Download Introduction to cosmology I

History of Science
Part I Pythagoras - Newton
Early mythology
Babylonians, Egyptians and Hebrews (6000 BC)
Earth in the center of an oyster, covered by dome
Water underneath and overhead, closed in on all sides
Moderate dimensions
Sun, moon and stars progress across dome
Universe guided by deity, explained by myth
Chaldean priests (3800 BC)
Timetables of the motion of the stars and the planets
Stars stationary, planets move across a lane in the sky (zodiac)
Computed the length of the year
Astronomy and astrology, formed calenders
Predicted astronomical events
Observation without explanation
1
Chap I
Greek Heroic Age
1. Ionian philosophers (6th cent BC)
Natural causes: not concerned with deities
Thales of Miletos: abstract geometry
What is the basic material of the Universe? Water
Anaximander: universe infinite in time and space:
Raw material a substance without definite properties
Mechanical model of the universe:
Anaximenes: stars attached to a transparent sphere that turns
around the earth
2. Pythagoras of Samos (6th cent BC)
Founder of science
Mathematization of experience: numbers sacred and eternal
Highest form of philosophy
All things have form, all form defined by numbers
2
Pitch of a note depends on the length of string that produces it
Intervals in the scale produced by simple numeric ratios
Reality could be reduced to number series and number ratios
16 is a square number, 12 is oblong, 6 a triangle
Relations between number-shapes found
Addition of successive odd numbers gives square:
e.g. 1+3 =4, 4+5=9, 9+7=16, 16+9 =25
Addition of even numbers gives oblong numbers
e.g. 2+4 =6, 6+6=12, 12+8=20 etc
Similarily, cubic and pyramid numbers obtained.
Theorem: Areas of the two smaller squares of the sides of
right-angled triangle will equal the area of the larger square
Could all the secrets of the Universe be revealed by numbers?
Phythagoran astronomy: earth is a sphere (navigation, eclipses)
Around it, sun, moon and planets revolve in concentric circles
Each planet hums on a different pitch
Intervals between orbits governed by the laws of harmony
Inspired Kepler
3
3. Downfall of the Pythagoran Brotherhood
Discovery of irrational numbers: the diagonal of a square
Breakdown in point-to-point correspondence between
arithmetic and geometry
Tried to keep secret
Dissolution of brotherhood
(also due to egalitarian practices, socialist nature)
Pythagoras: founder of European culture, source of Platonism
4
4. Legacy of Pythagoras
Spherical earth
(ships on horizon, lunar eclipses, shape of moon and sun)
Earth must attract everything to its center
Aristarchus of Samos: (310 BC)
"On the sizes and distances of the sun and moon"
Calculated relative distance of sun and moon
Eratosthenes:
Measured circumference of earth from summer solstice
Deduced relative size of moon (from lunar eclipse)
Deduced distance of moon from earth (from geometry)
Sun-earth/moon-earth distance (from half-moon)
Deduced sun-earth distance
Deduced relative size of sun (from solar eclipse)
rS/ dS = rM /dM
5
Philolaus and Aristarchus:
Earth sphere has motion: rotates about its own axis
Daily revolution of the sky caused by earth's own motion
Separated day and night, annual motion of the planets
Earth orbits sun
First suggestion of heliocentric system
Quoted by Archimedes: yet heliocentric system was discarded
1. Objects fell towards earth
2. No wind blowing against us
3. No obvious motion of stars
(stars too far away to observe stellar parallax)
→
Heliocentric model rejected
Geocentic model retained
Snag: motion of planets
6
Chap II
Plato and Aristotle
Heroic age followed by decline
(Should have been Aristarchus - Copernicus, Archimedes-Galileo)
Plato: dismissed the visible world, dismissed natural science
Philosophy: shape of the world must be a perfect sphere
All motion perfect circles at uniform speed
Science dominated by Aristotle (logician)
Aristotle: God spins the world from outside it, not from center
Earth and moon space subject to change: nowhere else
All celestial bodies orbit earth in perfect circles
7
2. Academic dogma
Planetary motion must be shown to be result of circular motions
Aristotle: used 54 spheres to account for motion of the planets
Ptolemy (AD 150) : ultimate earth-centered model
Complicated epicycle system for circular motion of celestial objects
(Ferris Wheel universe)
Enshrined in ‘He Magele Syntaxis’ ( later ‘The Almagest’)
Kept alive by Islamic scholars during the middle ages
Re-introduced to Europe in 1175 - 1600
New dogma dismissed reality: 3 fundamental conceits
1. dualism of celestial and terrestrial motion
2. immobililty of earth in the center
3. all heavenly motion perfectly circular
8
Chap III
Middle Ages
Platonism adopted by Christianity (St Augustine etc)
Ignored early Greeks, adopted only Plato's philosophy: neoplatonism
11cent AD: same view as 5th cent BC
Medieval philosophers: Aristotle's 55 spheres, Ptolemy's 40 epicyles
replaced by10 revolving spheres: disregarded stellar observation
