An introduction to electromagnetism

Vivid stained glass windows with colourful light effects in a historic church or cathedral setting.

Electromagnetism essentially describes the force between electrically charged particles conveyed by electromagnetic fields.

 

Initial thoughts

In everyday experience, interactions between objects are often straightforward to visualise. We forcefully push open a jammed door or hammer a nail into wood. A strong gale can topple a tree, while a gentle summer breeze merely causes leaves to flutter. These interactions feel intuitive because we understand what it means when one thing pushes, pulls, or resists another. However, at an atomic level, most of these mechanical forces are produced by electromagnetic force. The interactions between atoms and molecules within objects are governed by electromagnetism, and this underlying reality explains many of the mechanical forces that shape the world around us.

Electromagnetism also plays a key role in other everyday actions, such as perceiving the world around us, turning on a light at the stitch, cooking with a microwave or induction hob, or changing channels using a TV remote.

  • Simply looking around at the world involves light waves, a feature of electromagnetism, entering our eyes and triggering chemical reactions that produce signals transmitted to our brains.
  • Switching on a light allows an electric current—another phenomenon governed by electromagnetism—to pass through a circuit containing an incandescent filament, a fluorescent gas, or an LED, each of which produces artificial light.
  • Microwaves and induction hobs both rely on electromagnetic waves. Microwaves use specific frequencies of electromagnetic radiation to heat food, while induction hobs use rapidly changing magnetic fields to induce currents in cookware, generating heat.
  • Most modern TV remotes send signals to a TV using infrared light, which is part of the electromagnetic spectrum.
Aim of the article

This article explores the intricate world of electromagnetism, laying the groundwork for understanding how we perceive colour and interpret the world around us. These themes resonate throughout the resources available on lightcolourvision.org.

To appreciate the role of electromagnetism in visual perception, it is essential to examine its dual role: shaping the macro-scale visible world we interact with and the micro-scale interactions of electrically charged particles. These two realms are distinct yet interconnected:

Understanding these different scales begins with recognising the connections between them. Charged particles, and the systems they form, generate electromagnetic forces and fields. The positive and negative charges of particles govern their interactions, forming the basis of electromagnetism. Without charged particles, electromagnetic phenomena could not exist.

Classical electromagnetism describes charged particles as generating electric and magnetic fields that exert forces on other charges. This framework explains macroscopic phenomena, such as the behaviour of objects that attract or repel one another, and the propagation of electromagnetic waves, including visible light. A key feature of this perspective is the representation of electromagnetism as continuous lines of force seamlessly extending through space and time, linking particles, fields, and forces while treating them as distinct entities.

Quantum Electrodynamics (QED), on the other hand, extends our understanding by introducing a quantised view of electromagnetic fields. It depicts these fields as comprising discrete energy units called photons. In QED, interactions between charged particles occur through photon exchange, with each photon carrying a specific amount of energy and momentum determined by its frequency. This granular perspective redefines fundamental physical properties such as energy, charge, and angular momentum, offering a microscopic view of electromagnetic interactions.

While classical and quantum frameworks both recognise charged particles as the sources of electromagnetic forces and fields, they differ in representation. Classical physics envisions smooth, continuous fields, whereas QED reveals a dynamic interplay of discrete photon exchanges. Together, these perspectives allow us to bridge the macroscopic and microscopic worlds, providing a comprehensive understanding of electromagnetism and its evolution as a scientific concept.

 

View diagrams that map out the relationship between core concepts.

A classical perspective on electromagnetism

Classical electromagnetism

Classical electromagnetism is a foundational part of classical field theory, which describes how physical fields, such as electric and magnetic fields, interact with matter and propagate through space and time. Classical field theory encompasses a broad range of phenomena, including electromagnetism, gravitation – explained by Newton’s law of universal gravitation and refined by Einstein’s General Relativity—and fluid dynamics, where fields describe properties like velocity and pressure.

A central focus of classical electromagnetism is the relationship between matter and energy. Charged objects generate electric and magnetic fields, which influence the motion and configuration of other charged objects, shaping the behaviour of matter.

