Space, Time and Matter: the shape & size of the cosmos
Course Description
Course Description
How old is the universe? What is its shape and size? Indeed, is it even meaningful to ask such questions in the first place?
This module is concerned with the primitive concepts of space, time and of matter, examined in their historical context as well as where this leads in the light of modern physics, specifically Einstein’s general theory of relativity. Students will explore the nature of space and time, mass and energy, in relation to their usefulness towards an understanding of physical reality. The evolution of our understanding of these fundamental concepts from the pre-Socratic philosophers to Einstein is addressed and our exploration will involve three strands, namely the philosophical, mathematical and physical. Starting with intuitive notions of space, time and of gravity, we shall investigate why and how basic ideas were revised, sometimes radically, in order to describe nature correctly. We adopt a largely visual approach to geometry as the framework for examining the central issues involved.
The module gradually leads the student to the modern physical viewpoint of Einsteinian relativity in which space, time and matter are not only intimately related, but in a sense actually unified. We hope to impart a critical appreciation of the concepts discussed as well as the ability to perform simple calculations that quantitatively explore some of the implications of these profound ideas for cosmology - the study of the large scale structure and evolution of the universe. The treatment will in general emphasise the role of fundamental or primitive concepts and ideas in the evolution of our theoretical or mental picture of the physical universe and how these were modified and extended by taking into account new ‘facts’ provided by observation and experiment.
To adapt a quote from the preface to the book ‘The Evolution of Physics’ by Einstein and Infeld: “… You may find it boring or interesting, dull or exciting, but our aim will be accomplished if this module gives you some idea of the eternal struggle of the inventive human mind for a fuller understanding of the laws governing physical phenomena.”
Schedule
Schedule
This module comprises weekly lectures as well as tutorials, commencing Tuesday, 9th August 2022 at 12 noon sharp. However, as 9th August is a public holiday, there will be no lecture on that day; instead the relevant material will be circulated to students and this is to be read before coming to the Thursday/Friday tutorial during which students will be asked questions pertaining to the readings.
Thereafter, the schedule is as follows:
Lectures - Tuesday, 12 noon - 2.00pm (USP-TR1)
Tutorials - Group 1: Thursday, 12.00 noon - 2.00pm (USP-SR3)
Group 2: Friday, 12 noon - 2.00pm (USP-SR3)
For further information or clarifications, you may contact Assoc. Prof. Ali Namazie at uspmman@nus.edu.sg or mman@nus.edu.sg
NB. Many of the basic concepts we shall encounter are subtle as well as deep and, correspondingly, difficult to appreciate upon a first encounter. It is important therefore to raise any doubts or questions, directly they arise, in class and of reviewing the relevant assigned readings prior to the week’s tutorial session. Likewise, to be useful, homework tutorial questions should be attempted during the week(s) they are assigned and not left till later on in the course; students should manage their time to allow for this!
