de Broglie Matter Waves and Quantum Interpretations

endowed with a certain mass $m$ will therefore find itself naturally associated with • a characteristic Energy $E = mc^2$ which represents the energy enclosed by the rest mass of the particle (Rest energy of the particle) • a relative associated frequency $\nu = \frac{mc^2}{h}$ (de Broglie wave frequency) • a characteristic Length $\lambda = \frac{h}{mc}$ for which wave effects begin to be relevant (Compton wavelength of the particle) Epistemological Problems de Broglie's hypothesis on the wave nature of matter was confirmed in 1927 by the Davisson and Germer experiments on electrons. From that moment experiments have continued until today where de Broglie's hypothesis has been confirmed on material objects not only on elementary particles, but even on molecules and small material aggregates. Since de Broglie's hypothesis that matter behaves like a wave has proven experimentally valid, it is therefore more than legitimate, at this point, to ask the simplest and most immediate question: matter behaves like a wave, but a wave of what? Light is an electromagnetic wave, sound is a wave of air pressure, but matter is a wave of what? This question, however simple and immediate, has not yet found a unanimous answer. According to de Broglie and subsequently Bohm, the described wave is a wave that really exists in space and time and guides the particle in motion. According to Born's interpretation, instead, this wave described by de Broglie is nothing but a probability wave that matter has to be found in a certain point. But what would be the meaning to attribute to such probability? Would this probability perhaps be only a measure of our ignorance, as Einstein maintained? Or would this probability be a real indetermination of nature as Bohr and Heisenberg maintained with what today is called the Copenhagen interpretation? None of these questions has yet found an answer. General Relativity In the previous chapter we identified the three fundamental conceptual categories to which physicists resort to explain the reality that surrounds us, namely space, time and energy. Subsequently we highlighted which