Galileo and Einstein Text for Physics 109, Fall 2009

Total Page:16

File Type:pdf, Size:1020Kb

Galileo and Einstein Text for Physics 109, Fall 2009 Galileo and Einstein Text for Physics 109, Fall 2009 Michael Fowler, UVa Physics 8/21/2009 2 TABLE OF CONTENTS 1 INTRODUCTION: WHAT IS THIS COURSE ABOUT? ......................................................... 12 1.1 Some Basic Ideas .......................................................................................................................... 12 1.2 Babylonians and Greeks ................................................................................................................ 12 1.3 Greek Classics Come to Baghdad................................................................................................... 12 1.4 Monasteries and Universities ....................................................................................................... 13 1.5 Galileo .......................................................................................................................................... 13 1.6 Newton ......................................................................................................................................... 13 1.7 From Newton to Einstein .............................................................................................................. 13 1.8 What about Other Civilizations? ................................................................................................... 14 1.9 Plan of the Course ......................................................................................................................... 14 2 COUNTING IN BABYLON ............................................................................................................ 16 2.1 The Earliest Written Language ...................................................................................................... 16 2.2 Weights and Measures: 60s everywhere! ..................................................................................... 16 2.3 Number Systems: Ours, the Roman and the Babylonian ............................................................... 17 2.4 Fractions ....................................................................................................................................... 19 2.5 Ancient Math Tables ..................................................................................................................... 19 2.6 How Practical are Babylonian Weights and Measures? ................................................................. 20 2.7 Pythagoras’ Theorem a Thousand Years before Pythagoras.......................................................... 20 2.8 Babylonian Pythagorean Triplets .................................................................................................. 21 3 EARLY GREEK SCIENCE: THALES TO PLATO ...................................................................... 22 3.1 The Milesians ................................................................................................................................ 22 3.2 Early Geometry ............................................................................................................................. 23 3 3.3 Early Geometry According to Proclus ............................................................................................ 24 3.4 The Pythagoreans: a Cult with a Theorem, and an Irrational Discovery ........................................ 26 3.5 The Square on the Hypotenuse ..................................................................................................... 26 3.6 Rational and Irrational Numbers ................................................................................................... 27 3.7 What’s so Important about Irrational Numbers? .......................................................................... 30 3.8 Change and Constancy in the Physical World ................................................................................ 30 3.9 Hippocrates and his Followers ...................................................................................................... 31 3.10 Plato ......................................................................................................................................... 32 3.11 References ............................................................................................................................... 33 4 MOTION IN THE HEAVENS: STARS, SUN, MOON, PLANETS ........................................... 34 4.1 Introduction .................................................................................................................................. 34 4.2 Looking at the Stars ...................................................................................................................... 34 4.3 Motion of the Sun ......................................................................................................................... 34 4.4 Motion of the Moon against the Starry Vault ............................................................................... 37 4.5 Motion of the Planets ................................................................................................................... 38 5 ARISTOTLE .................................................................................................................................... 40 5.1 Beginnings of Science and Philosophy in Athens ........................................................................... 40 5.2 Plato’s Idea of a Good Education .................................................................................................. 40 5.3 Aristotle and Alexander ................................................................................................................ 40 5.4 Aristotle Founds the Lyceum ......................................................................................................... 41 5.5 Aristotle’s Science ......................................................................................................................... 42 5.6 Aristotle’s Method ........................................................................................................................ 42 5.7 “Causes” ....................................................................................................................................... 