Course Structure
Course Structure*
Weeks 1 to 4: The philosophy, physics & mathematics of SPACE
Readings:
Masks of the Universe: changing ideas on the nature of the cosmos by Harrison; Chapter 1, Introducing the Masks
Cosmology by Harrison; Chapter 1, What is Cosmology? & Chapter 2, Early Scientific Cosmology
Physics, the Human Adventure: From Copernicus to Einstein and Beyond by Gerald Holton & Stephen G. Brush; Chapter 1, The Astronomy of Ancient Greece & Chapter 2, Copernicus’ Heliocentric Theory
Measuring the universe: The Cosmological Distance Ladder by Stephen Webb; Chapter 2, First Step: the Earth
Poetry of the Universe by R. Osserman; Chapter 1, Measuring the Unmeasurable; Chapter 2, Encompassing the Earth;
Chapter 3, The Real World, Chapter 4; Imaginary Worlds & Chapter 5, Curved Space
Six Not-so-Easy Pieces by R.P. Feynman Chapter 6, Curved Space pages 111-125
Measuring very large distances
Weeks 5 to 6: Motion in SPACE & TIME
Readings:
Cosmological Koans by A. Aguirre; Chapter 1, The Arrow
Physics, the Human Adventure: From Copernicus to Einstein and Beyond by Gerald Holton & Stephen G. Brush; Chapter 6, Mathematics and the Description of Motion; Chapter 7, Galileo and the Kinematics of Free Fall; Chapter 8, Projectile Motion & Chapter 9, Newton's Laws of Motion
The Birth of a New Physics by I. Bernard Cohen; Chap. 5, Towards an Inertial Physics & Chap. 7, The Grand Design
Resolving Zeno’s Paradoxes by W.I. MacLauglin
Mathematical Principles of Natural Philosophy by Isaac Newton (trans. Andrew Motte)
Newton’s Views on Space, Time and Motion
Space and Time: inertial frames
Absolute and Relational Theories of Space and Motion
RECESS WEEK
Weeks 7 to 9: The relativity of TIME & SPACETIME
Readings:
What is Time? by G.J. Whitrow, Chap 5, Time & relativity, p.75-91
Physics, the Human Adventure: From Copernicus to Einstein and Beyond by Gerald Holton & Stephen G. Brush; Chapter 30, Einstein's Theory of Relativity, p.462-477
Physics: Structure & Meaning by Leon Cooper, p. 261-264 Temps Perdu
Conventionality of Simultaneity
The Relativity of Simultaneity
Spacetime & spacetime intervals
Weeks 10 to 13: MATTER & the geometry of ‘curved’ SPACETIME
Readings:
What is Time? by G.J. Whitrow, Chap 6, Time, gravitation and the universe, p.92-113
Relativity: The Special and the General Theory by Albert Einstein, p.61-82
Inertia by D.W. Sciama
Six Not-so-Easy Pieces by R.P. Feynman Chapter 6, Curved Space pages 125-144
Introduction to General Relativity
Einstein’s Philosophy of Science
Gravitational orbits in a strong gravity field
*Tentative sequence only; the actual lectures may depart from this by addition/subtraction of either topics or material at the discretion of the lecturer.
Course Texts
Course Texts
The following may usefully be referred to throughout the course for discussions of the physics, the ideas as well as their historical contexts, underlying the various topics to be explored in this course:
- Physics, the Human Adventure: From Copernicus to Einstein and Beyond by Gerald Holton & Stephen G. Brush; Rutgers Univ. Press, ISBN 0-8135-2908
- Physics: Structure and Meaning by Leon N Cooper; University Press of New England, 1992; ISBN 0-87451-592-0
The above books are available in the Scholar’s reading room.
Supplementary Reading Material
Supplementary Reading Material
The books listed below are to be regarded as a comprehensive list of resource materials relevant to this module; part of the weekly readings for this course are extracts taken from some of them. Additionally, for various parts of this module, or as source material for essay assignments, students might profit from consulting relevant chapters or sections of some of these books:
HISTORICAL & GENERAL
The Birth of a New Physics by I. Bernard Cohen (Penguin 1985; ISBN 0 14 013633 9)
What is Time? by G.J. Whitrow (Oxford University Press, 1972; ISBN 0-19-860781-4)
Einstein’s Clocks, Poincare’s Maps: Empires of Time by Peter Galison (QB209EIN2003); (Norton, 2003; ISBN 0-393-32604-7)
The Evolution of Physics by A. Einstein and L. Infeld (Simon & Schuster, 1966; ISBN0-671-20156-5)
The Philosophy of Space & Time by H. Reichenbach (Dover Publications, 1958; ISBN 0-486-60443-8)
Poetry of the Universe: a mathematical exploration of the cosmos by R. Osserman (Anchor Books, 1995; ISBN 0-385-47429-6)
Measuring the universe: The Cosmological Distance Ladder by Stephen Webb (Springer, 1999; ISBN 1-85233-106-2)
Afterglow of Creation by M. Chown (University Science Books, 1996; ISBN 0-935702-40-7)
Cosmology: The Science of the Universe by E. Harrison (Cambridge University Press, 2000; ISBN 052166148X)
Masks of the Universe: changing ideas of the nature of the cosmos by E. Harrison (Cambridge University Press, 2003; ISBN 0-521-77351-2)
The Book of the Cosmos – imagining the universe from Heraclitus to Hawking by D.R. Danielson (Perseus Publishing, 2000; ISBN 0-7382-0498-6)
Cosmology – historical, literary, philosophical, religious and scientific perspectives by N.S. Hetherington (Garland Reference Library of the Humanities, 1993; ISBN 0-8153-0934-1)
THEORY OF RELATIVITY, GRAVITATIONAL PHYSICS & COSMOLOGY
Einstein’s Universe: The Layperson’s Guide by Nigel Calder (Penguin, 1990;
ISBN 0 14 013516 2)
Great Ideas in Physics by Alan Lightman (McGraw Hill, 2000; ISBN 0-07-135738-6)
The Feynman Lectures on Physics Vol. 1 by R.P. Feynman (NL214FEY); Addision-Wesley Publishing Co.
