Sinusoidal waveforms as a rotating complex vector
Phasors are a clever human abstraction. We represent a sinusoidal waveform as a rotating complex vector, allowing us to compress time-domain behavior into simple algebra.
Phasors: Why Rotate?
But what does this rotation represent in CA terms?
In CA, phasor rotation reflects the dynamic equilibrium of potential and field inertia.
- It’s the circular symmetry of the electromagnetic field pair (E and B).
- Each complete rotation represents one full coherence cycle between stored and released field energy.
- The angle of the phasor isn’t just math — it maps to the lag between electric and magnetic field evolution in space.
This offers a physical intuition: we’re not watching waves “flow,” but rather watching energy slosh between potential (E) and kinetic (B) states, spatially constrained by impedance.
- Each complete rotation represents one full coherence cycle between stored and released field energy.
- The angle of the phasor isn’t just math — it reflects the lag between electric and magnetic field evolution in space.
- Rather than “waves flowing,” we see energy sloshing between potential (E) and kinetic (B) states — a dynamic equilibrium constrained by local impedance.
CA reframes phasor rotation as more than a convenience: it is a signature of coherent oscillation, a spatial marker of evolving field states.
Instead of abstract rotation, think of it as coherence choreography — the stepwise alignment of local energy densities through space and time.