"A Briefer History of Time" by Stephen Hawking

• In one second, a beam of light will travel 186,000 miles, so a light-year is a very long distance.
• The nearest star, other than our sun, is called Proxima Centauri (also known as Alpha Centauri C), which is about four light-years away.
• The fact that a ship’s masts, rising high above the hull, are the first part of the ship to poke up over the horizon is evidence that the earth is a ball.
• A theory is a good theory if it satisfies two requirements. It must accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements, and it must make definite predictions about the results of future observations.
• Any physical theory is always provisional, in the sense that it is only a hypothesis: you can never prove it. On the other hand, you can disprove a theory by finding even a single observation that disagrees with the predictions of the theory.
• The eventual goal of science is to provide a single theory that describes the whole universe.
• Today scientists describe the universe in terms of two basic partial theories--the general theory of relativity and quantum mechanics.
• The general theory of relativity describes the force of gravity and the large-scale structure of the universe.
• Quantum mechanics deals with phenomena on extremely small scales.
• One of the major endeavours in physics today, and the major theme of this book, is the search for a new theory that will incorporate them both [general relativity and quantum mechanics]--a quantum theory of gravity.
• The real effect of a force is always to change the speed of a body.
• Whenever a body is not acted on by any force, it will keep on moving in a straight line at the same speed.
• The body will accelerate, or change its speed, at a rate that is proportional to the force.
• Every body attracts every other body with a force that is proportional to the mass of each body.
• Newton’s law of gravity also tells us that the farther apart the bodies, the lesser the force.
• The concept of motion makes sense only as it relates to other objects.
• The kinetic energy of a moving object is identical to the energy you must expend in causing it to move.
• Only light, or other waves that have no intrinsic mass, can move at the speed of light.
• Maxwell’s equations predicted that there could be wavelike disturbances in the electromagnetic field and that these waves would travel at a fixed speed, like ripples on a pond. When he calculated this speed, he found it to match exactly the speed of light!
• Waves with wavelengths shorter than those of visible light are now known as ultraviolet light, X-rays, and gamma rays. Waves with longer wavelengths are called radio waves (a meter or more), microwaves (around a centimeter), or infrared radiation (less than one ten-thousandth of a centimeter but more than the visible range).
• Maxwell’s theory implied that radio or light waves would travel at a certain fixed speed.
• Einstein’s fundamental postulate of the theory of relativity, as it was called, stated that the laws of science should be the same for all freely moving observers, no matter what their speed.
• The requirement that all observers must agree on how fast light travels forces us to change our concept of time.
• The theory of relativity requires us to put an end to the idea of absolute time! Instead, each observer must have his own measure of time, as recorded by a clock carried with him, and identical clocks carried by different observers need not agree.
• 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.
• In the spacetime of relativity, any event--that is, anything that happens at a particular point in space and at a particular time--can be specified by four numbers or coordinates.
• Another well-known consequence of relativity is the equivalence of mass and energy, summed up in Einstein’s famous equation E=mc^2.
• The equation also tells us that if the energy of an object increases, so does its mass, that is, its resistance to acceleration, or change in speed.
• The kinetic energy of a moving object is identical to the energy you must expend in causing it to move. Therefore, the faster an object moves, the more kinetic energy it possess. But according to the equivalence of energy and mass, kinetic energy adds to an object’s mass, so the faster an object moves, the harder it is to further increase the object’s speed.
• 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. According to the theory of relativity, an object 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.
• Only light, or other waves that have no intrinsic mass, can move at the speed of light.
• Einstein’s theory of general relativity is based on the revolutionary suggestion that gravity is not a force like other forces but a consequence of the fact that spacetime is not flat, as had been previously assumed. In general relativity, spacetime is curved, or “warped,” by the distribution of mass and energy in it. Bodies such as the earth are not made to move on curved orbits by a force called gravity; instead they move in curved orbits because they follow the nearest thing to a straight path in a curved space, which is called a geodesic.
• In general relativity, bodies always follow geodesics in four-dimensional space-time. In the absence of matter, these geodesics in four-dimensional spacetime correspond to straight lines in three-dimensional space.