43 5.8 Biology .......................................................................................................................................... 44 4 5.9 Elements ....................................................................................................................................... 44 5.10 Dynamics: Motion, And Why Things Move ............................................................................... 45 5.11 Natural Motion and Violent Motion ......................................................................................... 45 5.12 Aristotle’s Laws of Motion ....................................................................................................... 46 5.13 Planetary Dynamics .................................................................................................................. 47 5.14 Aristotle’s Achievements .......................................................................................................... 47 6 MEASURING THE SOLAR SYSTEM .......................................................................................... 48 6.1 How Big is the Earth? .................................................................................................................... 48 6.2 How High is the Moon? ................................................................................................................. 49 6.3 How Far Away is the Sun? ............................................................................................................. 51 7 GREEK SCIENCE AFTER ARISTOTLE ..................................................................................... 53 7.1 Strato ............................................................................................................................................ 53 7.2 Aristarchus .................................................................................................................................... 53 7.3 Euclid ............................................................................................................................................ 54 7.4 Plato, Aristotle and Christianity .................................................................................................... 54 7.5 Archimedes ................................................................................................................................... 55 7.6 Archimedes’ Principle ................................................................................................................... 55 7.7 Archimedes and Leverage ............................................................................................................. 57 7.8 Apollonius ..................................................................................................................................... 59 7.9 Hypatia ......................................................................................................................................... 59 8 BASIC IDEAS IN GREEK MATHEMATICS .............................................................................. 60 8.1 Closing in on the Square Root of 2 ................................................................................................ 60 8.2
Recommended publications
  • Galileo in Rome Galileo in Rome
    Galileo in Rome Galileo in Rome The Rise and Fall of a Troublesome Genius William R. Shea and Mariano Artigas Oxford New York Auckland Bangkok Buenos Aires Cape Town Chennai Dar es Salaam Delhi Hong Kong Istanbul Karachi Kolkata Kuala Lumpur Madrid Melbourne Mexico City Mumbai Nairobi São Paulo Shanghai Taipei Tokyo Toronto Copyright © 2003 by Oxford University Press, Inc. First published by Oxford University Press, Inc., 2003 198 Madison Avenue, New York, New York 10016 www.oup.com Issued as an Oxford University Press paperback, 2004 ISBN 0-19-517758-4 (pbk) Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. The Library of Congress has catalogued the cloth edition as follows: Artigas, Mariano. Galileo in Rome : the rise and fall of a troublesome genius / Mariano Artigas and William R. Shea. p. cm. Includes bibliographical references and index. ISBN 0-19-516598-5 1. Galilei, Galileo, 1564-1642—Journeys—Italy—Rome. 2. Religion and science—History—16th century. 3. Astronomers—Italy—Biography. I. Shea, William R. II. Title. QB36.G2 A69 2003 520'.92—dc21 2003004247 Book design by planettheo.com 9 8 7 6 5 4 3 2 1 Printed in the United States of America on acid-free paper CONTENTS ACKNO W L E D G E M E N T S vii I N TRO D U C TIO N ix CHA P TER O N E Job Hunting and the Path
    [Show full text]
  • It's the Question That You Ask Galileo Galilei
    THE NEW JERSEY ITALIAN HERITAGE COMMISSION It's the Question That You Ask Galileo Galilei Grade Level: 6-12 Subject: Science / World History / World Languages Categories: Arts and Sciences / History and Society Standards: Please see page 8 of the lesson plan for complete New Jersey Student Learning Standards alignment. Objectives: Students will be able to: 1. explain why the proper question can lead to a more accurate answer. 2. conduct an experiment using the scientific method. 3. demonstrate why scientific experiments will explain the "how" things happen. Materials: • Five five-pound free weights and one ten-pound weight • A high place, e.g. football stands, second floor window. • Duct tape • Notebook Abstract: The lesson includes Galileo’s investigation of gravity. It emphasizes the shift from Aristotelian deductive reasoning to empiricism by changing the investigative question from why things fall to earth to how things fall to earth. Background: Ancient Greece gave birth to systematic thinking, i.e., philosophy. Through philosophy, men began to use reason and the observation of the natural world to explain the causes of things. Aristotle brought his mentor, Plato's abstract investigation of causes to his own investigation of the physical world. Aristotle, however, did not conduct scientific experiments in the modern sense. Like other Greek philosophers, he believed that all knowledge could be deduced through reason. Page 1 of 9 Copyright 2019 – New Jersey Italian Heritage Commission U3-LP-004 Aristotle reasoned that the cause of falling was "heaviness." He deduced that the heavier an object, the faster it would fall to earth. To Aristotle, the world was made up of combinations of the four elements, Earth, Fire, Air, and Water.
