The Physics Book

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PHYTSHEICS BOOK

PHYTSHEICS BOOK

DK LONDON DK DELHI First American Edition, 2020 Published in the United States by DK Publishing SENIOR ART EDITOR PROJECT ART EDITOR 1450 Broadway, Suite 801, New York, NY 10018 Gillian Andrews Pooja Pipil Copyright © 2020 Dorling Kindersley Limited SENIOR EDITORS ART EDITORS DK, a Division of Penguin Random House LLC Camilla Hallinan, Laura Sandford Meenal Goel, Debjyoti Mukherjee 20 21 22 23 24 10 9 8 7 6 5 4 3 2 1 EDITORS ASSISTANT ART EDITOR 001–316670–Mar/2020 John Andrews, Jessica Cawthra, Joy Evatt, Nobina Chakravorty SENIOR EDITOR All rights reserved. Claire Gell, Richard Gilbert, Tim Harris, Suefa Lee Without limiting the rights under the copyright Janet Mohun, Victoria Pyke, Dorothy Stannard, reserved above, no part of this publication may be ASSISTANT EDITOR reproduced, stored in or introduced into a retrieval Rachel Warren Chadd Aashirwad Jain system, or transmitted, in any form, or by any means US EDITOR (electronic, mechanical, photocopying, recording, SENIOR JACKET DESIGNER or otherwise), without the prior written permission Megan Douglass Suhita Dharamjit ILLUSTRATIONS of the copyright owner. James Graham SENIOR DTP DESIGNER Published in Great Britain by JACKET DESIGN Neeraj Bhatia Dorling Kindersley Limited DEVELOPMENT MANAGER DTP DESIGNER A catalog record for this book Sophia MTT Anita Yadav is available from the Library of Congress. PRODUCER, PRE-PRODUCTION PROJECT PICTURE RESEARCHER ISBN: 978–1–4654–9102–2 Gillian Reid Deepak Negi PRODUCER DK books are available at special discounts when Nancy-Jane Maun PICTURE RESEARCH MANAGER purchased in bulk for sales promotions, premiums, SENIOR MANAGING ART EDITOR Taiyaba Khatoon fund-raising, or educational use. For details, contact: Lee Griffiths DK Publishing Special Markets, 1450 Broadway, Suite MANAGING EDITOR PRE-PRODUCTION MANAGER Gareth Jones Balwant Singh 801, New York, NY 10018 ASSOCIATE PUBLISHING DIRECTOR [email protected] Liz Wheeler PRODUCTION MANAGER Printed in China ART DIRECTOR Pankaj Sharma A WORLD OF IDEAS: Karen Self MANAGING ART EDITOR SEE ALL THERE IS TO KNOW DESIGN DIRECTOR Sudakshina Basu www.dk.com Philip Ormerod SENIOR MANAGING EDITOR PUBLISHING DIRECTOR Rohan Sinha Jonathan Metcalf original styling by STUDIO 8

CONTRIBUTORS DR. BEN STILL, CONSULTANT EDITOR Scientific American, and Forbes. He has also appeared as a space expert on several radio and television shows, and is currently A prize-winning science communicator, particle physicist, and working on a series of educational science books for children. author, Ben teaches high school physics and is also a visiting research fellow at Queen Mary University of London. After a master’s MUKUL PATEL degree in rocket science, a PhD in particle physics, and years of research, he stepped into the world of outreach and education in Mukul Patel studied natural sciences at King’s College Cambridge 2014. He is the author of a growing collection of popular science and mathematics at Imperial College London. He is the author of books and travels the world teaching particle physics using LEGO®. We’ve Got Your Number, a children’s math book, and over the last 25 years has contributed to numerous other books across scientific JOHN FARNDON and technological fields for a general audience. He is currently investigating ethical issues in AI. John Farndon has been short-listed five times for the Royal Society’s Young People’s Science Book Prize, among other awards. A widely ROBERT SNEDDEN published author of popular books on science and nature, he has written around 1,000 books on a range of subjects, including Robert Snedden has been involved in publishing for 40 years, internationally acclaimed titles such as The Oceans Atlas, Do researching and writing science and technology books for young You Think You’re Clever?, and Do Not Open, and has contributed people on topics ranging from medical ethics to space exploration, to major books such as Science and Science Year By Year. engineering, computers, and the internet. He has also contributed to histories of mathematics, engineering, biology, and evolution, and TIM HARRIS written books for an adult audience on breakthroughs in mathematics and medicine and the works of Albert Einstein. A widely published author on science and nature for both children and adults, Tim Harris has written more than 100 mostly GILES SPARROW educational reference books and contributed to many others. These include An Illustrated History of Engineering, Physics Matters!, A popular science author specializing in physics and astronomy, Great Scientists, Exploring the Solar System, and Routes of Science. Giles Sparrow studied astronomy at University College London and science communication at Imperial College London. He is the author HILARY LAMB of books including Physics in Minutes, Physics Squared, The Genius Test and What Shape Is Space?, as well as DK’s Spaceflight, and has Hilary Lamb studied physics at the University of Bristol and science contributed to bestselling DK titles including Universe and Science. communication at Imperial College London. She is a staff journalist at Engineering & Technology Magazine, covering science and JIM AL-KHALILI, FOREWORD technology, and has written for previous DK titles, including How Technology Works and Explanatorium of Science. An academic, author, and broadcaster, Jim Al-Khalili FRS holds a dual professorship in theoretical physics and the public engagement JONATHAN O’CALLAGHAN in science at the University of Surrey. He has written 12 books on popular science, translated into over 20 languages. A regular With a background in astrophysics, Jonathan O’Callaghan has been presenter on British TV, he is also the host of the Radio 4 program a space and science journalist for almost a decade. His work has The Life Scientific. He is a recipient of the Royal Society Michael appeared in numerous publications including New Scientist, Wired, Faraday Medal, the Institute of Physics Kelvin Medal, and the Stephen Hawking Medal for science communication.

6 CONTENTS 10 INTRODUCTION 38 The most wonderful 76 The minute parts of matter productions of the are in rapid motion MANEDASMUORTEIMONENT mechanical arts Fluids Measuring time PHYSICS AND THE 80 Searching out the fire-secret EVERYDAY WORLD 40 All action has a reaction Heat and transfers Laws of motion 18 Man is the measure 82 Elastical power in the air of all things 46 The frame of the system The gas laws Measuring distance of the world Laws of gravity 86 The energy of the universe 20 A prudent question is constant is one half of wisdom 52 Oscillation is everywhere Internal energy and the first law The scientific method Harmonic motion of thermodynamics 24 All is number 54 There is no destruction 90 Heat can be a cause The language of physics of force of motion Kinetic energy and Heat engines 32 Bodies suffer no resistance potential energy but from the air 94 The entropy of the universe Free falling 55 Energy can be neither tends to a maximum created nor destroyed Entropy and the second law 36 A new machine for The conservation of of thermodynamics multiplying forces energy Pressure 100 The fluid and its vapor 56 A new treatise on become one 37 Motion will persist mechanics Changes of state and Momentum Energy and motion making bonds 58 We must look to the 104 Colliding billiard balls heavens for the measure in a box of the Earth The development of statistical SI units and physical mechanics constants 112 Fetching some gold from ENERGY AND MATTER the sun Thermal radiation MATERIALS AND HEAT 68 The first principles of the universe Models of matter 72 As the extension, so the force Stretching and squeezing

7 EMLAEGCNTERTIICSIMTY AND 158 An encyclopedia on the head 192 These mysterious waves of a pin we cannot see TWO FORCES UNITE Nanoelectronics Electromagnetic waves 122 Wondrous forces 159 A single pole, either north 196 The language of spectra is Magnetism or south a true music of the spheres Magnetic monopoles Light from the atom 124 The attraction of electricity SOUND AND LIGHT 200 Seeing with sound Electric charge Piezoelectricity and ultrasound THE PROPERTIES OF WAVES 128 Potential energy becomes 202 A large fluctuating echo palpable motion 164 There is geometry in the Seeing beyond light Electric potential humming of the strings Music THE QUANTUM WORLD 130 A tax on electrical energy 168 Light follows the path OUR UNCERTAIN UNIVERSE Electric current and of least time resistance Reflection and refraction 208 The energy of light is distributed discontinuously 134 Each metal has a certain 170 A new visible world in space power Focusing light Energy quanta Making magnets 176 Light is a wave 212 They do not behave like 136 Electricity in motion Lumpy and wavelike light anything that you have The motor effect ever seen 180 Light is never known to Particles and waves 138 The dominion of magnetic bend into the shadow forces Diffraction and interference 216 A new idea of reality Induction and the generator Quantum numbers effect 184 The north and south sides of the ray 218 All is waves 142 Light itself is an Polarization Matrices and waves electromagnetic disturbance Force fields and Maxwell’s 220 The cat is both alive equations and dead Heisenberg’s uncertainty 148 Man will imprison the power principle of the sun Generating electricity 152 A small step in the control of nature Electronics 156 Animal electricity Bioelectricity 157 A totally unexpected 188 The trumpeters and the scientific discovery wave train Storing data The Doppler effect and redshift

8 222 Spooky action at a distance 248 Dreadful amounts of 276 Does Oxford stop at Quantum entanglement energy this train? Nuclear bombs and power Special relativity 224 The jewel of physics Quantum field theory 252 A window on creation 280 A union of space and time Particle accelerators Curving spacetime 226 Collaboration between parallel universes 256 The hunt for the quark 281 Gravity is equivalent Quantum applications The particle zoo and quarks to acceleration The equivalence principle PNHUYCSLIECASR AND PARTICLE 258 Identical nuclear particles do not always act alike 282 Why is the traveling INSIDE THE ATOM Force carriers twin younger? Paradoxes of special relativity 236 Matter is not infinitely 260 Nature is absurd divisible Quantum electrodynamics 284 Evolution of the stars Atomic theory and life 261 The mystery of the missing Mass and energy 238 A veritable transformation neutrinos of matter Massive neutrinos 286 Where spacetime Nuclear rays simply ends 262 I think we have it Black holes and wormholes 240 The constitution of matter The Higgs boson The nucleus 290 The frontier of the 264 Where has all the known universe 242 The bricks of which atoms antimatter gone? Discovering other galaxies are built up Matter–antimatter asymmetry Subatomic particles 294 The future of the universe 265 Stars get born and die The static or expanding 244 Little wisps of cloud Nuclear fusion in stars universe Particles in the cloud chamber RUENLIVAETRIVSIETY AND THE 296 The cosmic egg, exploding 246 Opposites can explode at the moment of creation Antimatter OUR PLACE IN THE COSMOS The Big Bang 247 In search of atomic glue 270 The windings of the 302 Visible matter alone The strong force heavenly bodies is not enough The heavens Dark matter 272 Earth is not the center 306 An unknown ingredient of the universe dominates the universe Models of the universe Dark energy 274 No true times or true 308 Threads in a tapestry lengths String theory From classical to special relativity 312 Ripples in spacetime Gravitational waves 275 The sun as it was about eight minutes ago 316 DIRECTORY The speed of light 324 GLOSSARY 328 INDEX 335 QUOTATIONS 336 ACKNOWLEDGMENTS

