Quantum Electrodynamics Explained: QED & Feynman Diagrams

Einstein's equation E=mc² establishes a fundamental correspondence between energy and mass. The c² factor is purely dimensional, meaning mass can be transformed into energy and vice versa. This is remarkable because mass is an ontological property (what makes an electron an electron) while energy is a contingent property (how much energy an object has). The spacetime interval (time squared minus distance squared) generalizes the Pythagorean theorem to spacetime. The key property is that this interval is invariant—it does not depend on which reference frame is used to measure it.

Total energy equals relativistic mass times c squared: E = Mc². This includes rest energy (m₀c²) plus kinetic energy. Energy and mass are interchangeable—when mass disappears in nuclear reactions, it converts directly to energy via ΔE = ΔMc². Because c² is enormous, tiny mass losses release huge energy, explaining nuclear power. More fundamentally, special relativity replaces absolute space and time with unified spacetime. The only invariant quantity is the spacetime interval, behaving like a length. Four-vectors transform under Lorentz transformations identically to 3D vectors rotating in space, implying space and time are truly blended into a single fabric.

Einstein unified space and time into a four-dimensional spacetime. While different observers measure different times and lengths, they all agree on the spacetime interval. The speed of light is invariant for all observers and represents the maximum possible speed. Mass and energy are equivalent: E = mc². The relativistic mass increases with velocity: m = m₀/√(1 - v²/c²). As velocity approaches c, mass approaches infinity, making it impossible to accelerate massive objects to light speed. Only massless particles like photons can travel at c.

Hermann Minkowski proposed that space and time should be treated as a unified four-dimensional structure called spacetime. Just as rotating a 3D object mixes its dimensions, moving through spacetime mixes space and time dimensions. The invariant interval (time² - distance²) is the same for all observers. Einstein's equation E = mc² shows that mass and energy are equivalent - they are different forms of the same thing. As an object's speed increases, its relativistic mass increases, preventing it from reaching light speed. In relativistic collisions, the resulting mass is greater than the sum of original masses because kinetic energy has been converted to mass.

Special relativity introduces spacetime as a continuum of events shared by all observers, yet each observer has their own coordinate system leading to subjective measurements of space and time. The theory provides conversion formulas between frames, producing counterintuitive effects like length contraction and time dilation. To connect this theory to mass-energy equivalence, we examine classical quantities: kinetic energy (motion-dependent energy) and momentum (recoil in collisions). Both depend on velocity, which bridges space-time concepts with mass and energy. This foundation enables understanding how relativistic principles lead to Einstein's revolutionary equation.

This comprehensive section covers classical electromagnetism principles. Electric field direction is from high potential to low potential, or from positive to negative. Any charged particle experiences force F = qE, with force direction matching field for positive charges and opposite for negative charges. Stationary particles experience zero magnetic force. When charged particles accelerate through potential difference ΔV, they gain kinetic energy qΔV with final velocity v = √(2qΔV/m). When entering electric fields with initial velocity perpendicular to the field, particles follow parabolic paths described by y = (qE/2mv²)x². The electric field between parallel plates is uniform: E = ΔV/d. Magnetic force on moving particles is F = q(v × B), always perpendicular to both velocity and field. When velocity is perpendicular to magnetic field, particles move in circular paths with radius r = mv/qB and time period T = 2πm/qB, independent of velocity and radius.

Classical electromagnetism studies electric and magnetic fields generated by charged particles. Matter consists of atoms with positively charged nuclei (protons) and negatively charged electrons. In neutral matter, equal numbers of protons and electrons balance the charge. Every physical interaction—from holding objects to walking on surfaces—is governed by electromagnetic forces. Light emerges when charged particles accelerate, producing oscillating electric and magnetic fields that propagate as electromagnetic waves. The course covers electrostatics (stationary charges), multipole expansions for complex charge distributions, and dielectric materials where polarization creates bound charges. These fundamental principles form the theoretical foundation for understanding all electromagnetic phenomena in nature and technology.

