"SIX EASY PIECES: ESSENTIALS OF PHYSICS EXPLAINED BY ITS MOST BRILLIANT TEACHER" by Richard P. Feynman, Robert B. Leighton, Matthew Sands

• Science is a people-driven activity like all human endeavor, and just as subject to fashion and whim. In this case fashion is set not so much by choice of subject matter, but by the way scientists think about the world.
• Theoretical physics is one of the toughest intellectual exercises, combining abstract concepts that defy visualization with extreme mathematical complexity.
• A summation of his teaching philosophy was found among his papers in the Caltech archives, in a note he had scribbled to himself while in Brazil in 1952: First figure out why you want the students to learn the subject and what you want them to know, and the method will result more or less by common sense.
• It’s impossible to learn very much by simply sitting in a lecture, or even by simply doing problems that are assigned.
• Each piece, or part, of the whole of nature is always merely an approximation to the complete truth, or the complete truth so far as we know it. In fact, everything we know is only some kind of approximation, because we know that we do not know all the laws as yet.
• The principle of science, the definition, almost, is the following: The test of all knowledge is experiment. Experiment is the sole judge of scientific “truth.”
• all things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another.
• Now the jiggling motion is what we represent as heat: when we increase the temperature, we increase the motion.
• order to confine a gas we must apply a pressure.
• Air consists almost entirely of nitrogen, oxygen, some water vapor, and lesser amounts of carbon dioxide, argon, and other things.
• An ion is an atom which either has a few extra electrons or has lost a few electrons.
• Everything is made of atoms.
• From the point of view of basic physics, the most interesting phenomena are of course in the new places, the places where the rules do not work—not the places where they do work!
• The ultimate basis of an interaction between the atoms is electrical.
• the chemical properties depend upon the electrons on the outside, and in fact only upon how many electrons there are.
• Magnetic influences have to do with charges in relative motion, so magnetic forces and electric forces can really be attributed to one field, as two different aspects of exactly the same thing.
• The electromagnetic field can carry waves; some of these waves are light, others are used in radio broadcasts, but the general name is electromagnetic waves.
• The only thing that is really different from one wave to another is the frequency of oscillation.
• If we increase the frequency to 500 or 1000 kilocycles (1 kilocycle = 1000 cycles) per second, we are “on the air,” for this is the frequency range which is used for radio broadcasts.
• Instead, it was discovered that things on a small scale behave nothing like things on a large scale.
• there is a rule in quantum mechanics that says that one cannot know both where something is and how fast it is moving.
• it is not possible to predict exactly what will happen in any circumstance.
• We just have to take what we see, and then formulate all the rest of our ideas in terms of our actual experience.
• There is no distinction between a wave and a particle. So quantum mechanics unifies the idea of the field and its waves, and the particles, all into one.
• The fact that a particle has zero mass means, in a way, that it cannot be at rest. A photon is never at rest; it is always moving at 186,000 miles a second.
• To summarize it, I would say this: outside the nucleus, we seem to know all; inside it, quantum mechanics is valid—the principles of quantum mechanics have not been found to fail. The stage on which we put all of our knowledge, we would say, is relativistic space-time; perhaps gravity is involved in space-time. We do not know how the universe got started, and we have never made experiments which check our ideas of space and time accurately, below some tiny distance, so we only know that our ideas work above that distance.
• All proteins are not enzymes, but all enzymes are proteins.
• Proteins have a very interesting and simple structure. They are a series, or chain, of different amino acids.
• But the most remarkable discovery in all of astronomy is that the stars are made of atoms of the same kind as those on the earth.
• It is important to realize that in physics today, we have no knowledge of what energy is.
• The general name of energy which has to do with location relative to something else is called potential energy.
• In quantum mechanics it turns out that the conservation of energy is very closely related to another important property of the world, things do not depend on the absolute time.
• What is this law of gravitation? It is that every object in the universe attracts every other object with a force which for any two bodies is proportional to the mass of each and varies inversely as the square of the distance between them.
• First of all, Kepler found that each planet goes around the sun in a curve called an ellipse, with the sun at a focus of the ellipse.
• Kepler’s second observation was that the planets do not go around the sun at a uniform speed, but move faster when they are nearer the sun and more slowly when they are farther from the sun,
• Thus Kepler’s three laws are: I. Each planet moves around the sun in an ellipse, with the sun at one focus. II. The radius vector from the sun to the planet sweeps out equal areas in equal intervals of time. III. The squares of the periods of any two planets are proportional to the cubes of the semimajor axes of their respective orbits: T ∝ a3/2.
• Any great discovery of a new law is useful only if we can take more out than we put in.
• The moon pulls the water up under it and makes the tides—people
• If a law does not work even in one place where it ought to, it is just wrong.
• so far as we now know, gravity seems to go out forever inversely as the square of the distance.
• Even light, which has an energy, has a “mass.”
• “Quantum mechanics” is the description of the behavior of matter in all its details and, in particular, of the happenings on an atomic scale.