9 FOREWORD I fell in love with physics as a boy when I discovered we make observations and conduct experiments, that this was the subject that best provided answers revising and improving on what we know. Often, to many of the questions I had about the world around we take wrong turns or discover after many years me—questions like how magnets worked, whether that a particular description or theory is wrong, or space went on forever, why rainbows form, and how only an approximation of reality. Sometimes, new we know what the inside of an atom or the inside discoveries are made that shock us and force us to of a star looks like. I also realized that by studying revise our view entirely. physics I could get a better grip on some of the more profound questions swirling around in my head, such One beautiful example of this that has happened as: What is the nature of time? What is it like to fall in my lifetime was the discovery, in 1998, that the into a black hole? How did the universe begin and universe is expanding at an accelerating pace, leading how might it end? to the idea of so-called dark energy. Until recently, this was regarded as a complete mystery. What Now, decades later, I have answers to some of was this invisible field that acted to stretch space my questions, but I continue to search for answers against the pull of gravity? Gradually, we are learning to new ones. Physics, you see, is a living subject. that this is most likely something called the vacuum Although there are many things we now know with energy. You might wonder how changing the name of confidence about the laws of nature, and we have used something (from “dark energy” to “vacuum energy”) this knowledge to develop technologies that have can constitute an advance in our understanding. But transformed our world, there is still much more we the concept of vacuum energy is not new. Einstein had do not yet know. That is what makes physics, for me, suggested it a hundred years ago, then changed his the most exciting area of knowledge of all. In fact, mind when he thought he’d made a mistake, calling it I sometimes wonder why everyone isn’t as in love his “biggest blunder.” It is stories like this that, for me, with physics as I am. make physics so joyous. But to bring the subject alive—to convey that sense This is also why The Physics Book is so enjoyable. of wonder—requires much more than collecting Each topic is made more accessible and readable with together a mountain of dry facts. Explaining how the introduction of key figures, fascinating anecdotes, our world works is about telling stories; it is about and the timeline of the development of the ideas. Not acknowledging how we have come to know what we only is this a more honest account of the way science know about the universe, and it is about sharing in progresses, it is also a more effective way of bringing the joy of discovery made by the many great scientists the subject alive. who first unlocked nature’s secrets. How we have come to our current understanding of physics can be I hope you enjoy the book as much as I do. as important and as joyful as the knowledge itself. Jim Al-Khalili This is why I have always had a fascination with the history of physics. I often think it a shame that we are not taught at school about how concepts and ideas in science first developed. We are expected to simply accept them unquestioningly. But physics, and indeed the whole of science, isn’t like that. We ask questions about how the world works and we develop theories and hypotheses. At the same time,

INTRODU

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12 INTRODUCTION W e humans have a people were free to wonder about marvels from east to west. Ideas heightened sense of our place in the universe. First the from this wealth of culture drew our surroundings. We Greeks, then the Romans tried to Europe out of the dark ages and evolved this way to outmaneuver make sense of the world through into a new age of enlightenment stronger and faster predators. To patterns they observed in nature. known as the Renaissance. A achieve this, we have had to predict Thales of Miletus, Socrates, Plato, revolution of our world view began the behavior of both the living Aristotle, and others began to reject as ideas from ancient civilizations and the inanimate world. Knowledge supernatural explanations and became updated or outmoded, gained from our experiences was produce rational answers in the quest replaced by new ideas of our place passed down through generations to create absolute knowledge—they in the universe. A new generation via an ever-evolving system of began to experiment. of experimenters poked and prodded language, and our cognitive prowess nature to extract her secrets. In and ability to use tools took our At the fall of the Roman Empire, Poland and Italy, Copernicus and species to the top of the food chain. so many of these ideas were lost to Galileo challenged ideas that had the Western world, which fell into a been considered sacrosanct for two We spread out of Africa from dark age of religious wars, but they millennia—and they suffered harsh around 60,000 years ago, extending continued to flourish in the Arab persecution as a result. our abilities to survive in world and Asia. Scholars there inhospitable locations through sheer continued to ask questions and Then, in England in the ingenuity. Our ancestors developed conduct experiments. The 17th century, Isaac Newton’s laws techniques to allow them to grow language of mathematics was of motion established the basis of plentiful food for their families, and invented to document this new- settled into communities. found knowledge. Ibn al-Haytham Whosoever studies works of and Ibn Sahl were just two of the science must … examine tests Experimental methods Arab scholars who kept the flame Early societies drew meaning from of scientific knowledge alive in the and explanations with the unrelated events, saw patterns that 10th and 11th centuries, yet their greatest precision. did not exist, and spun mythologies. discoveries, particularly in the Ibn al-Haytham They also developed new tools and fields of optics and astronomy, methods of working, which required were ignored for centuries outside advanced knowledge of the inner the Islamic world. workings of the world—be it the seasons or the annual flooding of the A new age of ideas Nile—in order to expand resources. With global trade and exploration In some regions, there were periods came the exchange of ideas. of relative peace and abundance. In Merchants and mariners carried these civilized societies, some books, stories, and technological

INTRODUCTION 13 classical physics, which was to thermodynamics. British physicist One cannot help but be in reign supreme for more than two James Clerk Maxwell produced awe when he contemplates centuries. Understanding motion equations to describe the close allowed us to build new tools— relationship of electricity and the mysteries of eternity, machines—able to harness energy magnetism—electromagnetism. of life, of the marvellous in many forms to do work. Steam engines and water mills were two By 1900, it seemed that there structure of reality. of the most important of these— were laws to cover all the great Albert Einstein they ushered in the Industrial phenomena of the physical world. Revolution (1760–1840). Then, in the first decade of the 20th Physics has evolved over the century, a series of discoveries sent years as a science, branching The evolution of physics shock waves through the scientific out and breaching new horizons In the 19th century, the results community, challenging former as discoveries are made. Arguably, of experiments were tried and “truths” and giving birth to modern its main areas of concern now lie at tested numerous times by a new physics. A German, Max Planck, the fringes of our physical world, international network of scientists. uncovered the world of quantum at scales both larger than life and They shared their findings through physics. Then fellow countryman smaller than atoms. Modern papers, explaining the patterns Albert Einstein revealed his theory physics has found applications in they observed in the language of of relativity. Others discovered the many other fields, including new mathematics. Others built models structure of the atom and uncovered technology, chemistry, biology, and from which they attempted to the role of even smaller, subatomic astronomy. This book presents the explain these empirical equations particles. In so doing, they launched biggest ideas in physics, beginning of correlation. Models simplified the the study of particle physics. New with the everyday and ancient, complexities of nature into digestible discoveries weren’t confined to then moving through classical chunks, easily described by simple the microscopic—more advanced physics into the tiny atomic world, geometries and relationships. These telescopes opened up the study of and ending with the vast expanse models made predictions about new the universe. of space. ■ behaviors in nature, which were tested by a new wave of pioneering Within a few generations, experimentalists—if the predictions humanity went from living at the were proven true, the models were center of the universe to residing on deemed laws which all of nature a speck of dust on the edge of one seemed to obey. The relationship of galaxy among billions. Not only had heat and energy was explored by we seen inside the heart of matter French physicist Sadi Carnot and and released the energy within, we others, founding the new science of had charted the seas of space with light that had been traveling since soon after the Big Bang.

MANEDASMUORTEI physics and the everyday world

MONENT

16 INTRODUCTION The Egyptians The Greek philosopher Italian astronomer Nicolaus Dutch physicist Christiaan use the cubit Euclid writes Copernicus publishes De Huygens invents the to measure Revolutionibus orbium distance and Elements, one of the coelestium (On the pendulum clock, allowing manage farmland. foremost texts of the scientists to accurately time about geometry Revolutions of the Heavenly measure the motion Spheres), marking the start of of objects. and mathematics. the Scientific Revolution. 3000 BCE 3RD CENTURY BCE 1543 1656 1603 4TH CENTURY BCE 1361 Aristotle develops the French philosopher Nicholas Galileo Galilei shows scientific method Oresme proves the mean that balls rolling speed theorem, which using inductions from describes the distance down inclined planes observations to draw accelerate at the covered by objects undergoing deductions about constant acceleration. same rate regardless the world. of their mass. O ur survival instincts have purchase plentiful goods cheaply were unrivalled for millennia and made us creatures of in one location before transporting devise farming systems to feed comparison. Our ancient and selling them for a higher price the burgeoning population. As struggle to survive by ensuring that in another location where that trade with ancient Egypt became we found enough food for our family commodity was scarce. As trade global, the idea of a common or reproduced with the correct in goods grew to become global, language of measurement mate has been supplanted. These local leaders began taxing trade spread around the world. primal instincts have evolved with and imposing standard prices. To our society into modern equivalents enforce this, they needed standard The Scientific Revolution such as wealth and power. We measures of physical things to (1543–1700) brought about a new cannot help but measure ourselves, allow them to make comparisons. need for these metrics. For the others, and the world around us by scientist, metrics were to be metrics. Some of these measures Language of measurement used not for trading goods but are interpretive, focusing upon Realizing that each person’s as a tool with which nature could personality traits that we experience is relative, the ancient be understood. Distrusting their benchmark against our own Egyptians devised systems that instincts, scientists developed feelings. Others, such as height, could be communicated without controlled environments in which weight, or age, are absolutes. bias from one person to another. they tested connections between They developed the first system different behaviors—they For many people in the ancient of metrics, a standard method experimented. Early experiments and modern world alike, a measure for measuring the world around focused on the movement of of success was wealth. To amass them. The Egyptian cubit allowed everyday objects, which had fortune, adventurers traded goods engineers to plan buildings that a direct effect upon daily life. across the globe. Merchants would Scientists discovered patterns

