In 1923, Arthur Holly Compton introduced what today is known as the Compton wavelength. Even if the Compton scattering derivation by Compton is relativistic in the sense that it takes into account the momentum of photons traveling at the speed of light, the original Compton derivation indirectly assumes that the electron is stationary at the moment it is scattered by electrons, but not after it has been hit by photons. Here, we extend this to derive Compton scattering for the case when the electron is initially moving at a velocity v.
A. H. Compton. A quantum theory of the scattering of x-rays by light elements. Physical Review, 21(5):483, 1923. URL https://doi.org/10.1103/PhysRev.21.483.
S. Prasannakumar, S. Krishnaveni, and T. K. Umesh. Determination of rest mass energy of the electron by a Compton scattering experiment. European Journal of Physics, 33(1):215, 2012. URL https://doi.org/10.1088/0143-0807/33/1/005.
P. Dirac. The quantum theory of the electron. Proc. Roy. Soc. London, (117):610, 1928. URL https://doi.org/10.1098/rspa.1928.0023.
E. Schrodinger. Experimental test of Heisenberg’s measurement uncertainty relation based on statistical distances. ¨ Physical Review, 28(6):104–1070, 1928.
de. L. Broglie. Waves and quanta. Nature, 112:540, 1923. URL https://doi.org/10.1038/112540a0.
de. L. Broglie. An introduction to the Study of Wave Mechanics. Metheum & Co., Essex, 1930.
B. Haisch, A. Rueda, and Y. Dobyns. Inertial mass and the quantum vacuum fields. Annalen der Physik, 10(5):393, 2001.
E. G. Haug. Collision space-time: Unified quantum gravity. Physics Essays, 33(1):46, 2020. URL https://doi.org/10.4006/0836-1398-33.1.46.
E. G. Haug. Quantum Gravity Hidden In Newton Gravity And How To Unify It With Quantum Mechanics. in the book: The Origin of Gravity from the First Principles, Editor Volodymyr Krasnoholovets, NOVA Publishing, New York, 2021.
E. G. Haug. Unified quantum gravity field equation describing the universe from the smallest to the cosmological scales. Physics Essays, 35:61, 2022. URL https://doi.org/10.4006/0836-1398-35.1.61.
H. Chauhan, S. Rawal, and R. K. Sinha. Wave-particle duality revitalized: Consequences, applications and relativistic quantum mechanics.
A. I. Lvovsky. Quantum Physics: An Introduction Based on Photons. Springer, 2018.
H. A. Lorentz. Simplified theory of electrical and optical phenomena in moving systems. Proc. Acad. Scientific, Amsterdam, 1, 1899.
L. B. Okun. The concept of mass. Physics Today, 42, 1989. URL https://doi.org/10.1063/1.881171
C. G. Adler. Dose mass really depends on velocity dad? American Journal of Physics, 55:739, 1987. URL https://doi.org/10.1119/1.15314.
E. Hecht. Einstein never approved the relativistic mass formula. The Physics Teacher, 47:336, 2009. URL https://doi.org/10.1119/1.3204111.
E. F. Taylor and J. A. Wheeler. Spacetime Physics, Introduction To Special Relativity. W. H. Freeman and Company, New York, 1992.
Wolfgang Rindler. Relativity, Special, General and Cosmology, Second Edition. Oxford University Press, 2006.
M. Jammer. Concepts of Mass in Contemporary Physics and Philosophy. Princeton University Press, 2000.
E. A. Milne. On the foundations of dynamics. Proceedings of the Royal Society A, 154:22, 1936. URL https://doi.org/10.1098/rspa.1936.0034.
Ø Grøn. Introduction to Einstein’s Theory of Relativity, From Newton’s Attractive Gravity to the Repulsive Gravity of Vacuum Energy, Second Edition. Springer Verlag, 2020.
E. G. Haug. Modern physics incomplete absurd relativistic mass interpretation. and the simple solution that saves Einstein’s formula. Journal of Modern Physics, 9(14), 2018. URL https://doi.org/110.4236/jmp.2018.914163.
E. G. Haug. Planck speed: the missing speed of physics? Absolute still without breaking Lorentz symmetry! European Journal of Applied Physics, 4 (1):15, 2022a. URL https://www.ej-physics.org/index.php/ejphysics/article/view/144.
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