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 Eλ = 2/3 hf, where the Planck constant h can be expressed in terms of the unit charge, e, the vacuum permeability, μ0, the velocity of light, c, and a numerical factor as h = 1.1049*2π3e2μ0c=6.62607*10-34 [kgm2/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 Eλ = 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 α=1/(1.1049*4π3) = 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.
When interpreted with the standard theory of cosmology, recent observations of the apparent magnitude vs. redshift of Type Ia supernovae suggest an accelerating expansion of space. The acceleration is justified by assuming the presence of an unknown dark energy working against gravitation at cosmological distances. The assumption of dark energy is equivalent to Einstein's cosmological constant, which he originally proposed to prevent a collapse of spherically closed space which he assumed to be static. If Einstein's spherically closed space, the surface of a 4-sphere, is allowed to expand in a zero energy balance between the energies of motion and gravitation, no cosmological constant or dark energy is needed. In a thorough analysis of such expansion, the apparent magnitude, m, versus redshift, z, obtains the form m = M0 + 5 log(z) + 2.5 log(z+1), which completely agrees with the Type Ia supernovae observations [1,2]. Due to the assumed spherical geometry and the zero energy balance, the obtained magnitude prediction is absolute in its nature; it has no free parameters like omega(m), omega(lamda), or the Hubble constant H(0) that are needed in the corresponding equation derived from the standard cosmology model. In space, described as a dynamic 4-sphere, the fourth dimension is geometrical in its nature, allowing a universal time coordinate. The velocity of light becomes directly linked to the velocity of space in the direction of the 4-radius and the rest energy of mass gets the meaning of the energy of motion mass possesses mass due to the expansion of space. As further consequences of the zero-energy balance, buildup of mass centers in space result in local bending of space allowing solutions of the perihelion advance of planetary orbits, the bending of light and the Shapiro delay in closed mathematical form. The characteristic absorption and emission frequencies of atomic objects become linked to local motion and gravitation, which means that the concept of proper time is replaced by a direct effect of motion and gravitation on the frequencies of atomic oscillators. In dynamic spherical space the well known equality between the total gravitational energy and the rest energy of mass in space reflects the zero energy balance driving the expansion of spherically closed space.