Electricity is charged particles (electrons) flowing through wires. These particles are attracted or repelled by magnetic fields - opposite charges attract, like charges repel. This can be understood through an analogy of a paddle wheel paddling water through a loop, but instead of water, it's charged particles. Electric and magnetic fields can travel through empty space - they don't need a medium to propagate. This is different from sound waves, which need air or a solid medium to travel through.

Classical electromagnetism studies interactions between electric charges and currents using the classical Newtonian model, providing excellent descriptions when quantum effects are negligible. The theory emerged from Michael Faraday's experiments suggesting electromagnetic fields and James Clerk Maxwell's differential equations in his treatise. The Lorentz force law describes how electromagnetic fields exert forces on charged particles: F = q(E + v × B), where the cross product produces a force perpendicular to both velocity and magnetic field, while the electric component acts parallel to the field. The electric field is defined as force per unit test charge, calculated using Coulomb's law for discrete charges or integrals for continuous distributions.

Electric fields arise from electric charges, following Coulomb's law where like charges repel and unlike charges attract. Moving charges create magnetic fields; bar magnets result from aligned electron orbital motions creating current loops. Electric and magnetic fields influence each other, producing electromagnetic waves including visible light. Maxwell's equations provide a complete classical description of electromagnetic behavior, explaining how electric and magnetic fields generate and interact with each other.

All matter and radiation consists of elementary particles. Photons are the fundamental particles of electromagnetic radiation—including radio waves, visible light, and gamma rays—distinguished by their energy levels. Einstein and Planck's discoveries (1900-1905) established light as quantized particles. Electrons are another fundamental particle encountered daily, used in television tubes where they are generated, accelerated, and deflected to create images. Particle physicists measure energy in electron volts (eV), where 1 eV equals the energy gained by an electron accelerated through 1 volt. Television tubes operate at ~5,000 volts, giving electrons ~5 keV of energy. These two particles form the foundation for understanding all other particle physics phenomena.

According to the Standard Model of particle physics, electrons and photons are considered fundamental particles with no known substructure; electrons are massive leptons whose mass arises from interaction with the Higgs field, while photons are massless bosons whose energy comes from their momentum (E=pc) rather than mass, and both are described as point-like excitations of quantum fields rather than tiny solid objects.

Photons are quantum packets of electromagnetic energy with six key properties: (1) Discrete energy packets (quanta), (2) Travel at speed of light (3 × 10⁸ m/s), (3) Energy given by E = hν = hc/λ, (4) Zero rest mass, (5) Momentum p = E/c = h/λ, (6) Electrically neutral (cannot be deflected by fields). Electrons are charged particles with: (1) Negative charge (-1.60 × 10⁻¹⁹ C), (2) Constant mass (9.11 × 10⁻³¹ kg), (3) Kinetic energy KE = ½mv², (4) de Broglie wavelength λ = h/p, (5) Can be controlled by electromagnetic fields. These properties distinguish photons from electrons and explain their different behaviors in atomic and subatomic processes.

This section covers the fundamental properties of electrons and photons. Electrons are elementary particles with charge 1.6 × 10^-19 C and mass 9.1 × 10^-31 kg. The work function (W₀) is the minimum energy for electron escape from metal surfaces. Electron emission includes thermionic, field, photoelectric, and secondary emission types. When electrons accelerate through potential V, kinetic energy gain equals eV. One electron volt (eV) equals 1.6 × 10^-19 J. According to Planck's quantum theory, electromagnetic waves travel as discrete energy packets called photons. Photons travel at light speed, have zero rest mass, and their energy equals hν or hc/λ, while momentum equals hν/c or h/λ.

Electrons have mass and can therefore have internal clocks, while photons cannot. The mass of an electron creates a natural frequency (Compton wavelength) that serves as a timing mechanism. According to the Standard Model, electrons are excitations of quantum fields with two coupled components that constantly interact through the Higgs field, creating the electron's mass. Electrons are stable particles that cannot be destroyed under normal conditions, while photons can be absorbed and re-emitted. This fundamental difference explains why sunlight reaching Earth consists of different photons than those originally emitted by the Sun.