In classical electromagnetism:

  • Electric fields store energy associated with the arrangement of charged particles and exert forces that cause attraction or repulsion between charges. These forces follow Coulomb’s law and decrease in strength with distance.
  • Magnetic fields are generated by moving charges and currents, transferring energy and interacting with other magnetic materials or moving charges.
  • Electromagnetic waves, such as light, consist of oscillating electric and magnetic fields that carry energy through space and interact with matter via processes like absorption and reflection, transferring energy in the process.

This classical view presents energy as continuously distributed and transferred through fields, shaping the behaviour of matter. However, energy itself is not a physical substance but a property of systems that can be transferred or converted from one form to another. The interplay between matter and energy is evident across all scales, from the microscopic interactions of atoms to the vast structures of the universe.

While the classical perspective treats matter and energy as distinct entities, Einstein’s equation, E=mc^2, reveals their interchangeability under certain conditions, offering a more nuanced understanding of this relationship.

Electromagnetic force

In classical physics, electromagnetic force is evident through electric and magnetic fields, which vary continuously and predictably. The strength of these fields depends on the amount of charge, the distance between charged particles, and the momentum of moving charges. Fields make the force measurable, enabling the calculation of interactions between charges. This understanding underpins a range of phenomena, from light as electromagnetic waves to electric circuits and magnetic interactions.

James Clerk Maxwell (1831–1879) unified the behaviour of electric and magnetic fields through a set of four equations, known as Maxwell’s equations. These equations describe how fields interact with charges, currents, and each other, summarised as:

  • Electric charges produce electric fields.
  • A changing magnetic field induces an electric field.
  • Electric currents and changing electric fields produce magnetic fields.
  • Magnetic field lines form closed loops.
Electric & Magnetic Fields

Electric and magnetic fields are fundamental concepts in classical electromagnetism:

  • The electric field (E) describes the force experienced by a charged particle due to other nearby charges. It is generated by stationary electric charges, which can be positive or negative.
  • The magnetic field (B) represents the influence of moving charged particles, electric currents, and magnetic materials plus the forces they generate.
Classical waves

In the classical view, light is understood as electromagnetic waves propagating through space in a vacuum at the “speed of light”. These waves consist of oscillating electric and magnetic fields, oriented perpendicular (at right angles) to each other and the direction of propagation. This wave-like behaviour explains classical wave phenomena such as reflection, refraction, polarisation, and interference. Classical electromagnetism does not address photons, which are central to the quantum mechanical understanding of light.

Deterministic nature of interactions

In classical electromagnetism, interactions between charged particles and fields are deterministic. This means that Maxwell’s equations allow precise predictions of how electric and magnetic fields behave and the forces they exert.

The term “deterministic” signifies that, given a system’s initial conditions, its future state can be accurately predicted. This implies that events unfold as inevitable consequences of preceding conditions, with no inherent randomness.

Continuous interaction

The electromagnetic force is conceived as a continuous interaction across space and time. Electric and magnetic fields are represented by continuous lines of force, which change smoothly and predictably over distance and time. These lines enable the uninterrupted transmission of electromagnetic effects, such as visible light and radio waves, in contrast to the discrete, step-like changes characteristic of quantized systems.

Visualisations of fields use field lines to depict the direction and strength of the force experienced by a positively charged particle. For electric fields, lines emanate from positive charges and terminate at negative charges, while magnetic field lines form closed loops, circulating from the north to the south pole of a magnet. This is a convention: the direction of an electric field (E) is defined as the direction of the force exerted on a positive test charge, and for magnetic fields, the direction is determined assuming the presence of positive test charges.

Classical laws of physics

The classical laws governing electromagnetic interactions are derived from Maxwell’s equations, which provide a comprehensive mathematical framework:

  • Gauss’s Law for Electricity: Electric charges generate electric fields.
  • Gauss’s Law for Magnetism: There are no isolated magnetic poles; magnetic field lines form closed loops.
  • Faraday’s Law of Induction: A changing magnetic field induces an electric field.
  • Ampère’s Law (with Maxwell’s correction): Oscillating electric fields and electric currents produce magnetic fields.

These equations unify electricity and magnetism and reveal their connection to light by demonstrating that light is an electromagnetic wave. Maxwell’s unification marked a turning point in physics and laid the groundwork for quantum electrodynamics (QED), the modern theory describing electromagnetic interactions at the quantum level.

