Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

# The Time Domain Transition Radiation as a Vehicle to Probe Qualitatively the Connection between the Elementary Charge, Heisenberg’s Uncertainty Principle and the Size of the Universe

Version 1 : Received: 18 April 2017 / Approved: 18 April 2017 / Online: 18 April 2017 (12:13:18 CEST)
Version 2 : Received: 18 July 2017 / Approved: 19 July 2017 / Online: 19 July 2017 (08:57:09 CEST)

A peer-reviewed article of this Preprint also exists.

Cooray, V. and Cooray, G. (2017) Classical Electromagnetic Fields of Moving Charges as a Vehicle to Probe the Connection between the Elementary Charge and Heisenberg’s Uncertainty Principle. Natural Science, 9, 219-230. doi: 10.4236/ns.2017.97022. Cooray, V. and Cooray, G. (2017) Classical Electromagnetic Fields of Moving Charges as a Vehicle to Probe the Connection between the Elementary Charge and Heisenberg’s Uncertainty Principle. Natural Science, 9, 219-230. doi: 10.4236/ns.2017.97022.

Journal reference: Natural Science 2017, 9, 219-230
DOI: 10.4236/ns.2017.97022

## Abstract

The energy, momentum and the action associated with the time domain transition radiation fields are investigated. The results show that for a charged particle moving with speed $v$, the longitudinal momentum associated with the transition radiation is approximately equal to $E/c$ for values of $1-v/c$ smaller than about 10-3 where $E$ is the total radiated energy and c is the speed of light in free space. The action of the transition radiation, defined as the product of the energy dissipated and the duration of the emission, increases as $1-v/c$ decreases and, for an electron, it becomes equal to $h/4\pi$ when $v=c-{v}_{m}$ where ${v}_{m}$ is the speed associated with the lowest energy state of a particle confined inside the universe and h is the Plank constant. Combining these results with Heisenberg’s uncertainty principle, an expression for the electronic charge based on other fundamental physical constants is derived. The best agreement between the experimentally observed electronic charge and the theoretical prediction is obtained when one assumes that the actual size of the universe is about 250 times larger than the visible universe.

## Keywords

transition radiation; Heisenberg’s uncertainty principle; electronic charge; size of the universe

## Subject

PHYSICAL SCIENCES, General & Theoretical Physics

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