The expression E = h × f is misleading because it implies the distribution of a photon quantum over 299 792 458 m, while the expression E = (h × c)/λ enables us to explain the particle-wave duality

Abstract

The two equations E = h × f and E = (h × c)/λ for the quantum of energy of electromagnetic radiation provide the same result but describe electromagnetic radiation very differently. E = (h × c)/λ describes the quantum of energy of electromagnetic radiation to be located already in one wavelength and therefore like a particle. E = h × f describes the quantum of energy distributed over 299 792 458 m and therefore like a wave. To obtain h × f for the quantum of energy, we have to refer the quantum of energy to 299 792 458 m. Only then we obtain from E = (h × c)/(299 792 458 m), as the distance of 299 792 458 m of the velocity c is cancelling out now, E = h × 1/s = h × Hz, which is the precondition to obtain the correct value for the quantum of energy by multiplying Planck’s constant h by the frequency f. This already indicates the necessity of today's physics to have to speak of a particle-wave duality. It turns out that electromagnetic radiation consists of the first wavelength that carries the quantum of energy and behaves like a particle, which today is called “photon,” and a few following wavelengths that do not carry a further quantum of energy and behave like a wave, which today is called “electromagnetic wave.” By this knowledge, the particle-wave duality vanishes, and we obtain one single physical phenomenon, which I call “photon-wave.” The strange behavior of quantum objects at a single slit, at double-slits, and at beam splitters can now be understood in a causal way. “God does not play dice!” Einstein was right.