1000 AD: Portolano charts for navigation
12-16th century: Aristotlean philosophy adopted
Muslims: carried fragments of Euclid , Archimedes and Aristotle to Europe
Improved Calendric astronomy and planetary tables
Important Indian numerals (including zero) and algebra
Christianity and Aristotelianism (Thomas Aquinas)
Roger Bacon and Albert the Great: study of nature
Revival of learning: Universities of Bologna, Paris, Oxford and Cambridge
Medieval science divorced mathematics from science
Principle: "things only move when they are pushed" handicapped science
Aquinas: first proof of God's existence (based on Aristotelian physics)
Unmoved mover = God
9
Summary (Chap II-III)
By 1500 AD, Europe knew less than Archimedes in 200 BC
1. Splitting of Universe into 2 spheres
2. Geocentric dogma
3.Uniform motion in perfect circles dogma
4.Divorce of mathematics from science
5. Inability to realise tendency of a body in motion to stay in motion
These 5 handicaps were to be overcome by
Copernicus, Kepler and Galileo
10
Chap IV
Renaissance Science
Moderns: Roger Bacon, William of Ockham rejected Aristotle
William of Occam school: Ockham’s razor philosophy
“all other things equal, simpler explanation more likely’’
Nicole d’Oresme: geocentric universe not proven
Nicholas of Cusa: earth not hub of universe
1. Canon Nicolas Copernicus (1473-1543)
"On the Revolutions of the Heavenly Spheres"
Studied at the Universities of Bologna, Padua and Krakow
Simple instruments for observing the sky
Relied on the observations of the Chaldeans and the Greeks
Improved astronomical tables
Published Commentariolus (1514)
11
Copernicus - Commentariolus (1514) : 7 axioms
1. Heavenly bodies do not share a common center
2. Earth is not the centre of the universe
3. Centre of the universe is near the sun
4. Earth’s distance to sun negligible compared to distance to stars
5. Daily motion of stars is due to rotation of the earth
6. Earth, planets revolve around sun
7. Observed motion of the planets is due to moving platform (earth)
Summ: earth cannot be stationary, Ptotelmy system inconsistent
Instead: heliocentric system (influenced by Pythagoras, Aristarchus)
Book of the Revolutions of the Heavenly Spheres (1543)
Published with aid of Georg von Lauchen (Rheticus)
Problems: undermined by preface
Ahead of its time (earth just a planet like others)
Less accurate predictions of planetary motion
Copernican system quite complicated (48 epicycles)
Universe de-centralized: no natural center of directions
12
2. Tycho de Brahe (1546-1601)
Danish nobleman
Lifetime of astronomical observations
Observational astronomy to new level (own observatory)
Expensive instruments: precise and continuous data
Sympathetic to Copernican ideas
‘Mixed’ model of universe (1588): planets orbit sun, sun orbits earth
Migrated to Prague (imperial mathematician)
Employed Kepler to study Mars: noted interpreter of data
Gave data sparingly to Kepler
Died from drink (1600)
Kepler free to interpret all of Tycho planetary data
13
3. Johannes Kepler (1571-1630)
Low born: founder of modern astronomy
University of Tubingen
Teacher of mathematics and astronomy in Graz, Austria
1. Defended Copernicus while still a young priest
Mysterium Cosmographicum (1596):
1st public commitment by professional astronomer to Copernican system
1600: Kepler goes to work with Tycho de Brahe
Given Mars project, but limited data
Tycho dies after a few months
Kepler becomes Imperial Mathematicus (1601-1612)
Solved Mars problem in sun-centered model (8 years, not 8 days)
Result:
"Astronomia Nova " (Kepler, 1609)
First accurate sun-centered model of universe
14
Kepler’s planetary laws
1. Planets move in elliptical orbits (not circles)
2. Planets continuously vary their speed (not uniform)
3. Sun is at focus of ellipse (not center of circle)
Discovered orbit equation empirically (from data)
Natural laws: precise, verifiable statements based on physical data
Simple, elegant model
Material bodies acted upon by forces
Accurate predictions (tides, gravity explained)
Ignored by Germans and Italians (incl. Galileo)
Accepted by British: (Thomas Harriot, Jeremiah Horrocks, Newton)
Kepler’s other work: founded instrumental optics
Optics (1604): study of refraction by lenses
Light intensity α 1/r2
Principle of sight, spectacles
Camera obscura
15
Chap V Galileo and Newton
1. Galileo Galilei (1564-1642)
Student: noticed period of pendulum constant
(depends only on length, not angle or weight)
Invented pendulum timing device
Appointed lecturer in mathematics at the University of Pisa (1589)
Chair of Mathematics at the University of Padua (1592)
Studied mechanics in detail, laid foundations of dynamics
Laws of motion of falling bodies
Galileo’s Astronomy
Improved Dutch model of telescope (mag x 60)
Discovered Lunar surface not smooth (contradicts Ptolemy)
Discovered moons of Jupiter : (earth not center of all things)
Discovered phases of Venus (as predicted by Copernicus)
Discovered innumerable stars in Milky Way
