Abstract
By the end of the second decade of the nineteenth century—long before the discovery of X-rays and the invention of the electron microscope—it would still have been possible, using nothing more than a beam of light and two polarizing crystals (e.g., calcite), to determine that the intrinsic structure of at least some molecules was three dimensional (assuming one believed in molecules then [1]). The tell-tale “optical activity”—a rotation of the plane of polarization of the light upon transmission through the sample as shown in Figure 6.1—does not occur for all molecules, but only for those which cannot be superimposed upon their mirror image. Such a structure, subsequently termed “dissymmetric” by Louis Pasteur but referred to as “chiral” (derived from the Greek for “hand”) in current terminology—must necessarily be three dimensional, for a flat object and its mirror image could always be made to superimpose. Reflection, as illustrated in Figure 6.2, reverses the chirality or “handedness” of an object, thereby interchanging, for example, the right and left winding of a helix or screw.
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References
Skepticism over the atomic theory of matter by reputable scientists existed into the twentieth century, i.e., until the conclusive experiments in 1908–1909 on Brownian motion by Jean Perrin based on the theoretical predictions of Einstein (1905–1906). See, for example, G.L. Trigg, Crucial Experiments in Modern Physics (Crane, Russak, New York, 1975), Chapter 4.
Optically active substances can also be constructed from mirror-inequivalent arrangements of achiral molecules. Crystalline quartz is one such example; repeating units of silicon dioxide wind in helical fashion (with left or right circulations) about the optic axis. Unlike substances composed of intrinsically chiral molecules, however, the chirality, and therefore the optical activity, vanish when these “enantiomorphic” forms are melted or dissolved in solution. Thus, fused quartz exhibits no optical activity.
Thorough discussions of the problem of biomolecular homochirality may be found in Origins of Optical Activity in Nature edited by D.C. Walker (Elsevier, Amsterdam, 1979), and in the special issue of Chiral Symmetry Breaking in Physics, Chemistry, and Biology of Biosystems 20, No. 1 (1987).
It is a common error to think that the electric vector of circularly polarized light traces out a circle in time. Since the light wave is advancing as the electric vector is rotating, the actual locus of points traced out would resemble something like a twisted ribbon.
M.P. Silverman, Reflection and Refraction at the Surface of a Chiral Medium: Comparison of Gyrotropic Constitutive Relations Invariant or Noninvariant under a Duality Transformation,J. Opt. Soc. Amer. A 3, 830 (1986).
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We have again separated the center of mass motion and the internal or relative motion. Equation (37) specifies the force on the “relative” particle in a two-particle system—i.e., the hypothetical particle whose mass is the reduced mass m 1 m 2/( m 1 + m 2) and whose velocity is the relative velocity v2 — Vj. If the mass of one particle is much greater than that of the other, then the motion of the bound particle with smaller mass is virtually the same as that of the “relative” particle.
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Silverman, M.P. (1995). The Quantum Physics of Handedness. In: More Than One Mystery. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2504-1_6
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