• Light rays too must follow geodesics in spacetime.
• General relativity predicts that gravitational fields should bend light.
• Another prediction of general relativity is that time should appear to run slower near a massive body such as the earth.
• In the theory of relativity there is no unique absolute time; instead, each individual has his own personal measure of time that depends on where he is and how he is moving.
• The nearest star, Proxima Centauri, is about four light-years, or twenty-three million million miles, away. Most of the other stars that are visible to the naked eye lie within a few hundred light-years of us. Our sun, for comparison, is a mere eight light-minutes away!
• We now know that the Milky Way--our galaxy--is about one hundred thousand light-years across and is slowly rotating; the stars in its spiral arms orbit around its center about once every several hundred million years. Our sun is just an ordinary, average-sized yellow star near the inner edge of one of the spiral arms.
• We can see about five thousand stars, only about .0001 percent of all the stars in just our own galaxy, the Milky Way. The Milky Way itself is but one of more than a hundred billion galaxies that can be seen using modern telescopes--and each galaxy contains on average some one hundred billion stars.
• Any material body, such as a star, will give off light or other radiation when heated. The light such glowing objects give off is due to the thermal motion of the atoms within them. It is called blackbody radiation. The spectrum of blackbody radiation is hard to mistake: it has a distinctive form that varies with the temperature of the body. The light emitted by a glowing object is therefore like a thermometer reading.
• Since we know that each chemical element absorbs a characteristic set of very specific colors, by matching these to those that are missing from a star’s spectrum we can determine exactly which elements are present in that star’s atmosphere.
• To physicists, the shifting of color or frequency is known as the Doppler effect.
• The different wavelengths of light are what the human eye sees as different colors, with the longest wavelengths appearing at the red end of the spectrum and the shortest wavelengths at the blue end.
• The further a galaxy is, the faster it is moving away!
• It is in fact expanding; the distance between the different galaxies all the time.
• The discovery that the universe is expanding was one of the great intellectual revolutions of the twentieth century.
• Even if at some time the universe had been static, it wouldn’t have remained static because the mutual gravitational attraction of all the stars and galaxies would soon have started it contracting. In fact, even if the universe was expanding fairly slowly, the force of gravity would cause it eventually to stop expanding, and it would start to contract. However, if the universe was expanding faster than a certain critical rate, gravity would never be strong enough to stop it, and it would continue to expand forever.
• The amount of dark matter greatly exceeds the amount of ordinary matter in the universe.
• There appears to be far less matter in the universe than would be needed to halt its expansion.
• The universe will continue to expand at an ever-increasing rate.
• All our theories of cosmology are formulated on the assumption that spacetime is smooth and nearly flat. That means that all our theories break down at the big bang: a spacetime with infinite curvature can hardly be called nearly flat! Thus even if there were events before the big bang, we could not use them to determine what would happen afterward, because predictability would have broken down at the big bang. Correspondingly, if, as is the case, we know only what has happened since the big bang, we cannot determine what happened beforehand.
• Atoms are made of smaller particles: electrons, protons, and neutrons. The protons and neutrons themselves are made of yet smaller particles called quarks. In addition, corresponding to each of these subatomic particles there exists an antiparticle. Antiparticles have the same mass as their sibling particles but are opposite in their charge and other attributes.
• When an antiparticle and particle meet, they annihilate each other.
• Light energy comes in the form of another type of particle, a mass-less particle called a photon.
• The strong force is a short-range attractive force that can cause protons and neutrons to bind to each other, forming nuclei.
• Absolute zero, -273 degrees Celsius, is the temperature at which substances contain no heat energy, and thus the lowest possible temperature.
• Paradoxically, the more fuel a star starts off with, the sooner it runs out. This is because the more massive the star is, the hotter it needs to be to balance its gravitational attraction. And the hotter the star, the faster the nuclear fusion reaction and the sooner it will use up its fuel.
• When a star runs out of fuel, it starts to cool off and gravity takes over, causing it to contract.
• By the wave/particle duality of quantum mechanics, light can be regarded as both a wave and a particle. The descriptors wave and particle are concepts humans created, not necessarily concepts that nature is obliged to respect by making all phenomena fall into one category or the other!
