Heuristic Estimation of the Vacuum Energy Density of the Universe: Part II-Analysis Based on Frequency Domain Electromagnetic Radiation

In Part I of this paper, an inequality satisfied by the vacuum energy density of the universe was derived using an indirect and heuristic procedure. The derivation is based on a proposed thought experiment, according to which an electron is accelerated to a constant and relativistic speed at a distance L from a perfectly conducting plane. The charge of the electron was represented by a spherical charge distribution located within the Compton wavelength of the electron. Subsequently, the electron is incident on the perfect conductor giving rise to transition radiation. The energy associated with the transition radiation depends on the parameter L. It was shown that an inequality satisfied by the vacuum energy density will emerge when the length L is pushed to cosmological dimensions and the product of the radiated energy, and the time duration of emission is constrained by Heisenberg’s uncertainty principle. In this paper, a similar analysis is conducted with a chain of electrons oscillating sinusoidally and located above a conducting plane. In the thought experiment presented in this paper, the behavior of the energy radiated by the chain of oscillating electrons is studied in the frequency domain as a function of the length L of the chain. It is shown that when the length L is pushed to cosmological dimensions and the energy radiated within a single burst of duration of half a period of oscillation is constrained by the fact that electromagnetic energy consists of photons, an inequality satisfied by the vacuum energy density emerges as a result. The derived inequality is given by where is the vacuum energy density. This result is consistent with the measured value of the vacuum energy density, which is 5.38 × 10-10 J/m. The result obtained here is in better agreement with experimental data than the one obtained in Part I of this paper with time domain radiation.

Heuristic Estimation of the Vacuum Energy Density of the Universe: Part I—Analysis Based on Time Domain Electromagnetic Radiation

In this paper, an inequality satisfied by the vacuum energy density of the universe is derived using an indirect and heuristic procedure. The derivation is based on a proposed thought experiment, according to which an electron is accelerated to a constant and relativistic speed at a distance L from a perfectly conducting plane. The charge of the electron is represented by a spherical charge distribution located within the Compton wavelength of the electron. Subsequently, the electron is incident on the perfect conductor giving rise to transition radiation. The energy associated with the transition radiation depends on the parameter L. It is shown that an inequality satisfied by the vacuum energy density will emerge when the length L is pushed to cosmological dimensions and the product of the radiated energy and the time duration of emission are constrained by Heisenberg’s uncertainty principle. The inequality derived is given by ρΛ ≤ 9.9×10-9J/m3 where ρΛ is the vacuum energy density. This result is consistent with the measured value of the vacuum energy density, which is 0.538 × 10-9J/m. Since there is a direct relationship between the vacuum energy density and the Einstein’s cosmological constant, the inequality can be converted directly to that of the cosmological constant.

Hints of the Photonic Nature of the Electromagnetic Fields in Classical Electrodynamics

Several recent publications show that the electromagnetic radiation generated by transmitting antennas satisfy the following universal conditions: The time domain radiation fields satisfy the condition A ≥ h/4π ⇒q ≥ e where A is the action of the radiation field, which is defined as the product of the radiated energy and the duration of the radiation, h is the Planck constant, e is the electronic charge and q is the charge associated with the radiating system. The frequency domain radiation fields satisfy the condition U ≥ hv ⇒q ≥ e where U is the energy radiated in a single burst of radiation of duration T/2 and v is the frequency of oscillation. The goal of this paper is to show that these conditions, which indeed are expressions of the photonic nature of the electromagnetic fields, are satisfied not only by the radiation fields generated by physical antennas but also by the radiation fields generated by accelerating or decelerating electric charges. The results presented here together with the results obtained in previous studies show that hints of the photonic nature of the electromagnetic radiation remain hidden in the field equations of classical electrodynamics, and they become apparent when the dimension of the radiating system is pushed to the extreme limits as allowed by nature.

Lorentz Force from a Current-Carrying Wire on a Charge in Motion under the Assumption of Neutrality in the Symmetrical Frame of Reference

It is commonly assumed that a wire conducting an electric current is neutral in the laboratory frame of reference (the rest frame of the lattice of positive ions). Some authors consider that the wire is neutral only in a symmetrical frame of reference, in which the velocities of electrons and protons have equal norm and opposite direction. In this paper, we discuss the Lorentz transformation between different frames of reference in the context of the special theory of relativity for a current-carrying conducting wire and a probe charge in motion with respect to the wire. A simple derivation of the Lorentz force in the laboratory frame of reference for the assumed neutrality in a symmetrical frame of reference is presented. We show that the Lorentz force calculated assuming neutrality in the symmetrical frame of reference and the one assuming neutrality in the laboratory frame of reference differ by a term corresponding to a change in the test charge speed of one half the drift velocity of the electrons.

Characteristics of different charge transfer modes in upward flashes inferred from simultaneously measured currents and fields

The authors present an analysis of different charge transfer modes during upward negative flashes.The analysis includes a total number of 94 pulses that occurred during two upward negative flashes recorded at the Säntis Tower.The pulses included 59 mixed-mode(MM)initial continuous current(ICC)pulses,17 M-component-type ICC(M-ICC)pulses,8 returnstroke pulses,and 10 classical M-component(MC)pulses.It is found that the initial stage of the flash is responsible for the largest share of the total charge transferred to the ground.Simulation results for the electric fields associated with the considered charge transfer modes are presented and discussed.Return stroke(RS)and MM pulses were simulated adopting the MTLE model,while MCs and M-ICC pulses were simulated using the guided wave model of Rakov et al.The simulated results are shown to be in good agreement with simultaneous records of electric fields measured at a distance of 15 km from the Säntis Tower.The inferred velocities for MCs and M-ICC pulses range from 2.0×10^(7) to 9.0×10^(7) m/s,and the corresponding junction point heights range from 1.0 to 2.0 km.The inferred pulse velocities for RSs and MM pulses range from 1.3×10^(8) to 1.65×10^(8) m/s.The inferred current attenuation constants of the MTLE model obtained in this study range from 0.3 to 0.8 km,lower than the value of 2 km previously suggested for RSs in downward flashes.The obtained results support the assumption that the mode of charge transfer to the ground giving rise to MM pulses is similar to that of RSs.The results are also in support of the generally assumed similarity between M-ICC pulses and classical MCs.