"A Brief History of Time" by Stephen Hawking

• 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.
• The eventual goal of science is to provide a single theory that describes the whole universe.
• In the theory of relativity there is no unique absolute time, but instead each individual has his own personal measure of time that depends on where he is and how he is moving.
• 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. They are the great intellectual achievements of the first half of this century.
• 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.
• The fundamental postulate of the theory of relativity was that the laws of science should be the same for all freely moving observers, no matter what their speed. This simple ideas has some remarkable consequences. Perhaps the best known are the equivalence of mass and energy, summed up in Einstein’s famous equation E = mc^2, and the law that nothing may travel faster than the speed of light.
• 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.
• 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.
• Einstein made the revolutionary suggestion that gravity is not a force like other forces, but is a consequence of the fact that spacetime is not flat, as had been previously assumed: it is curved, or “warped,” by the distribution of mass and energy in it.
• Another prediction of general relativity is that time should appear to run slower near a massive body like the earth.
• In the theory of relativity there is no unique absolute time, but instead each individual has his own personal measure of time that depends on where he is and how he is moving.
• We live in a galaxy that 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.
• The different frequencies of light are what the human eye sees as different colors, with the lowest frequencies appearing at the red end of the spectrum and the highest frequencies at the blue end.
• If the source [of light] is moving away from us, the frequency of the waves we receive will be lower. In the case of light, therefore, this means that stars moving away from us will have their spectra shifted toward the red end of the spectrum (red-shifted) and those moving toward us will have their spectra blue-shifted.
• The further a galaxy is, the faster it is moving away!
• The distance between the different galaxies is growing all the time.
• All our theories of science are formulated on the assumption that spacetime is smooth and nearly flat, so they break down at the big bang singularity, where the curvature of spacetime is infinite.
• Using the way light cones behave in general relativity together with the fact that gravity is always attractive, he [Roger Penrose] showed that a star collapsing under its own gravity is trapped in a region whose surface eventually shrinks to zero size. And, since the surface of the region shrinks to zero, so too must its volume. All the matter in the star will be compressed into a region of zero volume, so the density of matter and the curvature of spacetime become infinite. In other words, one has a singularity contained within a region of space-time known as a black hole.
• Heisenberg Principle--the more accurately you try to measure the position of a 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.
• Heisenberg’s uncertainty principle is a fundamental, inescapable property of the world.
• 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.
• We now know the neither the atoms nor the protons and neutrons within them indivisible.
• Quantum mechanics tells us that all particles are in fact waves.
• We now know that every particle has an antiparticle, with which it can annihilate.
• By the wave/particle duality of quantum mechanics, light can be regarded as both a wave and a particle. Under the theory that light is made up of waves, it was not clear how it would respond to gravity. But if light is comprised of particles, one might expect them to be affected by gravity in the same way that cannonballs, rockets, and planets are.
• The whole history of science had been the gradual realization that events do not happen in an arbitrary manner, but that they reflect a certain underlying order, which may or may not be divinely inspired.
• With the advent of quantum mechanics, we have come to recognize that events cannot be predicted with complete accuracy but that there is always a degree of uncertainty.
• The rate of progress is so rapid that what one learns at school or university is always a bit out of date.
• anthropic principle: We see the universe the way it is because if it were any different, we would not be here to observe it.
• general relativity: Einstein’s theory based on the idea that the laws of science should be the same for all observers, no matter how they are moving. It explains the force of gravity in terms of the curvature of a four-dimensional space-time.
• Planck’s quantum principle: The idea that light (or any other classical waves) can be emitted or absorbed only in discrete quanta, whose energy is proportional to their frequency.
• quantum mechanics: The theory developed from Planck’s quantum principle and Heisenberg’s uncertainty principle.
• special relativity: Einstein’s theory based on the idea that the laws of science should be the same for all freely moving observers no matter what their speed.
• uncertainty principle: One can never be exactly sure of both the position and the velocity of a particle; the more accurately one knows the one, the less accurately one can know the other.