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“There is a philosophy that says that if something is unobservable -- unobservable in principle -- it is not part of science. If there is no way to falsify or confirm a hypothesis, it belongs to the realm of metaphysical speculation, together with astrology and spiritualism. By that standard, most of the universe has no scientific reality -- it's just a figment of our imaginations.”
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
“Dick Feynman was a genius of visualization (he was also no slouch with equations): he made a mental picture of anything he was working on. While others were writing blackboard-filling formulas to express the laws of elementary particles, he would just draw a picture and figure out the answer.”
― The Cosmic Landscape: String Theory and the Illusion of Intelligent Design
― The Cosmic Landscape: String Theory and the Illusion of Intelligent Design
“There is so much to groak; So little to groak from.”
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
“the three-dimensional world of ordinary experience—the universe filled with galaxies, stars, planets, houses, boulders, and people—is a hologram, an image of reality coded on a distant two-dimensional surface. This new law of physics, known as the Holographic Principle, asserts that everything inside a region of space can be described by bits of information restricted to the boundary.”
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
“I would guess that there are limits to what we can understand. But old people always think there are limits to what we can understand. It's the young people who push past those limits.”
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“We often say that the earth is a sphere, but to be precise, the term sphere refers only to the surface. The correct mathematical term for the solid earth is a ball.”
― The Cosmic Landscape: String Theory and the Illusion of Intelligent Design
― The Cosmic Landscape: String Theory and the Illusion of Intelligent Design
“The great tragedy of science—the slaying of a beautiful hypothesis by an ugly fact.” — THOMAS HENRY HUXLEY”
― The Cosmic Landscape: String Theory and the Illusion of Intelligent Design
― The Cosmic Landscape: String Theory and the Illusion of Intelligent Design
“If a system is chaotic (most are), then it implies that however good the resolving power may be, the time over which the system is predictable is limited. Perfect predictability is not achievable, simply because we are limited in our resolving power.”
― The Theoretical Minimum: What You Need to Know to Start Doing Physics
― The Theoretical Minimum: What You Need to Know to Start Doing Physics
“Before World War II, when physics was primarily a European enterprise, physicists used the Greek language to name particles. Photon, electron, meson, baryon, lepton, and even hadron originated from the Greek. But later brash, irreverent, and sometimes silly Americans took over, and the names lightened up. Quark is a nonsense word from James Joyce’s Finnegan’s Wake, but from that literary high point, things went downhill. The distinctions between the different quark types are referred to by the singularly inappropriate term flavor. We might have spoken of chocolate, strawberry, vanilla, pistachio, cherry, and mint chocolate chip quarks but we don’t. The six flavors of quarks are up, down, strange, charmed, bottom, and top. At one point, bottom and top were considered too risqué, so for a brief time they became truth and beauty.”
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
“Unforeseen surprises are the rule in science, not the exception. Remember: Stuff happens.”
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“Quantum mechanics can be appreciated, to some degree, on a purely qualitative level. But mathematics is what brings its beauty into sharp focus. We have tried to make this amazing body of work fully accessible to mathematically literate nonphysicists.”
― Quantum Mechanics: The Theoretical Minimum
― Quantum Mechanics: The Theoretical Minimum
“From time to time, we hear physicists claim that Einstein didn’t understand Quantum Mechanics and therefore wasted his time with naive classical theories. I very much doubt that this is true. His arguments against Quantum Mechanics were extremely subtle, culminating in one of the most profound and most cited papers in all of physics.12 My guess is that Einstein was disturbed by the same thing that bothered the slow student. How could the ultimate theory of reality be about nothing more concrete than our own degree of surprise at the outcome of an experiment?”
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
“The units that we use reflect our own size. The origin of the meter seems to be that it was used to measure rope or cloth: it’s about the distance from a person’s nose to his or her outstretched fingers. A second is about as long as a heartbeat. And a kilogram is a nice weight to carry around. We use these units because they are convenient, but fundamental physics doesn’t care that much about us. The”
― Quantum Mechanics: The Theoretical Minimum
― Quantum Mechanics: The Theoretical Minimum
“world seems filled with people who are genuinely, deeply interested in physics but whose lives have taken them in different directions. This book is for all of us.”
― Quantum Mechanics: The Theoretical Minimum
― Quantum Mechanics: The Theoretical Minimum
“If necessity is the mother of invention, laziness is the father. The Einstein summation convention is the offspring of this happy marriage.”
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“Tides and the 2,000-Mile Man What causes the seas to rise and fall as if they were breathing two big breaths every day? It’s the Moon, of course, but how does it do it, and why twice a day? I will explain, but first let me tell you about the fall of the 2,000-Mile Man. Imagine the 2,000-Mile Man—a giant who measures 2,000 miles from the tip of his head to the bottoms of his feet—as he falls, feet-first, from outer space toward the Earth. Far out in outer space, gravity is weak—so weak that he feels nothing. But as he gets closer to the Earth, strange sensations arise in his long body—sensations not of falling but of being stretched. The problem is not the giant’s overall acceleration toward the Earth. The cause of his discomfort is that gravity is not uniform throughout space. Far from the Earth, it is almost entirely absent. But as he draws closer, the pull of gravity increases. For the 2,000-Mile Man, this presents difficulties even while he is in free fall. The poor man is so tall that the pull on his feet is much stronger than the pull on his head. The net effect is an uncomfortable feeling that his head and feet are being pulled in opposite directions. Perhaps he can avoid being stretched by falling in a horizontal position, legs and head at the”
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
“At some point we have to give up and say that's just the way it is. Or, not give up and push on.”