Six Easy Pieces by R.P. Feynman (NL018); Addision-Wesley Publishing Co.,ISBN 0-201-40825-2
Six Not-so-Easy Pieces by R.P. Feynman (NL193FEY); Addision-Wesley Publishing Co.,ISBN 0-14-027667-X
(the last two titles being reprint volumes of selected chapters of The Feynman Lectures)
It’s About Time: Understanding Einstein’s Relativity by N.David Mermin; (Princeton University Press, 2005; ISBN 0-691—12201-6)
A Journey into Gravity & Spacetime by J.A. Wheeler (Scientific American Library, W.H. Freeman 1999; ISBN 1040-3213)
Relativity by A. Einstein (Routledge, 2001; ISBN 0 415 25384 5)
General Relativity from A to B by Robert Geroch (Univ. of Chicago Press, 1978; ISBN 0226288641)
Black Holes & Time Warps: Einstein’s Outrageous Legacy by Kip S. Thorne (Pan Macmillan, 1995; ISBN 0333639693)
Was Einstein Right? Putting General Relativity to the Test by Clifford M. Will (The Perseus Books Group, 1993; ISBN 0465090869)
Time Travel in Einstein’s Universe by J.R. Gott (Houghton Mifflin Company, 2001; ISBN 0395955637)
Cosmic Time Travel: A Scientific Odyssey by B. Parker (Perseus Publishing, 1991; ISBN 0738206326)
The Future of Spacetime by S.W. Hawking, K.S. Thorne et al (W.W. Norton & Co., 2002; ISBN 0393020223)
Cosmology by M. Rowan-Robinson (Oxford University Press, 2000; ISBN 0-19851884-6)
A Short History of the Universe by J. Silk (Scientific American Library, 1997; ISBN 0-7167-6020-7)
The Big Bang by J. Silk (W.H Freeman & Co, New York, 2001; ISBN 0-7167-3878-3)
The First Three Minutes by Steven Weinberg (Basic Books, New York, 1988; ISBN 0-465-02437-8)
Our Cosmic Habitat by Martin Rees (Princeton University press, 2001; ISBN 0-691-08926-4)
After the First Three Minutes by T Padmanabhan (Cambridge University press, 1998; ISBN 0-521-62972-1)
The Accelerating Universe by Mario Livio ( John Wiley & Sons, 2000; ISBN 0-47132969-X)
Genesis of the Big Bang by R.A. Alpher and R. Herman (Oxford University Press, 2001; ISBN 0-19-511182-6)
Towards the Edge of the Universe: A Review of Modern Cosmology by Stuart Clark (Springer- Praxis Publishing, 1999; ISBN 1-85233-098-8)
Cosmology and Controversy – the historical development of two theories of the universe by H. Kragh (Princeton University Press, 1996; ISBN 0-691-00546-X)
Assessment
Assessment
| Mid-term paper | 20% |
| Group projects | 20% |
| Tutorial questions, participation and oral presentations | 25% |
| Final Term paper | 35% |