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....

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....

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....

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....

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....

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....

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....

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....

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....

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....

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....

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....

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....

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....

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?...

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?...

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....

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....

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....

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....

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....

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....

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....

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....

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