Chapter 14.

Newtonian Cosmology

14.1. Elements of Newtonian Cosmology

• Copernican principle (Aristarchus)
  • We are not privileged occupants of the Universe and are consequently not at its center.
• Galilean relativity principle
  • All laws of mechanics observed in one reference frame are equally valid in any other reference frame moving with a constant velocity relative to the first.
  • Consequence: from observation of motion within one reference frame, one can not determine whether or not that frame of reference is moving relative to another reference frame.
• Newtonian space
  • "Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies...because the parts of space cannot be seen, or distinguished from one another by our senses, therefore in their stead we use sensible measures of them...instead of absolute places and motions, we use relative ones; and that without any inconvenience in common affairs; but in philosophical disquisitions, we ought to abstract from our senses, and consider things themselves, distinct from what are only sensible measures of them. For it may be that there is no body really at rest, to which the places and motions of others may be referred (no absolute standard of rest, Descartes)."
• Newtonian time
  • "Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year."
• Newtonian spacetime
  • Space and time are absolutes and exist independent of existence of matter in the Universe; space and time precede material Universe's existence and survive its demise
  • God forms matter--stars, galaxies, etc.--and places them in to the framework provided by space and time
• Newtonian universe
  • Gravity demands that the universe be centerless, edgeless, and of reasonably uniform and infinite extent in all directions.
• Newton's letter to Richard Bentley of 1692
  • "It seems to me, that if the matter of our Sun and planets, and all the matter of the Universe, were evenly scattered through all the heavens, and every particle had an innate gravity towards all the rest, and the whole space throughout which this matter was scattered, was finite, the matter on the outside of this space would by its gravity tend towards all the matter on the inside, and by consequence fall down into the middle of the whole space, and there compose one great spherical mass. But, if the matter were evenly disposed throughout an infinite space, it could never convene into one mass, but some of it would convene into one mass and some into another, so as to make an infinite number of great masses, scattered great distances from one to another throughout all that infinite space. And thus might the Sun and fixed stars be formed, supposing the matter were of a lucid nature."
• Stability of Newtonian universe
  • Newtonian universe is stable on global (or cosmic) scale, but is unstable on local (or finite) scale where local gravity can cause irregularities by condensing matter in to heavenly bodies.
• Paradoxes of Newtonian universe
  • Olber's paradox (Henrich Olbers 1823): an infinite universe would produce an infinite amount of light at our position (or any point for that matter), so "why is the night sky dark?" (Paradox probably known since at least Kepler's time; certainly Cheseaux and Halley, probably Newton, discussed it at length.)
  • Gravity paradox (Newton): an infinite universe would produce an infinite gravitational attraction at our position (or at any point for that matter). (Newton assumed that resolution of paradox was that stars are uniformly spaced and there is, consequently, an exact cancellation of their collective effects--not a likely scenario.)
  • Absolute position paradox (Newton): Newtonian theory of motion precludes existence of an absolute standard of rest which in turn means that one can not give an event an absolute position in space. (Example: throwing a ball up on a train; observer on train says ball comes down at same spot from which it started; observer beside track says ball comes down at very different spot from which it started.) This seems to contradict Newton's concept of absolute space. But, absolute time concept does not seem to be violated.
  • Solutions of these paradoxes comes in modern times.

14.2. Controversy Over The Clockwork Universe

• Gottfried Whilhelm Leibniz (1646-1716)
  • German philosopher-mathematician
  • Developed differential calculus; controversy with Newton's followers as to whom credit belonged
  • Did not support Newton's absolute space and time; "I hold space to be something purely relative, as time is."
  • Ironies of history of science that one man, Newton, whose work by 19th century had done most to establish concept that world is like a machine or clock (clockwork universe) was most eager to reject that idea.
• Newton:
  • God"...is himself the author and continual preserver of [the world's] original forces or moving powers,... "it is "...not a diminution, but the true glory of His workmanship, that nothing is done without his continual government and inspection. The notion of the world's being a great machine, going on without the interposition of God, as a clock continues to go without the assistance of a clockmaker, is the notion of materialism and fate, and tends to exclude providence and God's government in reality out of the world."
• Liebniz:
  • "Sir Isaac Newton, and his followers, have also a very odd opinion concerning the work of God. According to their doctrine, God almighty needs to wind up his watch from time to time; otherwise it would cease to move. He had not, it seems sufficient foresight to make it a perpetual motion. Nay, the machine of God's making, is so imperfect, according to these gentlemen, that he is obliged to clean it now and then by an extraordinary concourse, and even to mend it, as a clockmaker mends his work; who must consequently be so much the more unskillful a workman, as he is often obliged to mend his work and set it right. According to my opinion, the same force and vigour [energy] remains always in the world, and only passes from one part to another, agreeably to the laws of nature, and the beautiful pre-established order...."
• Triumph of clockwork universe without God
  • Newton argued that clockwork universe, far from being complimentary to God, as Robert Boyle, Leibniz, and others claimed, was likely to lead instead to atheism.
  • Newton predicted that skeptics could push creation--first and last acts of God--further back in time and eventually conclude that the Universe has always existed as it does now.
  • Further development of Newtonian world system by:
    • Leonhard Euler (1707-1783): Swiss mathematician
    • Joseph Louis Lagrange (1736-1813): Italian-French mathematician
    • Pierre Simon de Laplace (1749-1827): French astronomer-physicist
    • Simon Denis Poisson (1781-1840): French mathematician
  • Exchange between Napoleon and Laplace; Napoleon could find no mention of God in Laplace's masterpiece Celestial Mechanics, Laplace replied that "Sir, I have no need of that hypothesis!"
  • World as a machine had triumphed.

14.3. Goal of Newton's Work (Speculation)

• Mechanics - to discover mathematics underlying motion; successful in publication of Principia
• Chemistry - to discover mathematics underlying transformation; unsuccessful, no unifying publication
• Theology - to prove that God is a mathematician; unsuccessful, no unifying publication

14.4. Energy Concept

• Last of great mechanical concepts
  • Historical development of concept and law of energy conservation was lengthy and involved
  • 150 years passed between first attempts at quantitative formulation and final form of concept
  • Grew out of problem of how motion of bodies changes when they collide with on another (same problem as momentum)
• Christian Huygens (1629-1695)
  • Dutch physicist-mathematician, equal of Galileo and Newton in many respects
  • Concept of centripetal force
  • Conservation law of elastic impact
  • Theory of oscillating systems
  • Theory of wave nature of light
• Energy definition
  • Is the ability of a physical system to perform useful work when it undergoes a describable change
  • Kinetic energy is energy a body possesses by virtue of its state of motion
  • Potential energy is energy a body possesses by virtue of its position in field of force, such as Earth's gravitational field
• Conservation of energy
  • Julius Robert Mayer (1814-1878): German physicist
  • James Prescott Joule (1818-1889): English physicist
  • Energy may neither be created or destroyed, but only transformed from one form to another; total energy in the Universe is finite and remains constant.