Beginnings and Endings

14 March 2018

Stephen Hawking follows a geodesic path through spacetime. Jim Campbell/Aero-News Network
Stephen Hawking follows a geodesic path through spacetime.

Each of us has a beginning and an ending. We awake to explore the universe for a brief time, then return to our cosmic slumber. Stephen Hawking was no different. He was born in January of 1942, and he died on 14 March 2018. He was fascinated with beginnings and endings.

For his doctoral dissertation, Hawking focused on the nature of the big bang, specifically whether it began as a singularity. A singularity is where the very nature of space and time break down. The curvature of space at a singularity becomes infinite, and matter at a singularity has infinite density. They first appeared in the context of black holes (still hypothetical at the time) where it was thought that the matter of a large dead star would collapse forever under its own weight. Hawking showed that general relativity required the big bang to be a singularity, hence the idea that the universe began as a single point of infinite energy density. Years later Hawking and others demonstrated that a big bang singularity wasn’t necessary. Because of quantum mechanics, a singularity might not even be possible. Whether the universe began as a singularity or merely as a hot dense state is still an issue of much debate.

The work Hawking is most known for concerned black holes. In general relativity, black holes have an event horizon. That is, a boundary surrounding a black hole that is a cosmic point of no return. Cross the event horizon, and you are forever trapped. But this caused several problems in theoretical physics. For example, if an event horizon were truly a point of no return, and not even light can escape, then black holes would be absolutely cold. According to thermodynamics, every object gives off some light as thermal heat. General relativity said that black holes have a temperature of absolute zero, which thermodynamics says is impossible.

Hawking found that this contradiction could be solved through quantum mechanics. General relativity is a classical theory, meaning that objects have an absolute position in space and time. But in quantum theory the location of objects is fuzzy. The wavelike nature of quantum objects means they can’t be pinned down to a specific location. This means that quantum objects can’t be trapped forever within a black hole. There is always a small chance that they could escape, taking a bit of the black hole’s mass with it. This escaped radiation came to be known as Hawking radiation. Through Hawking radiation black holes not only had a temperature, but their temperature increased as they radiated away. Thus black holes are not immortal. Like everything else in the universe, they exist for a finite time.

Of course the beginning and ending of things is rooted in the nature of time. While it seems obvious that time flows from past to present to future, in physics things aren’t so clear. The mathematical equations we use are time symmetric, meaning they work just as well going from past to future as they do going from future to past. It seems that there is nothing inherent to the laws of physics that requires a direction to time. This is known as the arrow of time problem. Why do we experience a direction in time?

The answer seems to lie within thermodynamics. One of the fundamental rules of thermodynamics is that heat flows from warmer objects to colder objects. This is related to the amount of entropy a system has. Entropy increases over time, and this seems to give a direction to time. In studying this problem Hawking found entropy could account for the arrow of time, but it could also have strange effects. If an expanding universe experiences an arrow of time that moves from past to future, a contracting universe could have an arrow of time that points from future to past.

Throughout his life, Stephen Hawking explored some of the most challenging and subtle questions in physics and cosmology. He focused on ideas and their implications, not experiments. As a result, none of his ideas have been proven experimentally. Some of his ideas such as Hawking radiation are widely thought to be correct, but that is far from being proven. The legacy Hawking leaves us is in many ways a challenge. Prove that his ideas are correct, or find better answers to the questions he raised.

And in that way the story of Stephen Hawking is just beginning.