Stephen Hawking's scientific legacy: Black holes, event horizons and an exit from eternal inflation
From singularity theorems to the multiverse, we explore his ideas with Prof Paul Shellard of the Centre for Theoretical Cosmology in Cambridge
‘He was one of the greatest figures of theoretical physics in the 20th century. He made at least five breakthroughs that would be enough to make someone famous in the scientific community.”
Professor Paul Shellard is well placed to offer this verdict on the achievements of Stephen Hawking.
His PhD on quantum effects in the early universe was supervised by Prof Hawking.
And now he is director of the Centre for Theoretical Cosmology at the University of Cambridge, established by Prof Hawking to “develop theories of the universe that are both mathematically consistent and observationally testable”.
There was no doubting his ambition in doing so.
Much of what Prof Hawking sought to achieve revolved inexorably around one of the biggest puzzles facing physicists today: reconciling two apparently incompatible theories.
“The two big ideas in the 20th century for physical theory are quantum mechanics – the idea of uncertainty on very small scales – and general relativity, which describes the very large scales in the universe: galaxies and stars and black holes,” explains Prof Shellard. “They are incompatible in the sense of there being no theory that joins them together.
“Stephen thought about their connection in the context of the black hole. He came up with this idea of an event horizon around a black hole, which cloaks the singularity at the centre from view.”
A singularity is a point of infinite density, with a gravitational pull so immense that it was thought that nothing – not even light – could escape.
But Prof Hawking explored how a black hole might affect the production of matching pairs of particles and anti-particles – a process that quantum theory states is happening all the time in space.
“Stephen thought about quantum mechanical effects near this horizon. He realised a black hole is not entirely black. It could emit particles through quantum effects – little fluctuations that created particles that escaped from the black hole. This is Hawking radiation. And so the black hole would radiate its energy away slowly and thereby shrink, as energy has to be conserved.
“If it was a tiny black hole, it would be a lot hotter and would radiate more quickly.
“This is the first successful marriage of quantum theory with general relativity. It brings together the largest scales and the smallest scales. It’s a touchstone for people exploring the ‘theory of everything’ – bringing the two big ideas together in a theory of quantum gravity.”
Prof Hawking’s idea dates from 1974 but is still driving research today, not least because it has yet to be observed in space.
“If we found a tiny black hole then that would radiate quite strongly and we would be able to see it,” explains Prof Shellard. “But Stephen always remarked that if we found a tiny black hole he would have received a Nobel Prize…
“Other researchers have been trying to recreate analogues of black holes in the laboratory with fluid systems or condensed matter systems and look for the analogue of Hawking radiation from a horizon in those systems. It’s an active area of research.”
Since 2010 there have been claims that such analogues of Hawking radiation have been observed in the lab. But that remains a matter for debate.
Prof Hawking, however, expanded on his idea.
“This idea of radiation from a horizon he then applied to the universe,” says Prof Shellard. “A natural progression is that the universe itself has a horizon.
“The early universe, where it expands very rapidly – it’s a period we call inflation these days – can radiate as well. It’s very similar to black hole radiation.
“It creates tiny little ripples in the early universe and these ripples are believed to be the primordial seeds around which all the structure in the universe forms.
“These tiny fluctuations grow gravitationally to become stars and planets and everything we see.
“This is called inflationary fluctuation. Stephen was the first person in the West to propose this idea.
“And it’s now believed to be the case. It’s been tested by several satellite experiments.”
Such experiments probe the Cosmic Microwave Background (CMB), the relic radiation left over from the Big Bang.
“It provides a snapshot of the early universe,” explains Prof Shellard. “About 10 per cent of the signal on an old TV when it’s all fuzzy and you haven’t tuned it to a station is the CMB.
“With these satellite experiments you can get an exquisite map of these fluctuations – they are at about one part in 100,000.
“Another of Stephen’s major breakthroughs was that he recognised that the area of the event horizon always had to increase. It’s like the second law of thermodynamics.
“When two black holes collided the area of the final horizon of the two black holes together had to be larger. He was able to use this insight to predict the maximum amount of gravitational waves that two black holes produce.”
He explored this in the 1960s and 1970s but it took until February 2016 for the first observation of gravitational waves, which are a disturbance in the fabric of space-time, generated by accelerated masses.
“Stephen was also important in establishing that black holes are very simple solutions mathematically. He proved that black holes are symmetric about their axis of rotation.”
The beginning – and ending – of time
“Stephen started his career by looking at the question of whether the universe has a beginning in time,” says Prof Shellard.
“When the evidence from the Cosmic Microwave Background came out, that was strong evidence that as you go backwards in time, the universe gets much smaller and hotter because this is radiation left over from a hot, early phase of the Big Bang. He looked at the implications for the universe getting smaller like this in Einstein’s Theory of General Relativity.