"SEVEN BRIEF LESSONS ON PHYSICS" by Carlo Rovelli

• The gravitational field is not diffused through space; the gravitational field is that space itself. This is the idea of the general theory of relativity. Newton’s “space,” through which things move, and the “gravitational field” are one and the same thing.
• A momentous simplification of the world: space is no longer something distinct from matter—it is one of the “material” components of the world.
• Planets circle around the sun, and things fall, because space curves.
• Space curves where there is matter.
• The whole of space can expand and contract.
• Einstein’s equation shows that space cannot stand still; it must be expanding.
• space and gravitational field are the same thing.
• Einstein showed that light is made of packets: particles of light. Today we call these “photons.”
• In quantum mechanics no object has a definite position, except when colliding headlong with something else.
• Science begins with a vision.
• Scientific thought is fed by the capacity to “see” things differently than they have previously been seen.
• The things we see are made of atoms. Every atom consists of a nucleus surrounded by electrons. Every nucleus consists of tightly packed protons and neutrons.
• Electrons, quarks, photons, and gluons are the components of everything that sways in the space around us. They are the “elementary particles” studied in particle physics.
• There is no such thing as a real void, one that is completely empty.
• Quantum mechanics and experiments with particles have taught us that the world is a continuous, restless swarming of things, a continuous coming to light and disappearance of ephemeral entities.
• Our world may have actually been born from a preceding universe that contracted under its own weight until it was squeezed into a tiny space before “bouncing” out and beginning to re-expand, thus becoming the expanding universe that we observe around us.
• A hot substance is a substance in which atoms move more quickly.
• Cold air is air in which atoms, or rather molecules, move more slowly. Hot air is air in which molecules move more rapidly.
• Heat, as we know, always moves from hot things to cold.
• Friction produces heat.
• The difference between past and future exists only when there is heat. The fundamental phenomenon that distinguishes the future from the past is the fact that heat passes from things that are hotter to things that are colder.
• Heat does not move from hot things to cold things due to an absolute law: it does so only with a large degree of probability. The reason for this is that it is statistically more probable that a quickly moving atom of the hot substance collides with a cold one and leaves it a little of its energy, rather than vice versa.
• It is not impossible for a hot body to become hotter through contact with a colder one: it is just extremely improbable.
• To trust immediate intuitions rather than collective examination that is rational, careful, and intelligent is not wisdom: it is the presumption of an old man who refuses to believe that the great world outside his village is any different from the one that he has always known.
• There is a detectable difference between the past and the future only when there is the flow of heat.
• To be free doesn’t mean that our behavior is not determined by the laws of nature. It means that it is determined by the laws of nature acting in our brains.
• Our free decisions are freely determined by the results of the rich and fleeting interactions among the billion neurons in our brain: they are free to the extent that the interaction of these neurons allows and determines.
• There is not an “I” and “the neurons in my brain.” They are the same thing. An individual is a process: complex, tightly integrated.
• It is not against nature to be curious: it is in our nature to be so.
• Life is precious to us because it is ephemeral.