MEASUREMENT AND MOTION 17 English cleric John Isaac Newton Swiss mathematician British physicist Wallis suggests that publishes Principia Leonhard Euler’s James Joule conducts and revolutionizes experiments that show momentum, the our understanding laws of motion define that energy is neither product of mass and linear momentum lost nor gained when velocity, is conserved of how objects it is converted from one move on Earth and and the rate of in all processes. change of angular form to another. in the cosmos. momentum. 1668 1687 1752 1845 1663 1670 1740 1788 2019 French physicist Blaise French astronomer and French mathematician French physicist The units Pascal’s law about the mathematician Gabriel Émilie du Châtelet Joseph-Louis with which we uniform distribution of Mouton suggests the benchmark our pressure throughout a discovers how to figure Lagrange produces liquid in an enclosed metric system of the kinetic energy of equations to universe are space is published. units using the meter, redefined to depend a moving object. simplify calculations on nature alone. liter, and gram. about motion. in linear, circular, and repetitive on his laws of motion, English international (SI) collection of oscillating motion. These patterns physicist Isaac Newton invented metrics to convey their results. became immortalized in the calculus, which brought a new The value of each of these SI language of mathematics, a gift ability to describe the change metrics and their link to the world from ancient civilizations that had in systems over time, not just around us are defined and decided then been developed in the Islamic calculate single snapshots. To upon by an international group of world for centuries. Mathematics explain the acceleration of falling scientists known as metrologists. offered an unambiguous way objects, and eventually the nature of sharing the outcomes of of heat, ideas of an unseen entity This first chapter charts these experiments and allowed scientists called energy began to emerge. early years of the science we today to make predictions and test these Our world could no longer be call physics, the way in which predictions with new experiments. defined by distance, time, and the science operates through With a common language and mass alone, and new metrics experimentation, and how results metrics, science marched forward. were needed to benchmark the from these tests are shared across These pioneers discovered links measurement of energy. the world. From the falling objects between distance, time, and speed that Italian polymath Galileo Galilei and set out their own repeatable and Scientists use metrics to convey used to study acceleration to the tested explanation of nature. the results of experiments. Metrics oscillating pendulums that paved provide an unambiguous language the way to accurate timekeeping, Measuring motion that enables scientists to interpret this is the story of how scientists Scientific theories progressed the results of an experiment and began to measure distance, time, rapidly and with them the language repeat the experiment to check energy, and motion, revolutionizing of mathematics changed. Building that their conclusions are correct. our understanding of what makes Today, scientists use the Système the world work. ■

18 MMALEALANSTIUHSRINTEHGOESF MEASURING DISTANCE IN CONTEXT W hen people began to to the tip of the outstretched build structures on an middle finger. Of course, not KEY CIVILIZATION organized scale, they everyone has the same length of Ancient Egypt needed a way to measure height forearm and middle finger, so this and length. The earliest measuring “standard” was only approximate. BEFORE devices are likely to have been c.4000bce Administrators use primitive wooden sticks scored Imperial measure a system of measuring field with notches, with no accepted As prodigious architects and sizes in ancient Mesopotamia. consistency in unit length. The first builders of monuments on a widespread unit was the “cubit,” grand scale, the ancient Egyptians c. 3100 bce Officials in ancient which emerged in the 4th and 3rd needed a standard unit of distance. Egypt use knotted cords—pre- millennia bce among the peoples of Fittingly, the royal cubit of the Old stretched ropes tied at regular Egypt, Mesopotamia, and the Indus Kingdom of ancient Egypt is the intervals—to measure land and Valley. The term cubit derives from first known standardized cubit survey building foundations. the Latin for elbow, cubitum, and measure in the world. In use since was the distance from the elbow at least 2700 bce, it was 20.6–20.8 in AFTER (523–529 mm) long and was divided 1585 In the Netherlands, Cubit into 28 equal digits, each based Simon Stevin proposes a on a finger’s breadth. decimal system of numbers. Palm Archaeological excavations of 1799 The French government The Egyptian royal cubit was based pyramids have revealed cubit rods adopts the meter. on the length of the forearm, measured of wood, slate, basalt, and bronze, from the elbow to the middle fingertip. which would have been used as 1875 Signed by 17 nations, Cubits were subdivided into 28 digits measures by craftsmen and the Meter Convention agrees a (each a finger’s breadth in length) and architects. The Great Pyramid at consistent length for the unit. a series of intermediary units, such as Giza, where a cubit rod was found palms and hands. in the King’s Chamber, was built 1960 The eleventh General to be 280 cubits in height, with a Conference on Weights and base of 440 cubits squared. The Measures sets the metric Egyptians further subdivided system as the International cubits into palms (4 digits), hands System of Units (“SI,” from the (5 digits), small spans (12 digits), French Système international). large spans (14 digits, or half a cubit), and t’sers (16 digits or

MEASUREMENT AND MOTION 19 See also: Free falling 32–35 ■ Measuring time 38–39 ■ SI units and physical Changing definitions constants 58–63 ■ Heat and transfers 80–81 In 1668, English clergyman 4 palms). The khet (100 cubits) was Cubit rods—such as this example John Wilkins followed Stevin’s used to measure field boundaries from the 18th dynasty in ancient proposal of a decimal-based and the ater (20,000 cubits) to Egypt, c. 14th century bce—were used unit of length with a novel define larger distances. widely in the ancient world to achieve definition: he suggested that consistent measurements. 1 meter should be set as the Cubits of various length were distance of a two-second used across the Middle East. The male’s thumb—foot, and mile. pendulum swing. Dutch Assyrians used cubits in c. 700 bce, The Roman mile was 1,000 paces, physicist Christiaan Huygens while the Hebrew Bible contains or mille passus, each of which was (1629–1695) calculated this to plentiful references to cubits— five Roman feet. Roman colonial be 39.26 in (997 mm). particularly in the Book of Exodus’s expansion from the 3rd century bce account of the construction of the to the 3rd century ce introduced In 1889, an alloy bar of Tabernacle, the sacred tent that these units to much of western platinum (90%) and iridium housed the Ten Commandments. Asia and Europe, including (10%) was cast to represent The ancient Greeks developed their England, where the mile was the definitive 1-meter length, own 24-unit cubit, as well as the redefined as 5,280 feet in 1593 but because it expanded and stade (plural stadia), a new unit by Queen Elizabeth I. contracted very slightly at representing 300 cubits. In the different temperatures, it was 3rd century bce, the Greek scholar Going metric accurate only at the melting Eratosthenes (c. 276 bce–c. 194 bce) In his 1585 pamphlet De Thiende point of ice. This bar is still estimated the circumference of (The Art of Tenths), Flemish kept at the International Earth at 250,000 stadia, a figure he physicist Simon Stevin proposed a Bureau of Weights and later refined to 252,000 stadia. The decimal system of measurement, Measures in Paris, France. Romans also adopted the cubit, forecasting that, in time, it would When SI definitions were along with the inch—an adult be widely accepted. More than two adopted in 1960, the meter centuries later, work on the metric was redefined in terms of the You are to make upright system was begun by a committee wavelength of electromagnetic frames of acacia wood for of the French Academy of Sciences, emissions from a krypton the Tabernacle. Each frame with the meter being defined as atom. In 1983, yet another is to be ten cubits long and one ten-millionth of the distance definition was adopted: the a cubit and a half wide. from Earth’s equator to the North distance that light travels Pole. France became the first nation in a vacuum in 1/299,792,458 Exodus 26:15–16 to adopt the measurement, in 1799. of a second. The Bible International recognition was A mile shall contain eight not achieved until 1960, when the furlongs, every furlong forty Système international (SI) set the meter as the base unit for distance. poles, and every pole It was agreed that 1 meter (m) is shall contain sixteen equal to 1,000 millimeters (mm) or 100 centimeters (cm), and 1,000 m foot and a half. make up 1 kilometer (km). ■ Queen Elizabeth I

20 IN CONTEXT QOWAUNPIEESRSDUHTODAIMOELNFNTOISF KEY FIGURE Aristotle (c. 384–322 bce) THE SCIENTIFIC METHOD BEFORE 585 bce Thales of Miletus, a Greek mathematician and philosopher, analyzes movements of the sun and moon to forecast a solar eclipse. AFTER 1543 Nicolaus Copernicus’s De Revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres) and Andreas Vesalius’s De humani corporis fabrica (On the Workings of the Human Body) rely on detailed observation, marking the beginning of the Scientific Revolution. 1620 Francis Bacon proposes the inductivist method, which involves making generalizations based on accurate observations. C areful observation and a questioning attitude to findings are central to the scientific method of investigation, which underpins physics and all the sciences. Since it is easy for prior knowledge and assumptions to distort the interpretation of data, the scientific method follows a set procedure. A hypothesis is drawn up on the basis of findings, and then tested experimentally. If this hypothesis fails, it can be revised and reexamined, but if it is robust, it is shared for peer review— independent evaluation by experts. People have always sought to understand the world around them, and the need to find food and

MEASUREMENT AND MOTION 21 See also: Free falling 32–35 ■ SI units and physical constants 58–63 ■ Focusing light 170–175 ■ Models of the universe 272–273 ■ Dark matter 302–305 The starting point for Scientists form a the scientific method is hypothesis (a theory an observation. to explain the observation). An experiment is carried out to test the hypothesis. Data from the experiment is collected. Aristotle If the data supports If the data refutes The son of the court physician the hypothesis, the the hypothesis, the of the Macedonian royal experiment is repeated hypothesis is revised. family, Aristotle was raised to make sure the results by a guardian after his parents died when he was young. At are correct. around the age of 17, he joined Plato’s Academy in Athens, The hypothesis is eventually accepted as fact. the foremost center of learning in Greece. Over the next two understand changing weather were who sought to interpret the world decades, he studied and wrote matters of life and death long before and record their findings. One of about philosophy, astronomy, ideas were written down. In many the first to reject supernatural biology, chemistry, geology, societies, mythologies developed explanations of natural phenomena and physics, as well as to explain natural phenomena; was the Greek thinker Thales of politics, poetry, and music. He elsewhere, it was believed that Miletus. Later, the philosophers also traveled to Lesvos, where everything was a gift from the gods Socrates and Plato introduced he made ground-breaking and events were preordained. debate and argument as a method observations of the island’s of advancing understanding, but it botany and zoology. Early investigations was Aristotle—a prolific investigator The world’s first civilizations— of physics, biology, and zoology— In c. 343 bce, Aristotle was ancient Mesopotamia, Egypt, who began to develop a scientific invited by Philip II of Macedon Greece, and China—were method of inquiry, applying logical to tutor his son, the future sufficiently advanced to support reasoning to observed phenomena. Alexander the Great. He “natural philosophers,” thinkers He was an empiricist, someone ❯❯ established a school at the Lyceum in Athens in 335 bce, where he wrote many of his most celebrated scientific treatises. Aristotle left Athens in 322 bce and settled on the island of Euboea, where he died at the age of about 62. Key works Metaphysics On the Heavens Physics

