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Paradox: The Nine Greatest Enigmas in Physics by Jim Al-Khalili
Albert Einstein, Albert Michelson, anthropic principle, Arthur Eddington, butterfly effect, clockwork universe, complexity theory, dark matter, Edmond Halley, Edward Lorenz: Chaos theory, Ernest Rutherford, Henri Poincaré, invention of the telescope, Isaac Newton, Johannes Kepler, Laplace demon, luminiferous ether, Magellanic Cloud, Olbers’ paradox, Pierre-Simon Laplace, Schrödinger's Cat, Search for Extraterrestrial Intelligence, The Present Situation in Quantum Mechanics, Wilhelm Olbers
Library of Congress Cataloging-in-Publication Data Al-Khalili, Jim, 1962- Paradox: the nine greatest enigmas in physics / Jim Al-Khalili. — 1st ed. p. cm. 1. Science—Miscellanea. I. Title. Q173.A395 2012 500—dc23 2012005011 eISBN: 978-0-307-98680-1 Illustrations: Patrick Mulrey Cover design: Kyle Kolker Cover photography: istockphoto v3.1 To Julie, David, and Kate Contents Cover Title Page Copyright Dedication Preface 1 The Game Show Paradox 2 Achilles and the Tortoise 3 Olbers’ Paradox 4 Maxwell’s Demon 5 The Pole in the Barn Paradox 6 The Paradox of the Twins 7 The Grandfather Paradox 8 The Paradox of Laplace’s Demon 9 The Paradox of Schrödinger’s Cat 10 Fermi’s Paradox 11 Remaining Questions Acknowledgments About the Author Preface Paradoxes come in all shapes and sizes. Some are straightforward paradoxes of logic with little potential for investigation, while others sit atop icebergs of entire scientific disciplines.
Here, the paradox has nothing to do with tricks of logic, but everything to do with the even stranger tricks that nature seems able to play down at the tiny scale of atoms—tricks that we are only beginning to understand. Zeno’s paradoxes have taken us from the very birth of physics to cutting-edge ideas in the twenty-first century. All the other paradoxes in this book arose somewhere in between. In resolving them we will have to travel to the furthest reaches of the Universe and explore the essence of space and time themselves. Hold on tight. 3 OLBERS’ PARADOX Why does it get dark at night? Several years ago I was on holiday with my family and a group of friends in France. We were staying in an idyllic country farmhouse in the Limousin region of the Massif Central, one of the most sparsely populated areas of the country. Late one evening, with the children asleep, we adults were sitting outside enjoying a last glass or three of the local red wine, looking up at the clear, sparkling night sky and commenting on how France is big enough for one still to find uninhabited swathes of countryside where the light pollution is low, and how unaccustomed we were, living in the densely populated southeast of England, to being able to see so many stars overhead.
After all, even a child knows that night falls when the Sun “sets” below the horizon, and that since there is nothing else in the night sky anywhere near as bright as the Sun we have to make do with the feeble reflected light from the Moon and the even more feeble light emanating from the distant planets and stars. And yet it turns out this question is far more significant than it first appears. Indeed, astronomers puzzled over it for hundreds of years before they found the correct answer. It is known today as Olbers’ Paradox. Here, then, is the problem. We have good reason to believe that even if the Universe is not infinite in size (and it may well be), it is so enormous that to all intents and purposes it goes on forever. Thus, in every direction we care to look out into space, we should see a star, and the sky should be even brighter than it normally becomes during the day; in fact, it should be so bright, all the time, that it should not even matter whether it is day or night according to our Sun.