"The Little Book of Scientific Principles, Theories, & Things" by Surendra Verma

• A postulate (or axiom) claims something is true or is the basis for an argument. A theorem is a proven proposition, which is a statement with logical constraints.
• Archimedes Principle explains why things float. If an object is less dense than the fluid that surrounds it (that is, it weighs less than an equal volume of the fluid), it will float, since the apparent loss of weight will be greater than its weight in air. If it is denser than the fluid, the apparent loss in weight will be less than its weight in air and it will sink.
• All circles are similar and the ratio of the circumference to the diameter of a circle is always the same number, known as the constant pi.
• It is impossible to find the exact value of pi; however, the value can be calculated to any required degree of accuracy.
• Fibonacci numbers: A series of numbers in which each successive term is the sum of the preceding two. The ratio of successive terms approaches the number 1.618. This ratio is known as the golden ratio and is denoted by the Greek letter phi.
• Ockham’s Razor: This guiding principle in developing scientific ideas insists that you should prefer the simplest explanation to fit the facts. In other words, the explanation requiring the fewest assumptions is most likely to be correct.
• Scientific laws must be based on observations and experiments.
• The essence of his [Bacon’s Scientific Method] is as follows: collect masses of facts by observations and experiments, analyze facts by drawing up tables of negative, affirmative, and variable instances of the phenomenon, draw hypotheses from the evidence, collect further evidence to proceed toward a more general theory. The most important aspect of this method was the idea of drawing up tentative hypothesis from available data and then verifying them by further investigations.
• Refraction is the change in direction of a ray of light when it crosses the boundary between two media. It happens because light has different speeds in different media.
• Pascal’s Law: When pressure is applied anywhere to an enclosed fluid, it is transmitted uniformly in all directions.
• Light, but not sound, can travel through a vacuum.
• Calculus has now become an important branch of mathematics dealing with the behavior of functions.
• Newton’s Law of Gravitation: Any two bodies attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
• Newton’s Laws of Motion:
• An object at rest will remain at rest and an object in motion will remain in motion at that velocity until an external force acts on the object.
• The sum of all the forces (F) that act on an object is equal to the mass (m) of the object multiplied by the acceleration, or F = ma.
• To every action, there is an equal and opposite reaction.
• We now know that biological clocks are an internal timing system that regulates metabolism in all forms of life.
• Hundreds of cellular, physiological, and behavioral patterns have been observed to follow a 24-hour cycle in humans. For this reason the biological clock is also called circadian rhythm (from the Latin circa diem, about a day).
• Bernoulli’s Principle: As the velocity of a liquid or gas increases, its pressure decreases; and when the velocity increases, its pressure increases. It can be summed up simply as the faster the flow the lower the pressure.
• The Celsius Temperature Scale: The temperature difference between the freezing point and the boiling point of water is a hundred degrees.
• The mnemonic, My Very Educated Mother Just Served Us Nine Pizzas, may help you to remember the order of nine planets, outwards from the sun.
• In an arithmetic series of numbers there is common difference between any number and its successor, while in a geometric series each number is a constant multiple of the preceding number.
• Young’s Principle of Interference: Interference between waves can be constructive or destructive. Two identical waves traveling together either reinforce each other (constructive interference) or cancel each other out (destructive interference).
• Oersted’s Theory of Electromagnetism: Electric current produces a magnetic field.
• The distant galaxies are moving away from us at a speed so high that it diminishes the intensity of light we receive from them.
• Ampere’s Law: Two current-carrying wires attract each other if their currents are in the same direction, but repel if their currents are opposite. The force of attraction or repulsion is directly proportional to the strength of the current and inversely proportional to the square of the distance between them.
• Ohm’s Law: The electric current in a conductor is proportional to the potential difference.
• Faraday’s Law of Induction: A changing magnetic field around a conductor produces an electric current in the conductor. The size of the voltage is proportional to the rate of change of the magnetic field.
• Gases have no fixed volume; they expand to fill the entire volume of their container.
• Gauss’ Law: The electric flux through a closed surface is proportional to the sum of the electric charges within the surface.
• Doppler Effect:; Any source of sound or light moving away from an observer changes in frequency with reference to the observer.
• First Law of Thermodynamics: Heat is a form of energy and energy is conserved. It’s simply a restatement of the law of conservation of energy: energy is neither created nor destroyed, but may be changed from one form to another.
• Kirchhoff’s Laws:
• At any junction point in an electrical circuit, the sum of all currents entering the junction must equal the sum of all currents leaving the junction.