22 THE SCIENTIFIC METHOD All truths are Anatomical drawings from 1543 easy to understand reflect Vesalius’s mastery of dissection and set a new standard for study of the once they are human body, unchanged since the discovered; the point Greek physician Galen (129–216 ce). is to discover them. greater authority. In fact, the Galileo Galilei geocentric view of the universe was held to be true—due in part to its enforcement by the Catholic Church, which discouraged ideas that challenged its interpretation of the Bible—until it was superseded in the 17th century by the ideas of Copernicus, Galileo, and Newton. who believes that all knowledge is Testing and observation point of a luminous object radiates based on experience derived from Arab scholar Ibn al-Haytham light along every straight line and the senses, and that reason alone (widely known as “Alhazen”) was in every direction. is not enough to solve scientific an early proponent of the scientific problems—evidence is required. method. Working in the 10th and Unfortunately, al-Haytham’s 11th centuries ce, he developed his methods were not adopted beyond Traveling widely, Aristotle own method of experimentation the Islamic world, and it would be was the first to make detailed to prove or disprove hypotheses. 500 years before a similar approach zoological observations, seeking His most important work was emerged independently in Europe, evidence to group living things by in the field of optics, but he also during the Scientific Revolution. behavior and anatomy. He went made important contributions to But the idea that accepted theories to sea with fishermen in order to astronomy and mathematics. may be challenged, and overthrown collect and dissect fish and other Al-Haytham experimented with if proof of an alternative can be marine organisms. After discovering sunlight, light reflected from produced, was not the prevailing that dolphins have lungs, he judged artificial light sources, and refracted view in 16th-century Europe. Church they should be classed with whales, light. For example, he tested—and authorities rejected many scientific not fish. He separated four-legged proved—the hypothesis that every ideas, such as the work of Polish animals that give birth to live astronomer Nicolaus Copernicus. young (mammals) from those that Earth Moon He made painstaking observations lay eggs (reptiles and amphibians). Mercury Mars of the night sky with the naked eye, Saturn explaining the temporary retrograde However, in other fields Aristotle Sun (“backward”) motion of the planets, was still influenced by traditional Venus which geocentrism had never ideas that lacked a grounding in accounted for. Copernicus realized good science. He did not challenge Jupiter the phenomenon was due to Earth the prevailing geocentric idea Copernicus’s heliocentric model, and the other planets moving that the sun and stars rotate around so-called because it made the sun around the sun on different orbits. Earth. In the 3rd centurybce, another (helios in Greek) the focus of planetary Although Copernicus lacked the Greek thinker, Aristarchus of orbits, was endorsed by some scientists tools to prove heliocentrism, his use Samos, argued that Earth and the but outlawed by the Church. known planets orbit the sun, that stars are very distant equivalents of “our” sun, and that Earth spins on its axis. Though correct, these ideas were dismissed because Aristotle and his student Ptolemy carried

MEASUREMENT AND MOTION 23 If a man will begin with recorded observations on matters of facts to create axioms (a process certainties, he shall end in as varied as the movement of the known as “inductivism”), while doubts, but if he will be content planets, the swing of pendulums, being careful to avoid generalizing to begin with doubts, he and the speed of falling bodies. He beyond what the facts tell us; produced theories to explain them, then gathering further facts to shall end in certainties. then made more observations to produce an increasingly complex Francis Bacon test the theories. He used the new base of knowledge. technology of telescopes to study of rational argument to challenge four of the moons orbiting Jupiter, Unproven science accepted thinking set him apart as proving Copernicus’s heliocentric When scientific claims cannot be a true scientist. Around the same model—under geocentrism, all verified, they are not necessarily time, Flemish anatomist Andreas objects orbited Earth. In 1633 wrong. In 1997, scientists at the Vesalius transformed medical Galileo was tried by the Church’s Gran Sasso laboratory in Italy thinking with his multi-volume work Roman Inquisition, found guilty of claimed to have detected evidence on the human body in 1543. Just as heresy, and placed under house- of dark matter, which is believed Copernicus based his theories on arrest for the last decade of his to make up about 27 percent of detailed observation, Vesalius life. He continued to publish by the universe. The most likely analyzed what he found when smuggling papers to Holland, away source, they said, were weakly dissecting human body-parts. from the censorship of the Church. interacting massive particles (WIMPs). These should be detected Experimental approach Later in the 17th century, as tiny flashes of light (scintillations) For Italian polymath Galileo Galilei, English philosopher Francis Bacon when a particle strikes the nucleus experimentation was central to the reinforced the importance of a of a “target” atom. However, scientific approach. He carefully methodical, skeptical approach to despite the best efforts of other scientific inquiry. Bacon argued research teams to replicate the that the only means of building experiment, no other evidence true knowledge was to base of dark matter has been found. axioms and laws on observed It is possible that there is an facts, not relying (even if only unidentified explanation—or the partially) on unproven deductions scintillations could have been and conjecture. The Baconian produced by helium atoms, which method involves making systematic are present in the experiment’s observations to establish verifiable photomultiplier tubes. ■ facts; generalizing from a series The scientific method in practice Photo 51, taken by Franklin, is Deoxyribonucleic acid (DNA) was diffraction pattern would be a 1952 X-ray diffraction image of identified as the carrier of genetic X-shaped. British scientist human DNA. The X-shape is due information in the human body in Rosalind Franklin tested this to DNA’s double-helix structure. 1944, and its chemical composition theory by performing X-ray was shown to be four different diffraction on crystallized pure molecules called nucleotides. DNA, beginning in 1950. After However, it was unclear how refining the technique over a genetic information was stored period of two years, her analysis in DNA. Three scientists—Linus revealed an X-shaped pattern Pauling, Francis Crick, and (best seen in “Photo 51”), James Watson—put forward the proving that DNA had a helical hypothesis that DNA possessed structure. The Pauling, Crick, a helical structure, and realized Watson hypothesis was proven, from work done by other scientists forming the starting point for that if that was the case, its X-ray further studies on DNA.

NAULMLBIESR THE LANGUAGE OF PHYSICS



26 THE LANGUAGE OF PHYSICS IN CONTEXT P hysics seeks to understand Number is the ruler of forms the universe through and ideas, and the cause of KEY FIGURE observation, experiment, Euclid of Alexandria and building models and theories. gods and daemons. (c. 325–c. 270 bce) All of these are intimately entwined Pythagoras with mathematics. Mathematics is BEFORE the language of physics—whether prediction increased. Power was 3000–300 bce Ancient used in measurement and data tied to knowledge of astronomical Mesopotamian and Egyptian analysis in experimental science, cycles and seasonal patterns, civilizations develop number or to provide rigorous expression such as flooding. Agriculture and systems and techniques to for theories, or to describe the architecture required accurate solve mathematical problems. fundamental “frame of reference” in calendars and land surveys. which all matter exists and events The earliest place value number 600–300 bce Greek scholars, take place. The investigation of systems (where a digit’s position including Pythagoras and space, time, matter, and energy is in a number indicates its value) Thales, formalize mathematics only made possible through a prior and methods for solving equations using logic and proofs. understanding of dimension, shape, date back more than 3,500 years symmetry, and change. to civilizations in Mesopotamia, AFTER Egypt, and (later) Mesoamerica. c. 630 ce Indian Driven by practical needs mathematician Brahmagupta The history of mathematics is one Adding logic and analysis uses zero and negative of increasing abstraction. Early The rise of ancient Greece brought numbers in arithmetic. ideas about number and shape about a fundamental change in developed over time into the most focus. Number systems and c. 820 ce Persian scholar general and precise language. al-Khwarizmi sets down In prehistoric times, before the the principles of algebra. advent of writing, herding animals and trading goods undoubtedly c. 1670 Gottfried Leibniz and prompted the earliest attempts Isaac Newton each develop at tallying and counting. calculus, the mathematical study of continuous change. As complex cultures emerged in the Middle East and Mesoamerica, demands for greater precision and Euclid Although his Elements were the loose ideas of other scholars. immensely influential, few details Thus, the theorems of the of Euclid’s life are known. He was 13 books of Euclid’s Elements born around 325bce, in the reign are not original, but for two of Egyptian pharaoh Ptolemy I millennia they set the standard and probably died around 270bce. for mathematical exposition. He lived mostly in Alexandria, then The earliest surviving editions an important center of learning, but of the Elements date from the he may also have studied at Plato’s 15th century. academy in Athens. Key works In Commentary on Euclid, written in the 5th century ce, the Elements Greek philosopher Proclus notes Data that Euclid arranged the theorems Catoptrics of Eudoxus, an earlier Greek Optics mathematician, and brought “irrefutable demonstration” to

MEASUREMENT AND MOTION 27 See also: Measuring distance 18–19 ■ Measuring time 38–39 ■ Laws of motion 40–45 ■ SI units and physical constants 58–63 ■ Antimatter 246 ■ The particle zoo and quarks 256–257 ■ Curving spacetime 280 1⁄16 1⁄8 1⁄4 1⁄2 1 Central to calculus is the idea of calculating infinitesimals (infinitely The dichotomy paradox is one of Zeno’s paradoxes that show motion to small quantities), which was be logically impossible. Before walking a certain distance a person must anticipated by Archimedes of walk half that distance, before walking half the distance he must walk a Syracuse, who lived in the 3rd quarter of the distance, and so on. Walking any distance will therefore entail century bce. To calculate the an infinite number of stages that take an infinite amount of time to complete. approximate volume of a sphere, for instance, he halved it, enclosed measurement were no longer which cannot be exactly expressed the hemisphere in a cylinder, then simply practical tools; Greek as one whole number divided by imagined slicing it horizontally, scholars also studied them for their another) by the Pythagorean from the top of the hemisphere, own sake, together with shape and philosopher Hippasus; according where the radius is infinitesimally change. Although they inherited to legend, he was murdered by small, downward. He knew that much specific mathematical scandalized colleagues. the thinner he made his slices, the knowledge from earlier cultures, more accurate the volume would such as elements of Pythagoras’s Titans of mathematics be. Reputed to have shouted theorem, the Greeks introduced the In the 5th century bce, the Greek “Eureka!” on discovering that the rigor of logical argument and an philosopher Zeno of Elea devised upward buoyant force of an object approach rooted in philosophy; the paradoxes about motion, such as immersed in water is equal to the ancient Greek word philosophia Achilles and the tortoise. This weight of the fluid it displaces, means “love of wisdom.” was the idea that, in any race Archimedes is notable for applying where the pursued has a head start, math to mechanics and other The ideas of a theorem (a the pursuer is always catching up— branches of physics in order to general statement that is true eventually by an infinitesimal solve problems involving levers, everywhere and for all time) and amount. Such puzzles, which were screws, pulleys, and pumps. proof (a formal argument using logical—if simple to disprove in the laws of logic) are first seen in the practice—would worry generations Archimedes studied in geometry of the Greek philosopher of mathematicians. They were Alexandria, at a school established Thales of Miletus in the early 6th resolved, at least partially, in the by Euclid, often known as the century bce. Around the same 17th century by the development of “Father of Geometry.” It was by ❯❯ time, Pythagoras and his followers calculus, a branch of mathematics elevated numbers to be the building that deals with continuously blocks of the universe. changed quantities. For the Pythagoreans, numbers Greek philosophers drew in the sand had to be “commensurable”— when teaching geometry, as shown measurable in terms of ratios or here. Archimedes is said to have been fractions—to preserve the link drawing circles in the sand when he with nature. This world view was was killed by a Roman soldier. shattered with the discovery of irrational numbers (such as √2,