    [Show full text]
  • Galileo Galilei: Un Hombre Contra La Oscuridad
    Rev.R.Acad.Cienc.Exact.Fís.Nat. (Esp). Vol. 107, Nº. 1­2, pp 55­78, 2014 XVI. Programa de Promoción de la Cultura Científica y Tecnológica. GALILEO GALILEI: UN HOMBRE CONTRA LA OSCURIDAD. FERNANDO BOMBAL GORDÓN *. * Real Academia de Ciencias Exactas, Físicas y Naturales. Valverde 22, 28004 Madrid. Facultad de Matemáticas. Universidad Complutense. 28040 Madrid. Prefiero descubrir un solo hecho, por pequeño que sea, a discutir largamente los grandes temas sin descubrir nada en absoluto. GALILEO GALILEI. Galileo Galilei (1564-1642) es probablemente el “La filosofía está escrita en ese grandísimo libro personaje que mejor evoca el proceso de cambio y —me refiero al Universo— que tenemos abierto ante evolución que marca la transición de la concepción los ojos, pero no se puede comprender si antes no se medieval del mundo al nacimiento de la Ciencia mo- aprende el idioma y a interpretar los caracteres en que está escrito. Está escrito en el lenguaje de las matemá­ derna en el Occidente europeo. ticas y sus caracteres son triángulos, círculos y otras figuras geométricas, sin las cuales es imposible entender una sola palabra. Sin ese lenguaje, navegamos en un oscuro laberinto”. incluidas en su obra Il Saggiatore (El Ensayador, 1623; una polémica dirigida contra la dialéctica de los jesui- tas) se consideran como la declaración funda cional del método científico. La defensa a ultranza de sus ideas sobre el diseño racional de la Naturaleza, le hizo enfrentarse al oscu- rantismo de su tiempo y le han convertido en el para- digma de la libertad de pensamiento. De sus descubrimientos, sus ideas y su vida en la apasionante Italia de la época trata esta Conferencia.
    [Show full text]
  • Prof.Bignami
    Industry and Astronomy By Prof. Giovanni Bignami Galileo too had started like this. That is, by building telescopes for the Serenissima Republic of Venice, in 1609, as soon as he learned that some glass specialist in Flanders has discovered a lens combination which allowed one to see things afar as if they were near-by. Galileo, who had been professor in Padua for over 17 years, knew very well that Venice has the best glass in the world, and went personally to Murano to order lenses of various sizes and curvatures. But then he immediately realized that a lens is just as good as it is polished, and thus proceeded to polish his lenses by his own hand. In this he was amorously supported by a young and beautiful girl from Venice, Marina Gamba, who was then living with Galileo “in sin”(and had given him three children..). Galileo mounted his lenses, polished to the same optical quality as for reading glasses (occhiale, in Italian), at both ends of a tube, resembling a small cannon, and, pronto, there was a “cannocchiale” (cannone + occhiale…), i.e. what today we call telescope with a fancy Greek name. The rest, as they say, it’s history: it was the birth of observational astronomy. EIE, alas, did not exist at the time, and Mestre was just a hamlet of fishermen who did not for a moment think about telescopes. Nor did INAF exist (nor even Italy), and even less so ESO or a united Europe. Today, on the other hand, we are all here to celebrate EIE, which 25 years ago started in Mestre, more or less like Galileo, but with no need of Dutch people to take optics lessons from (this is true even today, after all).
