What fills space—and how does matter respond?
Modern physics replaces the idea of action-at-a-distance with fields defined throughout spacetime. Charges source electromagnetic fields; those fields carry energy and momentum; particles respond locally to the fields they encounter. Quantization adds another layer: individual field modes exchange energy in discrete quanta.
∇·E = ρ/ε₀F = q(E + v×B)S = (1/μ₀)E×BEₙ = (n+½)ℏωElectric fields are local maps of influence.
Drag the positive and negative charges. The arrows show the net electric-field direction and relative strength at each location.
Fields can carry energy through empty space.
An ideal plane electromagnetic wave has electric and magnetic fields perpendicular to the direction of propagation. Polarization is set by the relative amplitude and phase of transverse electric-field components. Change amplitude, frequency and relative phase.
Particles respond to the field where they are.
Launch a classical charged particle into uniform electric and magnetic fields. Magnetic forces bend motion without doing work; electric fields can change the particle's kinetic energy.
A field mode can exchange energy in discrete quanta.
Quantize one ideal electromagnetic cavity mode. Mathematically, that single mode behaves like a quantum harmonic oscillator. Increase or decrease the occupation number and watch the energy ladder and field-amplitude uncertainty change.
Scientific boundary
Experiments 1–3 use classical electromagnetism and classical particle dynamics. Experiment 4 uses the standard quantization of one electromagnetic mode. In quantum field theory, the electromagnetic field contains infinitely many modes and interacting matter fields require a relativistic quantum description. “Particle = field excitation” is a useful modern statement, but particles should not be pictured as tiny classical beads sitting inside a classical field.