28 THE LANGUAGE OF PHYSICS analyzing geometry itself that precise, symbolic language of Imaginary numbers are a fine Euclid established the template modern mathematics—which is and wonderful refuge of the for mathematical argument for significantly more effective for divine spirit … almost an the next 2,000 years. His 13-book analyzing problems and universally amphibian between being treatise, Elements, introduced understood—is relatively recent. the “axiomatic method” for Around 250ce, however, the Greek and non-being. geometry. He defined terms, mathematician Diophantus of Gottfried Leibniz such as “point,” and outlined five Alexandria introduced the partial axioms (also known as postulates, use of symbols to solve algebraic French mathematician François or self-evident truths), such as “a problems in his principal work Viète finally pioneered the use of line segment can be drawn Arithmetica, which influenced the symbols in equations in his 1591 between any two points.” From development of Arabic algebra after book, Introduction to the Analytic these axioms, he used the laws the fall of the Roman Empire. Arts. The language was not yet of logic to deduce theorems. standard, but mathematicians could The study of algebra flourished now write complicated expressions By today’s standards, Euclid’s in the East during the Golden Age in a compact form, without resorting axioms are lacking; there are of Islam (from the 8th century to the to diagrams. In 1637, French numerous assumptions that 14th century). Baghdad became philosopher and mathematician a mathematician would now the principal seat of learning. Here, René Descartes reunited algebra expect to be stated formally. at an academic center called the and geometry by devising the Elements remains, however, House of Wisdom, mathematicians coordinate system. a prodigious work, covering not could study translations of Greek only plane geometry and three- texts on geometry and number More abstract numbers dimensional geometry, but also theory or Indian works discussing Over millennia, in attempts to solve ratio and proportion, number theory, the decimal place-value system. different problems, mathematicians and the “incommensurables” that In the early 9th century, Muhammad have extended the number system, Pythagoreans had rejected. ibn Musa al-Khwarizmi (from expanding the counting numbers whose name comes the word 1, 2, 3 … to include fractions and Language and symbols “algorithm”) compiled methods for irrational numbers. The addition In ancient Greece and earlier, balancing and solving equations of zero and negative numbers scholars described and solved in his book al Jabr (the root of the indicated increasing abstraction. algebraic problems (determining word “algebra”). He popularized In ancient number systems, zero unknown quantities given certain the use of Hindu numerals, which had been used as a placeholder—a known quantities and relationships) evolved into Arabic numerals, way to tell 10 from 100, for instance. in everyday language and by using but still described his algebraic By around the 7th century ce, geometry. The highly-abbreviated, problems in words. Islamic scholars gather in one of Baghdad’s great libraries in this 1237 image by the painter Yahya al-Wasiti. Scholars came to the city from all points of the Islamic Empire, including Persia, Egypt, Arabia, and even Iberia (Spain).

MEASUREMENT AND MOTION 29 negative numbers were used In differential calculus, Integrating a curve’s for representing debts. In 628 ce, the gradient (slope) of the equation between two the Indian mathematician tangent to a curve at a Brahmagupta was the first to treat point shows the rate of xvalues of gives the negative integers (whole numbers) change at that point just like the positive integers for area under the curve arithmetic. Yet, even 1,000 years y between those values later, many European scholars still considered negative numbers 5 y unacceptable as formal solutions to equations. 4 5 4 The 16th-century Italian 3 3 polymath Gerolamo Cardano not 2 only used negative numbers, but, 2 1 in Ars Magna, introduced the idea of complex numbers (combining a 1 01234 x real and imaginary number) to INTEGRAL CALCULUS solve cubic equations (those with x 5 at least one variable to the power 012345 of three, such as x3, but no higher). DIFFERENTIAL CALCULUS Complex numbers take the form Differential calculus examines the rate of change a + bi, where a and b are real over time, shown geometrically here as the rate of numbers and i is the imaginary change of a curve. Integral calculus examines the unit, usually expressed as i = √-1. areas, volumes, or displacement bounded by curves. The unit is termed “imaginary” set down the first rules for using new methods and techniques because when squared it is complex and imaginary numbers, emerged. One of the most negative, and squaring any real it took a further 200 years before significant for physics, was the number, whether it is positive or Swiss mathematician Leonhard development of “infinitesimal” negative, produces a positive methods in order to study curves number. Although Cardano’s Euler introduced the symbol i to and change. The ancient Greek contemporary Rafael Bombelli method of exhaustion—finding the denote the imaginary unit. area of a shape by filling it with A new, a vast, and a powerful Like negative numbers, complex smaller polygons—was refined in language is developed for the order to compute areas bounded numbers were met with resistance, by curves. It finally evolved into future use of analysis, in right up until the 18th century. a branch of mathematics called which to wield its truths so Yet they represented a significant integral calculus. In the 17th that these may become of advance in mathematics. Not century, French lawyer Pierre more speedy and accurate only do they enable the solution de Fermat’s study of tangents to practical application for the of cubic equations but, unlike real curves inspired the development numbers, they can be used to of differential calculus—the purposes of mankind. solve all higher-order polynomial calculation of rates of change. Ada Lovelace equations (those involving two or more terms added together and Around 1670, English physicist British computer scientist Isaac Newton and German higher powers of a variable x, such philosopher Gottfried Leibniz as x4 or x5). Complex numbers independently worked out a theory that united integral emerge naturally in many branches and differential calculus into of physics, such as quantum infinitesimal calculus. The mechanics and electromagnetism. underlying idea is of approximating a curve (a changing quantity) by ❯❯ Infinitesimal calculus From the 14th century to the 17th century, together with the increasing use of symbols, many

30 THE LANGUAGE OF PHYSICS Euclidean and non-Euclidean geometries In Euclidean geometry, space is In hyperbolic geometry, developed In elliptic geometry, the surface assumed to be “flat.” Parallel lines by Bolyai and Lobachevsky, the surface curves outward like a sphere and remain at a constant distance from curves like a saddle and lines on the parallel lines curve toward each one another and never meet. surface curve away from each other. other, eventually intersecting. considering that it is made up is not on that line, exactly one line (hyperbolic geometry) in which of many straight lines (a series of can be drawn through the given the fifth postulate is false and different, fixed quantities). At the point and parallel to the given parallel lines never meet. In their theoretical limit, the curve is line. Throughout history, various geometry, the surface is not flat as identical to an infinite number mathematicians, such as Proclus in Euclid’s, but curves inward. By of infinitesimal approximations. of Athens in the 5th century or the contrast, in elliptic geometry and Arabic mathematician al-Haytham, spherical geometry, also described During the 18th and 19th have attempted in vain to show in the 19th century, there are no centuries, applications of calculus that the parallel postulate can be parallel lines; all lines intersect. in physics exploded. Physicists derived from the other postulates. could now precisely model dynamic In the early 1800s, Hungarian German mathematician (changing) systems, from vibrating mathematician János Bolyai and Bernhard Riemann and others strings to the diffusion of heat. Russian mathematician Nicolai formalized such non-Euclidean The work of 19th-century Scottish Lobachevsky independently geometries. Einstein used physicist James Clerk Maxwell developed a version of geometry Riemannian theory in his general greatly influenced the development theory of relativity—the most of vector calculus, which models Out of nothing I have created a advanced explanation of gravity— change in phenomena that have strange new universe. All that in which mass “bends” spacetime, both quantity and direction. Maxwell I have sent you previously is making it non-Euclidean, although also pioneered the use of statistical space remains homogeneous techniques for the study of large like a house of cards in (uniform, with the same properties numbers of particles. comparison with a tower. at every point). Non-Euclidean geometries János Bolyai Abstract algebra The fifth axiom, or postulate, on By the 19th century, algebra geometry that Euclid set out in in a letter to his father had undergone a seismic shift, his Elements, is also known as to become a study of abstract the parallel postulate. This was symmetry. French mathematician controversial, even in ancient Évariste Galois was responsible for times, as it appears less self-evident a key development. In 1830, while than the others, although many investigating certain symmetries theorems depend on it. It states exhibited by the roots (solutions) that, given a line and a point that of polynomial equations, he

MEASUREMENT AND MOTION 31 developed a theory of abstract In the 1950s and 1960s, physicists Emmy Noether was a highly creative mathematical objects, called used group theory to develop the algebraist. She taught at the University groups, to encode different kinds Standard Model of particle physics. of Göttingen in Germany, but as of symmetries. For example, a Jew was forced to leave in 1933. all squares exhibit the same Modeling reality She died in the US in 1935, aged 53. reflectional and rotational Mathematics is the abstract study symmetries, and so are associated of numbers, quantities, and shapes, instance, the application of with a particular group. From his which physics employs to model 19th-century group theory to research, Galois determined that, reality, express theories, and modern quantum physics. There unlike for quadratic equations (with predict future outcomes—often are also many examples of a variable to the power of two, such with astonishing accuracy. For mathematical structures driving example, the electron g-factor— insight into nature. When British as x2, but no higher), there is no a measure of its behavior in an physicist Paul Dirac found twice as electromagnetic field—is computed many expressions as expected in general formula to solve polynomial to be 2.002 319 304 361 6, while the his equations describing the equations of degree five (with terms experimentally determined value behavior of electrons, consistent is 2.002 319 304 362 5 (differing by with relativity and quantum such as x5) or higher. This was a just one part in a trillion). mechanics, he postulated the existence of an anti-electron; it dramatic result; he had proved that Certain mathematical models was duly discovered, years later. there could be no such formula, no have endured for centuries, matter what future developments requiring only minor adjustments. While physicists investigate occurred in mathematics. For example, German astronomer what “is” in the universe, Johannes Kepler’s 1619 model of mathematicians are divided as to Subsequently, algebra grew into the solar system, with some whether their study is about nature, the abstract study of groups and refinements by Newton and or the human mind, or the abstract similar objects, and the symmetries Einstein, remains valid today. manipulation of symbols. In a they encoded. In the 20th century, Physicists have applied ideas strange historical twist, physicists groups and symmetry proved vital that mathematicians developed, researching string theory are now for describing natural phenomena sometimes much earlier, simply suggesting revolutionary advances at the deepest level. In 1915, to investigate a pattern; for in pure mathematics to geometers German algebraist Emmy Noether (mathematicians who study connected symmetry in equations geometry). Just exactly how this with conservation laws, such as the illuminates the relationship conservation of energy, in physics. between mathematics, physics, and “reality” is yet to be seen. ■ Mathematics is an abstract, concise, symbolic language of quantity, pattern, symmetry, and change. Physicists’ mathematical models of nature have great predictive power. Mathematics must be a true (if partial) description of the universe.