• For any closed loop in an electrical circuit, the sum of the voltages must add up to zero.
• Second Law of Thermodynamics: Heat does not flow spontaneously from a colder to a hotter body.
• The third law of thermodynamics dictates that it is impossible to cool an object to a temperature of absolute zero.
• Boolean Logic: Logical operations can be expressed in mathematical symbols rather than words and can be solved in a manner similar to ordinary algebra.
• Boolean algebra has three main logical operations: NOT, AND, OR.
• Darwin’s Theory of Evolution: All present-day species have evolved from simpler forms of life through a process of natural selection.
• Evolution through natural selection is opportunistic and it takes place steadily.
• Four equations [Maxwell’s Equations] that express mathematically the way electric and magnetic fields behave.
• The equations [Maxwell’s Equations] are complex, but in simple words they describe:
• a general relationship between electric field and electric charge
• a general relationship between magnetic field and magnetic poles
• how a changing magnetic field produces electric current
• how an electric current or a changing electric field produces a magnetic field
• Radio waves can be produced by electric sparks. They have the same speed as light and behave the same as light. We are now familiar with all the types of electromagnetic waves that make up the complete electromagnetic spectrum they all travel with the speed of light and differ from each other in their frequency -- and we measure this frequency in hertz (Hz), a unit named in Hertz's honor.
• The transmission of high-voltage alternating current (AC) over long distances is more efficient than the transmission of direct current (DC).
• Quantum Theory: Energy is not a continuous quantity but it is quantized, that is, it flows in discrete bundles or quanta (singular quantum). When particles emit energy they do so only in quanta.
• Special Theory of Relativity
• The relativity principle: All laws of science are the same in all frames of reference.
• Constancy of the speed of light: The speed of light in a vacuum is constant and is independent of the speed of the observer.
• The theory [Special Relativity] says that time is not an absolute quantity. Our measurements of time are affected by our motion.
• The theory [Special Relativity] also says that the mass of a moving object increases as its speed increases. At the speed of light, which is about 186,300 miles per second, the mass becomes infinite and therefore nothing can move faster than light.
• The energy of a body (E) equals its mass (m) times the speed of light (c) squared.
• Mass and energy are mutually convertible under certain conditions.
• The mass-energy equation is a consequence of Einstein’s theory of special relativity.
• Superconductivity: At very low temperature, some materials conduct electricity without any resistance; that is, virtually without any loss of energy.
• Theory of General Relativity: Objects do not attract each other by exerting pull, but the presence of matter in space causes space to curve in such a manner that a gravitational field is set up. Gravity is the property of space itself.
• In quantum mechanics, elementary particles can, in some instances, behave like waves. The waves - which are really waves of probability - describe where a particle is most likely to be at a given moment.
• Heisenberg’s Uncertainty Principle: It is impossible to determine exactly both the position and momentum of a particle (such as an electron) simultaneously.
• Dirac’s Antimatter Theory: Every fundamental particle has an antiparticle -- a mirror twin with the same mass but opposite charge.
• When antimatter and ordinary matter meet, they annihilate each other and disappear in a violent explosion in which mass is converted into energy as dictated by Einstein’s equation E = mc^2.
• Hubble’s Law: Galaxies are moving away from us and each other at an ever-increasing rate. The more distant the galaxy, the faster it is moving away.
• Asimov’s Three Laws of Robotics
• A robot may not injure a human being or, through inaction, allow a human being to come to harm.
• A robot must obey orders given it by human beings, except where such orders would conflict with the first law.
• A robot must protect its own existence as long as such protection does not conflict with the first or second law.
• Radiocarbon Dating: The radioactive isotope of carbon, carbon-14, is present in all living things. When life stops carbon-14 begins to decay. From the rate of decay, the age (or time of death) of an organism can be calculated.
• The Big Bang Theory: The universe began when a single point of infinitely dense and infinitely hot matter exploded spontaneously.
• Murphy’s Law: If anything can go wrong, it will.
• Moore’s Law: The number of transistors on a computer chip doubles every 18 months or so.
• The Scientific Method involves the following:
• observations and search for data
• hypothesis to explain observations
• experiments to test hypothesis
• formulation of theory
• experimental confirmation of theory
• mathematical or empirical confirmation of theory into scientific law
• use of scientific law to predict behavior of nature
• Hypothesis -- a tentative explanation of observed facts. Every theory or law in science begins as a hypothesis.
• Theory -- a theory is a hypothesis that has been tested by experiments, and to which exceptions have been found.
• Scientific Law -- a theory that has been verified mathematically.

