For more than a century, quantum mechanics and electromagnetism have been taught as fundamentally different kinds of theories: one built from a single wavefunction, the other from two real fields that generate each other. This work shows that the difference was never essential. Beneath the familiar formalism, both matter and light share the same underlying architecture: each is a real two‑component system whose parts sustain one another through first‑order propagation. In this framework, the wavefunction is not an abstract complex object but a real pair of internal quadratures selected by a physical clock axis. Maxwell’s electric and magnetic fields are another such pair, selected by the same axis and transported by the same geometric connection. The unity is not metaphorical — it is encoded directly in the action. The same internal direction that determines matter’s internal rotation also determines the electromagnetic sector that survives at long range. Nothing in this reinterpretation alters the tested predictions of quantum mechanics or electromagnetism. What changes is the meaning: phase becomes real geometry, the wavefunction becomes a two‑quadrature field, and electromagnetism emerges as the about‑axis transport of the same clock structure that governs matter. This reveals a simple, coherent propagation principle underlying two pillars of physics.
Abstract Developments since Einstein are summarized. Our systems of units and their relationship to the speed of light. Light propagation in vacuum—what stuff is an electric field made of? Quantum field theory ideas. The Casimir force and energy. Olbers’ paradox and the cosmic horizon. Effect of gravity on speed of light. Schemes for messaging at speeds greater than that of light. The Einstein–Rosen–Podolsky paper of 1935 and its interpretation in simple terms. The reality of the quantum world. Hidden variable theories and Bell’s theorem. Interpretation of many-body quantum wavefunctions—Bohm, Born, Schrӧdinger, Heisenberg, de Broglie, their lives and contributions to physics. The Copenhagen interpretation of quantum mechanics and others. The measurement problem and collapse of the wavefunction. Entangled states. The unreasonable effectiveness of mathematics in the natural sciences.
We consider rectilinear free-space propagation of electromagnetic wavepackets using electromagnetic field theory, scalar wavepacket propagation, and quantum-mechanical formalism. We demonstrate that spatially localized wavepackets are inherently characterized by a subluminal group velocity and a superluminal phase velocity, whose product equals
c2. These velocities are also known as the 'energy' and 'momentum' velocities, introduced by K. Milton and J. Schwinger. We illustrate general conclusions by explicit calculations for Gaussian and higher-order beams and wavepackets, and also highlight subtleties of the quantum-mechanical description based on the 'photon wavefunction'.