A Mathematical Extension That Reveals Deeper Structure of Light Beyond Quantum Electrodynamics

Quantum Electrodynamics (QED) currently provides the most accurate description of electromagnetic interactions, yet it treats photon energy quantization exclusively through frequency. Motivated by conceptual limitations in the photon hypothesis, the Einsmax Theory of Light Quanta and Massless Particles introduces a complementary quantization framework in which amplitude plays a primary mathematical role. In this paper, a unified theoretical and mathematical formulation is presented that fully preserves Maxwellian wave propagation, the Planck–Einstein relation, and relativistic momentum conservation. Discrete amplitude quantum levels at fixed frequency are derived and shown to provide deeper explanatory power for interference, black-body radiation, and image formation in darkness. This work establishes amplitude as an active quantum variable, offering a mathematically grounded extension to the foundations of optical physics.

Theoretical Physics (Quantum Optics / Electromagnetic Theory)

1. Dirac, P.A.M. (1927). The Quantum Theory of the Emission and Absorption of Radiation. Proc. Roy. Soc. A, 114, 243-265. [Google Scholar] [Crossref]

2. Einstein, A. (1905). Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt. Ann. Phys., 17, 132-148. [Google Scholar] [Crossref]

3. Feynman, R.P. (1949). Space-Time Approach to Quantum Electrodynamics. Phys. Rev., 76, 769-789. [Google Scholar] [Crossref]

4. Planck, M. (1900). Zur Theorie des Gesetzes der Energieverteilung im Normalspektrum. Verh. Dtsch. Phys. Ges., 2, 237-245. [Google Scholar] [Crossref]

5. Raja, S. (2025). Replaced Hypothesis of Light Quanta. IJRIAS, Vol. X, Issue Y, 45-60. [Google Scholar] [Crossref]

6. Maxwell, J.C. (1873). A Treatise on Electricity and Magnetism. Oxford University Press. [Google Scholar] [Crossref]

7. Jackson, J.D. (1999). Classical Electrodynamics. 3rd Edition, Wiley. [Google Scholar] [Crossref]

8. Born, M., & Wolf, E. (1999). Principles of Optics. 7th Edition, Cambridge University Press. [Google Scholar] [Crossref]

9. Schwinger, J. (1948). On Quantum-Electrodynamics and the Magnetic Moment of the Electron. Phys. Rev., 73, 416-417. [Google Scholar] [Crossref]

10. Weinberg, S. (1995). The Quantum Theory of Fields. Cambridge University Press. [Google Scholar] [Crossref]

11. Heitler, W. (1954). The Quantum Theory of Radiation. Oxford University Press. [Google Scholar] [Crossref]

12. Tomonaga, S. (1946). On a Relativistically Invariant Formulation of the Quantum Theory of Wave Fields. Prog. Theor. Phys., 1, 27-42. [Google Scholar] [Crossref]

13. Lamb, W.E., & Retherford, R.C. (1947). Fine Structure of the Hydrogen Atom by a Microwave Method. Phys. Rev., 72, 241-243. [Google Scholar] [Crossref]

14. Bethe, H.A. (1947). The Electromagnetic Shift of Energy Levels. Phys. Rev., 72, 339-341. [Google Scholar] [Crossref]

15. Pais, A. (1982). Subtle is the Lord: The Science and the Life of Albert Einstein. Oxford University Press. [Google Scholar] [Crossref]

16. Compton, A.H. (1923). A Quantum Theory of the Scattering of X-rays by Light Elements. Phys. Rev., 21, 483-502. [Google Scholar] [Crossref]

17. Millikan, R.A. (1916). A Direct Photoelectric Determination of Planck's "h". Phys. Rev., 7, 355-388. [Google Scholar] [Crossref]

18. Bohr, N. (1913). On the Constitution of Atoms and Molecules. Phil. Mag., 26, 1-25. [Google Scholar] [Crossref]

19. de Broglie, L. (1924). Recherches sur la théorie des quanta. Ann. Phys., 3, 22-128. [Google Scholar] [Crossref]

20. Heisenberg, W. (1925). Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen. Z. Phys., 33, 879-893. [Google Scholar] [Crossref]

21. Schrödinger, E. (1926). Quantisierung als Eigenwertproblem. Ann. Phys., 79, 361-376. [Google Scholar] [Crossref]

22. Pauli, W. (1925). Über den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplexstruktur der Spektren. Z. Phys., 31, 765-783. [Google Scholar] [Crossref]