    [Show full text]
  • Galileu Galilei: El Naixement De La Ciència Moderna
    Galileu Galilei: el naixement de la ciència moderna Victòria Rosselló Rosselló, V. (2016). Galileu Galilei: el naixement de la ciència moderna. In: Ginard, A.; Vicens, D. i Pons, G.X. (eds.). Idees que van canviar el món. Mon. Soc. Hist. Nat. Balears, 22; 53-65. SHNB - UIB. ISBN 978-84-608-9162-8. Disponible on-line a shnb.org/SHN_monografies Resum: El pensament de Galileu suposa el punt de partida de la Revolució Científica amb l’aparició d’una ciència on l’experimentació hi té un paper fonamental en contraposició a la ciència aristotèlica vigent al segle XVI. Amb el seu esforç intel·lectual, Galileu va fer trontollar l’edifici conceptual del seu temps amb el canvi d’actitud mental davant els problemes físics. La física galileana suposà una nova manera de mirar el món, que pretenia descobrir les lleis físiques que regulen els processos naturals. La nova manera d’analitzar els fenòmens de la naturalesa fou un procés que pot descriure’s com el pas de la recerca de causes a la recerca de lleis. La física aristotèlica s’ocupava del canvi (motio) i tenia com a objectiu comprendre els fenòmens de la naturalesa mitjançant l’examen de les causes. El coneixement pràctic (techne) havia estat exclòs per Aristòtil de la Filosofia Natural per considerar-lo inferior al coneixement científic (episteme). La Revolució Científica va consistir en bona mesura en la progressiva dissolució d’aquesta diferenciació i en la reconciliació del coneixement adquirit amb la pràctica amb l’obtingut mitjançant la raó. 54 Idees que van canviar el món Galileu Galilei va néixer el 15 de febrer de 1564 a Pisa i fou el primer de sis germans.
    [Show full text]
  • 2011 Medals & Awards Gsa President's Medal
    2011 MEDALS & AWARDS GSA PRESIDENT’S I was born in 1947 in the Bronx, right near the Bronx Zoo and the New York MEDAL Botanical Garden, so that I could walk to Presented to either by myself from an early age. My best Dava Sobel academic credential is undoubtedly my diploma from the Bronx High School of Science. My home life, too, provided excellent career preparation, since my mother had trained as a chemist, and no one in my family thought it odd or unusual for a girl to be interested in science. I am extremely gratified by the warm reception my books have received—not just in terms of good reviews or ratings on bestseller lists, but also events that followed their publication. Longitude helped place a memorial to John Harrison in Westminster Abbey. Astronomers who read Galileo’s Daughter named a crater on Venus for Suor Maria Celeste, and also a feature on the asteroid Eros for her mother, Marina Gamba. Dava Sobel Thanks to The Planets, an asteroid discovered Author “Galileo’s Daughter and Longitude” in 1994 by David Levy and Carolyn Shoemaker has been officially registered as (30935) Davasobel. Beginning fresh out of college as a Right now I am writing a play about technical writer for IBM, I moved quickly Copernicus and the events that made him into journalism in 1970, just in time for the buck common sense and received wisdom to first Earth Day. My favorite jobs were as defend the Earth’s motion around the Sun. science writer for the Cornell University News The theme of the piece is a familiar favorite of Bureau, where my beat included everything mine: the great transformation of humankind’s from astronomy to veterinary medicine, and worldview through science.
    [Show full text]
  • Galileo Galilei 1 Galileo Galilei
    Galileo Galilei 1 Galileo Galilei « La filosofia è scritta in questo grandissimo libro che continuamente ci sta aperto innanzi a gli occhi (io dico l'universo), ma non si può intendere se prima non s'impara a intender la lingua, e conoscer i caratteri, ne' quali è scritto. Egli è scritto in lingua matematica, e i caratteri son triangoli, cerchi, ed altre figure geometriche, senza i quali mezzi è impossibile a intenderne umanamente parola; senza questi è un aggirarsi vanamente per un oscuro laberinto. » (Galileo Galilei, Il Saggiatore, Cap. VI) Galileo Galilei Galileo Galilei (Pisa, 15 febbraio 1564 – Arcetri, 8 gennaio 1642) è stato un fisico, filosofo, astronomo e matematico italiano, padre della scienza moderna. Il suo nome è associato ad importanti contributi in dinamica[1] e in astronomia - fra cui il perfezionamento del telescopio, che gli permise importanti osservazioni astronomiche[2] - e all'introduzione del metodo scientifico (detto spesso metodo galileiano o metodo scientifico sperimentale). Di primaria importanza furono il suo ruolo nella rivoluzione astronomica e il suo sostegno al sistema eliocentrico e alle teorie copernicane. Accusato di voler sovvertire la filosofia naturale aristotelica e le Sacre Scritture, Galileo fu per questo condannato come eretico dalla chiesa cattolica e costretto, il 22 giugno 1633, all'abiura delle sue concezioni astronomiche, nonché a trascorrere il resto della sua vita in isolamento. Biografia La giovinezza (1564-1588) Galileo Galilei nacque il 15 febbraio 1564 a Pisa, [3] primogenito dei sette
    [Show full text]
  • Galileo Galilei
    Galileo Galilei . And the Optik Tube Galileo’s Italy . Pisa Vincenzo & Guilia Galilei Born in Pisa, Feb. 15, 1564 Oldest of six kids (four survived) Baptized in Cathedral of Pisa Santa Maria di Vallombrosa (monastery) University of Pisa (1581) Pendulum Motion 1592 – University of Padua Hydrostatic Balance The “Sector” Marina Gamba Hans Lippershey (1570-1619) A quick review . • Heavens are perfect • Earth is fixed, doesn’t move • Circles are perfect • Uniform circular motion • Use of epicycles to explain “retrograde” motion Geocentric problems • Planets “orbit” imaginary points. Why? • Why to closer planets always stay near the Sun? What confines them there? • More distant planets only retrograde when opposite the Sun from Earth. • What the hell is an “equant?” • Is it truly Geocentric now? • However . Is this a good “scientific theory?” Planetary configurations Nicholas Copernicus • Polish doctor • Found it “pleasing” that the Earth might orbit the Sun • Heliocentric idea • Feared criticism • Still used perfect circles for orbits De Revolutionibus, 1543 Galileo’s “Optik Tube” (1609) . He wrote it down! “Sidereus Nuncius” (Mar. 1610) Saturn has “ears” “smaismrmilmepoetaleumibunenugttausras” How do you “look” at the Sun? December 1615 – Heads to Rome 1616 decree . Cardinal Bellarmine Pope Urban VIII Santa Maria Sopra Minerva “Discourse and Mathematical Demonstrations Relating to Two New Sciences” “E pur si muove” Died: January 8, 1642 Galileo Museum, Florence POWER!!! The “nasty five-letter word” Different “powers” • Magnification – “making things larger” • Light Gathering – “collecting more light than your eye.” Depends on “aperture,” or diameter of light collector. • Resolving – “the ability to see fine detail.” Depends on quality, aperture & sky conditions. Measured in arc seconds.
    [Show full text]
  • Life of Galileo
    previous index next Life of Galileo Michael Fowler, UVa Physics Department NOTE: Many books have been written about Galileo, and, in particular, about his interaction with the Church. An excellent short biography is Galileo, Stillman Drake, Oxford. One classic is The Crime of Galileo, Giorgio de Santillana, 1955, University of Chicago Press. A fairly recent biography by a journalist is Galileo, a Life, James Reston, Jr., HarperCollins. (I am certainly no expert in this complex field of study, and just present a collection of facts below to try to give the flavor of Galileo’s life and times.) Galileo was born in Pisa, Tuscany in 1564, the son of Florentine musician Vincenzo Galilei. Actually, Vincenzo was a revolutionary musician—he felt the formal church music that then dominated the scene had become sterile, and that classic Greek poetry and myths had a power the church music lacked, that perhaps could be translated into modern music. He attempted some of this, and his work began the development that culminated in Italian opera. To understand something of Galileo’s early upbringing, here is a quote from his father, Vincenzo Galileo: “It appears to me that those who rely simply on the weight of authority to prove any assertion, without searching out the arguments to support it, act absurdly. I wish to question freely and to answer freely without any sort of adulation. That well becomes any who are sincere in the search for truth.” (I took this from Reston, Page 9) At age 17, Galileo went to the University of Pisa. He enrolled as a medical student, following his father’s advice, but turned to math, after persuading his father that he didn’t want to be a doctor.
