Superlumen: Phase Velocity Faster Than Light
Relativity & Gravity arc, page 43 of 193. Back to The Pixelated Physics Universe
Who they are
Superlumen has one line, and says it often: “Phase velocity above c. no information sent.”
Superlumen is a character of the Relativity & Gravity arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Phase velocity can exceed c in dispersive media while the signal (front) velocity does not; no information travels faster than light.
$$ \begin{gathered} v_p = \frac{\omega}{k} = \frac{c}{n} \\ v_g = \frac{d\omega}{dk} = \frac{c}{n + \omega\,\dfrac{dn}{d\omega}} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $v_p$ | phase velocity | m/s |
| $v_g$ | group velocity | m/s |
| $\omega$ | angular frequency | rad/s |
| $k$ | wavenumber | m^{-1} |
| $c$ | speed of light | m/s |
| $n$ | refractive index | — |
Sources
- L. Brillouin, Wave Propagation and Group Velocity (Academic Press, 1960)
Crossovers
Superlumen meets Lenta (17 Metres per Second). Lenta slows a light pulse's group velocity to bicycle speed in an atomic cloud. Superlumen points to the phase velocity, which in a dispersive medium can exceed c. Neither of them carries information faster than light.
Superlumen meets Prematura (OPERA Faster-Than-Light Neutrino Anomaly). Prematura's claim fell to a timing error. Superlumen's faster-than-light phase velocity is real, but carries no signal. Two ways to seem faster than light, and neither one is.
Superlumen meets Lenta (17 Metres per Second). In a dispersive medium the phase and group velocities part ways. Superlumen's phase velocity can exceed c, while Lenta's group velocity can crawl. The signal front never beats c.
Wear the lore
Concept keywords: Phase Velocity Faster Than Light, Superlumen, Relativity & Gravity, physics lore, Pixelated Physics