(unlikely created for man's pleasure)
Discovered sunspots: sun subject to decay etc
16
Corresponded with Kepler
Private belief in Copernican system
Measurements confirmed by Jesuits
University Aristotelians opposed Galileo
Letter to Grand Duchess Christina
Defended Copernican system, suggested scriptures not literal
Church Charges brought against Galileo in 1615, dropped
Church demanded proof of Copernican system
Galileo refused (couldn't prove): ignored Kepler's findings
Holy decree (1616): Copernicus's teachings outlawed, Galileo censored
1623: New pope in favour of Galileo
1632: Galileo publishes "Dialogue on the Great World Systems"
Propounds Copernican system
Pope displeased, felt deceived (many changes over the years)
1633: Church Comission finds Galileo defied decree
Interrogated by Inquisition
House arrest
Dialogue prohibited: smuggled out to Europe
17
After trial
Dialogue Concerning Two New Sciences (1636)
Magnum Opus - dynamics
Postscript: his crusade damaged heliocentric system
precipitated the divorce of science from faith
18
Galileo: extra notes
Kinematics
Careful observation of falling bodies
Objects do not fall at rate proportional to their weight
s = vt
v = gt
s = ½ gt2
Inertia principle
Body will move forever if not acted upon
Projectile motion
Resultant of horizontal component (constant) and
vertical component (gravity-dependant)
19
Telescopic observation
Moons of Jupiter
Phases of venus
Sunspots
Promoted Copernicus
Censored
Defended Copernican system
Dialogue of the Two World Ssytems
Tried by the Inquisition (1633)
Discourse on Two New Sciences (1637): kinematics
No treatment of causes of motion
20
2. Isaac Newton (1642 – 1727)
Synthesised all that went before
1. Kepler's laws (planetary motion)
2. Galileo's laws (motion of bodies on earth)
Two problems:
What were the nature of the forces which drive the planets around?
What would a body do if left alone?
1st step
“identified Keplerian orbit of moon with Galilean
orbit of projectile”
Interaction of gravity with centrifugal force: cause of elliptical orbits
Law of Gravity (1666)
Force of attraction proportional to the masses,
inversly proportional to square of separation
Dropped for 20 years
Developed mechanics and calculus
Halley-Hooke-Wren worked on gravity
Newton goaded back to problem
21
1686: Newton computes force of earth's attraction for the moon
Explained observed motion: repeated for sun
Showed orbit produced by inverse-square law was Kepler ellipse
Showed Kepler's laws arise as consequence
Extended theory to include all motion
Newton’s Principia (1687):
4 basic laws for all motion
Law of inertia
Law of acceleration
Law of action and reaction
Law of gravity
Note:
synthesis of celestial and terrestrial dynamics
22
Newton: extra notes
Mathematics at Cambridge (TC) 1661
Studies interrupted by plague
Invented calculus
Elected fellow
Reflecting telescope
Light made up of components (1666)
Lucasian professor of mathematics (1668)
Halley : FG α 1/r2
Newton (1684): theoretical basis for Kepler’s laws
1687: Principia published
Law 1 Every body continues in its state of rest, or uniform motion
in a straight line, unless compelleed to change by forces acting on
it
Law 2: The change in motion is proportional to the force
impressed, and in the direction of the force
Law 3: To every action there is always an equal and opposite
reaction: the mutual actions of two bodies upon each other are
akways equal, and directed to contrary parts
23
First 3 Laws put the planets in elliptical orbits controlled by
inverse square law forces: centripetal forces
Law 4: Moon held in its orbit by force of gravity (like apple)
Compares gravitational pull needed to keep moon in orbit with
pendulum data
Law 5: Extends to other planets
Laws 6 and 7: Universal Law of Gravitation
FG = Gm1m2/r2
Optics (1704)
Experimental foundations of optics
Relection, refraction
Diffraction
Interference (Newton’s rings)
Light rays trajectories of small particles
Optical forces different in different media
Optical and grav phenomena transported by the ether
Suggests Atomism
By 1830, wave theory of Young supreme
24
Postscript
3. Albert Einstein (1867-1955)
Special Relativity (1905):
Breakdown of Newtonian mechanics
for bodies at high velocity
All motion is relative
Speed of light = fundamental const, limit
Distance, time and mass depend on velocity
Space+time = spacetime
General relativity (1915):
Breakdown of Newtonian mechanics
for bodies in high gravitational fields
Gravity = distortion of space-time
Mass distorts spacetime, causes other mass to move along curve
25
4. Schrodinger, Heisenberg and Dirac
Quantum Theory (1925-)
Breakdown of Newtonian mechanics at the atomic scale
Wave-particle duality of radiation (Planck, Einstein, Bohr)
Wave-particle duality of matter (de Broglie)
Schrodinger: wave equation, wave mechanics
Born: probability amplitude
Heisenberg: matrix mechanics, uncertainty principle
Dirac: quantum field theory (relativistic)
New ideas:
Indeterminancy
Probability
Entanglement
26