Vol. 68 , Issue 04
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STEPHEN HAWKING IN MEMORIAM On 14 March, esteemed physicist and activist Stephen Hawking passed away. Author of the record breaking A Brief History of Time and many research papers on cosmology, his work inspired many people during his life. In their pieces, The Eternal Professor? and A Theory Of Everything, Aryanne Caminschi and Andy Yin, respectively, will reflect on the Stephen Hawking they knew.
The Universe Will Never be the Same Text: Andy Yin Graphic: Clarence Lee and Sophie Bear When I heard that Stephen Hawking had died, I was dumbstruck. It seemed like he would be around forever. Even late in his life, he remained active in the public eye; he still delivered public lectures, and still voiced his opinions on matters like artificial intelligence and space travel. A revision to a paper he co-authored was submitted on March 4 this year, only ten days before he passed away. But, most of all, I think, I was struck because of what he represented. He was a person of our time, but when we heard him speak or read his writing, we were connected to a more mythical era, one linking back to Einstein. Hawking worked with the geometry of spacetime, with black holes, with the beginning of the universe. His discoveries were of the kind that changed how we thought of reality itself. Perhaps the earliest example of this is his 1966 doctoral thesis, Properties of Expanding Universes. It’s best known for its fourth and final chapter - a methodical, highly abstract, even enigmatic piece on a strange concept: spacetime singularities. It’s a mark of Stephen’s work that it is often hideously complicated, but its essential concepts are alluringly simple. Case in point: you probably already know what a singularity is. Think of the function y = 1/x. When x = 0, there is a singularity because division by zero is not well-defined. Roughly speaking, 1/0 ‘blows up’ to infinity. Singularities can also appear in models of spacetime - that is, the three-dimensional space plus one-dimensional time that we live in. For example, models that described black holes predict a point within where matter is concentrated to an infinite density, and where gravity is infinitely strong. Under Einstein’s general relativity, gravity is just the curvature of spacetime. According to it, objects don’t fall because they’re acted on by a force, but because
they’re following grooves in spacetime, like water following a channel. Therefore, the singularity is a point where spacetime is infinitely curved. Just as 1/0 isn’t defined, the model cannot even include or describe that point. Some found this worrisome; they countered that the singularity was nothing more than a mathematical artifact. To illustrate, we could say that a singularity exists on Earth: the North Pole. As you traverse it, your longitude abruptly changes by 180° and you’re suddenly facing south instead of north. This is a discontinuity, a kind of singularity. But if a different convention is used for north, it vanishes: if the North Pole is in London, suddenly there’s no singularity in the Arctic, and it’s in London instead. The singularity isn’t entirely real, just an artificial result of the mathematical model. Singularities in spacetime models are not as easily resolved, but were nonetheless considered by some to be unrealistic. Certain models displayed singularities only under very restrictive constraints - for example, a black hole that must be axially symmetrical, rotating, and electrically neutral. Some believed that, under more general conditions, the singularities would vanish like the North Pole. Chapter four of Hawking’s thesis refutes this: Hawking shows how more generalised models must also display singularities. The question: how is a singularity point in a spacetime model detected, if such a point can’t be included in the model? The answer: find out where things aren’t allowed to go. Hawking’s method involves geodesics: paths followed in spacetime by objects in freefall - that is, solely under the influence of gravity. Geodesics are curved by gravity because free-falling objects fall towards massive bodies like the Earth. A black hole’s gravity is so strong that nothing that falls in can escape – meaning that geodesics curve into it and
don’t come back out. At a singularity, geodesics must terminate. Hawking proves that a model must have a terminating geodesic under some constraining conditions. In succeeding sections, he removes or weakens a condition, and shows that a termination remains – that is, there is still a singularity. With the conditions sufficiently weakened, from highly specific models to more generalised models, Hawking’s proof could be applied to a model of the entire universe. Remember that y = 1/x displays a singularity at x = 0. Analogously, the universe displays a singularity at t = 0. Hawking’s thesis suggested that, at the beginning of the universe, the universe was compressed into an infinitely-dense singularity. Hawking would do further work on singularities with mathematician Roger Penrose, but it’s clear his thesis was already an astonishing result: that our universe at the Big Bang could be compared with a black hole. Yet it doesn’t actually say how the universe began. In fact, because there’s a singularity at the start of the universe, and because spacetime models break down at singularities, it means that general relativity can’t
explain the universe’s origin. Physicists would have to turn to quantum physics to bridge the gap. That’s why, I think, we were so struck when Stephen Hawking passed. His work was awe-inspiring in so many ways. On the one hand, he showed us what we knew about the universe, and what a strange and amazing place it is. On the other, he reminded us how much was yet to be known.