# Electrostatic Time Dilation and Redshift

## TL;DR

This paper explores the theoretical possibility of electrostatic time dilation and redshift effects, proposing a general relativistic framework and emphasizing the importance of ionic atomic clocks for experimental verification.

## Contribution

It introduces the concept of electrostatic time dilation, develops a relativistic scheme for it, and proposes an electrical equivalence principle analogous to gravity.

## Key findings

- Electrostatic redshift experiments yielded null results due to charge conservation.
- A general relativistic scheme for electrostatic time dilation is proposed.
- Ionic atomic clocks could potentially measure the electrostatic time dilation effect.

## Abstract

We first present the salient features of the gravitational time dilation and redshift effects in two ways; by considering the oscillation frequencies/rates of clocks at different heights/potentials and by considering the photons emitted by these clocks such as atoms/nuclei. We then point out to the extension of these gravitational effects to static electricity along with two experiments performed in the '30s with null results of the electrostatic redshift. We show that the absence of this redshift is a consequence of the conservation of electric charge. We discuss the electrical time dilation and redshift effects in detail and argue that the electrostatic time dilation in an electric field must be a fact of Nature. We then present a general relativistic scheme that explains this effect. We also introduce an electrical equivalence principle analogous to the gravitational one and demonstrate how to obtain the electrostatic time dilation by this principle. We emphasize the importance of ionic atomic clocks to measure this effect whose confirmation would support the general relativistic scheme presented. We finally go over an attempt in the literature to explain the impossibility of the experimental observation of the electrostatic redshift due to its smallness by employing the Reissner - Nordstr\"om metric in general relativity. We argue that the $Q^{\,2}$ - term in this metric is due to the minuscule contribution of the energy of the electric field of the central body to its gravitational field. Thus being gravitational, this metric cannot be used to calculate the amount of the alleged electrostatic redshift.