32 IN CONTEXT BBNTHUOOETDRIAFEEIRSSROISSMUTAFNFECRE KEY FIGURE Galileo Galilei (1564–1642) FREE FALLING BEFORE c. 350bce In Physics, Aristotle explains gravity as a force that moves bodies toward their “natural place,” down toward the center of Earth. 1576 Giuseppe Moletti writes that objects of different weights free fall at the same rate. AFTER 1651 Giovanni Riccioli and Francesco Grimaldi measure the time of descent of falling bodies, enabling calculation of their rate of acceleration. 1687 In Principia, Isaac Newton expounds gravitational theory in detail. 1971 David Scott shows that a hammer and a feather fall at the same speed on the moon. W hen gravity is the only force acting on a moving object, it is said to be in “free fall.” A skydiver falling from a plane is not quite in free fall— since air resistance is acting upon him—whereas planets orbiting the sun or another star are. The ancient Greek philosopher Aristotle believed that the downward motion of objects dropped from a height was due to their nature—they were moving toward the center of Earth, their natural place. From Aristotle’s time until the Middle Ages, it was accepted as fact that the speed of a free-falling object was proportional to its weight, and inversely proportional to the density

MEASUREMENT AND MOTION 33 See also: Measuring distance 18–19 ■ Measuring time 38–39 ■ Laws of motion 40–45 ■ Laws of gravity 46–51 ■ Kinetic energy and potential energy 54 If gravity is the only force acting on a moving object, it is in a state of free fall. Unless it moves in a In a vacuum, its Galileo Galilei vacuum, air resistance speed increases at a and/or friction will slow The oldest of six siblings, constant rate of Galileo was born in Pisa, Italy, it down. acceleration, regardless of in 1564. He enrolled to study medicine at the University of its size or weight. Pisa at the age of 16, but his interests quickly broadened Bodies suffer no resistance but from the air. and he was appointed Chair of Mathematics at the University of the medium it was falling free-falling body will fall more of Padua in 1592. Galileo’s through. So, if two objects of quickly than a lighter one—a view contributions to physics, different weights are dropped that had recently been challenged mathematics, astronomy, and at the same time, the heavier by several other scientists. engineering single him out as will fall faster and hit the ground one of the key figures of the before the lighter object. Aristotle In 1576, Giuseppe Moletti, Scientific Revolution in 16th- also understood that the object’s Galileo’s predecessor in the Chair and 17th-century Europe. He shape and orientation were factors of Mathematics at the University of created the first thermoscope in how quickly it fell, so a piece of Padua, had written that objects of (an early thermometer), unfolded paper would fall more different weights but made of the defended the Copernican slowly than the same piece of same material fell to the ground at idea of a heliocentric solar paper rolled into a ball. the same speed. He also believed system, and made important that bodies of the same volume ❯❯ discoveries about gravity. Because some of his ideas Falling spheres Nature is inexorable and challenged Church dogma, At some time between 1589 and immutable; she never he was called before the 1592, according to his student and transgresses the laws Roman Inquisition in 1633, biographer Vincenzo Viviani, Italian imposed upon her. declared to be a heretic, and polymath Galileo Galilei dropped Galileo Galilei sentenced to house arrest two spheres of different weight until his death in 1642. from the Tower of Pisa to test Aristotle’s theory. Although it was Key works more likely to have been a thought experiment than a real-life event, 1623 The Assayer Galileo was reportedly excited to 1632 Dialogue Concerning discover that the lighter sphere fell the Two Chief World Systems to the ground as quickly as the 1638 Discourses and heavier one. This contradicted the Mathematical Demonstrations Aristotelian view that a heavier Relating to Two New Sciences

34 FREE FALLING sacrosanct by the Catholic Church, in which Oresme served as a Fall of 1 ft (0.3 m) after 1 second bishop. It is not known whether Fall of 4 ft (1.2 m) after 2 seconds Oresme’s studies influenced the Fall of 9 ft (2.7 m) after 3 seconds later work of Galileo. Fall of 16 ft (4.9 m) Balls on ramps after 4 seconds From 1603, Galileo set out to investigate the acceleration of free- Fall of 25 ft falling objects. Unconvinced that (7.6 m) after they fell at a constant speed, he 5 seconds believed that they accelerated as they fell—but the problem was Galileo showed that objects of different mass Lighter ball how to prove it. The technology accelerate at a constant rate. By timing how long a ball Heavier ball to accurately record such speeds took to travel a particular distance down a slope, he could simply did not exist. Galileo’s figure out its acceleration. The distance fallen was always ingenious solution was to slow proportional to the square of the time taken to fall. down the motion to a measurable speed, by replacing a falling object but made of different materials uniformly, its speed increases in with a ball rolling down a sloping fell at the same rate. Ten years direct proportion to time, and the ramp. He timed the experiment later, Dutch scientists Simon Stevin distance it travels is proportional using both a water clock—a device and Jan Cornets de Groot climbed to the square of the time during that weighed the water spurting 33 ft (10 m) up a church tower in which it is accelerating. It was into an urn as the ball traveled— Delft to release two lead balls, one perhaps surprising that Oresme and his own pulse. If he doubled ten times bigger and heavier than should have challenged the the period of time the ball rolled, he the other. They witnessed them established Aristotelian “truth,” found the distance it traveled was hit the ground at the same time. which at the time was considered four times as far. The age-old idea of heavier objects falling faster than lighter ones Leaving nothing to chance, was gradually being debunked. Galileo repeated the experiment “a full hundred times” until he Another of Aristotle’s beliefs— had achieved “an accuracy such that a free-falling object descends that the deviation between two at a constant speed—had been observations never exceeded one- challenged earlier still. Around 1361, French mathematician Nicole Oresme had studied the movement of bodies. He discovered that if an object’s acceleration is increasing In this fresco by Giuseppe Bezzuoli, Galileo is shown demonstrating his rolling-ball experiment in the presence of the powerful Medici family in Florence.

MEASUREMENT AND MOTION 35 tenth of a pulse beat.” He also The hammer and the feather changed the incline of the ramp: as it became steeper, the acceleration In 1971, American astronaut walk, Scott dropped a 3-lb increased uniformly. Since Galileo’s David Scott—commander of geological hammer and a 1-oz experiments were not carried out in the Apollo 15 moon mission— falcon’s feather from a height a vacuum, they were imperfect— performed a famous free-fall of 5 ft. In the virtual vacuum the moving balls were subject to experiment. The fourth NASA conditions of the moon’s surface, air resistance and friction from expedition to land on the moon, with no air resistance, the the ramp. Nevertheless, Galileo Apollo 15 was capable of a ultralight feather fell to the concluded that in a vacuum, all longer stay on the moon than ground at the same speed as the objects—regardless of weight or previous expeditions, and its heavy hammer. The experiment shape—would accelerate at a crew was the first to use a was filmed, so this confirmation uniform rate: the square of the Lunar Roving Vehicle. of Galileo’s theory that all elapsed time of the fall is objects accelerate at a uniform proportional to the distance fallen. Apollo 15 also featured a rate regardless of mass was greater focus on science than witnessed by a television Quantifying gravitational earlier moon landings. At the audience of millions. acceleration end of the mission’s final lunar In spite of Galileo’s work, the question of the acceleration of free- The priests, who described their dense rocks near Earth’s surface. falling objects was still contentious methodology in detail, repeated If the constant acceleration of an in the mid-17th century. From 1640 the experiments several times. object in free fall near Earth’s to 1650, Jesuit priests Giovanni Riccioli and Francesco Grimaldi Riccioli believed that free-falling surface is represented by g, the conducted various investigations objects accelerated exponentially, height at which it is released is z0 in Bologna. Key to their eventual but the results showed him that and time is t, then at any stage in success were Riccioli’s time- he was wrong. A series of falling keeping pendulums—which were objects were timed by pendulums its descent, the height of the body as accurate as any available at the at the top and bottom of the tower. time—and a very tall tower. The They fell 15 Roman feet (1 Roman above the surface z = z0 – 1/2 gt2, two priests and their assistants foot = 11.6 in) in 1 second, 60 feet where gt is the speed of the body dropped heavy objects from various in 2 seconds, 135 feet in 3 seconds, and g its acceleration. A body of levels of the 321-ft (98-m) Asinelli and 240 feet in 4 seconds. The data, mass m at a height z0 above Earth’s Tower, timing their descents. published in 1651, proved that the distance of descent was surface possesses gravitational When Galileo caused proportional to the square of the balls … to roll down length of time the object was potential energy U, which can be an inclined plane, falling—confirming Galileo’s ramp calculated by the equation U = a light broke upon all experiments. And for the first time, mgz0 (mass  acceleration  height students of nature. due to relatively accurate time- Immanuel Kant keeping, it was possible to work above Earth’s surface). ■ out the value of acceleration due German philosopher to gravity: 9.36 (±0.22) m/s2. This In questions of science, figure is only about 5 percent less the authority of a than the range of figures accepted today: around 9.81 m/s2. thousand is not worth the humble reasoning The value of g (gravity) varies of a single individual. according to a number of factors: it Galileo Galilei is greater at Earth’s poles than at the equator, lower at high altitudes than at sea level, and it varies very slightly according to local geology, for example if there are particularly

