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 ...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<sup>-10</sup> 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.展开更多
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...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 ρ<sub>Λ</sub> ≤ 9.9×10<sup>-9</sup>J/m<sup>3</sup> where ρ<sub>Λ </sub>is the vacuum energy density. This result is consistent with the measured value of the vacuum energy density, which is 0.538 × 10<sup>-9</sup>J/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.展开更多
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 &...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.展开更多
文摘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<sup>-10</sup> 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.
文摘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 ρ<sub>Λ</sub> ≤ 9.9×10<sup>-9</sup>J/m<sup>3</sup> where ρ<sub>Λ </sub>is the vacuum energy density. This result is consistent with the measured value of the vacuum energy density, which is 0.538 × 10<sup>-9</sup>J/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.
文摘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.
