# A Brief History of Time (Stephen Hawking)
* As we shall see, the concept of time has no meaning before the beginning of the universe. (p. 8)
* But in 1929, Edwin Hubble made the landmark observation that wherever you look, distant galaxies are moving rapidly away from us. In other words, the universe is expanding. (p. 9)
* The lack of an absolute standard of rest meant that one could not determine whether two events that took place at different times occurred in the same position in space. (p. 18)
* Both Aristotle and Newton believed in absolute time. That is, they believed that one could unambiguously measure the interval of time between two events, and that this time would be the same whoever measured it, provided they used a good clock. (p. 18)
* The fact that light travels at a finite, but very high, speed was first discovered in 1676 by the Danish astronomer Ole Christensen Roemer. (p. 19)
* The fundamental postulate of the theory of relativity, as it was called, was that the laws of science should be the same for all freely moving observers, no matter what their speed. This was true for Newton’s laws of motion, but now the idea was extended to include Maxwell’s theory and the speed of light: all observers should measure the same speed of light, no matter how fast they are moving. (p. 20)
* As an object approaches the speed of light, its mass rises ever more quickly, so it takes more and more energy to speed it up further. It can in fact never reach the speed of light, because by then its mass would have become infinite, and by the equivalence of mass and energy, it would have taken an infinite amount of energy to get it there. For this reason, any normal object is forever confined by relativity to move at speeds slower than the speed of light. Only light, or other waves that have no intrinsic mass, can move at the speed of light. (p. 21)
* In other words, the theory of relativity put an end to the idea of absolute time! It appeared that each observer must have his own measure of time, as recorded by a clock carried with him, and that identical clocks carried by different observers would not necessarily agree. (p. 22)
* We must accept that time is not completely separate from and independent of space, but is combined with it to form an object called space-time. (p. 23)
* Another prediction of general relativity is that time should appear to run slower near a massive body like the earth. (p. 33)
* Space and time not only affect but also are affected by everything that happens in the universe. Just as one cannot talk about events in the universe without the notions of space and time, so in general relativity it became meaningless to talk about space and time outside the limits of the universe. (p. 34)
* The discovery that the universe is expanding was one of the great intellectual revolutions of the twentieth century (p. 41)
* General relativity is only an incomplete theory: it cannot tell us how the universe started off, because it predicts that all physical theories, including itself, break down at the beginning of the universe. (p. 53)
* In other words, the more accurately you try to measure the position of the particle, the less accurately you can measure its speed, and vice versa. Heisenberg showed that the uncertainty in the position of the particle times the uncertainty in its velocity times the mass of the particle can never be smaller than a certain quantity, which is known as Planck’s constant. (p. 57)
* Heisenberg’s uncertainty principle is a fundamental, inescapable property of the world. (p. 57)
* In general, quantum mechanics does not predict a single definite result for an observation. Instead, it predicts a number of different possible outcomes and tells us how likely each of these is. (p. 58)
* Each electron, therefore, must be passing through both slits at the same time! (p. 61)
* A nice way of visualizing the wave/particle duality is the so-called sum over histories introduced by the American scientist Richard Feynman. (p. 62)
* Force-carrying particles can be grouped into four categories according to the strength of the force that they carry and the particles with which they interact. It should be emphasized that this division into four classes is man-made; it is convenient for the construction of partial theories, but it may not correspond to anything deeper. Ultimately, most physicists hope to find a unified theory that will explain all four forces as different aspects of a single force. (p. 72)
* But a machine that was powerful enough to accelerate particles to the grand unification energy would have to be as big as the Solar System – and would be unlikely to be funded in the present economic climate. Thus it is impossible to test grand unified theories directly in the laboratory. However, just as in the case of the electromagnetic and weak unified theory, there are low-energy consequences of the theory that can be tested. (p. 76)
* The most interesting of these is the prediction that protons, which make up much of the mass of ordinary matter, can spontaneously decay into lighter particles such as antielectrons. (p. 77)
* We therefore believe that all galaxies are composed of quarks rather than antiquarks; it seems implausible that some galaxies should be matter and some antimatter. (p. 79)
* Black holes are one of only a fairly small number of cases in the history of science in which a theory was developed in great detail as a mathematical model before there was any evidence from observations that it was correct. (p. 95)
* How is it possible that a black hole appears to emit particles when we know that nothing can escape from within its event horizon? The answer, quantum theory tells us, is that the particles do not come from within the black hole, but from the ‘empty’ space just outside the black hole’s event horizon! (p. 109)
* A flow of negative energy into the black hole therefore reduces its mass. As the black hole loses mass, the area of its event horizon gets smaller, but this decrease in the entropy of the black hole is more than compensated for by the entropy of the emitted radiation, so the second law is never violated. (p. 110)
* What happens when the mass of the black hole eventually becomes extremely small is not quite clear, but the most reasonable guess is that it would disappear completely in a tremendous final burst of emission, equivalent to the explosion of millions of H-bombs. (p. 111)
* The existence of radiation from black holes seems to imply that gravitational collapse is not as final and irreversible as we once thought. (p. 116)
