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.
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.
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


11 thoughts on “How Stephen Hawking reconciled the irreconcilable

  1. With the nearest cinema being 150 km away I’m eagerly anticipating the DVD release of that film.

    I’m actually reading a book on Quantum Theory at the moment. One that explains it without using too much math😉

    1. It’s worth the wait! I think quantum physics can definitely be understood without the math – it’s as much a conceptual matter as anything else. Actually, even Einstein worked his stuff out by concept first, then back-filled the math…

      1. I had to read this again, Mathew. The physics involved is a teeny bit more complicated that the experiments with wave length I remember from school. So, basically, a black hole isn’t black, after all. And it’s finite, which is, I have to say, a bit of relief. Up till now whenever I’ve stopped to think about all this, which hasn’t been very often, I’ve imagined black holes out there gobbling up everything, infinitely. Thank goodness for Hawking Radiation.

        1. I have to agree on all points. Yeah, the physics of this one are extremely arcane. And it’s a testament to Hawking’s genius that he thought of it. As usual, these things seem obvious (I hesitate to say ‘simple’) to those familiar with the science, after the event – but that leap of understanding is usually almost insurmountable. It takes a genius – like Newton, or Einstein, or Hawking – to make those jumps.

  2. The last few years I’ve started wishing I was more into quantum mechanics when I was at university. I thought space-time physics was more the thing, alas. Lately I’ve been dabbling with it but I find that the math doesn’t come as easily for me as once it did. Fortunately, as you say, the concepts may be understood without too much math…! Anyway, thought-provoking and well explained, Matthew. Good luck to Dr. Hawking!

  3. I loved this post, Matthew and as you can see, I linked to it. For me, the Theory of Everything has taken on a new meaning–a bit of tongue-in-cheek-spooky–but thanks to this great post, I have a better understanding of the equation that is there and maybe not quite there. Thanks for that. And, I just know I will see that movie one day….😉 Thanks, Matthew!
    Karen

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