From: sarfatti@well.sf.ca.us (Jack Sarfatti)
Subject: footnotes Sarfatti Lectures I
Organization: Whole Earth 'Lectronic Link
Date: Sat, 22 Aug 1992 08:04:42 GMT



  The study of instantaneous rates of change (derivatives) and the areas
under curves (integrals).
  A vector is an arrow with a direction in space. The length of the
vector is the magnitude.
  Linear momentum is the product of the mass with the vector velocity
(i.e., instantaneous rate of change of position vector with time). Speed
is the magnitude of the velocity vector.  In uniform circular motion
there is a centripetal inward acceleration pointing toward the center of
the circle even though the speed is constant. The orbital angular
momentum for circular motion is the product of the mass times the square
of the radius of the circle times the rate of change of angular position
of the particle with time.
  A central force vector points along the line separating the two point
particles. If the mass is extended the point is the center of mass.
Central forces conserve orbital angular momentum. The orbits of
planets, comets and asteroids around the sun, moons and man-made
satellites around the planets are ellipses with the sun or planet at one
focus of the ellipse. A circle is a degenerate ellipse in which the two
foci squeeze together. A particle in an elliptical orbit is always
falling toward the focus where the source of gravity is. Conservation of
orbital angular momentum prevents the particle from crashing into the
focus. The total energy of bound orbits is always negative. The negative
potential energy of attraction must be greater than the positive kinetic
energy to prevent the particle from escaping to infinity.
 For example, if you are traveling at 100 mph on a straight freeway and
a police car starts to give chase at 70 mph your speed relative that of
the police is 30 mph - that's Galilean relativity.
 In physics the word absolute means "invariant".  Objective properties
are frame invariant - the same as viewed from different perspectives or
different points of view or different frames of reference. In the case
of relativity, Galilean or Einsteinian the different points of view are
those of different observers moving in a fixed direction at constant
speed relative to each other.
 In Scotland during the American Civil War.
 Faraday's empirical law of electromotive induction that Maxwell built
upon. Faraday induction makes electric generators work.
 The Lorentz force that makes electric motors work.
 This was Maxwell's great discovery of the "displacement current" on the
basis of an aesthetic formal symmetry idea that he had.
   Sound waves in air and water are longitudinal waves in which the tiny
periodic density variation is along the direction of propagation of the
wave front. In a transverse electromagnetic wave the electric field
arrow is perpendicular to the magnetic field arrow and both are
perpendicular to the direction of propagation of the wave front. In
other words, the electric and magnetic vectors are in the tangent plane
to the wave front at any point in space at any moment of time. We
imagine both plane waves and spherical waves as fundamental waves. Any
wave form can be built as a superposition of either a set of fundamental
plane waves or fundamental spherical waves. The polarization of light,
for example, is defined by the direction of the electric vector of the
wave. The light is linearly polarized if the direction of the electric
vector is fixed in direction as the wave front propagates. A wave front
at a fixed time is also called a surface of constant phase. If the
phases of different overlapping wave fronts are relatively steady then
we have a coherence in which the local intensity of the overlapping
superposition  can be significantly larger or smaller than the sum of
intensities of the separate waves.  Thus, coherence means that the whole
is more than the simple sum of its parts. The total energy of the
overlapping waves over an extended region of space is the same as the
simple sum of the energies of the separate waves because of conservation
of energy.  Coherence changes the distribution of the energy over that
region putting an excess (constructive interference) in one place and
compensating by putting a deficit (destructive interference) at another
place.  Light from the spontaneous emission of atomic electrons in
incandescent and neon bulbs is incoherent in both space and time
compared to light from the stimulated emission of pumped atoms in a
laser.
 Biological systems use other kinds of engines at fixed temperature
based upon "chemical potential" differences of concentrations of
electrically charged ions across permeable cellular membranes for
example.
 A hypothetical absolute frame of reference in which light moved at
300,000 km/sec which could not be detected.
 time dilation
 timelike subluminal geodesics have the longest proper time
 in the sense of the arithmetic of complex numbers which are arrows from
an origin to points on the "complex plane" or on the surface of the
"Riemann sphere". The complex plane is connected to the Riemann sphere
by a sterographic "spinor" mapping.
 Bell's theorem and the Einstein-Podolsky-Rosen (EPR)effect.
 equivalence principle



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