QI: The Book of General Ignorance - The Noticeably Stouter Edition by Lloyd, John, Mitchinson, John
Admiral Zheng, Albert Einstein, Barry Marshall: ulcers, British Empire, discovery of penicillin, Dmitri Mendeleev, Fellow of the Royal Society, Ignaz Semmelweis: hand washing, invention of the telephone, James Watt: steam engine, Kickstarter, Kuiper Belt, lateral thinking, Magellanic Cloud, Mars Rover, Menlo Park, Olbers’ paradox, On the Revolutions of the Heavenly Spheres, placebo effect, Pluto: dwarf planet, trade route, V2 rocket, Vesna Vulović
A few weeks after the announcement to the American Astronomical Society, however, they had to admit they’d made a mistake in their calculations, and that the universe was, in fact, more a sort of dreary shade of taupe. Since the seventeenth century, some of the greatest and most curious minds have wondered why it is that the night sky is black. If the universe is infinite and contains an infinite number of uniformly distributed stars, there should be a star everywhere we look, and the night sky should be as bright as day. This is known as Olbers’ Paradox, after the German astronomer Heinrich Olbers who described the problem (not for the first time) in 1826. Nobody has yet come up with a really good answer to the problem. Maybe there is a finite number of stars, maybe the light from the furthest ones hasn’t reached us yet. Olbers’ solution was that, at some time in the past, not all the stars had been shining and that something had switched them on.
H. 1 Morris, Desmond 1 Mortensen, Christian 1 mosquitoes 1, 2, 3 moths flames and 1 stimulating 1 mountains highest 1 tallest 1 Mount Augustus 1 Mount Chimborazo 1 Mount Conner 1 Mount Everest 1 and asthmatics 1 Mount Kilimanjaro 1 Mount Olga 1 Mozart, middle name of 1 Mumford, Louis 1 Murray, George 1 muscles strongest in human beings 1 use of, in smiling and frowning 1 mushroom, as largest organism 1 music La Marseillaise 1 Nero’s instruments 1 ‘ring-a-ring o’ roses’ 1 and snake charming 1 nacre 1 Naismith, James 1 Namaqua people 1 names of boys, most popular 1 Namibia 1, 2 NASA 1, 2, 3, 4, 5, 6, 7 Nast, Thomas 1 ‘Near Earth’ Asteroids (NEAs) 1 Near Earth Object (NEO) 1 neck ties 1 Nelson, Horatio 1 eye-patch 1 funeral 1 last words 1 preservation in brandy 1 and ventriloquism 1 Nepal 1 Neptune 1, 2 Nero 1, 2 Netherlands 1, 2, 3, 4, 5 nettles World Stinging Nettle Eating Championship 1 WWI German uniforms made from 1 neurons 1, 2, 3, 4 New Zealand 1, 2 Newton, Isaac 1 newts 1, 2 Nicholas, Saint 1 Nicot, Jean 1, 2 nicotine colour of 1 etymology 1 toxicity 1 Nile, river 1 ‘Night before Christmas, The’ (Moore) 1 nitrogen 1 Noah 1, 2 Noah’s Ark, sheep on 1 nociception 1 Nome, Alaska, naming of 1 North America, camels from 1 Norway 1, 2 nuclear war, most likely survivor of 1 numbers, unlucky 1 nuts, definition of 1 Oates, Titus 1 ocean, loudest noise in 1 Olazowa Cave 1 Olbers, Heinrich 1 Olbers’ Paradox 1 Old English Game fowl 1 Olsen, Lloyd 1 Olympics, modern 1, 2 Olympus Mons, see Mount Olympus