Strange Theory of Light and Matter: QED and Photon Interactions

Photons: Quanta of Light

Maxwell gave us beautiful equations in 1865—four laws unifying electricity and magnetism into electromagnetic fields. Electric charges source electric fields. Magnetic poles always come paired, never isolated. Changing magnetic fields disturb electric fields. Changing electric fields disturb magnetic fields. That last circularity is the key: electric and magnetic disturbances chase each other through space, creating waves that propagate at light speed. Maxwell predicted light itself must be electromagnetic radiation, and he was right.

But nature had more surprises. Einstein explained the photoelectric effect in 1905 by proposing light comes in discrete packets—photons with energy E = hν. The energy depends on frequency, not intensity. Shine dim violet light on metal, electrons pop out. Shine bright red light, nothing happens. Classical waves couldn’t explain it, but photon quanta could. Each photon either has enough energy to eject an electron or it doesn’t.

Then came Compton scattering in 1923. Photons bounced off electrons like billiard balls, their wavelength shifting by Δλ = h/mc(1-cosθ). The photon transferred momentum p = h/λ to the electron despite having zero mass. Light exhibited particle properties—discrete impacts, momentum transfer, energy quantization—while still showing wave properties in interference and diffraction experiments.

So what is light really? Quantum field theory resolved the paradox by treating the universe as fields permeating spacetime. The electromagnetic field is a mathematical fluid made of vectors expressed with real numbers. Photons emerge as quanta—discrete energy packets within this field. They can appear or disappear as field disturbances concentrate or dissipate. The electron field, by contrast, consists of spinors—complex numbers with both magnitude and phase. Electrons are wave-like disturbances propagating through their field. These fields coexist in spacetime but possess fundamentally different mathematical natures, which explains why electrons carry charge and mass while photons don’t.

Quantum electrodynamics—QED—became the relativistic quantum field theory unifying light and matter. The Lagrangian couples electron fields to photon fields through the covariant derivative: an interaction term -eψ̄γ^μψA_μ where electron current couples to the photon field. From this deceptively simple mathematical structure emerges all electromagnetic phenomena.

Diagrams: Particles as Lines

I invented my diagrams in 1948 as better calculation tools. The mathematics of quantum field theory was forbidding—infinite series of integrals, creation and annihilation operators, time-ordered products. My diagrams translated this abstract formalism into something visual and intuitive.

The rules are simple. External lines represent real particles—electrons in, photons out, positrons (drawn as electrons going backward in time). Internal lines represent virtual particles connecting vertices. These can be “off mass shell,” violating E²=p²c²+m²c⁴ temporarily. The uncertainty principle permits this for time Δt ~ ℏ/ΔE.

Each vertex represents an interaction point where an electron emits or absorbs a photon. Every vertex contributes a factor proportional to the fine structure constant α ≈ 1/137. This makes perturbation theory convergent: tree-level diagrams with two vertices contribute ~α, one-loop diagrams with four vertices contribute ~α², two-loop diagrams contribute ~α³, and so on. Each order is suppressed by another factor of 1/137, so the series converges rapidly.

Consider electron-electron scattering. Two electrons approach, one emits a virtual photon, the other absorbs it, both recoil. The photon exchange transfers momentum, creating what we observe as electromagnetic repulsion. Like two skaters throwing a ball back and forth—each throw recoils them apart. But this is quantum mechanics, so all possible photon exchanges happen simultaneously in superposition. You sum amplitudes over every Feynman diagram: one-photon exchange, two-photon exchange, three-photon exchange, infinite series. The math works out to finite predictions.

Or take Compton scattering: an electron absorbs an incoming photon, then re-emits one at different angle and frequency. Energy and momentum conservation determine the wavelength shift. Higher-order diagrams add tiny corrections at order α².

Pair production requires a nucleus nearby. A photon can’t spontaneously create an electron-positron pair in vacuum because momentum can’t be conserved. But near a nucleus, the nucleus absorbs recoil momentum, and the photon creates a pair. The reverse process—pair annihilation—produces two photons.