While Maxwell’s equations focus on the dynamics of fields, additional laws describe specific interactions between charges and fields:

  • Coulomb’s Law: States that the electrostatic force between two charges is directly proportional to their magnitudes and inversely proportional to the square of their distance.
  • Lorentz Force Law: Describes the force on a charged particle moving through electric and magnetic fields, a key principle for understanding devices like motors and particle accelerators.
A quantum perspective on electromagnetism

This section explores electromagnetism through the lens of quantum mechanics, focusing on Quantum Field Theory (QFT) and Quantum Electrodynamics (QED). Taken together, they extend our understanding of how charged particles interact with the electromagnetic field. They provide a framework for describing the exchange of force carriers (photons) between charged particles, explaining phenomena like electromagnetic forces and light emission and absorption in ways surpassing classical electromagnetism.

Quantum mechanics

Quantum mechanics has been pivotal in shaping the 20th century, revolutionising our understanding of nature and driving groundbreaking technological, societal, and economic changes. Its influence has transformed cultural perspectives and helped define modern and post-modern thought. In terms of electromagnetism and light, quantum mechanics provides an entirely new foundation distinct from the classical perspective.

Central to quantum mechanics are wavefunctions, mathematical descriptions of the probable distribution of particles within a system. The wavefunction describes the probability of finding a single particle in a particular state within the system, or the probability distribution of the entire system, encompassing the possible states and interactions of all the particles. A key facet of quantum mechanics states that the act of measurement causes a wavefunction to transition from a superposition of probabilities to a single definite state.  The act of measurement is understood to cause a wave function to ‘collapse’, resulting in a specific outcome and an observed property. Wave functions provide crucial insights into phenomena underlying technologies like lasers, optical fibres and MRI machines, which all rely on a deep understanding of the quantum behaviour of particles and their interactions.
Other key concepts that distinguish quantum mechanics from classical physics in the context of electromagnetism include:

  • Probability distributions: Quantum mechanics predicts the probability of finding a particle in a particular state, rather than providing definite values for properties like position and momentum. This inherent uncertainty is described by Heisenberg’s uncertainty principle.
  • Superposition: A fundamental principle in quantum mechanics, where a quantum system can exist in multiple states simultaneously until measured, at which point it collapses into a single observable state.
  • Quantisation of energy: Energy can only exist in discrete amounts or levels, rather than being continuous, as demonstrated by phenomena like atomic spectra and electron orbitals. Atomic spectra are unique patterns of electromagnetic radiation wavelengths emitted or absorbed by atoms, resulting from the quantised energy levels within them.
  • The dual wave-particle nature of matter and light: Reveals that particles such as electrons and photons can exhibit properties of both waves and particles depending on the experiment, leading to effects like interference and diffraction when behaving as waves, and discrete particle-like interactions in phenomena such as the photoelectric effect.

Building upon these fundamental concepts, Quantum Field Theory (QFT) and Quantum Electrodynamics (QED) offer a more advanced framework for understanding the quantum behaviour of particles and fields. QED, in particular, provides a unified description of the quantum aspects of electromagnetism and has been incredibly successful in accurately predicting the outcomes of a wide range of experiments in atomic and particle physics. Let’s explore these ideas in more detail, one step at a time.

Special relativity

A crucial implication of Special Relativity for electromagnetism is the conceptual unification of electric and magnetic fields into a single entity: the electromagnetic field. This establishes that electricity and magnetism are not fundamentally distinct forces, but rather different manifestations of the same core interaction.

Special Relativity, developed by Albert Einstein, also established that the laws of physics are the same for all observers moving at constant speeds, regardless of how fast they travel. This principle is foundational to both Quantum Field Theory (QFT) and Quantum Electrodynamics (QED), as it ensures that descriptions of electromagnetic interactions, such as those involving photons and electrons, are valid for all observers, no matter their relative motion. Relativity also guarantees consistency between energy, momentum, and the speed of light across different reference frames.

Using a simple example, imagine you’re on a train moving at a constant speed. You drop a ball. To you, it looks like it falls straight down. Special Relativity says that even if someone outside the train is watching, the laws of physics will look the same to them. They might see the ball move sideways because of the train’s motion, but the way it falls will follow the same rules of gravity for both observers.

