**In a lecture delivered at Starmus in 2016, Professor Stephen Hawking discussed some of his most groundbreaking theories, his children and his life**

## The Meaning of Life

*“Remember to look up at the stars and not down at your feet. Try to make sense of what you see and wonder about what makes the universe exist. Be curious. And however difficult life may seem, there is always something you can do and succeed at.”*

My work on black holes began with a eureka moment, shortly after the birth of my daughter, Lucy, while getting into bed. I realised the area theorem. If general relativity is correct, and the energy density is positive, the surface area of the event horizon, the boundary of a black hole, has the property that it always increases when additional matter or radiation falls into the black hole.

Moreover, if two black holes collide and merge to form a single black hole, the area of the event horizon around the resulting black hole is greater than the sum of the areas of the event horizons around the original black holes.

The area theorem can be tested experimentally by Ligo. On September 14, 2015, Ligo, for the first time, detected gravitational waves from the collision and merger of a black hole binary. The properties of black holes suggested that the area of a black hole was like what is called the entropy in thermodynamics.

Entropy can be regarded as a measure of the disorder of a system, or equivalently, as a lack of knowledge of its precise state. It would be a measure of how many states a black hole could have on the inside, for the same appearance on the outside. But the area couldn’t actually ~be the entropy, because as everyone thought they knew, black holes were completely black, and couldn’t be in equilibrium with thermal radiation.

We were so successful with the classical general theory of relativity that I was at a bit of a loose end in 1973. My work with Roger Penrose, had shown that general relativity broke down at singularities. So the obvious next step would be to combine general relativity, the theory of the very large, with quantum theory, the theory of the very small.

I had no background in quantum theory, and the singularity problem seemed too difficult for a frontal assault at that time. So as a warm-up exercise, I considered how particles and fields governed by quantum theory, would behave near a black hole.

I studied how quantum fields or particles would scatter off a black hole and was expecting that part of an incident wave would be absorbed, and the remainder scattered. To my great surprise, I found there seemed to be emissions from the black hole itself. At first I thought this must be a mistake in my calculation but what persuaded me that it was real was that the emission was exactly what was required; to identify the area of the horizon, with the entropy of a black hole.

Later work uncovered the deep reason for this formula. General relativity can be combined with quantum theory in an elegant manner, if one replaces ordinary time with so-called imaginary time. This is called the Euclidean approach because it makes time become a fourth direction of space.

Euclidean spacetime is smooth and contains no singularity at which the equations of physics could not be defined. It solved the fundamental problem that the singularity theorems of Penrose and myself had raised – that predictability would break down because of the singularity.

The radiation from a black hole will carry away energy, so the black hole will lose mass, and shrink. Eventually, it seems the black hole will evaporate completely, and disappear. This raised a problem that struck at the heart of physics. My calculation showed the radiation was exactly thermal and random, as it has to be, if the area of the horizon is to be the entropy of the black hole.

So how could the radiation left over carry all the information about what made the black hole? But if information is lost, this is incompatible with quantum mechanics. This paradox had been argued for thirty years, without much progress.

Eventually, I found what I think is its resolution. Information is not lost in black holes, but it is not returned in a useful way. It is like burning an encyclopedia. Information is not lost, but it is very hard to read.

In 1982, I proposed that the seeds for structures in our universe could be created by quantum effects during inflation. The original scenario for inflation was that the universe began with a big bang singularity. As the universe expanded, it was supposed somehow to get into an inflationary state, but I thought this was unsatisfactory.

Unless one knew what came out of the initial singularity, one could not calculate how the universe would develop. Cosmology would not have any predictive power. What was needed was a spacetime without singularity, like in the Euclidean version of a black hole.

Around this time, I decided to write a book. I thought I might make a modest amount to help support my children at school and the rising costs of my care, but the main reason was because I enjoyed it. While I was writing it, I visited CERN and I became critically ill with pneumonia and lost my voice due to a tracheostomy. I never expected *A Brief History of Time* to do as well as it did.

There are many ambitious experiments planned for the future. We will map the positions of billions of galaxies, and with the help of supercomputers like Cosmos, we will better understand our place in the Universe.

It has been a glorious time to be alive, and doing research in theoretical physics. The fact that we humans, who are ourselves mere collections of fundamental particles of nature, have been able to come this close to an understanding of the laws governing us, and our universe, is a great triumph.

Remember to look up at the stars and not down at your feet. Try to make sense of what you see, and wonder about what makes the universe exist. Be curious. And however difficult life may seem, there is always something you can do, and succeed at. It matters that you don’t just give up.

*This article was originally published in October 2016. The above extracts were taken from Stephen Hawking’s 2016 Starmus lecture titled*A Brief History of Mine*- the full speech was published in the third Starmus book.*