Oompa-Loompas orange 1 original, 1 orang utans 1 orange, words rhyming with 1 Orkney, polar bear in 1 osmium 1 ostriches 1, 2 owls on the Ark 1 colour-blindness of 1 eaten by Darwin 1 eyes of 1 sounds of 1 oysters 1 ozone 1, 2, 3 Palin, Michael 1 Panama 1, 2 Panama hats, origins of 1 panthers, colour of 1 papacy 1 paper, possible number of folds in 1 paper clip, invention of 1 Papua New Guinea cannibalism in 1, 2 lack of colour words 1 Parker, David 1 Parker, Hyde 1 Parkes, Alexander 1 Parr, Catherine 1 Parton, Dolly 1 Pascal, Blaise 1 Pasteur, Louis 1 Paterson, William 1 Patrick, Saint 1 Paul, Saint 1 Paul I, Czar of Russia 1, 2 peanuts 1 pearls, middle of 1 Pedro, King of Castile 1 pencils, consequences of sucking on 1 penicillin, discovery of 1 penises baculi 1 barnacles 1 in the Bible 1 blue whales 1, 2 European earwigs 1 length of, related to shoe size 1 replaced by sandwich 1 Penn, William 1 Penny Post, invention of 1 Pepys, Samuel 1 Perey, Marguerite 1 Periander 1 Pérignon, Dom 1 Perovski, Count Lev 1 perovskite 1 Perrault, Charles 1, 2 Perseus, virgin birth of 1 Peru 1, 2, 3, 4 Peter the Great 1 Pheidippides 1 philtrum 1 phorids 1 Piccadilly Circus, name of statue 1 Pierce, Franklin 1 pineapples 1 Pinker, Stephen 1 Pisa, Rustichello da 1 pistachios 1 planets naming of 1 number of 1 plaster of Paris 1 naming of 1 Pliny the Elder 1, 2, 3, 4, 5, 6, 7 Plunket, Saint Oliver 1 Plunkett, Roy 1 Plutarch 1 Pluto 1, 2, 3, 4 Poe, Edgar Allan 1 poisons antitdote to arsenic 1 ethyl gasoline 1 and Nero 1 and newts 1 and snakes 1 in tobacco 1 Poland 1, 2, 3 polar bears 1, 2, 3 Polo, Marco 1, 2 ‘pom’, as nickname 1 pomegranate 1, 2 Pony Express 1 porridge, origins of 1 Portugal 1, 2, 3, 4 potatoes evolutionary path of 1 introduction of 1, 2 nicotine in 1, 2 Potemkin, Grigori Alexandrovich 1 Procopius 1 proprioception 1 Prozac 1 Prussia 1 Ptolemy II 1 Puerto Rico 1, 2 puma 1, 2 punctuation 1 Punxsutawney Phil 1 Pythagoras 1 Quaker Oats, creation of 1 Quinion, Michael 1 rabbits 1, 2 raindrops, shape of 1 Raleigh, Walter 1 Rama I, King of Thailand 1 Randolph, Peyton 1 raspberries 1 rats, colour-blindness of 1 Recorde, Robert 1 Red Jungle Fowl, chickens descended from 1 Redi, Francesco 1 Reed, Carol 1 reindeer antler loss in 1 domestication of 1 speed of 1 Remarque, Erich Maria 1 Reyburn, Wallace 1, 2 rhinoceroses, horns of 1 Richardson, Lucy 1 Richter, Charles 1 Richter scale 1 rickshaw, invention of 1 ‘ring-a-ring o’ roses’, origin of 1 Roberts, Brushy Bill 1 Robin Hood 1 rock, biggest 1 Romania 1 Rome, ancient Britons considered cannibals 1 carrots as aphrodisiacs 1 fashions in dress 1 gladiators in 1 names for British 1 naming conventions 1 Nero and the fire 1 and number thirteen 1 postal service 1 running-with-a-ball game 1 vomitoria 1 Roosevelt, Robert 1 Roosevelt, Theodore 1, 2 Ross, Ronald 1 Rousseau, Jean-Jacques 1, 2 Rowbotham, Samuel Birley 1 Royal Society 1 rubber boots, invention of 1 rubidium 1, 2 Rudolph the Red-nosed Reindeer, gender of 1 rugby 1 Rugby School 1, 2 Rumsey, H.