• The speed required to escape from the gravitational field of a large body is called the minimum escape velocity. The escape velocity of a star depends on the strength of its gravitational pull. The more massive the star, the greater its escape velocity.
• If the star is massive enough, the speed of light will be less than the star’s escape velocity, and all light emitted by the star will fall back into it.
• A star that was sufficiently massive and compact would have such a strong gravitational field that light could not escape: any light emitted from the surface of the star would be dragged back by the star’s gravitational attraction before it could get very far. Such objects are what we now call black holes, because that is what they are: black voids in space.
• According to the theory of relativity, nothing can travel faster than light. Thus if light cannot escape, neither can anything else: everything is dragged back by the gravitational field. The collapsed star has formed a region of spacetime around it from which it is not possible to escape to reach a distant observer. This region is the black hole. The outer boundary of a black hole is called the event horizon.
• Because mathematics cannot really handle infinite numbers, by predicting that the universe began with the big bang, a time when the density of the universe and the curvature of spacetime would have been infinite, the theory of general relativity predicts that there is a point in the universe where the theory itself breaks down, or fails. Such a point is an example of what mathematicians call a singularity. When a theory predicts singularities such as infinite density and curvature, it is a sign that the theory must somehow be modified. General relativity is an incomplete theory because it cannot tell us how the universe started off.
• The higher the frequency of light, the greater its energy content.
• The uncertainty principle tells us that, contrary to Laplace’s belief, nature does impose limits on our ability to predict the future using scientific law.
• The more accurately you try to measure the position of the particle, the less accurately you can measure its speed, and vice versa.
• Heisenberg’s uncertainty principle is a fundamental, inescapable property of the world, and it has had profound implications for the way in which we view the world.
• One of the most important implications of Heisenberg’s uncertainty principle is that particles behave in some respects like waves.
• An important consequence of wave like behaviour in quantum mechanics is that one can observe what is called interference between two sets of particles.
• Quantum theory has been an outstandingly successful theory and underlies nearly all of modern science and technology. It governs the behavior of transistors and integrated circuits, which are the essential components of electronic devices such as televisions and computers, and it is also the basis of modern chemistry and biology.
• If you can travel faster than light, the theory of relativity implies you can also travel back in time.
• A wormhole is a thin tube of spacetime that can connect two nearly flat regions far apart.
• So wormholes, like any other possible form of travel faster than light, would allow you to travel into the past.
• In quantum mechanics, the forces or interactions between matter particles are all supposed to be carried by particles.
• Each force is transmitted by its own distinctive type of force-carrying particle.
• The force-carrying particles exchanged between matter particles are said to be virtual particles because, unlike real particles, they cannot be directly detected by a particle detector. We know they exists, however, because they do have a measurable effect: they give rise to forces between matter particles.
• Before string theory, each of the fundamental particles was thought to occupy a single point of space. In string theories, the basic objects are not point particles but things that have a length but no other dimension, like an infinitely thin piece of string.
• There are two version of the anthropic principle, the weak and the strong.
• The weak anthropic principle states that in a universe that is large or infinite in space and/or time, the conditions necessary for the development of intelligent life will be met only in certain regions that are limited in space and time. The intelligent beings in these regions should not be surprised if they observe that their locality in the universe satisfies the conditions that are necessary for their existence.
• The strong anthropic 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.
• Sometimes, when a very massive star collapses, the outer regions of the star may get blown off in a tremendous explosion called a supernova.
• In a supernova, some of the heavier elements produced near the end of the star’s life are flung back into the galaxy and provide some of the raw material for the next generation of stars.
• We certainly cannot predict future events exactly if we cannot even measure the present state of the universe precisely!
• One of the revolutionary properties of quantum mechanics is that it 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.
• If you can travel with unlimited speed, you can also travel backward in time. One cannot be possible without the other.
• An antiparticle can be regarded as a particle traveling backward in time.
• With the advent of quantum mechanics, we have come to recognize that events cannot be predicted with complete accuracy: there is always a degree of uncertainty.
• The fact that gravity is always attractive implies that the universe must be either expanding or contracting.