― The Theoretical Minimum: What You Need to Know to Start Doing Physics
― The Theoretical Minimum: What You Need to Know to Start Doing Physics
“Heat is the energy of random chaotic motion, and entropy is the amount of hidden microscopic information.”
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
“The fundamental theorem of calculus is one of the simplest and most beautiful results in mathematics. It asserts a deep connection between integrals and derivatives. What it says is that if F(T) = ∫ f(t) d t, then”
― The Theoretical Minimum: What You Need to Know to Start Doing Physics
― The Theoretical Minimum: What You Need to Know to Start Doing Physics
“the world seems filled with people who are genuinely, deeply interested in physics but whose lives have taken them in different directions. This book is for all of us.”
― Quantum Mechanics: The Theoretical Minimum
― Quantum Mechanics: The Theoretical Minimum
“There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy. —WILLIAM SHAKESPEARE, HAMLET”
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
“Differential calculus has to do with rates of change. Integral calculus has to do with sums of many tiny incremental quantities. It’s not immediately obvious that these have anything to do with each other, but they do.”
― The Theoretical Minimum: What You Need to Know to Start Doing Physics
― The Theoretical Minimum: What You Need to Know to Start Doing Physics
“In fact, before Hawking, all physicists would have claimed that black holes were indeed black bodies, but black bodies at absolute zero. Now, it's not correct to say that black bodies don't give off any light at all. Take a sooty pot and heat it to a few hundred degrees, low, and eventually it will have a bright bluish white appearance. Curiously, according to the physicists' definition, the sun is a black body. How odd, you say; the sun is about as far from being black as anything you can imagine. Indeed, the sun's surface radiates plenty of light, but it reflects none. To a physicist, that makes it a black body.”
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
“In most cases the tiniest differences in the initial conditions—the starting state—leads to large eventual differences in outcomes. This phenomenon is called chaos. If a system is chaotic (most are), then it implies that however good the resolving power may be, the time over which the system is predictable is limited.”
― The Theoretical Minimum: What You Need to Know to Start Doing Physics
― The Theoretical Minimum: What You Need to Know to Start Doing Physics
“The three-dimensional world of ordinary experience––the universe filled with galaxies, stars, planets, houses, boulders, and people––is a hologram, an image of reality coded on a distant two-dimensional surface”
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
“By itself, the Holographic Principle was not enough to win the Black Hole War. It was too imprecise, and it lacked a firm mathematical foundation. The reaction to it was skepticism: The universe a hologram? Sounds like science fiction. The fictitious future physicist Steve passing to the “other side” while the emperor and the count watch him being immolated? Sounds like spiritualism.”
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
“Classical mechanics is filled to the brim with mathematical abstractions—point masses, rigid bodies, inertial reference frames, positions, momenta, fields, waves—the list goes on and on. There’s nothing new about mathematical abstractions.” This is actually a fair point, and indeed the classical and quantum worlds have some important things in common. Quantum mechanics, however, is different in two ways:”
― Quantum Mechanics: The Theoretical Minimum
― Quantum Mechanics: The Theoretical Minimum
“Perhaps he can avoid being stretched by falling in a horizontal position, legs and head at the same altitude. Yet when the giant tries it, he finds a new discomfort; the stretching sensation is replaced by an equal feeling of compression. He feels as if his head is being pressed toward his feet. To understand why this is so, let’s temporarily imagine that the Earth is flat. Here is what it would look like. The vertical lines, together with the arrows, indicate the direction of the gravitational force—not surprisingly, straight down. But more than that, the strength of the gravitational pull is entirely uniform. The 2,000-Mile Man would have no trouble in this environment, whether he fell vertically or horizontally—not until he hit the ground anyway. But the Earth is not flat. Both the strength and the direction of gravity vary. Instead of pulling in a single direction, gravity pulls directly toward the center of the planet, like this: This creates a new problem for the giant if he falls horizontally. The force on his head and feet will not be the same because gravity, as it pulls toward the center of the Earth, will push his head toward his feet, leading to the strange sensation of being compressed. Let’s return”
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
“Let’s return to the question of the ocean tides. The cause of the twice-daily rising and falling of the seas is exactly the same as the cause of the 2,000-Mile Man’s discomfort: the non-uniformity of gravity. But in this case, it’s the Moon’s gravity, not the Earth’s. The Moon’s pull on the oceans is strongest on the side of the Earth facing the Moon and weakest on the far side. You might expect the Moon to create a single oceanic bulge on the closer side, but that’s wrong. For the same reason that the tall man’s head is pulled away from his feet, the water on both sides of the Earth—near and far—bulges away from it. One way to think about this is that on the near side, the Moon pulls the water away from the Earth, but on the far side, it pulls the Earth away from the water. The result is two bulges on opposite sides of the Earth, one facing toward the Moon and the other facing away. As the Earth turns one revolution under the bulges, each point experiences two high tides. The distorting forces caused by variations in the strength and direction of gravity are called tidal forces, whether they are due to the Moon, Earth, Sun, or any other astronomical mass. Can humans of normal size feel tidal forces—for example, when jumping from a diving board? No, we cannot, but only because we are so small that the Earth’s gravitational field hardly varies across the length of our bodies. Descent”
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
― The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics
“For example, we’ll see that the idea of a state in quantum mechanics is conceptually very different from its classical counterpart. States are represented by different mathematical objects and have a different logical structure.”
― Quantum Mechanics: The Theoretical Minimum
― Quantum Mechanics: The Theoretical Minimum




