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10 September 2009 Relativistic transformation of wavelength provides insights into the geometry of photons
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The wavelength has been a common denominator to the various wave-like and particle-like models of the photon - this wavelength being inversely proportional to the momentum and energy ascribed to the photon. The Lorentz transformation has been utilized with both wave-like and particle-like descriptions to generate the relativistic Doppler Effect and the associated transformation of the wavelength. The relativistic transformation of those models is reexamined here, noting the common feature that wavelength transforms as a specific time-length projected along the trajectory of the photon. While in the wave-model this length can be associated with the periodicity of the wave, in the particle-model this length can be associated with a real, quantized geometric property of the photon. This associated length can tie the photon to the description of components of other quantum particles modeled variously by strings or membranes. Whatever description for the structure of light we ultimately converge upon should integrate this real, geometric property of wavelength. A novel membrane-like model for the photon is discussed that integrates this geometric time-length and suggests the correlation to mass-energy.
© (2009) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Michael J. Mobley "Relativistic transformation of wavelength provides insights into the geometry of photons", Proc. SPIE 7421, The Nature of Light: What are Photons? III, 74210G (10 September 2009);

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