36 FFAOONRRECWMEUSMLTAICPHLIYNINEG PRESSURE IN CONTEXT W hile investigating Pascal’s findings weren’t published hydraulics (the until 1663, the year after his KEY FIGURE mechanical properties death, but they would be used by Blaise Pascal (1623–1662) of liquids), French mathematician engineers to make the operation and physicist Blaise Pascal made of machinery much easier. In BEFORE a discovery that would eventually 1796, Joseph Bramah applied the 1643 Italian physicist revolutionize many industrial principle to construct a hydraulic Evangelista Torricelli processes. Pascal’s law, as it press that flattened paper, cloth, and demonstrates the existence became known, states that if steel, doing so more efficiently of a vacuum using mercury pressure is applied to any part of and powerfully than previous in a tube; his principle is later a liquid in an enclosed space, that wooden presses. ■ used to invent the barometer. pressure is transmitted equally to every part of the fluid, and to the Small AFTER container walls. force 1738 In Hydrodynamica, Small Swiss mathematician Daniel The impact of Pascal piston Bernoulli argues that energy Pascal’s law means that pressure in a fluid is due to elevation, exerted on a piston at one end of Large motion, and pressure. a fluid-filled cylinder produces an piston equal increase in pressure on 1796 Joseph Bramah, another piston at the other end of Large a British inventor, uses the cylinder. More significantly, force Pascal’s law to patent the if the cross-section of the second first hydraulic press. piston is twice that of the first, the Liquids cannot be compressed force on it will be twice as great. and are used to transmit forces in 1851 Scottish–American So, a 2.2 lb (1 kg) load on the small hydraulics systems such as car jacks. inventor Richard Dudgeon piston will allow the large piston to A small force applied over a long patents a hydraulic jack. lift 4.4 lb (2 kg); the larger the ratio distance is turned into a larger force of the cross-sections, the more over a small distance, which can 1906 An oil hydraulic weight the large piston can raise. raise a heavy load. system is installed to raise and lower the guns of the See also: Laws of motion 40–45 ■ Stretching and squeezing 72–75 ■ Fluids US warship Virginia. 76–79 ■ The gas laws 82–85

MEASUREMENT AND MOTION 37 PMEORTSIOISNTWILL MOMENTUM IN CONTEXT W hen objects collide, A body in motion several things happen. is apt to continue KEY FIGURE They change velocity John Wallis (1616–1703) and direction, and the kinetic its motion. energy of motion may be converted John Wallis BEFORE to heat or sound. 1518 French natural still some loss of kinetic energy. In philosopher Jean Buridan In 1666, the Royal Society of The Geometrical Treatment of the describes “impetus,” the London challenged scientists to Mechanics of Motion, John Wallis measure of which is later come up with a theory to explain went further, correctly arguing that understood to be momentum. what happens when objects collide. momentum is also conserved in Two years later, three individuals inelastic collisions, where objects 1644 In his Principia published their theories: from become attached after they collide, Philosophiae (Principles of England, John Wallis and causing the loss of kinetic energy. Philosophy), French scientist Christopher Wren, and from One such example is that of a René Descartes describes Holland, Christiaan Huygens. comet striking a planet. momentum as the “amount of motion.” All moving bodies have Nowadays, the principles of momentum (the product of their conservation of momentum have AFTER mass and velocity). Stationary many practical applications, such 1687 Isaac Newton describes bodies have no momentum because as determining the speed of his laws of motion in his their velocity is zero. Wallis, Wren, vehicles after traffic accidents. ■ three-volume work Principia. and Huygens agreed that in an elastic collision (any collision in 1927 German theoretical which no kinetic energy is lost physicist Werner Heisenberg through the creation of heat or argues that for a subatomic noise), momentum is conserved as particle, such as an electron, long as there are no other external the more precisely its position forces at work. Truly elastic is known, the less precisely its collisions are rare in nature; the momentum can be known, nudging of one billiard ball by and vice versa. another comes close, but there is See also: Laws of motion 40–45 ■ Kinetic energy and potential energy 54 ■ The conservation of energy 55 ■ Energy and motion 56–57

38 PMTRHEOECDHMUAOCNSTITCIOAWNLOSANRODTFESRTFHUEL MEASURING TIME IN CONTEXT A pendulum takes the same time to swing in each direction because of gravity. KEY FIGURE Christiaan Huygens The longer the pendulum, The smaller the swing, (1629–1695) the more slowly it swings. the more accurately the BEFORE pendulum keeps time. c. 1275 The first all- mechanical clock is built. A pendulum is a simple An escapement timekeeping device. mechanism keeps the 1505 German clockmaker Peter Henlein uses the force pendulum moving. from an uncoiling spring to make the first pocket watch. T wo inventions in the mid the flow of water, or the burning of 1650s heralded the start a candle. These mechanical clocks 1637 Galileo Galilei has the of the era of precision relied on a “verge escapement idea for a pendulum clock. timekeeping. In 1656, Dutch mechanism,” which transmitted mathematician, physicist, and force from a suspended weight AFTER inventor Christiaan Huygens built through the timepiece’s gear train, c. 1670 The anchor the first pendulum clock. Soon a series of toothed wheels. Over escapement mechanism after, the anchor escapement was the next three centuries, there makes the pendulum clock invented, probably by English were incremental advances in more accurate. scientist Robert Hooke. By the the accuracy of these clocks, but 1670s, the accuracy of timekeeping they had to be wound regularly 1761 John Harrison’s fourth devices had been revolutionized. and still weren’t very accurate. marine chronometer, H4, passes its sea trials. The first entirely mechanical In 1637, Galileo Galilei clocks had appeared in Europe in had realized the potential for 1927 The first electronic clock, the 13th century, replacing clocks pendulums to provide more using quartz crystal, is built. reliant on the movement of the sun, accurate clocks. He found that 1955 British physicists Louis Essen and Jack Parry make the first atomic clock.

MEASUREMENT AND MOTION 39 See also: Free falling 32–35 ■ Harmonic motion 52–53 ■ SI units and physical Harrison’s marine constants 58–63 ■ Subatomic particles 242–243 chronometer Christiaan Huygens’ pendulum In the early 18th century, even clock dramatically improved the the most accurate pendulum accuracy of timekeeping devices. clocks didn’t work at sea—a This 17th-century woodcut shows the major problem for nautical inner workings of his clock, including navigation. With no visible toothed gears and pendulum. landmarks, calculating a ship’s position depended on accurate this, even the most advanced non- latitude and longitude pendulum clocks lost 15 minutes a readings. While it was easy to day; now that margin of error could gauge latitude (by viewing the be reduced to as little as 15 seconds. position of the sun), longitude could be determined only by a swinging pendulum was almost Quartz and atomic clocks knowing the time relative to isochronous, meaning the time it Pendulum clocks remained the a fixed point, such as the took for the bob at its end to return most accurate form of time Greenwich Meridian. Without to its starting point (its period) was measurement until the 1930s, clocks that worked at sea, this roughly the same whatever the when synchronous electric clocks was impossible. Ships were length of its swing. A pendulum’s became available. These counted lost and many men died, so, in swing could produce a more the oscillations of alternating 1714, the British government accurate way of keeping time than current coming from electric offered a prize to encourage the existing mechanical clocks. power supply; a certain number the invention of a marine clock. However, he hadn’t managed to of oscillations translated into build one before his death in 1642. movements of the clock’s hands. British inventor John Harrison solved the problem in Huygens’ first pendulum clock The first quartz clock was built 1761. His marine chronometer had a swing of 80–100 degrees, in 1927, taking advantage of the used a fast-beating balance which was too great for complete piezoelectric quality of crystalline wheel and a temperature- accuracy. The introduction of quartz. When bent or squeezed, compensated spiral spring to Hooke’s anchor escapement, it generates a tiny electric voltage, achieve remarkably accurate which maintained the swing of or conversely, if it is subject to timekeeping on transatlantic the pendulum by giving it a small an electric voltage, it vibrates. journeys. The device saved push each swing, enabled the use A battery inside the clock emits lives and revolutionized of a longer pendulum with a smaller the voltage, and the quartz chip exploration and trade. swing of just 4–6 degrees, which vibrates, causing an LCD display gave much better accuracy. Before to change or a tiny motor to move John Harrison’s prototype second, minute, and hour hands. chronometer, H1, underwent sea trials from Britain to Portugal in The first accurate atomic clock, 1736, losing just a few seconds built in 1955, used the cesium-133 on the entire voyage. isotope. Atomic clocks measure the frequency of regular electromagnetic signals that electrons emit as they change between two different energy levels when bombarded with microwaves. Electrons in an “excited” cesium atom oscillate, or vibrate, 9,192,631,770 times per second, making a clock calibrated on the basis of these oscillations extremely accurate. ■

RALEL AACTCIOTNIHOASNA LAWS OF MOTION



42 LAWS OF MOTION P rior to the late 16th surface. Smoke rises because it is century, there was little largely made of air. However, the IN CONTEXT understanding of why circular movement of celestial moving bodies accelerated or objects was not considered to be KEY FIGURES decelerated—most people governed by the elements—rather, Gottfried Leibniz (1646–1716), believed that some indeterminate, they were thought to be guided by Isaac Newton (1642–1727) innate quality made objects fall to the hand of a deity. the ground or float up to the sky. BEFORE But this changed at the dawn Aristotle believed that bodies c. 330 bce In Physics, Aristotle of the Scientific Revolution, when move only if they are pushed, expounds his theory that it scientists began to understand and once the pushing force is takes force to produce motion. that several forces are responsible removed, they come to a stop. for changing a moving object’s Some questioned why an arrow 1638 Galileo’s Dialogues velocity (a combined measure unleashed from a bow continues Concerning Two New of its speed and direction), to fly through the air long after Sciences is published. It is including friction, air resistance, direct contact with the bow has later described by Albert and gravity. ceased, but Aristotle’s views went Einstein as anticipating the largely unchallenged for more work of Leibniz and Newton. Early views than two millennia. For many centuries, the generally 1644 René Descartes accepted views of motion were In 1543, Polish astronomer publishes Principles in those of the ancient Greek Nicolaus Copernicus published Philosophy, which includes philosopher Aristotle, who his theory that Earth was not the laws of motion. classified everything in the center of the universe, but that it world according to its elemental and the other planets orbited the AFTER composition: earth, water, air, fire, sun in a “heliocentric” system. 1827–1833 William Rowan and quintessence, a fifth element Between 1609 and 1619, German Hamilton establishes that that made up the “heavens.” astronomer Johannes Kepler objects tend to move along For Aristotle, a rock falls to the developed his laws of planetary the path that requires the ground because it has a similar motion, which describe the shape least energy. composition to the ground (“earth”). and speed of the orbits of planets. Rain falls to the ground because Then, in the 1630s, Galileo 1907–1915 Einstein proposes water’s natural place is at Earth’s challenged Aristotle’s views on his theory of general relativity. falling objects, explained that a loosed arrow continues to fly Gottfried Leibniz Born in Leipzig (now Germany) unpublished ideas and passing in 1646, Leibniz was a great them off as his own. Although philosopher, mathematician, it was later generally accepted and physicist. After studying that Leibniz had arrived at his philosophy at the University ideas independently, he never of Leipzig, he met Christiaan managed to shake off the Huygens in Paris and determined scandal during his lifetime. to teach himself math and physics. He died in Hanover in 1716. He became a political adviser, historian, and librarian to the Key works royal House of Brunswick in Hanover in 1676, a role that gave 1684 “Nova methodus pro him the opportunity to work on a maximis et minimis” (“New broad range of projects, including method for maximums and the development of infinitesimal minimums”) calculus. However, he was also 1687 Essay on Dynamics accused of having seen Newton’s

