The Mechanical Universe

from Descartes to Laplace

France 1955

France 1942

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?