Figures 1.1 Graphical representation of the Liouville theorem page 12 1.2 Photoelectric effect 13 1.3 Mach-Zender interferometer 15 1.4 The Michelson-Morley interferometer 16 1.5 Interferometer for detecting gravitational waves 17 1.6 Interference in the Mach-Zender interferometer 17 1.7 Results of the experiment performed by Grangier,Roger,and Aspect 18 1.8 Oscillation of electric and magnetic fields 20 1.9 Polarization of classical light 21 1.10 Decomposition of an arbitrary vector la) 22 1.11 Poincare sphere representation of states 28 1.12 Mach-Zender interferometer with the lower path blocked by the screen S 30 1.13 Black-body radiation intensity corresponding to the formula of Rayleigh- Jeans (1),Planck (2),and Wien (3) 32 1.14 Planck's radiation curves in logarithmic scale for the temperatures of liquid nitrogen,melting ice,boiling water,melting aluminium,and the solar surface 33 1.15 Compton effect 34 1.16 Dulong-Petit's,Einstein's,and Debye's predictions for specific heat 36 1.17 Lyman series for ionized helium 37 1.18 The Stern-Gerlach Experiment 39 1.19 Momentum conservation in the Compton effect 41 2.1 Polarization beam splitter 44 2.2 Change of basis 52 2.3 Filters 62 2.4 Two sequences of two rotations of a book 65 2.5 Probability distributions of position and momentum for a momentum eigenfunction 85 2.6 Probability distributions of position and momentum for a position eigenfunction 86 2.7 Time evolution of a classical degree of freedom in phase space and graphical representation of the uncertainty relation 88 2.8 Inverse proportionality between momentum and position uncertainties 89 2.9 Smooth complementarity between wave and particle 90 2.10 Illustration of the distributive law 93 2.11 Proposed interferometry and resulting non-Boolean algebra and Boolean subalgebras 94Figures 1.1 Graphical representation of the Liouville theorem page 12 1.2 Photoelectric effect 13 1.3 Mach–Zender interferometer 15 1.4 The Michelson–Morley interferometer 16 1.5 Interferometer for detecting gravitational waves 17 1.6 Interference in the Mach–Zender interferometer 17 1.7 Results of the experiment performed by Grangier, Roger, and Aspect 18 1.8 Oscillation of electric and magnetic fields 20 1.9 Polarization of classical light 21 1.10 Decomposition of an arbitrary vector |a 22 1.11 Poincaré sphere representation of states 28 1.12 Mach–Zender interferometer with the lower path blocked by the screen S 30 1.13 Black-body radiation intensity corresponding to the formula of Rayleigh– Jeans (1), Planck (2), and Wien (3) 32 1.14 Planck’s radiation curves in logarithmic scale for the temperatures of liquid nitrogen, melting ice, boiling water, melting aluminium, and the solar surface 33 1.15 Compton effect 34 1.16 Dulong–Petit’s, Einstein’s, and Debye’s predictions for specific heat 36 1.17 Lyman series for ionized helium 37 1.18 The Stern–Gerlach Experiment 39 1.19 Momentum conservation in the Compton effect 41 2.1 Polarization beam splitter 44 2.2 Change of basis 52 2.3 Filters 62 2.4 Two sequences of two rotations of a book 65 2.5 Probability distributions of position and momentum for a momentum eigenfunction 85 2.6 Probability distributions of position and momentum for a position eigenfunction 86 2.7 Time evolution of a classical degree of freedom in phase space and graphical representation of the uncertainty relation 88 2.8 Inverse proportionality between momentum and position uncertainties 89 2.9 Smooth complementarity between wave and particle 90 2.10 Illustration of the distributive law 93 2.11 Proposed interferometry and resulting non-Boolean algebra and Boolean subalgebras 94