Quantum fields

At the heart of Quantum Field Theory (QFT) are quantum fields, which are understood to serve as the foundation for all particles. Each type of particle corresponds to a specific field: electrons arise from the electron field, photons from the electromagnetic field, quarks from the quark field, and so on. These fields permeate all of space, and what we perceive as ’empty’ space is the lowest energy state of various quantum fields. When these fields are excited, they manifest as particles (discrete packets of energy with specific properties) or as waves (propagating disturbances in the field).

The previous paragraph implies that in the absence of visible particles, fields like the electromagnetic field persist and can be excited to higher energy levels by interactions with other fields or external energy sources (such as EM radiation, charged particles or thermal energy). These excitations can display particle-like properties, as seen in phenomena such as the photoelectric effect, and wave-like properties, as seen in interference and diffraction patterns. Particles represent localised excitations confined to specific regions of space, while waves represent distributed excitations that spread energy and momentum across broader areas. Analogies, such as comparing particles to localised vibrations of a spring and waves to disturbances travelling along the spring, may help convey these concepts more intuitively.

Quantum Field Theory

Quantum Field Theory (QFT) unites classical field theory, special relativity, and quantum mechanics, providing a unified framework for understanding the fundamental forces of nature. A core feature of QFT is its focus on fields, where particles such as electrons and photons are viewed as excitations of their corresponding quantum fields. QFT provides a consistent description of how these particles interact and how forces are mediated by the exchange of other particles (like photons for the electromagnetic force).

Quantum Electrodynamics (QED)

Quantum Electrodynamics (QED) is the quantum mechanical theory that describes interactions between charged particles. These interactions, such as the repulsion between like charges, the attraction between opposite charges, and the emission and absorption of light by atoms, are central to electromagnetism. Such interactions are not fully explained by classical physics, which fails to account for phenomena like the photoelectric effect and the quantisation of energy. Building upon the concept of quantum fields, QED describes how excitations of the electromagnetic field, namely photons, mediate these interactions between charged particles.

QED elegantly unifies the concepts of charged particles, fields, and forces. It demonstrates that light waves, electromagnetic fields, and photon interactions are different manifestations of the same underlying reality. From a quantum perspective, our observations of the world around us arise from this fundamental interplay. For example, the wave-particle duality of light and the connection between classical electromagnetism and quantum phenomena are comprehensively explained within the framework of QED.
Developed in the mid-20th century by Richard Feynman, Julian Schwinger, and Sin-Itiro Tomonaga, QED employs tools like Feynman diagrams to streamline the calculation of particle interactions. These diagrams depict interactions between particles by representing them as exchanges of virtual and real photons. Virtual photons are temporary carriers of force, mediating interactions between charged particles. Real photons, on the other hand, are observable particles of light. The theory also highlights the probabilistic nature of both virtual and real photon interactions, offering profound insights into the particle dynamics that govern the electromagnetic force.

Electromagnetic field

In Quantum Electrodynamics (QED), the electromagnetic field is the fundamental, unified quantum field that permeates all of spacetime. It is the specific quantum field discussed in the context of QED. This field is the source of all electromagnetic interactions, and excitations within this quantised field give rise to photons – the discrete packets of energy that mediate these interactions. These interactions encompass a wide range of phenomena, including:

  • Forces between charged particles: The attraction between oppositely charged particles (like electrons and protons) and the repulsion between like charges.
  • Propagation of light: The transmission of electromagnetic waves, including visible light, through space.
  • Behaviour of electromagnetic waves: The properties and characteristics of various types of electromagnetic waves, such as radio waves, microwaves, and infrared radiation.

The electromagnetic field underpins the entire framework of electromagnetic theory, providing a unified explanation for the transmission of energy and the exchange of forces between charged particles within the quantum realm.

Duality of matter and energy

In both Quantum Field Theory (QFT) and Quantum Electrodynamics (QED) frameworks, matter and energy are unified as excitations of quantum fields. QFT provides a theoretical framework for understanding the wave-particle duality of both matter and energy. Particles, traditionally understood as the building blocks of matter, are characterised by their mass and the space they occupy. However, particles, like electrons, also exhibit wave-like behaviour, as demonstrated in electron diffraction experiments. This wave-particle duality – the ability of particles to behave both as discrete particles and as waves – reveals the interconnectedness of matter and energy.