23. Bell, J.S. (1964). On the Einstein Podolsky Rosen Paradox. Physics, 1, 195-200. [Google Scholar] [Crossref]

24. Aspect, A., Dalibard, J., & Roger, G. (1982). Experimental Test of Bell's Inequalities Using Time-Varying Analyzers. Phys. Rev. Lett., 49, 1804-1807. [Google Scholar] [Crossref]

25. Glauber, R.J. (1963). The Quantum Theory of Optical Coherence. Phys. Rev., 130, 2529-2539. [Google Scholar] [Crossref]

26. Mandel, L., & Wolf, E. (1995). Optical Coherence and Quantum Optics. Cambridge University Press. [Google Scholar] [Crossref]

27. Scully, M.O., & Zubairy, M.S. (1997). Quantum Optics. Cambridge University Press. [Google Scholar] [Crossref]

28. Cohen-Tannoudji, C., Dupont-Roc, J., & Grynberg, G. (1997). Photons and Atoms: Introduction to Quantum Electrodynamics. Wiley. [Google Scholar] [Crossref]

29. Loudon, R. (2000). The Quantum Theory of Light. 3rd Edition, Oxford University Press. [Google Scholar] [Crossref]

30. Griffiths, D.J. (2018). Introduction to Quantum Mechanics. 3rd Edition, Cambridge University Press. [Google Scholar] [Crossref]

31. Peskin, M.E., & Schroeder, D.V. (1995). An Introduction to Quantum Field Theory. Westview Press. [Google Scholar] [Crossref]

32. Stratton, J.A. (1941). Electromagnetic Theory. McGraw-Hill. [Google Scholar] [Crossref]

33. Peebles, P.J.E. (1993). Principles of Physical Cosmology. Princeton University Press. [Google Scholar] [Crossref]

34. Hawking, S.W. (1975). Particle Creation by Black Holes. Comm. Math. Phys., 43, 199-220. [Google Scholar] [Crossref]

35. Wheeler, J.A., & Feynman, R.P. (1945). Interaction with the Absorber as the Mechanism of Radiation. Rev. Mod. Phys., 17, 157-181. [Google Scholar] [Crossref]

36. Zee, A. (2010). Quantum Field Theory in a Nutshell. Princeton University Press. [Google Scholar] [Crossref]

37. Sakuri, J.J. (1967). Advanced Quantum Mechanics. Addison-Wesley. [Google Scholar] [Crossref]

38. Penrose, R. (2004). The Road to Reality. Alfred A. Knopf. [Google Scholar] [Crossref]

39. Misner, C.W., Thorne, K.S., & Wheeler, J.A. (1973). Gravitation. W. H. Freeman. [Google Scholar] [Crossref]

40. Landau, L.D., & Lifshitz, E.M. (1975). The Classical Theory of Fields. Pergamon Press. [Google Scholar] [Crossref]

41. Panofsky, W.K.H., & Phillips, M. (1962). Classical Electricity and Magnetism. Addison-Wesley. [Google Scholar] [Crossref]

42. Purcell, E.M. (1985). Electricity and Magnetism. McGraw-Hill. [Google Scholar] [Crossref]

43. Shankar, R. (1994). Principles of Quantum Mechanics. Plenum Press. [Google Scholar] [Crossref]

44. Merzbacher, E. (1998). Quantum Mechanics. Wiley. [Google Scholar] [Crossref]

45. Gottfried, K., & Yan, T.M. (2003). Quantum Mechanics: Fundamentals. Springer. [Google Scholar] [Crossref]

46. Itzykson, C., & Zuber, J.B. (1980). Quantum Field Theory. McGraw-Hill. [Google Scholar] [Crossref]

47. Greiner, W., & Reinhardt, J. (1996). Field Quantization. Springer. [Google Scholar] [Crossref]

48. Bjorken, J.D., & Drell, S.D. (1964). Relativistic Quantum Mechanics. McGraw-Hill. [Google Scholar] [Crossref]

49. Taylor, J.R. (2005). Classical Mechanics. University Science Books. [Google Scholar] [Crossref]

50. Goldstein, H. (2001). Classical Mechanics. 3rd Edition, Addison-Wesley. [Google Scholar] [Crossref]

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