How Stephen Hawking reconciled the irreconcilable

I finally caught up with The Theory of Everything the other week – an awesome biopic about Stephen Hawking, the British physicist whose life’s goal is to find a theory – a single equation – that explains – well, everything. And what they didn’t mention in the movie is that he’s already made the first big discovery along that path.

The Horsehead nebula, Barnard 33, as seen by Hubble. Wonderful, wonderful imagery.

Let me explain. There are two main theories of the universe. Albert Einstein’s ‘General Theory of Relativity’ of 1917 totally explains space-time – the macro-scale universe. Quantum physics, which emerged a little later at the hands of Paul Dirac, Max Planck, Neils Bohr and others, works brilliantly in the micro-world – specifically, scales around a Planck length (1.61619926 × 10^-35  metres). But the two don’t play nicely together. Not at all.

So far, nobody’s been able to reconcile them – despite the profusion of hypotheses such as string theory, where the maths work out fine, but where nobody has been able to find any evidence to prove it. (I can’t help thinking this is why Sheldon is a string theorist…)

Finding a ‘theory of everything’ has long been Hawking’s goal; and with Jacob Bekenstein he was the first to discover a way in which both Einstein’s General Relativity and the Copenhagen interpretation of quantum physics could work together. They found that way in 1975, at the extreme edge of the possible – inside a black hole. Here’s Hawking’s original paper, ‘Particle Creation By Black Holes’ Commun. math. Phys. 43, 199—220 (1975).

A bit of explanation first. A ‘black hole’ is actually a ‘singularity’, a mathematical point where the curvature of space-time becomes infinite. The normal laws of space-time – the ones our friend Albert Einstein described – totally fail at that point. Even causality doesn’t apply. As Hawking once pointed out in a lecture, we can’t even imagine what might happen inside a singularity (he suggested a singularity could emit Cthulthu – it wouldn’t violate the laws of physics. I disagree. I can’t even pronounce Cthulthu. I think it would emit Sauron instead.)

Artists impression of a GRB. Zhang Whoosley, NASA, public domain, via Wikipedia.

Luckily for us, the everyday universe is shielded from singularities by the event horizon – the point where the escape velocity of the singularity exceeds light-speed. Stuff can fall in. But nothing gets out. Hence the term ‘black hole’. Hawking disputed that. Quantum theory states that particle pairs – positive and negative – are always appearing out of nowhere, then annihilating each other. It doesn’t violate thermodynamics because the net energy outcome is still zero. The effect is known as ‘quantum vacuum fluctuation’.

What I’m about to describe is the heuristic overview – the physics of it is complex and involves some mind-exploding mathematics (‘Bogoliubov transformations’). Basically, Hawking reasoned that if a quantum vacuum fluctuation occurred on the event horizon, there was a chance that one particle, the negative, would be drawn in while the other escaped. They couldn’t annihilate each other, because nothing can escape the horizon. Being negative, the falling particle would reduce the mass of the black hole. Meanwhile the positive particle would escape – effectively as heat – from the black hole.

The result was that ‘black holes’ weren’t actually the black dead ends previously imagined. They were glowing. And they’d eventually evaporate. And THAT is Hawking Radiation.

This also meant that black holes had life limits, and while larger-mass holes had lifespans measured in billions of years, small ones would disappear quickly – which, incidentally, is why nobody’s worried about forming one with a few tens of particles in the Large Hadron Collider at CERN, which is about to be deployed at full power for the first time this year. It’d evaporate in way less than a microsecond. And so Hawking showed that, yes – at least in this extreme case – quantum physics and Einsteinian determinism could play nicely together.

The next question was whether the two could be reconciled in more everyday terms. And that’s been the stalling point. But if anybody can solve it – well, I figure it’ll be Hawking.

Copyright © Matthew Wright 2015