24
Lectures
30
minutes/lecture
1.
Why Time Is a Mystery
Begin your study of the physics of time with these questions: What is a clock? What does it mean to say that “time passes”? What is the “arrow of time”? Then look at the concept of entropy and how it holds the key to the one-way direction of time in our universe.
1.
Why Time Is a Mystery
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13.
Boltzmann Brains
One possible explanation for order in the universe is that it is a random fluctuation from a disordered state. Could the entire universe be one such fluctuation, now in the process of returning to disorder? Investigate a scenario called “Boltzmann brains” that suggests not.
13.
Boltzmann Brains
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2.
What Is Time?
Approach time from a philosophical perspective. “Presentism” holds that the past and future are not real; only the present moment is real. However, the laws of physics appear to support “eternalism”—the view that all of the moments in the history of the universe are equally real.
2.
What Is Time?
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14.
Complexity and Life
Discover that Maxwell’s demon from lecture 10 provides the key to understanding how complexity and life can exist in a universe in which entropy is increasing. Consider how life is not only compatible with, but is an outgrowth of, the second law of thermodynamics and the arrow of time.
14.
Complexity and Life
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3.
Keeping Time
How do we measure the passage of time? Discover that practical concerns have driven the search for more and more accurate clocks. In the 18th century, the problem of determining longitude was solved with a timepiece of unprecedented accuracy. Today’s GPS navigation units rely on clocks accurate to a billionth of a second.
3.
Keeping Time
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15.
The Perception of Time
Turn to the way humans perceive time, which can vary greatly from clock time. In particular, focus on experiments that shed light on our time sense. For example, tests show that even though we think we perceive the present moment, we actually live 80 milliseconds in the past.
15.
The Perception of Time
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4.
Time’s Arrow
Embark on the quest that will occupy the rest of the course: Why is there an arrow of time? Explore how memory and aging orient us in time. Then look at irreversible processes, such as an egg breaking or ice melting. These capture the essence of the one-way direction of time.
4.
Time’s Arrow
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16.
Memory and Consciousness
Remembering the past and projecting into the future are crucial for human consciousness, as shown by cases where these faculties are impaired. Investigate what happens in the brain when we remember, exploring different kinds of memory and the phenomena of false memories and false forgetting.
16.
Memory and Consciousness
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5.
The Second Law of Thermodynamics
Trace the history of the second law of thermodynamics, considered by many physicists to be the one law of physics most likely to survive unaltered for the next thousand years. The second law says that entropy—the degree of disorder in a closed system—only increases or stays the same.
5.
The Second Law of Thermodynamics
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17.
Time and Relativity
According to Einstein’s special theory of relativity, there is no such thing as a moment in time spread throughout the universe. Instead, time is one of four dimensions in spacetime. Learn how this “relative” view of time is usefully diagramed with light cones, representing the past and future.
17.
Time and Relativity
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6.
Reversibility and the Laws of Physics
Isaac Newton’s laws of physics are fully reversible; particles can move forward or backward in time without any inconsistency. But this is not our experience in the world, where the arrow of time is fundamentally connected to irreversible processes and the increase in entropy.
6.
Reversibility and the Laws of Physics
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18.
Curved Spacetime and Black Holes
By developing a general theory of relativity incorporating gravity, Einstein launched a revolution in our understanding of the universe. Trace how his idea that gravity results from the warping of spacetime led to the discovery of black holes and the big bang.
18.
Curved Spacetime and Black Holes
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7.
Time Reversal in Particle Physics
Explore advances in physics since Newton’s time that reveal exceptions to the rule that interactions between moving particles are fully reversible. Could irreversible reactions between elementary particles explain the arrow of time? Weigh the evidence for and against this view.
7.
Time Reversal in Particle Physics
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19.
Time Travel
Use a simple analogy to understand how a time machine might work. Unlike movie scenarios featuring dematerializing and rematerializing, a real time machine would be a spaceship that moves through all the intervening points between two locations in spacetime. Also explore paradoxes of time travel.
19.
Time Travel
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8.
Time in Quantum Mechanics
Quantum mechanics is the most precise theory ever invented, yet it leads to startling interpretations of the nature of reality. Probe a quantum state called the collapse of the wave function that may underlie the arrow of time. Are the indications that it shows irreversibility real or only illusory?
8.
Time in Quantum Mechanics
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20.
Black Hole Entropy
Stephen Hawking showed that black holes emit radiation and therefore have entropy. Since the entropy in the universe today is overwhelmingly in the form of black holes and there were no black holes in the early universe, entropy must have been much lower in the deep past.
20.
Black Hole Entropy
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9.
Entropy and Counting
After establishing in previous lectures that the arrow of time must be due to entropy, begin a deep exploration of this phenomenon. In the 1870s, physicist Ludwig Boltzmann proposed a definition of entropy that explains why it increases toward the future. Analyze this idea in detail.
