The existence of matter waves was established by the Davisson-Germer experiment in 1927. The physical concept of matter waves were predicted earlier in 1924 by the French physicist Prince Louis-Victor Pierre Raymond de Broglie (1892-1987). Subsequently, de Broglie was awarded the Nobel Prize for physics in 1929. He based his discovery on the simple equation that the product of wavelength and momentum is equal to Planck’s constant of action. In this formulation the momentum was still defined as the product of mass and velocity giving the wavelength: =ℎ/. This sole equation was the only one found in de Broglie’s doctoral thesis of 1924 and his advisor Paul Langevin was surprisingly nonplussed. Langevin showed it to Einstein, who had already established the existence of photon in 1905 of which he was awarded the Nobel Prize for physics in 1921, and Einstein gave his blessings by saying “I believe that it involves more than a mere analogy.” His approval gave de Broglie his PhD. Later, Einstein made a reference of this wavelength equation in a paper that caught Schrödinger’s attention. Consequently, Schrödinger discovered the formulated wave version of quantum mechanics contrasting Heisenberg’s matrix version.
This simple wavelength equation alone established the wave-particle duality of all modern quantum physics. It bears a subtle resemblance to Heisenberg’s uncertainty principle between position and momentum. Hence a potential controversial physical argument should have then emerged between position (a vector) and wavelength (a scalar). Are these two physically equivalent? If so then all concepts of length (e.g. Planck length) should then be equally definable as a matrix, especially a symmetric singular Hadamard matrix. The transformation of wavelength to matrix should not cause any problem for advanced quantum theories (QED, QCD, QFT, etc.) since position, velocity, momentum, angular momentum, and energy as well as squares of energy is now all considered as matrices.


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