One of my students this morning mentioned he'd seen a news article about scientists who suggested that time had a 50% chance of ending in the next 3.7 billion years, and that we have to accept this result if we accept the way we do our calculations.

The paper is arXiv:1009.4968, by Bousso *et al.* I have to admit that I am not in in the field, and so don't really know how people really do calculations for the probabilities of events in eternal inflation. But, as best I can tell, what this paper has done is taken a calculational tool that theorists use in order to make calculations tractable, and have interpreted it as *reality*.

Here's an analogy to what I think is going on. When you do "aperture photometry", you take a digital image of a star, and add up the number of counts in all the pixels that are less than a certain distance away from the center of that star. In reality, the probability distribution for photons from that star extend all the way out to the edge of the field, but it's not practical to try to add things up that way. So, if you care about the total light in the star (say because you're calculating your aperture correction, if you know what that means), you draw an aperture that's "big enough" that you know you're including 99.99% of the light from the star, and don't worry about the fact that you've thrown out the other 0.01% of the light of the star, as your other uncertainties and systematics are bigger than that anyway. The radius of your aperture is a cutoff you use in the calculation for purposes of making the calculation practical and tractable. It does not mean that you're interpreting your data to say that absolutely no light from the star can exist outside of that line. Yes, you're implicitly assuming that, but you don't really believe it. What's more, your calculation shouldn't be taken to mean that you require there to be no light outside your aperture for your measurement to have meaning, and to be useful.

As best I can tell, Bousso *et al.* are taking a similar cutoff that theorists use when doing calculations in an inflationary universe, and are interpreting that calculational cutoff as * The End Of Time* (dramatic chord).

Can somebody explain to me why this isn't just overinterpretation of an approximation made for the sake of finding numbers? Why this is any different from saying that "if you use Kepler's Laws to calculate the orbit of Mars, you will float away because the validity of your calculations depend on Earth having zero mass"?

Rob, although you are not a theorist, I believe you have discovered *exactly* what the major flaw of this paper is. Finding a limit of your model, well outside the model's range of applicability (i.e., we are no longer inflating eternally), is expected.

But where this paper goes -- discussing the physical implications of what happens in that situation -- isn't so much wrong as it is completely uninteresting physically.

Very interesting. But how do you arrive at the lower limit of "10^(10^30) times the size of the observable universe" ?