Abstract
In a recent paper, we have studied the nature of the electromagnetic energy radiated over a single period of oscillation by an antenna working in frequency domain under ideal conditions and without losses when the oscillating charge in the antenna is reduced to the elementary charge. Here we extend and expand that study. The energy radiated by an oscillating current in an antenna occurs in bursts of duration T/2, where T is the period of oscillation. The results obtained here, based purely on classical electrodynamics, can be summarized by the inequality U ≥hv→q0 ≥e where U is the energy radiated in a single burst of duration T/2, h is the Planck constant, ν is the frequency of oscillation and q0 is the magnitude of the oscillating charge associated with the current. The condition U=hv→q0=e is obtained when the length of the antenna is equal to the ultimate Hubble radius of the universe (i.e. the maximum value of the antenna length allowed by nature) and the wavelength is equal to the Bohr radius (resulting from the smallest possible radius of the conductor allowed by nature). The ultimate Hubble radius is directly related to the vacuum energy density. The inequality obtained here is in general agreement with the one obtained in the previous study. One novel feature of this extended analysis is the discovery of an expression, in terms of the elementary charge and other atomic constants, for the vacuum energy density of the universe. This expression predicts the vacuum energy density to be about 4×10-10 J/m3 which is in reasonable agreement with the measured value of 6×10-10 J/m3.
Highlights
In several recent publications, Cooray and Cooray [1] [2] investigated the lower limits of the radiated energy when the charge associated with the current in the antenna giving rise to the radiation is equal to the elementary charge
The energy radiated by an oscillating current in an antenna occurs in bursts of duration T/2, where T is the period of oscillation
The results obtained here, based purely on classical electrodynamics, can be summarized by the inequality U ≥ hν → q0 ≥ e where U is the energy radiated in a single burst of duration T/2, h is the Planck constant, ν is the frequency of oscillation and q0 is the magnitude of the oscillating charge associated with the current
Summary
Cooray and Cooray [1] [2] investigated the lower limits of the radiated energy when the charge associated with the current in the antenna giving rise to the radiation is equal to the elementary charge. In the case of antennas working in frequency domain it was shown in reference [1] (hereinafter referred to as Paper 1), that the radiation satisfy the order of magnitude relationship, U ≥ hν → q ≥ e where U is the energy dissipated over a period of oscillation and q is the charge associated with the oscillating current [1]. Subsequent analysis showed that the energy increases slowly (i.e. logarithmically) instead of reaching a steady value This slowly increasing nature of the emitted energy over a given time period with increasing L/λ and the limited range of L/λ over which the analysis was carried out in Paper 1 compelled us to revisit the work
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