“And he was able to show that if you go backwards in time, there must have been a Big Bang singularity. And that means there must have been a beginning to time.
“A Big Bang singularity means all the laws of physics break down because everything gets infinitely dense. That’s mathematical ‘proof’ of what we were observing, which is that the universe was smaller and hotter in the past. That’s another of his breakthroughs.”
Much of Prof Hawking’s work on singularity theorems was in collaboration with Oxford mathematician Roger Penrose.
But in the 1980s, and in The Brief History of Time, which sold 10 million copies, he revised his early ideas about the beginning of time.
“He was always troubled that he proved this breakdown of everything at the beginning of the universe and the fact that time had to begin,” explains Prof Shellard. “So he asked himself ‘Can I apply my quantum mechanical ideas to the origins of the universe itself?’
“This is what’s called his famous ‘No boundary proposal’. In A Brief History of Time, he tried to explain ‘imaginary time’. This is the idea that you didn’t go into a singularity, but you rounded it off. You had a beginning of the universe that was quantum mechanical in origin using imaginary time.
“But asked what were the things he wished he could have done, he said: ‘I wish I could have explained imaginary time better’.
“It’s a mathematical way of thinking about time – a calculational ‘trick’ if you like. But he thought about it much more literally, that somehow time changes its nature.
“His idea that the universe was created out of nothing, using his ‘No boundary’ proposal. He worked on this with Jim Hartle and more recently with Thomas Hertog.
“But unlike his ideas of inflationary fluctuations which have been confirmed, this is still a speculative proposal and it will be difficult to establish it observationally. This was Stephen’s character – he was trying to answer the big questions. He was trying to answer the question about the origin of the universe.”
The Hartle-Hawking state, as it is known, describes how as we go back in time towards the Big Bang, time gives way to space, so that there is only space and no time. Their argument was that the origin has no origin – and that the concept of a beginning is meaningless, because time did not exist before the Big Bang. The universe was a singularity in both space and time – it has no boundaries in either.
The 1983 work also suggested that Big Bang would have been accompanied by numerous other ‘Big Bangs’, creating a multiverse. This is the idea that our universe is just one of many.
It is a theme that Prof Hawking returned to with Prof Hertog – submitting his final paper, it has emerged, just two weeks before he died last Wednesday at the age of 76.
‘A Smooth Exit from Eternal Inflation’ proposes the mathematics needed for a space to find evidence for the existence of the multiverse in the cosmic background radiation. The paper is being reviewed by a leading scientific journal – and could yet prove to be Prof Hawking’s most groundbreaking.
Portentously, the paper also predicts that eventually the universe will fade to blackness as stars run out of energy.
Unique, ambitious and courageous
“Stephen was very unique,” says Prof Shellard. “The first thing that struck you was his courage in the face of grave disability. Every day was a battle for him. He was so dedicated to his work. He was in at work every day and every day was a struggle and frustration for him.
“He said about himself that it doesn’t matter how difficult life may seem, there is always something you can do and succeed at.
“He had this very optimistic frame of mind and he dwelled on what he could do and not on what he couldn’t.
“He realised he could think about big questions about the universe and his disability perhaps influenced him in that way.
“He was very ambitious. As a mentor, he set a great example for which anyone who has been near him is very indebted.
“He looked at the heart of the problem. He pushed aside the complex mathematical detail and went for the core conceptual ideas.
“He saw further than the rest of us. He was a towering figure in theoretical physics.
“The other thing is his tremendous sense of humour. Everything was a frustration for him. Communicating with him was very, very slow, but whenever you did there was always a joke or ironic remark and he had an impish smile.
“These two things – his sheer determination and his ability to look at the lighter side of life in the face of adversity – were his key qualities that got him through and gave him such a long life.”
Continuing Prof Hawking’s work at the Centre for Theoretical Cosmology in Cambridge
“Stephen’s work is so influential that it goes in the annals of scientific history without question,” says Prof Shellard. “But fortunately for the rest of us he left some unanswered questions and those are driving our interest in the Centre for Theoretical Cosmology.
“One of the two central open questions is the implication of black hole radiation – the seeming idea that information can be lost through the process.
“So tables and chairs can fall into a black hole and it can evaporate.
“The outcome seems to be random particles.
“Stephen presented this as information loss, which contradicts one of the central tenets of quantum mechanics.
“This is a big mystery that people continue to work on.
“The other one is the question about the origins of the universe itself, which goes back to his no boundary proposal.
“Can we find hints that give us more clues about the fundamental theory describing how our universe emerged, or putting it another way, can we find clues about fundamental theory from observations of the universe?
“We’ve got a flood of new information coming. I hope we’ll find clues about the early universe. Maybe there were extra dimensions; maybe there were extra fields. We’ll learn about fundamental theory and about the structure of everything we see. That’s our vision.”
Read more
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