On the Momentum Transported by the Radiation Field of a Long Transient Dipole and Time Energy Uncertainty Principle

Abstract

The paper describes the net momentum transported by the transient electromagnetic radiation field of a long transient dipole in free space. In the dipole a current is initiated at one end and propagates towards the other end where it is absorbed. The results show that the net momentum transported by the radiation is directed along the axis of the dipole where the currents are propagating. In general, the net momentum P transported by the electromagnetic radiation of the dipole is less than the quantity U / c , where U is the total energy radiated by the dipole and c is the speed of light in free space. In the case of a Hertzian dipole, the net momentum transported by the radiation field is zero because of the spatial symmetry of the radiation field. As the effective wavelength of the current decreases with respect to the length of the dipole (or the duration of the current decreases with respect to the travel time of the current along the dipole), the net momentum transported by the radiation field becomes closer and closer to U / c , and for effective wavelengths which are much shorter than the length of the dipole, P ≈ U / c . The results show that when the condition P ≈ U / c is satisfied, the radiated fields satisfy the condition Δ t Δ U ≥ h / 4 π where Δ t is the duration of the radiation, Δ U is the uncertainty in the dissipated energy and h is the Plank constant.