OK
Fazor!
As you know, several events would have to happen in order to blow up the world. First mBH's have to be created in the LHC. Then the mBH's have to be trapped within the Earth. Then they have to be metastable. Then they have to grow fast enough to eat out the Earth on the inside within 10 to the however many years in the future you think we should care about planet Earth.
Let's treat these in order.
For an mBH to form, the universe has to be made out of more than 4 dimensions in order for the plank distance to open up enough. But, apparently, on 5 or 6-D mBH's would be dangerous. So what's the probability that the universe is made out of 5 or 6 dimensions. I've heard theories that propose up to 23, and of course we need more than 3. So there are 20 possible dimensions. So what do you say we just give each dimension an equal a priori probability, and so the probability that it's 5 or 6 would be
(1) 5% each or 10% for both.
Then there's the probability that the mBH will be trapped. Pretty much everyone agrees that at least many of the mBH's will have velocities lower than the Earth's escape velocity, and so will be trapped.
(2) Shall we go with 90% for that one?
So what's the probability that the mBH's will be metastable. The main argument against stability is Hawking radiation, although Plaga tried to demonstrate that mBH's could grow to the Eddington limit even with Hawking radiation and that the Hawking radiation could be a threat in itself. However, G&M said Plaga was off by 23 orders of magnitude, so we can leave that out of our calculations. So what is the probability that Hawking radiation will fail? Well, noting that Hawking radiation has never been empirically detected, out of a poll of
(3) 15 PhD physicists, the median probability that Hawking radiation would fail was 2%. Want to go with that?
Then there's the probability that a metastable mBH will grow. Now, under several, consistent theories of black holes, such mBH's could grow, or maybe they might not. There's no telling.
(4) So it's a coin flip really. So let's call that 50%.
So this is where the white dwarfs come in. Since the possibility that an mBH could grow within Earth is poorly constrained by the first principles of physics, scientists have turned to astrophysics to try and constrain the probability of mBH growth better. So if one extrapolates the semiclassical approximation to multidimensional mBH's that exist deep with the quantum gravitational regime, then one can calculate that cosmic ray induced mBH's formed at white dwarfs would be trapped by white dwarfs because white dwarfs are dense enough. But
this probability depends on the validity of the extrapolation of the semiclassical approximation to a realm that it has never before been applied to. How shall we weigh this one? On the one hand, it
sounds plausible; on the other, we have a history of science full of genuine surprises. Ever read
The First Three Minutes? Who would have thought that the universe is actually expanding.
No one ever thought of that idea until the empirical data forced it. I mean, these are mBH's we are talking about, as well as quantum gravity! On the other hand, this is your last chance to come up with a real showstopper.
(5) Shall we go with 1 in a million--0.000001.
So here we go:
0.1 x 0.9 x 0.2 x 0.5 x 0.000001 = 9 x 10-9
Which is basically 1 in 100,000,000 or about twice as likely as winning the PowerBall lottery.