Enhancement of Electromagnetic Memory Effects

Abstract

We show that the amplitude of electromagnetic memory can be significantly enhanced in comparison to known estimates. In a Lorentz breaking phase of lowered phase velocity of light, there exist critical spacetime directions of memory-source emission along the effective light cone, about which the total memory offset receives order of magnitude increases. The same amplification is already present in the Lorentz preserving case by considering ultra-relativistic memory-source charges. These observations may pave the way for a first observation of the phenomenon of memory and laboratory tests of the concepts of asymptotic symmetries and soft theorems.

Figures (3)

• Figure 1: The ration of the total memory offset $\Delta A^T_\text{sup}$ [Eq. \ref{['eq:defememsup']}] with superluminal speed $v_q=1.1 \,v_\text{em}$ and $\Delta A^T_\text{sub}$ [Eq. \ref{['eq:defememsub']}] with subluminal value $v_q=0.978\,v_\text{em}$ as a density plot over the sphere of memory emission centered at the position of charge emission. The spacial direction of charge emission is indicated by a thin white line with the superluminal charge represented by a white particle. For a superluminal emission, there exists critical angles $\hat{\mathbf{n}}\cdot\hat{\mathbf{n}}_q=v_\text{em}/v_q$, around which the amplitude of electromagnetic memory is enhanced by several orders of magnitude. For visibility, the plot is clipped at the scale of an increase in two orders of magnitude.
• Figure 2: The total electromagnetic memory amplitude $\Delta A^T(1,\theta,\theta_q=0)$ [Eq. \ref{['eq:TotalMemOffsetSimp']}] in SI units of [Vs/m] for a unit charge $q=1$[C] and distance $r=1$[m], as a function of the azimuthal angle $\theta$ and for different values of charge emission speeds $v_q$. For concreteness, the phase velocity of light in the medium is set to $v_\text{em}=0.9c$, with $\mu=\mu_0$ and $\epsilon\approx 1.23 \,\epsilon_0$. For a superluminal emission of the charge $v_q>v_\text{em}$ (solid blue) there exists an unprotected direction of unbounded memory sourcing $\theta_c=\arccos[v_\text{em}/v_q]=0.2089$, indicated by a black dashed vertical line, around which the amplitude of electromagnetic memory is considerably enhanced. If $v_q=v_\text{em}$ (dotdashed orange) the critical angle coincides with the direction of emission of the source $\hat{\mathbf{n}}=\hat{\mathbf{n}}_q$. For a subluminal emission velocity $v_q<v_\text{em}$ (dashed green and dotted red), the electromagnetic memory offset remains finite for any values of $\theta$, although the amplitude is still significantly increased at low values of the angle $\theta$ as soon as $v_q \gtrsim 0.99\, v_\text{em}$.
• Figure 3: Causal cone of emission of a charge $q$ at a speed $1>v_q>v_\text{em}$ with $c=1$ (blue) intersecting a past null cone of a memory event (orange) admitting critical directions of memory enhancement. The angle $\alpha$ precisely corresponds to the critical angle identified in Eq. \ref{['eq:LightconeCond']}.