My diagrams aren’t pictures of what’s “really happening.” They’re calculation tools. Each diagram represents a complex amplitude contributing to the probability of some initial state evolving to some final state. Don’t ask what the electron is “doing”—just calculate amplitudes, square them, get probabilities, compare with experiment. Shut up and calculate, as the saying goes (though I never quite said it that way).

Renormalizing the Infinities

Here’s where things got controversial. Loop diagrams give divergent integrals. The electron constantly emits and reabsorbs virtual photons, creating a “cloud” around it. Calculate the mass correction: infinity. The charge correction: infinity. Many thought quantum field theory was broken.

Tomonaga, Schwinger, and I independently developed renormalization. The key insight: bare mass and charge are unobservable. You never measure the “naked” electron without its virtual photon cloud. What you measure is dressed mass m and dressed charge e—bare values plus corrections. Both are infinite, but chosen so their sum equals the finite measured values.

It sounds like cheating—redefining parameters to hide infinities. Dirac called it “sweeping infinities under the rug.” But it works with stunning precision. Once you’ve fixed mass and charge to measured values, every other prediction follows unambiguously. No more free parameters, no more arbitrariness.

The electron magnetic moment demonstrates this precision. Classical theory predicts g-factor = 2. Quantum corrections modify it. The first-order correction contributes α/2π ≈ 0.00116. Higher orders add tiny refinements. Calculating to five loops requires evaluating thousands of Feynman diagrams—brutal work even with computers. The theoretical prediction: g = 2.00231930436256(35). The experimental measurement: g = 2.00231930436256(35). Twelve significant figures matching. This is the most precise prediction in all of physics.

QED also introduced the renormalization group—the idea that coupling constants “run” with energy scale. The fine structure constant α isn’t truly constant; it increases slightly at higher energies as virtual particle loops screen charge differently. At electron-mass energies, α ≈ 1/137. At W-boson energies, α ≈ 1/128. This running coupling became crucial for understanding forces in the Standard Model.

Virtual Particles, Real Effects

Virtual particles appear in internal lines of Feynman diagrams. They violate energy-momentum conservation temporarily—the uncertainty principle permits ΔE·Δt ≥ ℏ/2. More energetic virtual photons disappear faster. Less energetic ones propagate farther.

You can’t observe virtual particles directly—observation would make them real. But their effects are measurable. The Lamb shift demonstrates this. In hydrogen, 2S₁/₂ and 2P₁/₂ levels should be degenerate by Dirac’s equation. Measurements in 1947 showed 1 GHz splitting. Virtual photon emission and absorption shifts energy levels. QED predicted this precisely.

The Casimir effect provides another confirmation. Two metal plates in vacuum experience attractive force. Between the plates, only virtual photons with wavelengths fitting the gap exist—a discrete set. Outside, all wavelengths contribute. The radiation pressure outside exceeds that inside, pushing plates together. Measured in 1958, this confirms virtual particles have observable consequences.

Vacuum polarization shows virtual electron-positron pairs screening electric charge. Get very close to an electron, you see stronger charge because you’ve penetrated the screening cloud. This modifies Coulomb’s law at short distances.

My philosophy: don’t ask what’s “really” happening at quantum scales. QED is a strange theory. Electron emitting a photon? Absorbing it? Both? Neither? These questions mislead. Calculate probability amplitudes by summing all possible scenarios—all Feynman diagrams. Get predictions. Compare with experiments. That’s science. The rest is poetry.

QED became the template for the Standard Model. Electroweak theory unified electromagnetism with weak interactions. Quantum chromodynamics applied similar field theory to quarks and gluons. All modern particle physics traces back to the QED framework we developed in the 1940s. In 1965, Tomonaga, Schwinger, and I shared the Nobel Prize “for fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles.”

Nature uses only the longest threads to weave her patterns. QED revealed one of those threads—how light and matter interact through photon exchange, how forces emerge from virtual particle exchanges, how probability amplitudes sum over all possible paths. The theory is strange, counterintuitive, mathematically demanding. But it works. And that’s what matters.