QED describes how excitations of the electromagnetic field, namely photons, exhibit both wave-like properties (as seen in the propagation of light) and particle-like properties (as seen in the photoelectric effect). Technologies like fibre optics, where light (exhibiting both wave-like and particle-like properties) is guided through optical fibres, and solar cells, which rely on the photoelectric effect (demonstrating the particle-like nature of light interacting with matter), illustrate this duality in action.

Particles of light

Quantum mechanics also alters our understanding of light. In Quantum Electrodynamics (QED), light is understood to consist of discrete, quantised particles called photons, which are the excitations of the electromagnetic field. Each photon carries a specific amount of energy and momentum. On a macroscopic level, photons interact with the photoreceptor cells in our retina, triggering biochemical responses that allow us to perceive light. In this sense, photons can be thought of as having both a measurable and tangible existence.

Quantum Electrodynamics (QED) also reveals the role of virtual particles at the subatomic scale. In interactions between elementary particles, such as electrons and protons, forces are mediated by “virtual particles.” These particles are not directly observable, but their effects can be observed through their influence on particle interactions. For example, electromagnetic interactions between charged particles are facilitated by “virtual photons.” Similarly, the strong nuclear force, which holds quarks together within protons and neutrons, is mediated by virtual gluons, and the weak nuclear force, responsible for processes like beta decay, is mediated by W and Z bosons.

Virtual particles

Virtual particles act as transient intermediaries in interactions between subatomic particles. They are described by mathematical models in quantum field theory and represent the smallest interactions over extremely short timescales. While virtual particles cannot be directly detected, their effects on stable particles and fields can be inferred and calculated. For example, in electromagnetic interactions, “virtual photons” mediate the exchange of energy and momentum between charged particles, explaining the subtle forces that govern these interactions.

Virtual particles emerge from temporary changes in quantum fields, known as quantum fluctuations. These fluctuations arise due to the Heisenberg uncertainty principle, which allows for brief and invisible violations of energy conservation over extremely short time intervals. This allows for the temporary creation of particles that would otherwise be forbidden by energy conservation laws. Virtual particles mediate forces between particles. For example, the electromagnetic force between two electrons can be understood as the exchange of virtual photons, which mediate their repulsion.

Although virtual particles are not directly observable, they are essential theoretical tools that help to understand how energy and momentum pass between particles on the smallest scales. They play a crucial role in many quantum phenomena, providing insights into the fundamental forces of nature.
This means that:

  • Virtual particles help us understand how forces work: While we can observe the effects of forces (like gravity or electromagnetism), virtual particles help us understand the mechanism behind these forces at the most fundamental level.
  • They explain how particles interact: They explain how particles interact with each other, like how two electrons repel each other.
  • When you see two magnets repelling each other, you know there’s a force at play, but you can’t see what’s actually causing it. Virtual particles are like the invisible “messengers” that carry this force between the magnets, even though you can’t directly observe them at work.
Photons

In 1905, Albert Einstein explained the photoelectric effect in terms of discrete packets of energy. While Einstein’s work was foundational to the development of quantum theory, the term “photon” was coined later in 1926 by Gilbert N. Lewis to describe these quantum units of light. In Quantum Electrodynamics (QED), as discussed earlier, the electromagnetic field is quantised, and photons are its quanta, or individual excitations.

It is crucial to distinguish between two types of photons: real photons and virtual photons. Real photons are observable particles of light, carrying energy and momentum. They can be detected by instruments and interact with matter in various ways, such as in the photoelectric effect. Virtual photons, on the other hand, are temporary carriers of force. They mediate interactions between charged particles, such as the electromagnetic force, but cannot be directly observed. While these are related phenomena within the framework of quantum field theory, they have distinct natures and play different roles in physical processes.

