Supersonic and Superluminal Energy and Speed of Information via Temporal Interference in a Dispersionless Environment

TL;DR

The paper investigates how temporal interference between direct and boundary-reflected acoustic paths in a dispersionless medium can yield wave packets whose energy envelopes propagate at speeds $c_{3d}=l_1/t_m$ that are supersonic relative to the phase speed $c$, while the information-carrying component remains subluminal. It derives exact 3D acoustic solutions using an image-source approach and analyzes information transfer via BER and matched-filter techniques, introducing $D( au,oldsymbol{ ho})=L_0( au,oldsymbol{ ho})-L_1( au,oldsymbol{ ho})$ and related quantities to quantify distinguishability. The results show that temporally interfering paths can increase the apparent energy-speed beyond $c$ yet do not violate causality, and they suggest a plausible EM extension with a rigorous bound that the speed of information does not exceed $c$. The work provides a framework for experimental tests of direct+reflected path effects, with potential implications for high-precision timing, localization, and fundamental discussions of information transfer in wave physics.

Abstract

Numerical implementation of a theory yields acoustic wave packets whose peak-to-peak speeds, $c_{3d}$, are supersonic in a dispersionless medium due to temporal interference between direct and boundary-reflected paths. The effect occurs when the source and receiver are near each other and at least one is within $c\tilde{δt}/2$ of the boundary, where $c$ is the phase speed of propagation in the medium, and $\tilde{δt}$ is the smallest temporal separation between the paths at which interference first occurs. This direct+reflected path effect is distinct from previously-observed superluminal phenomena and theories including quantum tunneling, cavity vacuum fluctuations, and group speeds due to anomalous dispersion. For temporally interfering direct+reflected paths, simulations yield a speed of information less than $c$. The speed of information from the interfering paths can exceed the speed derived from propagation only along the direct path. We conjecture these results will also hold for electromagnetic (EM) wave propagation. If so, we prove the speed of information is less than or equal to the speed of light in a vacuum, so the effect does not violate special relativity. These theoretical and simulation results, as well as their conjectured EM extension, should be readily accessible to experimental verification.

Figures (6)

• Figure 1: Signal propagates from source ${\bf s}$ to receiver ${\bf r}$ along direct and boundary reflected paths with lengths, $l_1$ and $l_2$, and propagation times, $t_1$ and $t_2$, respectively. The $y$ axis is not shown but the $x-y$ plane is perpendicular to the $z$ axis and the boundary is in a $x-y$ plane.
• Figure 2: Envelopes of ideal symbols following Eqs. \ref{['eq:ideal_before_0']} through \ref{['eq:t_max']}. Point of non-analyticity is time zero. Symbols 0 and 1 differ only at times exceeding zero with symbol 0 being dashed.
• Figure 3: Envelopes of received symbol 0 (dashed) and 1 (solid). Red line is time the point of non-analyticity arrives at receiver in absence of any finite bandwidth effects along the direct path.
• Figure 4: A) Envelope of wave packet for symbol 0 at receiver for direct (black) and temporally interfering paths (green). Red line indicates time when point of non-analyticity arrives if energy propagates at phase and group speed, $c$, in absence of delays from finite-bandwidth effects at source and receiver. B) Same except for symbol 1.
• Figure 5: A) Absolute value of Hilbert transform of cross-correlation between emitted and received symbol 0. Ideal time of arrival, $t_1$ is vertical dashed line. Red dot at peak. B) Same except for symbol 1 and $t_1$ at vertical solid line.