9.
Entropy and Counting
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21.
Evolution of the Universe
Follow the history of the universe from just after the big bang to the far future, when the universe will consist of virtually empty space at maximum entropy. Learn what is well founded and what is less certain about this picture of a universe winding down.
21.
Evolution of the Universe
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10.
Playing with Entropy
Sharpen your understanding of entropy by examining different macroscopic systems and asking, which has higher entropy and which has lower entropy? Also evaluate James Clerk Maxwell’s famous thought experiment about a demon who seemingly defies the principle that entropy always increases.
10.
Playing with Entropy
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22.
The Big Bang
Explore three different ways of thinking about the big bang—as the actual beginning of the universe; as a “bounce” from a symmetric version of the universe on the other side of the big bang; and as a region that underwent inflationary expansion in a much larger multiverse.
22.
The Big Bang
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11.
The Past Hypothesis
Boltzmann explains why entropy will be larger in the future, but he doesn’t show why it was smaller in the past. Learn that physics can’t account for this difference except by assuming that the universe started in a state of very low entropy. This assumption is called the past hypothesis.
11.
The Past Hypothesis
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23.
The Multiverse
Dig deeper into the possibility that the big bang originated in a multiverse, which provides a plausible explanation for why entropy was low at the big bang, giving rise to the arrow of time. But is this theory and the related idea of an anthropic principle legitimate science or science fiction?
23.
The Multiverse
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12.
Memory, Causality, and Action
Can physics shed light on human aspects of the arrow of time such as memory, cause and effect, and free will? Learn that everyday features of experience that you take for granted trace back to the low entropy state of the universe at the big bang, 13.7 billion years ago.
12.
Memory, Causality, and Action
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24.
Approaches to the Arrow of Time
Use what you have learned in the course to investigate a range of different possibilities that explain the origin of time in the universe. Professor Carroll closes by presenting one of his favorite theories and noting how much remains to be done before conclusively solving the mystery of time.
24.
Approaches to the Arrow of Time
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24
Lectures
30
minutes/lecture
1.
From Principles to Paradoxes and Back Again
Prepare to explore the thrilling frontier that separates the possible from the impossible by first looking at what scientists mean by these two terms, and how the boundaries can shift. Professor Schumacher notes that by pondering the impossible, scientists gain amazing insights into the nature of physical laws.
1.
From Principles to Paradoxes and Back Again
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13.
A Spinning Universe, Wormholes, and Such
Delve deeper into Einstein's theories to uncover some startling implications: The entire cosmos could be rotating on its axis, giving rise to several supposedly impossible phenomena, already dismissed. Weigh the evidence for and against "exotic" matter, wormholes, and other hypothetical features of space-time.
13.
A Spinning Universe, Wormholes, and Such
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2.
Almost Impossible
Many technological and scientific breakthroughs were thought to be impossible before they were achieved. Examine several famous cases in which foremost experts were proved wrong—about heavier-than-air flight, space travel, the chemical composition of stars, and the existence of life forms at ultrahigh temperatures.
2.
Almost Impossible
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14.
What Is Symmetry?
Something is symmetric if it is impossible to tell whether a particular transformation has been applied. Explore this fascinating boundary between the possible and impossible, which includes some of the deepest principles of physics—among them, the surprising connection between symmetry and conservation laws discovered by mathematician Emmy Noether.
14.
What Is Symmetry?
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3.
Perpetual Motion
Probe one of the most enduring of all impossible quests: the search for a perpetual motion machine. Learn how the futility of such a pursuit was explained four centuries ago by the Flemish mathematician Simon Stevin, whose work eventually led to the law of conservation of energy.
3.
Perpetual Motion
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15.
Mirror Worlds
Inspect the universe through three special mirrors. One is an ordinary mirror that reflects left and right. Another mirror exchanges matter and antimatter. The third switches the future and the past. Is it possible to tell these mirror-worlds from our own? What does that imply about the laws of nature?
15.
Mirror Worlds
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4.
On Sunshine and Invisible Particles
Investigate two challenges to the law of conservation of energy, also known as the first law of thermodynamics. In the 19th century, the source of the sun's energy seemed inexplicable, until the discovery of radioactivity. Then, in the 20th century, a type of radioactive decay appeared to violate energy conservation, until the discovery of an invisible elementary particle.
4.
On Sunshine and Invisible Particles
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16.
Invasion of the Giant Insects
Test a favorite plot device of science-fiction movies by examining whether supersize gorillas, insects as big as trucks, and other ordinary creatures enlarged to gigantic size can really exist. Is there a physical reason such monsters are in fact impossible?
16.
Invasion of the Giant Insects
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5.
