221 ;;Quote: solve algebraic equations by generalization of addition by iteration: get negative numbers and reciprocal powers from subtraction, fractions from division, irrationals from fractional powers, and complex numbers from the square root of 1

229 ;;Quote: complex imaginary powers are the same as sine and cosine; they oscillate; for small t, e^it = 1+it; for small t, cos t is nearly 1 and sin t is nearly 0

229+;;Quote: the most remarkable formula in mathematics: e^i \theta = cos \theta + i sin \theta

254 ;;Quote: linear systems are important because we can solve them and because the fundamental laws of physics are often linear, e.g., Maxwell's equations for electricity, the laws of quantum mechanics, and the approximations when displacements are small

262 ;;Quote: development of physical law: observe effect, measure it, make a table, find the rule

262+;;Quote: Ptolemy produce a table for the refraction of light in 140 A.D., Snell found the law of refraction in 1621

263 ;;Quote: the glory of science is to find a way of thinking that makes evident a law relating measurements

263+;;Quote: Fermat's principle of least time: light takes the path which requires the shortest time; it is an approximation for time differences of a period or longer

265 ;;Quote: use an ellipse to reflect all light from one point to another, i.e., all shortest paths have the same length

267 ;;Quote: the principle of least time: small changes to the path only make secondorder changes to the time, i.e., there are many nearby paths which take almost exactly the same time

281 ;;Quote: electromagnetic fields knit together the universe because they vary inversely to the first power of the distance instead of the inverse square

284 ;;Quote: Maxwell's equation for electrical force has three terms: an inverse square term for Coulomb's law, an inverse square correction for delay, and an inverse term for radiation

284+;;Quote: at a large enough distance, electrical force is proportional to the delayed transverse acceleration divided by the distance

291 ;;Quote: an electric field moves as a wave outward from the source; i.e., the electromagnetic field is delayed

292 ;;Quote: since ratio of the area of the surface of a cone to the kinetic energy due to an electric field is constant, the energy flux is never lost and the energy's amplitude varies as 1/r

311 ;;Quote: the electric field is the sum of the individual fields and the field of a single charge is given by its acceleration retarded by the speed c

311 ;;Quote: when light passes through glass it vibrates the electrons in the glass which in turn generate new fields; these fields effectively change the light's speed through the glass

312 ;;Quote: refraction, the bending of light, comes about because the speed of light is different in different materials; the only way for waves to fit at a boundary is to change the angle; yields Snell's law

314 ;;Quote: so far as problems involving light are concerned, electrons behave as though they were held by springs, i.e., oscillators with displacement proportional to force

316 ;;Quote: the natural frequency of electron oscillators in most ordinary gases and transparent substances corresponds to ultraviolet light

316+;;Quote: dispersion: as the driving frequency rises toward ultraviolet light, the index of refraction rises; so a prism spreads light

319 ;;Quote: dark spectral lines occur when the light frequency is nearly the natural frequency and the light is absorbed

319+;;Quote: from the sun's spectral lines we know that the chemical elements in the sun and stars are the same as those on earth

3110 ;;Quote: a screen is opaque when the electric fields generated by the screen exactly cancel the light's electric field; this requires a sufficiently thick screen even for gold

321 ;;Quote: a radiating atom loses 1/e'th of its energy in 10^8 seconds

325 ;;Quote: distinct light sources do not interfer only if measurements are averaged over more than 10^8 seconds

326 ;;Quote: the scattering of sunlight by air is proportional to the fourth power of the frequency; why the sky is blue

328 ;;Quote: the wavelength of light is about 5000 times the diameter of an atom; small groups of atoms scatter light more strongly, but larger droplets scatter red more strongly

329 ;;Quote: at right angles to a light beam, scattered light is polarized

341 ;;Quote: associated with a vibrating electric field is a vibrating magnetic field at right angles and 1/c of the intensity of the electric field

331 ;;Quote: all electric fields are polarized; unpolarized light is the overlapping of many different polarizations

3410 ;;Quote: light carries a momentum which is 1/c of its energy; from radiation pressure due to moving charges in a magnetic field

354 ;;Quote: brown light is a dark red and yellow mixture against a lighter background

355 ;;Quote: adding a light to two, indistinguishable spectral distributions is also indistinguishable

365 ;;Quote: it is impossible to turn both eyes out at the same time because the eye's muscles are controlled together

356 ;;Quote: any three differently colored lights whatsoever can always be mixed to produce any color whatsoever; may need to take one light from the other

366 ;;Quote: when light strikes strongly absorbing organic substances (e.g., rhodopsin), all electrons shift by one double bond; effectively moving an electron the width of the molecule

367 ;;Quote: the human eye is slightly sensitive to light polarization; can learn to tell the direction of the sun by rotating your head about the axis of vision

396 ;;Quote: the definition of equal temperature is the condition of two boxes of gas that sit next to each other long enough; i.e., the same mean kinetic energy of the centerofmass motions

3910 ;;Quote: from the ideal gas law equal volumes of different gases at the same pressure and temperature have the same number of molecules because of Newton's laws!

401 ;;Quote: kinetic theory is the description of matter from the point of view of collisions between the atoms

401+;;Quote: the gross properties of matter should be explainable in terms of the motion of its parts

408 ;;Quote: the first indication that classical physics was wrong was Maxwell's work on specific heats; molecules have discrete energy levels

413 ;;Quote: blackbody radiation: real matter always emits light and radiates energy; in a closed box, the radiation and matter reach thermal equilibrium

413+;;Quote: by classical theory, blackbody radiation (the color of a furnace) would predominate at high frequency with unbounded total energy

416 ;;Quote: Planck empirically determined the equation for blackbody radiation and found a simple derivation under the assumption that harmonic oscillators have discrete energy levels

416+;;Quote: in the limit, Planck's equation for blackbody radiation yields the classical equation, Rayleigh's law

418 ;;Quote: a single molecule of water receives 10^14 collisions per second; over a hundredth of a second the collisions are effectively random

497 ;;Quote: for linear systems independent of time, there are usually a series of special motions which vary exponentially in time; the most general motion is a superposition of these special motions; e.g., vibrating systems with imaginary exponentials

497 ;;Quote: quantum mechanics uses the amplitude of the probability of finding a system of electrons in a given configuration; since the function is linear it can be represented as the superposition of states of definite energy

501 ;;Quote: Pythagoras discovered that chords are pleasant when in ratios of small integers; first numerical relationship in nature outside of geometry

504 ;;Quote: notes sound dissonant if their upper harmonics have frequencies near enough to cause a rapid beat

504+;;Quote: consonant sounds have harmonics of the same frequency

521 ;;Quote: something is symmetrical if it is invariant under some transformation; e.g., Newtonian laws are symmetrical under translation

Table 521;;Quote: the laws of physics contain many symmetries: translation in space and time, rotation, uniform velocity, reversal in space and time, interchange of identical atoms, phase, matterantimatter

523 ;;Quote: the scale of an individual atom is definite; Galileo discovered the effect of scale on the strength of materials

523 ;;Quote: each of the symmetries in physical law corresponds to a conservation law: e.g., symmetry under translation is space means that momentum is conserved; e.g., conservation of energy, angular momentum, and electrical charge