Real photons

Real photons are the observable particles that constitute electromagnetic radiation, including visible light. These massless particles travel at the speed of light in a vacuum and are emitted or absorbed when electrons transition between energy levels within atoms. Their energy, frequency, and wavelength determine the characteristics of electromagnetic radiation, from radio waves to gamma rays. In Quantum Electrodynamics (QED), real photons are the excitations of the electromagnetic field. The energy of a real photon is related to its frequency by the equation E=hf, where E is energy, h is Planck’s constant, and f is frequency. Real photons can be emitted by various sources, such as the sun, lasers, and atomic transitions, and can travel vast distances without losing energy. They can also be reflected off surfaces or absorbed by particles such as electrons. For example, the energy from photons absorbed by electrons in the leaves of plants plays a crucial role in photosynthesis. Real photons exhibit wave-particle duality, behaving both as waves and particles and constitute the entire electromagnetic spectrum.

Virtual photons

In contrast to real photons, virtual photons are not directly observable particles. They are temporary excitations of the electromagnetic field that mediate interactions between charged particles. As discussed earlier, the uncertainty principle allows for brief and invisible fluctuations in energy and momentum, enabling the temporary creation of these virtual particles. They play a crucial role in mediating electromagnetic interactions. For example, virtual photons mediate the exchange of energy and momentum between charged particles, explaining the forces that govern their interactions, such as the repulsion between two electrons. Although they cannot be directly observed, virtual photons are essential for understanding the underlying mechanisms of how electromagnetic forces operate at the quantum level.

Quantized units

Quantum mechanics reveals that at the smallest scales, nature is both quantised and probabilistic. Instead of being continuous, all aspects of electromagnetism are reduced to discrete, probabilistic units or quanta. As discussed earlier, the electromagnetic field is quantised, consisting of discrete packets of energy called photons. This quantisation means that electromagnetic fields do not follow smooth, continuous trajectories but rather exist in discrete units. Each photon carries a specific amount of energy and momentum, which results in precise interactions between charged particles at subatomic scales.

At the atomic level, quantisation also governs the energy levels of electrons orbiting the nucleus. Electrons can only occupy specific, discrete energy levels, dictating their allowed orbital distances from the nucleus. This quantisation of electron energy levels leads to the emission and absorption of photons with specific energies, resulting in the characteristic line spectra of elements.

Other quantised units include:

  • Angular momentum: In quantum mechanics, the angular momentum of electrons in atoms is quantised. This means electrons can only have specific, discrete values of angular momentum.
  • Spin: Electrons (and other particles) possess an intrinsic property called spin, which is also quantised. It can only take on specific values, typically represented as +1/2 or -1/2.
  • Magnetic moment: The magnetic moment of an electron, which is related to its spin, is also quantised.
Probabilistic behaviour

Probabilistic behaviour in quantum mechanics is fundamentally tied to the uncertainty principle, which states that certain properties, such as the position and momentum of subatomic particles, cannot both be precisely known at the same time. This introduces inherent uncertainty to the act of measurement itself.

Heisenberg’s uncertainty principle establishes a fundamental limit to how precisely certain pairs of physical properties, like position and momentum, can be known simultaneously. This reflects a fundamental characteristic of the quantum world rather than a limitation of measurement tools.

Probabilistic behaviour, as governed by the uncertainty principle, highlights the fundamental limits of precision in what were once considered predictable fields of knowledge. While it has important real-world practical applications, such as enabling advancements in quantum computing and atomic clocks,  it predicts the likelihood of different outcomes rather than deterministic certainties.

Wave-Particle Duality

Particles such as electrons and photons exhibit both wave-like and particle-like behaviours, a phenomenon known as wave-particle duality. This duality underlies the probabilistic nature of quantum systems, where exact positions and momenta cannot be simultaneously determined. Instead, particles are described by probability distributions that depend on the type of measurement or experiment conducted. For example, particles can act like waves in an interference experiment or as discrete particles when measured individually.

Superposition Principle

The wave-like behaviour of particles is closely tied to the principle of superposition, which states that a quantum system can exist in multiple states simultaneously until measured. This principle provides a framework for understanding interference patterns, such as those observed in the double-slit experiment, where particles seem to traverse all possible paths before measurement determines their specific outcome.

Entanglement

Entanglement builds on the principles of wave-particle duality and superposition by linking the states of two or more particles. When particles become entangled, the measurement of one particle’s state instantaneously determines the state of the other, regardless of distance. This non-local phenomenon highlights the interconnectedness of quantum systems and challenges classical notions of separability and locality.

(Another article developing on this introduction is in the pipeline.)