Reflections on the Motive Power of Fire
Learn how the 19th-century French engineer Nicolas Carnot showed that only a temperature difference can be used to generate work, and that some waste heat must always be lost—ideas that led to the second law of thermodynamics and the important concept of entropy.
5.
Reflections on the Motive Power of Fire
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17.
The Curious Quantum World
With the discovery of quantum mechanics in the early 20th century, the accepted boundary between the possible and the impossible was changed in radical ways. Begin a series of lectures on the quantum realm with a look at three of its key features.
17.
The Curious Quantum World
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6.
Maxwell's Demon
Entropy always increases in a system in which work is being done. Investigate James Clerk Maxwell's famous "demon"—an imaginary being that, in principle, appears to violate the entropy law. See how the demon paradox was resolved by interpreting entropy as information.
6.
Maxwell's Demon
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18.
Impossible Exactness
In Newtonian physics, the position and velocity of a particle can both be specified to any level of precision. Not so in quantum mechanics, where these are limited by Heisenberg's famous uncertainty principle. Investigate the consequences of this fundamental restriction on what it's possible to know.
18.
Impossible Exactness
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7.
Absolute Zero
Learn how absolute zero (0 K or -273.15 degrees Celsius) is unattainable due to the third law of thermodynamics. Nonetheless, remarkable things happen on the way toward this impossible goal. For example, electrical resistance and viscosity drop to zero in certain substances, and weird quantum mechanical effects occur.
7.
Absolute Zero
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19.
Quantum Tunneling
Discover how phenomena deemed impossible in classical physics are a regular feature of the quantum world—notably quantum tunneling, which is the ability of a subatomic particle to surmount a seemingly impassable energy barrier. One result of this effect: Black holes emit a slow trickle of energy known as Hawking radiation.
19.
Quantum Tunneling
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8.
Predicting the Future
Consider a new kind of impossible thing: predicting the future in the presence of chaos. Even the slightest imprecision in present knowledge makes the long-term future unknowable. This is the phenomenon of dynamical chaos, also known as the "butterfly effect"—from the ability of a single flapping butterfly to radically affect future weather.
8.
Predicting the Future
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20.
Whatever Is Not Forbidden Is Compulsory
Explore a startling rule in quantum mechanics: Anything that can possibly happen, will happen. This means that whatever does not happen, whatever is truly impossible among the elementary particles, provides a clue to the fundamental laws of nature.
20.
Whatever Is Not Forbidden Is Compulsory
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9.
Visiting the Past
Explore the paradoxes of time travel. These are so fundamental that most physicists regard time travel as a near-absolute impossibility, yet science-fiction writers—and a few imaginative physicists—have proposed ways to avoid these difficulties. Look into some of their intriguing ideas.
9.
Visiting the Past
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21.
Entanglement and Quantum Cloning
Delve into the weirdest of all quantum phenomena: entanglement, which causes a pair of quantum particles to behave as if they are telepathically connected. By cloning quantum particles, this effect could, in theory, allow faster-than-light signals, but there are fundamental reasons this is impossible.
21.
Entanglement and Quantum Cloning
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10.
Thinking in Space-Time
Is the passage of time merely "a stubborn illusion," as Einstein believed? Investigate the revolutionary concept of space-time that emerges from his theory of relativity, which involved a major redrawing of the boundary between the possible and the impossible in physics.
10.
Thinking in Space-Time
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22.
Geometry and Conservation
Where do conservation laws come from? How does nature "enforce" them? Investigate these questions by performing a remarkable thought experiment: See how Maxwell's laws of electromagnetism and the geometry of space together imply the conservation of electric charge, even in a theoretical "electromagnetic-free" zone.
22.
Geometry and Conservation
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11.
Faster than Light
Nothing can travel faster than light. Is there a way around this prohibition? Learn that it all depends on what is meant by a "thing." By considering various thought experiments, discover that this ultimate speed limit applies fundamentally to information, which means it is impossible to send a message into the past.
11.
Faster than Light
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23.
Symmetry, Information, and Probability
Survey the landscape of the impossible by focusing on three recurring themes in the course: One, symmetries are among the deepest principles in physics; two, the idea of information is pervasive; three, many phenomena that appear to be impossible are only statistical impossibilities.
23.
Symmetry, Information, and Probability
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12.
Black Holes and Curved Space-Time
Einstein's general theory of relativity interprets gravity as a distortion of space-time near a massive object. Find out that for a very massive, dense object, this can result in a "black hole"—a region where the distortion is so strong that escape is impossible.
12.
Black Holes and Curved Space-Time
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24.
The Future of the Impossible
Professor Schumacher concludes the course with his million-dollar list—those things he would be willing to bet a million dollars will remain impossible even in the face of future discoveries. But first he challenges you to draw on your newly acquired knowledge of physics to propose your own list.
24.
The Future of the Impossible
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