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) 1
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Introduction to cosmology I - Antimatter | Life in a puzzling ... · Web viewAround it, sun, moon and planets revolve in concentric circles Each planet hums on a different pitch Intervals
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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
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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
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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
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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
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Chap III Middle Ages
Platonism adopted by Christianity (St Augustine etc)
Ignored early Greeks, adopted only Plato's philosophy: neoplatonism
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
After trial
17
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 motionResultant of horizontal component (constant) and vertical component (gravity-dependant)
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Telescopic observation
Moons of JupiterPhases of venus
Sunspots
Promoted CopernicusCensored
Defended Copernican system Dialogue of the Two World Ssytems
Tried by the Inquisition (1633)
Discourse on Two New Sciences (1637): kinematicsNo treatment of causes of motion
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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
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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
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Newton: extra notes
Mathematics at Cambridge (TC) 1661Studies interrupted by plagueInvented calculusElected fellow
Reflecting telescopeLight made up of components (1666)Lucasian professor of mathematics (1668)
Halley : FG α 1/r2
Newton (1684): theoretical basis for Kepler’s laws1687: 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
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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 opticsRelection, refractionDiffractionInterference (Newton’s rings)
Light rays trajectories of small particlesOptical forces different in different media
Optical and grav phenomena transported by the etherSuggests Atomism
By 1830, wave theory of Young supreme
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Postscript
3. Albert Einstein (1867-1955)
Special Relativity (1905): Breakdown of Newtonian mechanics for bodies at high velocity
All motion is relativeSpeed of light = fundamental const, limitDistance, time and mass depend on velocitySpace+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
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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 mechanicsBorn: probability amplitudeHeisenberg: matrix mechanics, uncertainty principleDirac: quantum field theory (relativistic)