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3 " During our glorious year of 1974–5, while I was dithering over gravitational waves, and Stephen was leading our merged group in black hole research, Stephen himself had an insight even more radical than his discovery of Hawking radiation. He gave a compelling, almost airtight proof that, when a black hole forms and then subsequently evaporates away completely by emitting radiation, the information that went into the black hole cannot come back out. Information is inevitably lost.
This is radical because the laws of quantum physics insist unequivocally that information can never get totally lost. So, if Stephen was right, black holes violate a most fundamental quantum mechanical law.
How could this be? The black hole’s evaporation is governed by the combined laws of quantum mechanics and general relativity—the ill-understood laws of quantum gravity; and so, Stephen reasoned, the fiery marriage of relativity and quantum physics must lead to information destruction.
The great majority of theoretical physicists find this conclusion abhorrent. They are highly sceptical. And so, for forty-four years they have struggled with this so-called information-loss paradox. It is a struggle well worth the effort and anguish that have gone into it, since this paradox is a powerful key for understanding the quantum gravity laws. Stephen himself, in 2003, found a way that information might escape during the hole’s evaporation, but that did not quell theorists’ struggles. Stephen did not prove that the information escapes, so the struggle continues.
In my eulogy for Stephen, at the interment of his ashes at Westminster Abbey, I memorialised that struggle with these words: “Newton gave us answers. Hawking gave us questions. And Hawking’s questions themselves keep on giving, generating breakthroughs decades later. When ultimately we master the quantum gravity laws, and comprehend fully the birth of our universe, it may largely be by standing on the shoulders of Hawking. "

Stephen Hawking , Brief Answers to the Big Questions

6 " This was a golden age, in which we solved most of the major problems in black hole theory even before there was any observational evidence for black holes. In fact, we were so successful with the classical general theory of relativity that I was at a bit of a loose end in 1973 after the publication with George Ellis of our book The Large Scale Structure of Space–Time. My work with 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. In particular, I wondered, can one have atoms in which the nucleus is a tiny primordial black hole, formed in the early universe? My investigations revealed a deep and previously unsuspected relationship between gravity and thermodynamics, the science of heat, and resolved a paradox that had been argued over for thirty years without much progress: how could the radiation left over from a shrinking black hole carry all of the information about what made the black hole? I discovered that information is not lost, but it is not returned in a useful way—like burning an encyclopedia but retaining the smoke and ashes.
To answer this, I studied how quantum fields or particles would scatter off a black hole. I was expecting that part of an incident wave would be absorbed, and the remainder scattered. But to my great surprise I found there seemed to be emission 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. This entropy, a measure of the disorder of a system, is summed up in this simple formula which expresses the entropy in terms of the area of the horizon, and the three fundamental constants of nature, c, the speed of light, G, Newton’s constant of gravitation, and ħ, Planck’s constant. The emission of this thermal radiation from the black hole is now called Hawking radiation and I’m proud to have discovered it. "

Stephen Hawking , Brief Answers to the Big Questions

14 " The human mind is an incredible thing. It can conceive of the magnificence of the heavens and the intricacies of the basic components of matter. Yet for each mind to achieve its full potential, it needs a spark. The spark of enquiry and wonder.
Often that spark comes from a teacher. Allow me to explain. I wasn’t the easiest person to teach, I was slow to learn to read and my handwriting was untidy. But when I was fourteen my teacher at my school in St Albans, Dikran Tahta, showed me how to harness my energy and encouraged me to think creatively about mathematics. He opened my eyes to maths as the blueprint of the universe itself. If you look behind every exceptional person there is an exceptional teacher. When each of us thinks about what we can do in life, chances are we can do it because of a teacher.
[...] The basis for the future of education must lie in schools and inspiring teachers. But schools can only offer an elementary framework where sometimes rote-learning, equations and examinations can alienate children from science. Most people respond to a qualitative, rather than a quantitative, understanding, without the need for complicated equations. Popular science books and articles can also put across ideas about the way we live. However, only a small percentage of the population read even the most successful books. Science documentaries and films reach a mass audience, but it is only one-way communication. "

Stephen Hawking , Brief Answers to the Big Questions

15 " When I was growing up it was still acceptable—not to me but in social terms—to say that one was not interested in science and did not see the point in bothering with it. This is no longer the case. Let me be clear. I am not promoting the idea that all young people should grow up to be scientists. I do not see that as an ideal situation, as the world needs people with a wide variety of skills. But I am advocating that all young people should be familiar with and confident around scientific subjects, whatever they choose to do. They need to be scientifically literate, and inspired to engage with developments in science and technology in order to learn more.
A world where only a tiny super-elite are capable of understanding advanced science and technology and its applications would be, to my
mind, a dangerous and limited one. I seriously doubt whether long-range beneficial projects such as cleaning up the oceans or curing diseases in the developing world would be given priority. Worse, we could find that
technology is used against us and that we might have no power to stop it.
I don’t believe in boundaries, either for what we can do in our personal lives or for what life and intelligence can accomplish in our universe. We stand at a threshold of important discoveries in all areas of science. Without doubt, our world will change enormously in the next fifty years. We will find out what happened at the Big Bang. We will come to understand how life began on Earth. We may even discover whether life exists elsewhere in the universe. While the chances of communicating with an intelligent extra-terrestrial species may be slim, the importance of such a discovery means we must not give up trying. We will continue to explore our cosmic habitat, sending robots and humans into space. We cannot continue to look inwards at ourselves on a small and increasingly polluted and overcrowded planet. Through scientific endeavour and technological innovation, we must look outwards to the wider universe, while also striving to fix the problems on Earth. And I am optimistic that we will ultimately create viable habitats for the human race on other planets. We will transcend the Earth and learn to exist in space.
This is not the end of the story, but just the beginning of what I hope will be billions of years of life flourishing in the cosmos.
And one final point—we never really know where the next great scientific discovery will come from, nor who will make it. Opening up the thrill and wonder of scientific discovery, creating innovative and accessible ways to reach out to the widest young audience possible, greatly increases the chances of finding and inspiring the new Einstein. Wherever she might be.
So 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. Unleash your imagination. Shape the future. "

Stephen Hawking , Brief Answers to the Big Questions

20 " There are only two types of waves that can travel across the universe bringing us information about things far away: electromagnetic waves (which include light, X-rays, gamma rays, microwaves, radio waves…); and gravitational waves.
Electromagnetic waves consist of oscillating electric and magnetic forces that travel at light speed. When they impinge on charged particles, such as the electrons in a radio or TV antenna, they shake the particles back and forth, depositing in the particles the information the waves carry. That information can then be amplified and fed into a loudspeaker or on to a TV screen for humans to comprehend.
Gravitational waves, according to Einstein, consist of an oscillatory space warp: an oscillating stretch and squeeze of space. In 1972 Rainer (Rai) Weiss at the Massachusetts Institute of Technology had invented a gravitational-wave detector, in which mirrors hanging inside the corner and ends of an L-shaped vacuum pipe are pushed apart along one leg of the L by the stretch of space, and pushed together along the other leg by the squeeze of space. Rai proposed using laser beams to measure the oscillating pattern of this stretch and squeeze. The laser light could extract a gravitational wave’s information, and the signal could then be amplified and fed into a computer for human comprehension.
The study of the universe with electromagnetic telescopes (electromagnetic astronomy) was initiated by Galileo, when he built a small optical telescope, pointed it at Jupiter and discovered Jupiter’s four largest moons. During the 400 years since then, electromagnetic astronomy has completely revolutionised our understanding of the universe. "

Stephen Hawking , Brief Answers to the Big Questions