TITLE:
Classical Electromagnetic Fields of Moving Charges as a Vehicle to Probe the Connection between the Elementary Charge and Heisenberg’s Uncertainty Principle
AUTHORS:
Vernon Cooray, Gerald Cooray
KEYWORDS:
Transition Radiation, Heisenberg’s Uncertainty Principle, Electronic Charge, Elementary Charge, Size of the Universe
JOURNAL NAME:
Natural Science,
Vol.9 No.7,
July
25,
2017
ABSTRACT: The
radiation fields generated when a charged particle is incident on or moving
away from a perfectly conducting plane are obtained. These fields are known in
the literature as transition radiation. The field equations derived thus are
used to evaluate the energy, momentum and the action associated with the
radiation. The results show that for a charged particle moving with speed ν,
the longitudinal momentum associated with the transition radiation is
approximately equal to ΔU/c for values of 1- ν/c smaller than about
10-3 where ΔU is the total radiated energy dissipated
during the interaction and cis the speed of light in free space.
The action of the radiation, defined as the product of the total energy
dissipated and the duration of the emission, increases as 1- ν/c decreases
and, for an electron, it becomes equal to h/4π when ν = c - νm where νm is
the speed pertinent to the lowest possible momentum associated with a particle
confined inside the universe andh is the Planck constant. Combining these
results with Heisenberg’s uncertainty principle, an expression that predicts
the value of the elementary charge is derived.