View
220
Download
1
Category
Preview:
Citation preview
Last time ....
Newton’s “natural theology” God sets up initial conditions for the machine Preserves stability of solar system over time Prevents gravitational collapse of universe by
intervention in present world Newton’s laws of motion and gravity
Two types of mass (inertial, gravitational) Requires action at a distance (occult quality?) Universalizes the laws (unproven assumption)
Mechanical philosophy re-places Aristotle’s physics
Aristotle’s physics 4 elements + aether, subjects, properties, movers,
natural desires, causes Untenable after Scientific Revolution
Mechanical philosophy Matter, motion, force(?): only tools for explanation Problems to be solved
Causes (non-Aristotelian) of motion? Principles and mathematics required (new mechanics)? Role of the “supreme mechanic” (God)?
Task of lecture
Examine several mechanical philosophiesof 17-18th centuries
Examine creation of mechanics by 18th-century mathematicians, culminating inwork of Laplace (who removes God fromthe Newtonian world) Mechanics now = laws of motion, not study of
artificial machines (ancient Greece) Formulation of conservation laws
Newton’s “System of theWorld” in Principia, Book 3
Explains Kepler’s laws (not just facts) Can weigh planets using Kepler’s 3d law Maskelyne measures value for G in 1774, Cavendish
in 1798 Explains comets as orbiting Sun
Confirmed by return of Halley’s 1682 comet in 1758 Explains oblate shape of Earth
Newton Descartes
Newton’s “System,” cont.
Explains twice daily tides
Explains perturbation of large planets Explains precession of Earth (26,000 yrs)
MoonEarth
Ocean
R1
R3
R2
Fg α 1/R2
F1>F2>F3
MoonOblate Earth
Newton’s “System,” cont.
Moon test (how to sample gravity atdifferent distances to test 1/R2 relation)
Falling apple is like “falling” Moon
Apple
Moon Recall: F = ma = Gmme/R2, i.e, a = Gme/R2
Falling appple: aa = F/ma = Gme/R2
Falling moon: am = F/mm = Gme/(60R)2
Or aa/am = 3600
Know aa = 980 cm/sec2
Thus, am should = 980/3600 = 0.27 cm/sec2
Matches observed value for fall of Moon “prettynearly” says Newton! So generalizes 1/r2 toentire cosmos.
60R
R
Newton’s mechanical phil.
Ontology: matter, motion, force Extends to chemistry, optics, elasticity,
cohesion of solid bodies Where do forces come from in “dead” matter?
“Hypotheses non fingo” = I feign no hypotheses(Principia, 3d edition, General Scholium) Alchemical tradition of “active powers”?
• Elevated mercury levels in Newton’s body at his death! Speculated on aether and ‘electrical matter’ to
avoid action-at-a-distance in unpublished essays
Descartes’ mechanical phil.
Provided foil for Newton’s Principia (1687)with Principles of Philosophy (1644) Only matter & motion (no forces!)
Plenum universe (no “empty” space) God originates all motion at creation All subsequent motion governed by:
Linear inertia “Quantity of motion” [mv] remains unchanged Impact between particles governed by 6 laws
(mostly wrong or self-contradictory)
Cartesian cosmology
3 types of matter Sensible objects Insensible spheres Aether dust
Plenum cosmos All “natural” motionfrom swirling vortices No quantitativekinematics of motion
Cartesian physics
Examples of mechanical explanation Light as pressure, color as rotation of spheres Gravity as special vortex around earth Magnetism as screw-shaped particles
Explanation without closure, remains ad hoc Matter becomes dead, inert, passive “Clockwork” cosmos runs itself with no divine
intervention after creation Defeated by return of Halley’s comet 1758
Other 18c mechanicalphilosophies
Malebranche (d. 1715) and occasionalism Priest, mathematician, academician (Paris) Ontology: matter, motion, God’s continuous action Rejects force as a “power without God,” or aethism
Leibniz (d. 1716) and monads Philosopher, mathematician, librarian, academician (Berlin) Ontology: matter, motion, monads (=centers of reason & will,
all preprogrammed thru eternity)
Boskovic (d. 1787) and point-force law Jesuit, itinerant scholar (Paris, London, Milan, Poland) Ontology: only centers of forces (no matter!) Combined chemistry and gravity
Boskovic’s force law
Theory of natural philosophy, reduced to a single law of the forces existing innature, 1758
No physical contact between centers Not quantitative for chemistry, no links to
laboratory studies (speculative)
+
-Distance
F α 1/R2
Force
GravityChemistry
18c mathematical physics
New techniques of math analysis Approximation techniques for N-bodies
What is conserved in the universe? Descartes’ “quantity of motion” (mv)?
[Momentum, conserved in isolated system] Leibniz’s “living force” (mv2)?
Elastic collisions: mv2 conserved in visible bodies Inelastic collisions: mv2 conserved in invisible particles inside
visible bodies Kinetic energy: Ek = (1/2) mv2, change in Ek is measure of
work done by a force (defined in 19c)
Laplace’s (d. 1827)mechanical world
Solar system stable overtime (almost!)
Nebular hypothesis Newton’s laws explain
origin of solar system “Fixed” stars now in
orbits with proper motion Deterministic, clockwork
universe with no Godintervening “Sir, I have no need of that
hypothesis!” Like Descartes’ clockwork
cosmos
Conclusions
Two threads in 18th-century mechanics Philosophical: specify ontology, God’s role (the why) Mathematical: describe all motions exactly (the how)
Newtonian mechanics reigns supreme Oblateness measured in 1740s Return of Halley’s comet in 1758 Lunar theory and longitude problem Enlightenment ideology of order, reason, balance
Could Newtonian mechanics also explain: Light, electricity, magnetism, heat, capillarity,
physiological functions of animal bodies, mentalfunctions?
Recommended