How two disturbances can produce a third echo
In physics, an echo is not just a sound bouncing off a wall. It is a delayed, concentrated response that emerges after a system has been disturbed and its internal motions have had time to get out of sync and then partially re-align. The key requirement for an 'echo of an echo' is a second disturbance. In a collisionless system—one where particles or stars move without frequent collisions—a first perturbation sets up a response that spreads out in phase space, the abstract space of position and velocity. A second, later perturbation does the same. The two spread-out responses can then interact nonlinearly and produce a third, macroscopic echo-like response, even though no third perturbation was applied [4].
This was first worked out in plasma physics in the 1960s and has now been adapted to galaxies. In a model of vertical motion in the Milky Way, researchers derived the galactic version of this plasma echo theory and confirmed the predicted behavior in idealized simulations, with and without the added effect of diffusion from stars scattering off molecular clouds [4]. The same basic logic appears in quantum systems: a collection of atoms in a weakly anharmonic trap, hit by two successive pulses, shows pulse-like responses at times that are multiples of the delay between the pulses—most clearly at twice the delay—and these are called echoes [5].
Revival echoes: when the original response reassembles
There is a second, richer way an echo can have an echo. In the trapped-atom system, even a single perturbation produces 'revivals': the initial response dies away, then reassembles at regular revival times, because the trap's slight anharmonicity causes different parts of the quantum wavefunction to re-phase [5]. When a second, smaller perturbation is added, the revivals and the echo response combine. The result is a family of 'revival echoes'—localized responses that appear before and after the revival times, at times shifted by the delay between the two perturbations. Depending on the shape and size of the perturbations, the principal revival echoes can be much larger than the simple echo at twice the delay [5].
This matters for the question because it shows that 'an echo of an echo' is not a single phenomenon. In the plasma and galactic case, the third response comes from two perturbations coupling nonlinearly [4]. In the quantum case, the extra responses come from the interplay between the echo caused by the second perturbation and the natural revivals of the first response [5]. Both are real, predicted, and in the quantum case numerically verified against the time-dependent Schrödinger equation, but they are different mechanisms.
The phrase outside physics: copies that still carry a trace
The idea also shows up as a metaphor. A study of contemporary Swiss nationalism describes the Heidi figure as 'an echo of an echo, a simulation of a simulation,' where each iteration adds distortion but also preserves a trace, a longing, a question [2]. Similarly, a 1952 essay on poetry in broadcasting likens expressions of hope for poetry on the radio to 'the echo of an echo of an echo'—a faint, distant repetition of an original enthusiasm [3]. In both cases, the echo-of-an-echo is not a physical signal but a cultural copy that has been repeated enough to blur, yet not enough to erase, its source.
So can an echo have an echo?
In the physical sense, yes—provided the system is the right kind and is disturbed at least twice. The third response is not a literal sound echoing off a second wall, but a delayed, concentrated signal that emerges from the interaction of two earlier responses. The galactic work cautions that the specific 'Snail' structure in the Milky Way's stellar phase space is unlikely to be a pure echo effect, but the underlying physics is generic enough that such echoes are expected to be common in disc galaxies [4]. The quantum work shows that the timing and strength of the extra echoes depend on the symmetry and size of the perturbations, and that atom-atom interactions affect the phenomenon [5]. In the metaphorical sense, the phrase is already in use for cultural repetitions that carry a trace of the original [2][3].
Sources used in this answer
Magnetic Resonance Elastography of Intervertebral Discs: Spin‐<scp>Echo Echo</scp>‐Planar Imaging Sequence Validation
A spin-echo echo-planar imaging sequence for magnetic resonance elastography of intervertebral discs produced stiffness measurements that correlated well with the standard gradient-recalled-echo method, were highly reproducible, and reduced scan time by at least 51%.
Homeland as Echo, Nostalgia as Strategy: Rethinking Heimat through the Figure of Heidi
The figure of Heidi in contemporary Swiss nationalism is described as 'an echo of an echo, a simulation of a simulation,' where each iteration adds distortion but preserves a trace of longing.
Broadcast Poetry: A Lost Art?
A 1952 essay likens hopes for poetry in broadcasting to 'the echo of an echo of an echo,' a faint and distant repetition.
Galactic echoes
In a collisionless system perturbed twice, the two responses can mix nonlinearly to produce a third macroscopic echo response without a third perturbation; this phase-space echo physics is derived for galaxies and verified in simulations, though the Gaia Snail itself is unlikely to be a pure echo effect.
Echoes and revival echoes in systems of anharmonically confined atoms
Atoms in a weakly anharmonic trap subjected to two successive perturbations show echoes at multiples of the delay and 'revival echoes' before and after natural revival times, with principal revival echoes sometimes much larger than the simple echo at twice the delay.