User:Tohline/Appendix/CGH/QuantumTransitions

Speculation Regarding Quantum Transitions

The contents of this "Ramblings Appendix" chapter are pure speculation. I am definitely not an authority on quantum mechanics, but I have for some time been interested in interpretations of the wave function. It is this, along with my quantitative interests in digital holography, that have led to the set of thoughts presented below.

Digital Holography

When a ray of coherent, monochromatic light passes through a square aperture, a specific diffraction pattern is created. The same result is achieved by bouncing the light off of one side of a cube [serving as the square aperture]. In this manner, information about a localized structure (the aperture) is preserved in a (diffraction) pattern that formally extends to infinity. A hologram is created by "storing" the diffraction pattern (amplitude with no phase) as an image.

This process can be reversed. A ray of coherent, monochromatic light that bounces off of (or shines through) the holographic image will — at the appropriate distance from the hologram — display an image of the original compact aperture.

Note that, either way — that is, whether the aperture is being used to create the diffraction pattern or vise versa — the diffraction pattern/hologram can be viewed as a probability distribution.

This sounds suspiciously like an atomic transition: When an electron is bound to an atomic nucleus, information regarding its position/momentum is viewed as a wave function (probability distribution). When a photon (of the proper frequency) strikes the atom, it can react with the wave function in such a manner that it ejects the electron. That is to say, the result of the light passing through (bouncing off of) the wave function (hologram) is to form a compact entity (the electron).

See Also

• Tohline, J. E., (2008) Computing in Science & Engineering, vol. 10, no. 4, pp. 84-85 — Where is My Digital Holographic Display? [ PDF ]
• Diffraction (Wikipedia)
• Various Google hits:
  • Single Slit Diffraction (University of Tennessee, Knoxville)
  • Diffraction from a Single Slit; Young's Experiment with Finite Slits (University of New South Wales, Sydney, Australia)
  • Single Slit Diffraction Pattern of Light (University of British Columbia, Canada)
  • Fraunhofer Single Slit (Georgia State University)
• Hydrogen Atom (Wikipedia)

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