    [Show full text]
  • Galileo Biography
    Galileo Biography Astronomer, Scientist (1564–1642) Quick Facts Name Galileo Occupation Astronomer , Scientist Birth Date February 15 , 1564 Death Date January 8 , 1642 Education Monastery school at Vallombrosa, near Florence, University of Pisa Place of Birth Pisa , Italy Place of Death Arcetri , Italy AKA Galileo Nickname "The Father of Modern Science" Full Name Galileo Galilei Italian scientist and scholar Galileo made pioneering observations that laid the foundation for modern physics and astronomy. Synopsis Born on February 15, 1564, in Pisa, Italy, Galileo Galilei was a mathematics professor who made pioneering observations of nature with long-lasting implications for the study of physics. He also constructed a telescope and supported the Copernican theory, which supports a sun-centered solar system. Galileo was accused twice of heresy by the church for his beliefs, and wrote books on his ideas. He died in Arcetri, Italy, on January 8, 1642. Early Life Galileo Galilei was born on February 15, 1564, in Pisa in the Duchy of Florence, Italy. He was the first of six children born to Vincenzo Galilei, a well-known musician and music theorist, and Giulia Ammannati. In 1574, the family moved to Florence, where Galileo started his formal education at the Camaldolese monastery in Vallombrosa. In 1583, Galileo entered the University of Pisa to study medicine. Armed with high intelligence and talent, he soon became fascinated with many subjects, particularly mathematics and physics. While at Pisa, Galileo was exposed to the Aristotelian view of the world, then the leading scientific authority and the only one sanctioned by the Roman Catholic Church.
    [Show full text]
  • Historical Journeys Walk in Galileo's Footsteps in Rome, Florence, And
    Historical journeys Walk in Galileo’s footsteps in Rome, Florence, and other haunts of the great Experience astronomer. Galileo’sby William Sheehan Italy t isn’t hard to find the influence of Galileo Galilei (1564–1642) on the history of astronomy. After all, he was the first to use a telescope to study the heavens systematically and objectively. He discovered the Moon’s craggy mountains, Jupiter’s four major Isatellites, and the phases of Venus. But that’s Galileo the scientist. Who was the man? To find some clues, I went to Rome and Florence, where Galileo spent the prime of his life and ended up under house arrest for life after a disastrous encounter with the Roman Catholic Church. I decided to retrace the master’s footsteps in Italy — to visit the places where he lived and worked in hopes of absorbing some- thing of the spirit of the times in the 17th century when Galileo helped Galileo Galilei (1564–1642) was born in Pisa and taught mathematics at Padua. overturn what people thought they He lived in Florence after 1610, where he wrote his greatest scientific works. understood about the celestial realm. Science Museum Pictorial 56 Astronomy • May© 092010 Kalmbach Publishing Co. This material may not be reproduced in any form without permission from the publisher. www.Astronomy.com 1609 Galileo presents a telescope Astronomer and mathematician to the Venetian Senate, which Galileo Galilei lived portions of bestows on him life tenure at his life in Pisa and Padua, but he the University of Padua. considered himself a Florentine.
    [Show full text]
  • Famous Men of Science
    Famous Men of Science By Sarah Knowles Bolton Famous Men of Science GALILEO GALILEI "The same memorable day is marked by the setting of one of the most brilliant stars in the firmament of art and the rising of another in the sphere of science, which was to enlighten the world with beams of equal splendor. On the 18th of February, 1564, Michael Angelo Buonarotti closed his eyes at Rome, and Galileo Galilei first saw the light at Pisa." Thus writes young Karl von Gebler, in the best life of Galileo ever written, his dying contribution to literature. Some other authorities place Galileo's birth on February 15. He was the oldest in a family of five children born to Vincenzo Galilei, a Florentine noble, and Giulia Ammanati, who also belonged to an ancient family. Vincenzo wrote learnedly about music, and taught his boy to play on the lute and the organ; but he was poor and life was a struggle. However beneficial poverty may be in the development of character, most of us do not crave it for our children, so Vincenzo decided to place his son where he could earn a comfortable support. Music did not bring money. Galileo therefore should become a dealer in cloth; a necessity of life, rather than a luxury. GALILEO GALILEI. GALILEO GALILEI. But the boy soon showed great skill in music, surpassing his father. He excelled in drawing and color, and could have become a noted artist. He loved poetry, and had a decided taste for mechanics, making machines of great ingenuity.
    [Show full text]