◼️ Tom⇒maths: How long have we got left?

How long have we got left?

A question from Jo:

'Following all the hoo-hah and scaremongering over the Large Hadron Collider possibly creating black holes and ending the world, my question is this:

If the LHC did create the tiny black holes that the doom-mongers say it might, how long would it take for the world to end? And on that note, what actually would happen to it and, more importantly, me?! What might I notice/feel?'

Not a real black hole

First up:

A crash course in creating black holes (don't try this at home)

As far as I understand it, there are two ways to create a black hole:

1. Get lots of matter and put it all in the same place. By 'lots' I mean at least three times as much stuff as there is in our sun.

If you have enough mass, it will collapse in on itself. Now, gravity is a very weak force which is why you need so much stuff to make it all worthwhile; too little stuff and you get things like planets forming instead of black holes. A bit more stuff, and you get things like our star: the matter collapses in on itself until the energy released from this collapse ignites the matter and you get the big burning fireball that allows us to live. When the fuel for this fire runs out, the sun's matter will collapse a bit more and form a white dwarf, eventually cooling to become a brown dwarf, but not a black hole.

Even more mass in one place, and you still get a burning fireball, but more interesting things happen once the fuel has run dry. If your leftovers have a bit more mass than the sun has, they'll collapse further than the white dwarf stage and form a neutron star. This happens when there is enough mass to ensure that the combined forces of gravity can overcome the much stronger forces inside an atom that keep the protons and electrons apart: ram them together and you get neutrons.

With even more mass left over (I repeat, at least three times what's in the sun), even the forces that stop neutrons from being crushed into other neutrons (known as the 'neutron degeneracy pressure'*) are no match for the force of gravity, and everything goes weird: a black hole is formed.

2. Get a couple of particles and smack them into each other at very, very, very high speeds.

Whichever way you want to make a black hole, neutron degeneracy pressure has to be overcome. One way to do this is by crushing lots of mass together as above. Another way is to crash two particles together at very high speeds (or energies). One possibility for this is high energy cosmic rays striking the Earth's atmosphere. Another is within the confines of a particle accelerator experiment, such as the LHC, the Large Hadron Collider.

So is the unthinkable likely to happen?

Anybody who has seen any kind of science fiction film, or has any kind of interest in space science at all knows that nothing can escape from a black hole. One thing that most people don't know is that black holes aren't completely black. They give off energy called Hawking radiation** which actually causes a loss in mass of the black hole. Now, for really massive black holes the amount of energy lost is a lot smaller than the amount they absorb just from the cosmic microwave background***, so the net effect is that they keep getting bigger. But an interesting effect of the calculations is that the smaller a black hole, the more radiation it emits. So, for a really small black hole, of the kind of size we're talking about being possibly created in one of the LHC's experiments, the science predicts that it will evaporate in a tiny, tiny, teeny, insy-winsy spider-sized fraction of a second after it has been created. It wouldn't have time to start accreting matter, and the biggest problem facing particle physicists would be even noticing it was there in the first place.

In short, the processes that CERN's scientists are trying to recreate have been happening around us naturally for billions of years. We're unlikely to be swallowed up by a black hole of our own making; if it was going to happen the odds are that it would have done so by now!

But what if...

O.k, o.k, just saying it's incredibly unlikely and leaving it there is a bit boring, isn't it? I'm afraid the "yeah, but what if it did happen," response isn't that interesting either.

What would you notice? Not much. You wouldn't have time. If we were sucked into a microscopic black hole, everyone and everything you have ever known would be collectively crushed down to occupy a space around the size of an average garden pea. This would happen in less than a second. It would be accompanied by a belching of radiation off into space, but you wouldn't be around long enough to notice it.

Interestingly, because the mass of the Earth would still be the same, if occupying a significantly smaller volume, it's gravitational effect on the surrounding space would be the same as always. The Moon (and any other satellites, natural or artificial, that had escaped the collapse) would orbit just as they had before: to a casual, visual observer it would look like they were orbiting nothing at all. Weird.