Time Reversal

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Run Time Reversal Mirror

What Is It?

This experiment is a time-reversal mirror rather than an exact state rewind. A short wave packet is emitted from near the bottom of a two-dimensional telegraph cavity, then scatters from a masked circular obstacle.

During the forward pass, the field records both disturbance and velocity on a two-cell-thick inner boundary strip. During the reverse pass, that recorded boundary strip is replayed in reverse time as a driven boundary condition. The field then refocuses toward the original emitter region, partially reconstructing the broken wave.

What It Tests

The experiment asks whether a local field can reconstruct a scattered packet when only boundary information is replayed backwards. It does not restore the whole state. It records a finite aperture and uses that aperture as an active time-reversal mirror.

This makes the test useful because it separates exact reversibility from practical reconstructability. A perfect rewind would require the complete state and lossless inverse stepping. This experiment asks a narrower question: how much of a scattered wave can be recovered from recorded boundary data alone?

How It Works

The field is stored as a scalar disturbance and velocity pair, conventionally written as φ and v. A local telegraph update advances the mediator through a masked domain. The outer wall is clamped, so the experiment records an inner strip rather than the zero-valued wall itself.

In the forward phase, a smooth source pulse is stamped near the bottom. The packet propagates, scatters around the circular obstacle and reaches the inner boundary strip. At each tick, the experiment records φ and v for each strip cell.

In the reverse phase, the recorded strip is imposed in reverse order, both before and after the local update, so the boundary acts as a driven time-reversal mirror. The simulation then alternates forward and reverse continuously, without a fade, blank or reset.

What Is Not Hard-Coded

• No analytic propagation formula is used.
• No FFT is used.
• No closed-form inverse is supplied.
• No global solve reconstructs the source.
• No stored full-frame history is rewound.

The mediator continues to evolve by strictly local stencil updates. The only replayed information is the recorded boundary strip.

Why It Matters

Time reversal is a useful trap for careless simulations. A system may look reversible if the code simply restores previous frames. This experiment does not do that. It keeps the interior evolving and drives only the boundary from recorded data.

For CAELIX, the distinction matters. It lets the experiment expose finite-aperture loss, discrete constraints and gradual degradation across cycles. The result is a practical reconstruction test, not a theatrical rewind.