F. 1 sleep, healthy amount of 1 sloths as most dangerous animal 1 metabolism of 1 three-toed 1 two-toed 1, 2 Slovakia, smallest dog from 1 smallpox 1, 2 smoking 1, 2, 3, 4 snakes charming of 1 poisonous, not venomous 1 probability of a bite 1 rattlesnakes on 1970s TV 1 tolerant of poison 1 snow, Eskimo words for 1 soccer 1 Solanges, Comte de 1 solanine 1 sound barrier, first invention to break 1 South Africa 1, 2, 3 South America 1, 2, 3 cannibalism in 1 flamingos in 1 guinea pigs in 1 peanuts in 1 Spanish pronunciation in 1 South China tigers 1, 2 Spain 1, 2, 3, 4, 5, 6, 7, 8, 9 cannibalism in 1 pronunciation in, and the ‘lisp’ 1 Spam 1 Spears, Britney 1 Spencer, Herbert 1 sperm and division of labour 1 of dogs 1 sensitivity to scents 1 sperm whales 1 Sphinx 1 spiders 1, 2, 3 spirulina 1 Spitfire 1 ‘sport of kings’ 1 squirrels, fur of 1 stamps 1 stars Boomerang Nebula 1 names of constellations 1 Olbers’ paradox 1 shape of 1 visible 1 steam engine, inventor of 1 stomach ulcers, cause of 1 Stone Age peoples, habitats of 1 strawberries 1 Strutt, William John, Lord Rayleigh 1 Stuart, Gilbert 1 Suetonius 1 suicide rate, highest 1 Sundblom, Haddon 1, 2 superconductors 1, 2 superstitions, and pragmatism 1 ‘survival of the fittest’, coining of term 1 Sweden 1, 2, 3 suicide rate in 1 Swiss Family Robinson, surname of 1 Switzerland biscuits in 1 inventions of 1 St Bernards 1 Swiss rolls 1 synaesthesia 1 Tammann, Gustav 1 Tanzania 1 tartans, origins of 1 Taylor, David 1 Taylor, Montague 1 Tchaikovsky, Pyotr Ilyich 1 tea 1, 2, 3 teeth celluloid 1, 2 decay of, and bacteria 1 dental statistics (modern) 1 Washington’s false teeth 1, 2, 3 ‘Waterloo teeth’ 1 Teflon, discovery of 1 telephone, inventor of 1 television, effects on health 1 Tennant, Smithson 1 Thailand 1, 2 capital of 1 chicken ancestor in 1 Theory of Relativity, inventor of 1 thermoception 1 Thom, Charles 1 Thoreau, Henry David 1 Thule 1 Tibet 1 tigers 1 age of, when dangerous 1 highest concentration of 1 see also South China tigers tobacco 1 chemicals in 1 introduced to England 1 as a medicine 1 unusual fertilisers for 1 as world’s biggest killer 1 togas 1 Tokyo 1 toothpaste, bears and 1 Tour de France 1 Toynbee, Arnold 1 Trafalgar, Battle of 1 transport car accidents 1, 2 hydrofoil 1 railways 1 rickshaws 1 Treaty of Madrid 1 Treaty of Versailles 1 trees ‘anti-greenhouse effect’ 1 and loofahs 1 ozone released from 1 role of forest fires 1 in thunderstorms 1, 2 world’s most useful 1 Truman, Harry S. 1 tsunamis 1, 2 tulips, origins of 1 tungsten 1 Turkey 1, 2, 3, 4 turkeys farming techniques 1 origins of 1 Turner, Herbert Hall 1 Turner, J.
The Infinite Book: A Short Guide to the Boundless, Timeless and Endless by John D. Barrow
Albert Einstein, Andrew Wiles, anthropic principle, Arthur Eddington, cosmological principle, dark matter, Edmond Halley, Fellow of the Royal Society, Georg Cantor, Isaac Newton, mutually assured destruction, Olbers’ paradox, prisoner's dilemma, Ray Kurzweil, scientific worldview, short selling, Stephen Hawking, Turing machine
Everywhere your line of sight seems to end on the trunk of a tree (Figure 7.17). Halley realised that a universe containing an infinite number of stars creates exactly the same situation. If we look out into the sky we should find that every line of sight ends on the surface of a star. The result: the entire sky should shine like the surface of a star, day and night. But it doesn’t. And that is Halley’s Paradox – except that it’s called Olbers’ Paradox!29 There are some simple ways to avoid the paradox. Suppose that space goes on forever but the stars do not. Space is infinite but the material universe is finite. In this case there would be only a finite amount of light reaching us from the stars and our skies might grow dark when the Sun sets (see Figure 7.18). This seems an artificial solution. If the Universe has infinite spatial extent, why is there a little finite pocket of stars and planets somewhere within it?