"God and the New Physics" by Paul Davies

• Science and religion represent two great systems of human thought. For the majority of people on our planet, religion is the predominant influence over the conduct of their affairs.
• If religion has been displaced from people’s consciousness, it has certainly not been replaced by rational scientific thought.
• If the Church is largely ignored today it is not because science has finally won its age-old battle with religion, but because it has so radically reoriented our society that the biblical perspective of the world now seems largely irrelevant.
• The world’s major religions, founded on received wisdom and dogma, are rooted in the past and do not cope easily with changing times.
• The vast majority of people do not understand scientific principles, nor are they interested.
• Lip service may be paid to the importance of science and rational thought for ordering our society, but at the personal level most people still find religious doctrine more persuasive than scientific arguments.
• We live in a world that, in spite of appearances, is still fundamentally religious.
• No religion that bases its beliefs on demonstrably incorrect assumptions can expect to survive very long.
• It is ironical that although most religious extol the virtues of love, peace and humility, it is all too often hatred, war and arrogance that characterize the history of the world’s great religious organizations.
• The early attempts by the Church to hold back the floodgates of scientific advance have left a deep suspicion of religion among the scientific community. For their part, scientists have demolished a lot of cherished religious beliefs and have come to be regarded by many as faith-wreckers.
• Religion is founded on revelation and received wisdom.
• The trouble about revealed ‘Truth’ is that it is liable to be wrong, and even if it is right other people require a good reason to share the recipient's’ belief.
• Either the universe has always existed (in one form or another) or it began, more or less abruptly, at some particular moment in the past.
• The universe will eventually die, wallowing, as it were, in its own entropy. This is known among physicists as the ‘heat death’ of the universe.
• The universe cannot have existed for ever, otherwise it would have reached its equilibrium end state an infinite time ago. Conclusion: the universe did not always exist.
• Stars form, along with planets, as a result of the gradual contraction and fragmentation of huge, tenuous clouds of interstellar gas which consist mainly of hydrogen.
• The force of gravity powers all large-scale cosmic phenomena.
• The first instant of the big bang, where space was infinitely shrunken, represents a boundary or edge in time at which space ceases to exist. Physicists call such a boundary a singularity.
• To the physicist ‘nothing’ means ‘no space’ as well as no matter.
• Space is inextricably linked to time, and as space stretches and shrinks, so does time.
• By employing mathematics as a language, science can describe situations which are completely beyond the power of human beings to imagine.
• Failure of the human imagination to grasp certain crucial features of reality is a warning that we cannot expect to base great religious truths (such as the nature of the creation) on simple-minded ideas of space, time and matter, gleaned from daily experience.
• Hydrogen and helium together constitute over ninety-nine percent of the material in the universe.
• When antimatter encounters matter, the two annihilate each other with a violent release of energy -- the reverse process of matter creation.
• The cosmological argument is founded on the assumption that everything requires a cause, yet ends in the conclusion that at least one thing (God) does not require a cause.
• Today we know that time is linked inseparably to space, and that space-time is as much a part of the physical universe as matter.
• We may say that God is not so much a cause of the universe as an explanation.
• Atoms do not need to be ‘animated’ to yield life, they simply have to be arranged in the appropriate complex way.
• The earth is approximately 4.5 billion years old. Traces of developed life exist in the fossil record back to at least 3.5 billion years, and presumably some form of primitive life existed before this.
• In an infinite universe, anything that is possible must happen somewhere by pure chance.
• The existence of extraterrestrial intelligences would have a profound impact on religion, shattering completely the traditional perspective of God’s special relationship with man.
• At the neural (brain cell) level, the human brain is equally mechanical and subject to rational principles, yet this does not prevent us from experiencing feelings of indecision, confusion, happiness, boredom and irrationality.
• The materialist believes that mental states and operations are nothing but physical states and operations. At the other extreme is the philosophy of idealism which asserts that it is the physical world that does not exist; everything is perception.
• Axioms are the things you assume are true without proof (e.g. 1=1).
• There seems to be no scientific evidence for any special divine quality in man, and no fundamental reason is apparent why an advanced electronic machine should not, in principle, enjoy similar feelings of consciousness as ourselves.
• You can’t know where an atom, or electron, or whatever, is located and know how it is moving, at one and the same time.
• Einstein demonstrated that time is, in fact, elastic and can be stretched and shrunk by motion.
• Equally extraordinary effect afflict space, which is also elastic.
• When time is stretched, space is shrunk.
• The mutual distortions of space and time can be regarded as a conversion of space (which shrinks) into time (which stretches).
• The strong force glues the nuclear particles together, but there is also a very much weaker force. The weak force is responsible for causing some of the unstable nuclear particles to decay.
• The underlying assumption of the quark theory is that the quarks themselves are truly structureless, fundamental particles -- point-like objects with no internal parts.
• Leptons feel the weak force, quarks feel the strong force.
• Subatomic particles can be divided into two broad classes: leptons and quarks. Quarks are not found individually, but united in groups of two or three; they have fractional electric charge.
• Evolution of biological order by mutation and natural selection is now accepted virtually unanimously by scientists and theologians alike.
• However persuasive they may seem, arguments for the existence of God based on cosmology or suggestions of design in the natural world, are at best indirect.
• The ability of the scientific method to accommodate change in the light of new discoveries represents one of science’s great strengths.
• Religion is founded on dogma and received wisdom, which purports to represent immutable truth.

"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.

"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.