Secundar: Gauge Invariance
Electromagnetism & Plasma arc, page 86 of 193. Back to The Pixelated Physics Universe
Who they are
Secundar has one line, and says it often: “Pure gauge. nothing physical changed.”
Secundar is a character of the Electromagnetism & Plasma arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Gauge freedom: A → A + ∇χ, φ → φ − ∂χ/∂t leaves E and B unchanged. Gauge transformations change nothing physical.
$$ \begin{gathered} \mathbf{A} \to \mathbf{A} + \nabla\chi, \qquad \phi \to \phi - \frac{\partial \chi}{\partial t} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\mathbf{A}$ | magnetic vector potential | T·m |
| $\phi$ | scalar potential | V |
| $\chi$ | gauge function | T·m^2 |
| $t$ | time | s |
Sources
- J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999), §6.3
- H. Weyl, Z. Phys. 56, 330 (1929)
Crossovers
Secundar meets Papilla (Hofstadter's Butterfly). Papilla's butterfly depends only on the magnetic flux through each lattice cell. Secundar confirms that the vector potential behind it can be re-gauged freely, and the spectrum doesn't change, because only gauge-invariant quantities like flux appear in the physics.
Secundar meets Monopola (Dirac's Monopole). Monopola's existence would make electric charge quantised, through Dirac's condition. Secundar notes the subtle price: describing her with a vector potential needs a singular "string" that no gauge choice removes, only moves, and it must be invisible.
Secundar meets Lumidisk (Feynman's Disk Paradox). Lumidisk starts spinning when her coil switches off, which looks like angular momentum from nowhere. Secundar points to where it was hiding: in the electromagnetic field, whose angular momentum is gauge-invariant and real.
Wear the lore
Concept keywords: Gauge Invariance, Secundar, Electromagnetism & Plasma, physics lore, Pixelated Physics