The Fractalist by Benoit Mandelbrot
Albert Einstein, Benoit Mandelbrot, Brownian motion, business cycle, Claude Shannon: information theory, discrete time, double helix, Georg Cantor, Henri Poincaré, Honoré de Balzac, illegal immigration, Isaac Newton, iterative process, Johannes Kepler, John von Neumann, linear programming, Louis Bachelier, Louis Blériot, Louis Pasteur, mandelbrot fractal, New Journalism, Norbert Wiener, Olbers’ paradox, Paul Lévy, Richard Feynman, statistical model, urban renewal, Vilfredo Pareto
Distribution of Galaxies That the Milky Way is one of a number of similar “objects” in the sky is a surprisingly recent notion: it dates from the decade when I was born. So is the galaxy. Incredible but true, however, long before any evidence became available, the concepts of a galaxy and clusters of galaxies had been repeatedly invented and forgotten. Also, the natural assumption that faraway shining objects are uniformly distributed in space was analyzed and shown to lead to the embarrassing Olbers paradox, which argues that the sky must be uniformly and infinitely bright. A way to avoid this paradox was proposed by a science fiction writer, Edmund Fournier d’Albe, and developed by astronomer Carl Charlier. But the profession never took it seriously, largely because it required the universe to have a well-defined “cluster” and because relativity theory demands a well-defined overall density of mass.
Big Bang by Simon Singh
Albert Einstein, Albert Michelson, All science is either physics or stamp collecting, Andrew Wiles, anthropic principle, Arthur Eddington, Astronomia nova, Brownian motion, carbon-based life, Cepheid variable, Chance favours the prepared mind, Commentariolus, Copley Medal, cosmic abundance, cosmic microwave background, cosmological constant, cosmological principle, dark matter, Dava Sobel, Defenestration of Prague, discovery of penicillin, Dmitri Mendeleev, Edmond Halley, Edward Charles Pickering, Eratosthenes, Ernest Rutherford, Erwin Freundlich, Fellow of the Royal Society, fudge factor, Hans Lippershey, Harlow Shapley and Heber Curtis, Harvard Computers: women astronomers, Henri Poincaré, horn antenna, if you see hoof prints, think horses—not zebras, Index librorum prohibitorum, invention of the telescope, Isaac Newton, Johannes Kepler, John von Neumann, Karl Jansky, Kickstarter, Louis Daguerre, Louis Pasteur, luminiferous ether, Magellanic Cloud, Murray Gell-Mann, music of the spheres, Olbers’ paradox, On the Revolutions of the Heavenly Spheres, Paul Erdős, retrograde motion, Richard Feynman, scientific mainstream, Simon Singh, Solar eclipse in 1919, Stephen Hawking, the scientific method, Thomas Kuhn: the structure of scientific revolutions, unbiased observer, Wilhelm Olbers, William of Occam
For example, in 1823, when scientists assumed that the universe was infinite and eternal, the German astronomer Wilhelm Olbers wondered why the night sky was not ablaze with starlight. He reasoned that an infinite universe would contain an infinite number of stars, and if the universe was infinitely old then this would have allowed an infinite amount of time for the starlight to have reached us. Hence, our night sky ought to be flooded with an infinite amount of light from all these stars. The obvious lack of this infinite light from space is known as Olbers’ paradox. There are various ways to explain why the night sky is not infinitely bright, but the Big Bang explanation is perhaps the most convincing. If the universe was created just a few billion years ago, then the starlight would only have had enough time to reach us from a limited volume of space, because light travels at only 300,000 km/s. In short, a finite age for the universe and a finite speed of light results in a night sky with only a finite amount of light, which is what we observe.