The question I'm asking is pretty much: How do you convert PSI to Velocity? Everywhere I look it says You can't, but can you? And what would you need to know to do so if there is no direct way to convert?

For $f$ a compactly supported function on a spacetime $(\mathcal{M},g)$, one may define its integral over $\mathcal{M}$ by $$f\longmapsto \int_\mathcal{M}\star f,$$ where $\star$ is the Hodge star of $\mathcal{M}$. Since $\star$ is unique, this map is canonical. Suppose that $\Sigma$ is a null h...

Suppose I'm standing a few light minutes away from a light emitting object, as soon as the light is turned on, I project myself towards the object with some speed. Will the relative velocity of my speed and $c$ add up to give a velocity higher than speed of light?

I am confused by most discussions of analog Hawking radiation in fluids (see, for example, the recent experimental result of Weinfurtner et al. Phys. Rev. Lett. 106, 021302 (2011), arXiv:1008.1911). The starting point of these discussions is the observation that the equation of motion for f...