Why Louis Pasteur Didn't Prove Abiogenesis is Impossible

Christians often like to claim that Louis Pasteur proved abiogenesis was "impossible."  Here's the first example I came across in my search. It's a pretty professional-looking production. And it's short, so you won't hate me for wasting much of your life if you watch it. Seems like these guys understand the science and have thought it through, right?

Louis Pasteur in his laboratory.

A more careful review of his work demonstrates that he most certainly did nothing of the sort. In his experiment, Louis Pasteur experimented with relatively small quantities of liquid compared to the volume of liquid on earth. Let's pick an absurdly large number in order to give the Christian claim every possible benefit.  Suppose that Pasteur tested a thousand cubic meters of liquid. That's 260,000 gallons, larger than the Giant Ocean Tank at the New England Aquarium. Pasteur demonstrated that no life spontaneously generated in them over the course of his experiment. Let's assume that it was a decade-long experiment.  These would be very large numbers, considering the pictures available of him in his laboratory.  Pasteur's analysis did not demonstrate that life never spontaneously forms anywhere ever. It only showed only that life did not spontaneously generate in the large sample of broth over the time period he tested.  This puts a lower-bound on the mean time until life spontaneously forms in a given volume of liquid.  In other words, we can say with confidence that life sponteneously generates less often than once in $10^4 m^3  \cdot years$ . (for the sake of simplicity, I'm presuming that the spontaneous generation of life would follow Poisson distribution where each infinitesimal unit of liquid volume is as likely as any other to spontaneously generate life per unit time).

Now, compare that volume to the volume of water on earth ($1.386 \times 10^{18} m^3$) and we can then calculate a lower-bound on the global spontaneous generation rate:

$ f_{gen} < \frac{10^4 m^3/yr}{1.386\times 10^{18} m^3} $

$ f_{gen} < 1.386  \times 10^{14} year^{-1}  $

$ f_{gen} < 4.39 MHz $ [ref] 

That's right.  Pasteur's experiment shows that life spontaneously forms on Earth at a rate below 4.4 million times per second.  And that's with the generous assumption that he tested a thousand cubic meters of solution! Life could be forming all around the world at a rate of 4.4 MHz, and Pasteur's experiments would remain a valid measure. In 1000 cubic meters over a decade, life is unlikely to form.