the concept of colour charge.

Virtual gluons are massless exchange particles that mediate the strong nuclear force between quarks.

Because gluons also posses the quantum property of colour charge they also interact via the strong nuclear force with each other.

This leads to the property of the strong nuclear force whereby it remains constant in strength as two quarks as separated, eventually leading to the creation of a quark-antiquark pair. This is because the virtual gluons attract each other to form a narrow string, or flux tube, between the quarks.

This is in contrast with the virtual photons in quantum electrodynamics, which are electrically neutral and consequently do not act in this way when mediating the electromagnetic force.

Gluons can also bind together without quarks to form a particle known as a glueball. However, like a quark, an individual gluon cannot be isolated without it leading to the production of new gluons or quarks.

## Electroweak interaction

The Electroweak interaction is a unification of the electromagnetism and weak nuclear interactions.

## The Higgs Field and the Higgs Boson

The foundations of gauge theory suggests that all gauge bosons should have zero rest mass. However, the W and Z bosons, that mediate the weak nuclear interaction, all possess relatively large rest masses of around 80 GeV/c2.

In 1964, three different papers were published suggesting a solution to this problem, using related but slightly different approaches. They proposed the existence of a field that has a non-zero constant value throughout the whole of space, and that the W and Z particles could gain mass by interacting with this field. This became known as the Higgs field, after the author of one of the three papers, Peter Higgs.

Higgs also proposed in his 1964 paper that a quantum excitation of this field should be detectable as a scalar boson (scalar meaning that the particle would have a spin of 0), which later became known as the Higgs boson.

In 2012, the Large Hadron Collider discovered a new particle with all the properties predicted for the Higgs boson. This discovery is now considered to be experimental confirmation of Higgs’ theory. However, it should be noted that the Higgs particle is not directly responsible for the Higgs mechanism that couples particles to the Higgs field, although it’s discovery is important because it provides evidence for the field’s existence.

In addition to providing an explanation for the masses of the W and Z bosons, Steven Weinberg in 1967 showed that interaction with the Higgs field, through a mechanism known as Yukawa coupling, could also provide an explanation for the masses of the fundamental fermions – the quarks and charged leptons of the standard model of particle physics.

However, not all mass is derived via the Higgs mechanism. Einstein’s theory of relativity shows that all energy possesses mass through the relation E = mc2 (or more fully E2 = p2c2 + m2c4 including a term for an object’s momentum p). The Higgs mass from the three quarks that make up a proton, for example, contribute only around 1 per cent of the proton’s rest mass. The remainder is due to the quantum chromodynamic binding energy, which includes the kinetic energy (from momentum) of the quarks as well as the energy of the gluons that bind the quarks together.

Popular explanations of how the Higgs mechanism imparts mass to particles often invoke analogies such as a pearl moving through syrup or a celebrity trying to make their way through a crowd of fans. However, the Higgs mechanism also endows fundamental particles with gravitational mass, rather than just the inertial mass that these analogies suggest.

If this were not the case, then the principle of equivalence, which states that inertial mass and gravitational mass are identical would not apply to mass generated via the Higgs mechanism. However, the principle of equivalence has been tested to a high degree of accuracy, and any difference in the gravitation and inertial mass of the quarks and charged leptons would already have become evident.

This suggests that even the mass derived from the Higgs mechanism ultimately has the same origin in Einstein’s mass energy relationship. The energy derived from coupling with the Higgs field is essentially what gives the Z and W bosons as well the fundamental fermions their masses, similarly to the how the chromodynamic binding energy accounts for the majority of the proton’s mass.