Abstract

A radio engineer can hardly think about smaller amount of electromagnetic radiation than given by a single oscillation cycle of a unit charge in a dipole. When solved from Maxwell's equations for a dipole of one wavelength, the energy of the emitted radiation cycle obtains the form E_? = 2/3 hf, where the Planck constant h can be expressed in terms of the unit charge, e, the vacuum permeability, ?₀, the velocity of light, c, and a numerical factor as h = 1.1049⋅2?³e²?₀c = 6.62607⋅10³⁴ kg⋅m²/s. A point emitter like an atom can be regarded as a dipole in the fourth dimension. The length of such dipole is measured in the direction of the line element cdt, which in one oscillation cycle means the length of one wavelength. For a dipole in the fourth dimension, three space directions are in the normal plane which eliminates the factor 2/3 from the energy expression thus leading to Planck's equation E_? = hf for the radiation emitted by a single electron transition in an atom. The expression of the Planck constant obtained from Maxwell's equations leads to a purely numerical expression of the fine structure constant ? = 1/(1.1049⋅4?³) ~1/137 and shows that the Planck constant is directly proportional to the velocity of light. When applied to Balmer's formula, the linkage of the Planck constant to the velocity of light shows, that the frequency of an atomic oscillator is directly proportional to the velocity of light. This implies that the velocity of light is observed as constant in local measurements. Such an interpretation makes it possible to convert relativistic spacetime with variable time coordinates into space with variable clock frequencies in universal time, and thus include relativistic phenomena in the framework of quantum mechanics.