* The earth was initially very hot and without an atmosphere. In the course of time it cooled and acquired an atmosphere from the emission of gases from the rocks. This early atmosphere was not one in which we could have survived. It contained no oxygen, but a lot of other gases that are poisonous to us, such as hydrogen sulfide (the gas that gives rotten eggs their smell). There are, however, other primitive forms of life that can flourish under such conditions. It is thought that they developed in the oceans, possibly as a result of chance combinations of atoms into large structures, called macromolecules, which were capable of assembling other atoms in the ocean into similar structures. They would thus have reproduced themselves and multiplied. In some cases there would be errors in the reproduction. Mostly these errors would have been such that the new macromolecule could not reproduce itself and eventually would have been destroyed. However, a few of the errors would have produced new macromolecules that were even better at reproducing themselves. They would have therefore had an advantage and would have tended to replace the original macromolecules. In this way a process of evolution was started that led to the development of more and more complicated, self-reproducing organisms. The first primitive forms of life consumed various materials, including hydrogen sulfide, and released oxygen. This gradually changed the atmosphere to the composition that it has today, and allowed the development of higher forms of life such as fish, reptiles, mammals, and ultimately the human race. (p. 124)
* This is an example of the application of what is known as the anthropic principle, which can be paraphrased as, ‘We see the universe the way it is because we exist.’ (p. 128)
* However, suppose that only in the smooth regions were galaxies and stars formed and were conditions right for the development of complicated self-replicating organisms like ourselves who were capable of asking the question: why is the universe so smooth? (p. 128)
* Few people would quarrel with the validity or utility of the weak anthropic principle. Some, however, go much further and propose a strong version of the principle. According to this theory, there are either many different universes or many different regions of a single universe, each with its own initial configuration and, perhaps, with its own set of laws of science. (p. 129)
* Thus, in a sense, the gravitational field has negative energy. In the case of a universe that is approximately uniform in space, one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter. So the total energy of the universe is zero. (p. 133)
* This work on inflationary models showed that the present state of the universe could have arisen from quite a large number of different initial configurations. This is important, because it shows that the initial state of the part of the universe that we inhabit did not have to be chosen with great care. (p. 137)
* I’d like to emphasize that this idea that time and space should be finite ‘without boundary’ is just a proposal: it cannot be deduced from some other principle. Like any other scientific theory, it may initially be put forward for aesthetic or metaphysical reasons, but the real test is whether it makes predictions that agree with observation. (p. 141)
* If the universe really is in such a quantum state, there would be no singularities in the history of the universe in imaginary time. It might seem therefore that my more recent work had completely undone the results of my earlier work on singularities. But, as indicated above, the real importance of the singularity theorems was that they showed that the gravitational field must become so strong that quantum gravitational effects could not be ignored. This in turn led to the idea that the universe could be finite in imaginary time but without boundaries or singularities. When one goes back to the real time in which we live, however, there will still appear to be singularities. The poor astronaut who falls into a black hole will still come to a sticky end; only if he lived in imaginary time would he encounter no singularities. (p. 143)
* But if the universe is really completely self-contained, having no boundary or edge, it would have neither beginning nor end: it would simply be. What place, then, for a creator? (p. 146)
* Our subjective sense of the direction of time, the psychological arrow of time, is therefore determined within our brain by the thermodynamic arrow of time. Just like a computer, we must remember things in the order in which entropy increases. This makes the second law of thermodynamics almost trivial. Disorder increases with time because we measure time in the direction in which disorder increases. You can’t have a safer bet than that! (p. 151)
* To summarize, the laws of science do not distinguish between the forward and backward directions of time. However, there are at least three arrows of time that do distinguish the past from the future. They are the thermodynamic arrow, the direction of time in which disorder increases; the psychological arrow, the direction of time in which we remember the past and not the future; and the cosmological arrow, the direction of time in which the universe expands rather than contracts. I have shown that the psychological arrow is essentially the same as the thermodynamic arrow, so that the two would always point in the same direction. The no boundary proposal for the universe predicts the existence of a well-defined thermodynamic arrow of time because the universe must start off in a smooth and ordered state. And the reason we observe this thermodynamic arrow to agree with the cosmological arrow is that intelligent beings can exist only in the expanding phase. The contracting phase will be unsuitable because it has no strong thermodynamic arrow of time. (p. 156)
* We can accelerate particles to 99.99 percent of the speed of light, but however much power we feed in, we can’t get them beyond the speed-of-light-barrier. Similarly with spaceships: no matter how much rocket power they have, they can’t accelerate beyond the speed of light. (p. 163)
* In other words, quantum theory allows the energy density to be negative in some places, provided that this is made up for by positive energy densities in other places, so that the total energy remains positive. (p. 164)
* Thus the radiation by black holes shows that quantum theory allows travel back in time on a microscopic scale and that such time travel can produce observable effects. (p. 170)
* Thus the possibility of time travel remains open. But I’m not going to bet on it. (p. 170)
* Eternal inflation and the no boundary proposal together predict that our universe is not unique. Instead, from the quantum fuzz at the big bang many different universes emerge, possibly with different local laws of physics and chemistry. We may not live in the most probable of all universes. Rather, we live in one where the conditions are favorable for complexity and the development of life. (p. 192)
* The no boundary proposal and eternal inflation point increasingly strongly to the idea that our universe is just one of many. (p. 192)