Figure 1.1: Aristotle, circa 384-322 BC
Figure 1.2: The Christian Aristotelian cosmos, engraving from Peter Apian's Cosmographia, 1524
Figure 1.3: Ptolemy, AD 127-145
Figure 1.4: A ptolomaic construction of planetary motion, where E is the Earth, C the geometric center of the eccentric circle, Q the equant point, F the center of the epicycle, and P the planet.
Source: http://galileo.rice.edu/sci/theories/ptolemaic_system.html, From Michael J. Crowe, Theories of the World from Antiquity to the Copernican Revolution.
Figure 1.5: Nicolaus Copernicus (Mikolaj Kopernik), 1473-1643
Epicycle Center Earth Equant Deferent Celestial
Figure 1.6: Example of elliptical (first epicycle) and retrograde (second epicycle) orbits produced using epicycles.
Figure 1.7: Isaac Newton (1643 - 1727)
From a portrait by Kneller in 1689
Figure 1.8: Albert Einstein (1879 – 1955)
Figure 1.9: Renormalization in quantum electrodynamics: A single interaction (left) between a photon (g) and electron (e-) is replaced by multiple interactions (right).
Figure 1.10: Emmy Noether (1882-1935)
Figure 2.2: Thomas Young, 1773 - 1829
Figure 2.3: Augustin Fresnel, 1788 - 1827
Figure 2.4: George Gabriel Stokes, 1819 – 1903
Figure 2.5: James MacCullagh, 1809 - 1847
Figure 2.6: Joseph Boussinesq, 1842-1929
Figure 2.7: William Thomson (Lord Kelvin), 1824 - 1907
Figure 2.8: James Clerk Maxwell, 1831 - 1879
Figure 2.9: Albert Michelson, 1852-1931
Figure 2.10: Hendrik Lorentz, 1853 - 1928
Figure 2.11: Jules Henri Poincare, 1854 - 1912
Figure 2.12: Max Planck, 1858 - 1947
Figure 2.13: Neils Bohr, 1885-1962
Figure 2.14: Louis Victor de Broglie, 1892-1987
Figure 2.15: Clinton Davisson and Lester Germer in 1927
Figure 2.16: Images of diffraction from crystals of (a) x-rays and (b) electrons of similar wavelength
Copyright © 1997-2002 Catharine H. Colwell. All rights reserved. PhysicsLAB.
Figure 2.17: Time Dilation: The clock on O˘ ticks slower than the clock on O by the factor because waves travel farther between transmission and detection. Both O and O˘ measure the same number of clock cycles for a wave to propagate from their own sub to the fish and back. Hence they agree on distances perpendicular to the direction of relative motion.
Figure 2.18: Length Contraction: The true wave propagation time for the co-moving sub and fish is longer than for the stationary sub and fish by the factor 1/(1-v2/cs2). Since the moving clock runs slow, the perceived propagation time is longer only by the factor . Hence the stationary sub observes a shorter length than the moving sub.
Figure 2.19: Classical Doppler shifts for moving (approaching) source and detector differ by a factor of . This factor is not affected by reversal of the velocity direction.
Figure 2.20: Velocity Measurement: Radar signals sent simultaneously by O and O˘ will also be received simultaneously after reflection. Although O˘’s clock ticks slowly, the proportionality between radar pulse propagation time and total time elapsed is the same as for O. Therefore both O and O˘ measure the same relative velocity.
Figure 2.21: Energy, momentum, and mass have the same Pythagorean relation as light speed (c), velocity (u), and , respectively (with appropriate unit normalization).
Figure 2.22: Time Dilation: Moving matter waves propagate farther than stationary matter waves during each cycle. Therefore moving clocks tick more slowly than stationary clocks. dS = distance traveled in one cycle of stationary wave, dT = translational distance. The distance formula for the cycloid is exact only for an integer number of cycles.
Figure 3.1: J.J. Thomson, 1856-1940
Figure 3.2: Ernest Rutherford, 1871-1937
Figure 3.3: Arnold J.W. Sommerfeld, 1868-1951
Figure 3.4: Werner Heisenberg, 1901-1976
Figure 3.5: Erwin Schrodinger, 1887-1961
Figure 3.6: Wolfgang Pauli, 1900-1958
Figure 3.7: Paul Dirac, 1902-1984
Figure 3.8: Rotation of a single bar on a torsion wave machine results in mirror-symmetric waves propagating in opposite directions. This is a one-dimensional analogue of production of particles and anti-particles. Matter and anti-matter are also always produced in mirror-symmetric pairs.
Isaac Newton, 1643 – 1727
Pierre-Simon Laplace, 1749-1827
Lóránd Baron von Eötvös, 1848-1919
Albert Einstein, 1879 – 1955
David Hilbert, 1862 - 1943
Karl Schwarzschild, 1873-1916
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Figure: Rotation of a single bar on a torsion wave machine results in mirror-symmetric waves propagating in opposite directions. This is a one-dimensional analogue of production of particles and anti-particles. Anti-matter and matter behave exactly as if they are mirror images of each other.