The local five minute hypothesis is that the earth, with everything on it, and the environment five light-minutes out from it, come into existence five minutes ago.

Let’s estimate the probability of getting something like a local five minute hypothesis by placing particles at random in the observable universe. Of course, in a continuous spacetime the probability of getting *exactly* the arrangement we have is zero or infinitesimal. But we only need to get things right to within a margin of error of a Planck distance for all practical purposes.

The volume of the observable universe is about 10^{80} cubic meters. The Planck volume is about 10^{−105} cubic meters. So, getting a single particle at random within a Planck volume of where it has a probability of about 10^{−185}.

But, if we’re doing our back-of-envelope calculation in a non-quantum setting (i.e., with no uncertainty principle), we also need to set the velocity for the particles. Let’s make our margin of error be the equivalent of moving a Planck distance within ten minutes. So our margin of error for velocity in any direction will be about 10^{−35} meters in 600 seconds, or about 10^{−38} meters per second. Speeds range from 0 to the speed of light, or about 10^{8} meters per second, so the probability of getting each of the three components of the velocity right is about 10^{−46}, and since we have three directions right is something like 10^{−138}. The probability of getting both the position *and* velocity of a particle right is then 10^{−(185 + 138)} = 10^{−323}. Yeah, that’s small. Also, there are about 100 different types of particles, and there are a few other determinables like spin, so let’s multiply that by about 10^{−3} to get 10^{−326}.

The total mass of planetary stuff within around five light minutes of earth—namely, Earth, Mass and Venus—is around 10^{25} kilograms. There are no more than about 10^{25} atoms, and hence about 10^{27} particles, per kilogram. So, we have 10^{52} particles we need to arrange within our volume.

We’re ready to finish the calculation. The probability of arranging these many particles with the right types and within our position and velocity margins of error is:

- (10
^{−326})^{1052}≈ 10^{−102.5 × 1052}≈ 10^{−1055}.

Notice, interestingly, that most of the 55 comes from the number of particles we are dealing with. In fact, our calculations show that basically getting 10^{N} particles in the right configuration has, very roughly, a probability of around 10^{−10N + 3}.

So what? Well, Roger Penrose has estimated the probability of a universe with an initial entropy like ours at 10^{−10123}. So, now we have two hypotheses:

A universe like ours came into existence with a Big Bang

The localized five minute hypothesis.

If there is no intelligence behind the universes, and if probabilistic calculations are at all appropriate for things coming into existence *ex nihilo*, the above probability calculations seem about right, and the localized five minute hypothesis wins by a vast margin: 10^{−1055} to 10^{−10123} or, roughly, 10^{10123} to 1. And if probabilistic calculations are not appropriate, then we cannot compare the hypotheses probabilistically, and lots of scepticism also follows. Hence, if there is no intelligence behind the universe, scepticism about everything more than five minutes ago and more than five light minutes from us follows.