MEASUREMENT AND MOTION 43 See also: Free falling 32–35 ■ Laws of gravity 46–51 ■ Kinetic energy and potential energy 54 ■ Energy and motion 56–57 ■ The heavens 270–271 ■ Models of the universe 272–273 ■ From classical to special relativity 274 There is neither more nor Movement does not occur because of inherent, invisible less power in an effect than properties possessed by an object. there is in its cause. Forces act upon the object, causing it to move or come to rest. Gottfried Leibniz These forces can be calculated and predicted. because of inertia, and described Objects move at a constant Unless it moves in a vacuum, the role of friction in bringing to a speed and direction, or an object in motion is halt a book sliding across a table. remain at rest unless acted on subject to friction, which These scientists laid the basis by an external force. slows it down. for French philosopher René Descartes and German polymath Acceleration is proportional to an object’s mass and Gottfried Leibniz to formulate their the force applied to it. own ideas about motion, and for English physicist Isaac Newton Space and time are best understood as being relative between to draw all the threads together objects, and not as absolute qualities that remain constant in Mathematical Principles of everywhere, all the time. Natural Philosophy (Principia). thorough laws of motion in Newton’s three laws of motion A new understanding Principia, which—like Dynamics— (see pp.44–45) clearly explained In Principles in Philosophy, was also published in 1687. Newton the forces acting on all bodies, Descartes proposed his three respected Descartes’ rejection of revolutionizing the understanding laws of motion, which rejected Aristotelian ideas, but argued that of the mechanics of the physical Aristotle’s views of motion and the Cartesians (followers of world and laying the foundations a divinely guided universe, and Descartes) did not make enough for classical mechanics (the study explained motion in terms of use of the mathematical techniques of the motion of bodies). Not all of forces, momentum, and collisions. of Galileo, nor the experimental Newton’s views were accepted In his 1687 Essay on Dynamics, methods of chemist Robert Boyle. during his lifetime—one of those Leibniz produced a critique of However, Descartes’ first two who raised criticisms was Leibniz Descartes’ laws of motion. laws of motion won the support himself—but after his death they Realizing that many of Descartes’ of both Newton and Leibniz, and were largely unchallenged until criticisms of Aristotle were became the basis for Newton’s the early 20th century, just as justified, Leibniz went on to first law of motion. Aristotle’s beliefs about motion ❯❯ develop his own theories on “dynamics,” his term for motion and impact, during the 1690s. Leibniz’s work remained unfinished, and he was possibly put off after reading Newton’s

44 LAWS OF MOTION The bicycle is in motion due to the force Rider flies over handlebars, example, why does it eventually supplied by the pedalling of the rider, until the since he or she has not stop? In fact, as the ball rolls it external force of the rock acts upon it, causing been acted on by the experiences an outside force: it to stop. external force (the rock) friction, which causes it to decelerate. According to Newton’s second law, an object will accelerate Friction Forward in the direction of the net force. motion Since the force of friction is opposite to the direction of travel, this acceleration causes the object to slow and eventually stop. In interstellar space, a spacecraft Bicycle in motion due to force Rock supplies external will continue to move at the same supplied by rider’s pedaling force, greater in quantity than velocity because of an absence of being greater than friction and bicycle’s forward motion, friction and air resistance—unless drag (air resistance) bringing bicycle to a stop it is accelerated by the gravitational field of a planet or star, for example. had dominated scientific thinking object are known, it is possible to calculate the net external force— Change is proportional for the best part of 2,000 years. However, some of Leibniz’s views the combined total of the external Newton’s second law is one of the on motion and criticisms of Newton forces—expressed as ∑ F (∑ stands most important in physics, and were far ahead of their time, for “sum of”). For example, if a ball describes how much an object and were given credence by has a force of 23 N pushing it left, accelerates when a given net force Albert Einstein’s general theory and a force of 12 N pushing it right, is applied to it. It states that the of relativity two centuries later. ∑F = 11 N in a leftward direction. rate of change of a body’s Law of inertia It is not quite as simple as this, momentum—the product of its since the downward force of gravity mass and velocity—is proportional Newton’s first law of motion, which will also be acting on the ball, so to the force applied, and takes place is sometimes called the law of horizontal and vertical net forces in the direction of the applied force. inertia, explains that an object at also need to be taken into account. This can be expressed as rest stays at rest, and an object in There are other factors at play. ∑F = ma, where F is the net force, motion remains in motion with the Newton’s first law states that a a is the acceleration of the object in same velocity unless acted upon by moving object that is not acted the direction of the net force, and m an external force. For instance, if upon by outside forces should is its mass. If the force increases, so the front wheel of a bicycle being continue to move in a straight line does acceleration. Also, the rate of ridden at speed hits a large rock, at a constant velocity. But when a change of momentum is inversely the bike is acted upon by an ball is rolled across the floor, for proportional to the mass of the external force, causing it to stop. Unfortunately for the cyclist, he or she will not have been acted upon by the same force and will continue in motion—over the handlebars. For the first time, Newton’s law Low mass, enabled accurate predictions of high acceleration motion to be made. Force is defined as a push or pull exerted on one object by another and is measured High mass, in Newtons (denoted N, where 1 N low acceleration is the force required to give a 1 kg Two rockets with different masses but identical engines mass an acceleration of 1 m/s²). If will accelerate at different rates. The smaller rocket will the strength of all the forces on an accelerate more quickly due to its lower mass.

MEASUREMENT AND MOTION 45 The laws of motion … Notions of time, distance, and Motion is really nothing are the free acceleration are fundamental to an more than change of place. understanding of motion. Newton decrees of God. argued that space and time are So motion as we Gottfried Leibniz entities in their own right, existing experience it is nothing independently of matter. In 1715– object, so if the object’s mass 1716, Leibniz argued in favor of a but a relation. increases, its acceleration relationist alternative: in other words, Gottfried Leibniz decreases. This can be expressed that space and time are systems of relations between objects. While dismissed at the time, Einstein’s as a = ∑F∕m. For example, as a Newton believed that absolute time general theory of relativity (1907– exists independently of any observer 1915) made more sense of them two rocket’s fuel propellant is burned and progresses at a constant pace centuries later. While Newton’s laws during flight, its mass decreases throughout the universe, Leibniz of motion are generally true for and—assuming the thrust of its reasoned that time makes no sense macroscopic objects (objects that engines remains the same—it will except when understood as the are visible to the naked eye) under accelerate at an ever-faster rate. relative movement of bodies. Newton everyday conditions, they break argued that absolute space “remains down at very high speeds, at very Equal action and reaction always similar and immovable,” small scales, and in very strong Newton’s third law states that but his German critic argued that gravitational fields. ■ for every action there is an equal it only makes sense as the relative and opposite reaction. Sitting location of objects. Two Voyager spacecraft were down, a person exerts a downward launched in 1977. With no friction force on the chair, and the chair From Leibniz to Einstein or air resistance in space, the craft exerts an equal upward force on A conundrum raised by Irish bishop are still moving through space today, the person’s body. One force is and philosopher George Berkeley due to Newton’s first law of motion. called the action, the other the around 1710 illustrated problems reaction. A rifle recoils after it is with Newton’s concepts of absolute fired due to the opposing forces time, space, and velocity. It of such an action–reaction. When concerned a spinning sphere: the rifle’s trigger is pulled, a Berkeley questioned whether, if it gunpowder explosion creates was rotating in an otherwise empty hot gases that expand outward, universe, it could be said to have allowing the rifle to push forward motion at all. Although Leibniz’s on the bullet. But the bullet also criticisms of Newton were generally pushes backward on the rifle. The force acting on the rifle is the same as the force that acts on the bullet, but because acceleration depends on force and mass (in accordance with Newton’s second law), the bullet accelerates much faster than the rifle due to its far smaller mass.

SYSTEMTHE FRAME OF THE OF THE WORLD LAWS OF GRAVITY



48 LAWS OF GRAVITY IN CONTEXT Why do raindrops always They must be attracted fall downward? toward the center of KEY FIGURE Isaac Newton (1642–1727) Earth by gravity. BEFORE Could gravity also cause Could gravity extend 1543 Nicolaus Copernicus the moon’s orbit beyond the rain clouds? challenges orthodox thought around Earth? Could it reach the moon? with a heliocentric model of the solar system. If that’s the case, perhaps gravity is universal. 1609 Johannes Kepler P ublished in 1687, Newton’s model of the solar system, with publishes his first two laws of law of universal gravitation Earth and the planets orbiting the planetary motion in Astronomia remained—alongside his sun. According to him, “We revolve Nova (A New Astronomy), laws of motion—the unchallenged around the sun like any other arguing that the planets move bedrock of “classical mechanics” for planet.” His ideas, published in freely in elliptical orbits. more than two centuries. It states 1543, were based on detailed that every particle attracts every observations of Mercury, Venus, AFTER other particle with a force that is Mars, Jupiter, and Saturn made 1859 French astronomer directly proportional to the product with the naked eye. Urbain Le Verrier argues that of their masses, and inversely Mercury’s precessionary orbit proportional to the square of the Astronomical evidence (the slight variance in its axial distance between their centers. In 1609, Johannes Kepler rotation) is incompatible with published Astronomia Nova Newtonian mechanics. Before the scientific age in (A New Astronomy) which, as which Newton’s ideas were well as providing more support 1905 In his paper “On the formulated, the Western for heliocentrism, described the Electrodynamics of Moving understanding of the natural elliptical (rather than circular) Bodies,” Einstein introduces world had been dominated by the orbits of the planets. Kepler also his theory of special relativity. writings of Aristotle. The ancient discovered that the orbital speed Greek philosopher had no concept of each planet depends on its 1915 Einstein’s theory of of gravity, believing instead that distance from the sun. general relativity states heavy objects fell to Earth because that gravity affects time, that was their “natural place,” and Around the same time, Galileo light, and matter. celestial bodies moved around Galilei was able to support Kepler’s Earth in circles because they were view with detailed observations What hinders the perfect. Aristotle’s geocentric view made with the aid of telescopes. fixed stars from falling remained largely unchallenged When he focused a telescope on until the Renaissance, when Jupiter and saw moons orbiting upon one another? Polish–Italian astronomer Nicolaus the giant planet, Galileo uncovered Isaac Newton Copernicus argued for a heliocentric further proof that Aristotle had