sPaceNPilottime tunnels through another mystery

Imagine quantum tunneling not as a mysterious “ghost particle” leaking through a wall, but as a traveler finding a hidden shortcut through a hilly landscape. In the usual Bohmian picture, a particle’s velocity inside a barrier comes entirely from the wave’s phase, and if that phase flattens out, the particle stalls, zero speed inside the wall. That’s why a simple Bohmian account can’t explain Sharoglazova et al.’s experiment, which saw particles (or light in their optical analogue) actually speed up as their energy fell deeper below the barrier.

sPNP’s shortcut picture works like this:

Think of |Ψ|² as shaping the terrain.

Instead of walking on flat ground, the particle moves in a landscape whose hills and valleys are carved by the amplitude of the wavefunction.

Where |Ψ|² is small (inside the barrier), the landscape develops deep, narrow valleys; regions of negative curvature.

Geodesics are the quickest paths.

Just as a hiker in real mountains follows a winding trail that minimizes effort, our quantum traveler follows a “geodesic” in this curved information landscape.

These geodesics bend away from the highest parts of the hill and cut through valleys.

Curvature drives the speedup.

In a deep valley, the geodesic runs faster than it would on flat ground.

As you drop the particle’s energy further below the barrier height, the valley gets deeper (the curvature grows), and the geodesic speeds up more, exactly what Sharoglazova et al. measured.

A single smoothing scale ties it all together.

To keep the landscape well‑behaved (so it doesn’t pin the geodesic on sharp spikes), “blur” |Ψ|² over a small, fixed length (sPNP's Gaussian kernel).

That single choice of blur works for very different barrier shapes, smooth steps, gentle humps, even double bumps, without tweaking anything, and always gives the same “speed ∝ |E–V₀|½” trend.

Why it beats the naive Bohmian view

Bohmian particles slow to a halt whenever the phase gradient vanishes, so they can’t speed up in a deep barrier.

sPNP particles, guided by curvature rather than phase alone, automatically accelerate through deeper, narrower valleys of |Ψ|²—even when the phase is flat.

In plain terms: sPNP turns tunneling from a probabilistic leak into a geometric shortcut. The barrier isn’t just something you tunnel through, it’s a landscape you run across. Sharoglazova et al.’s optical‐waveguide experiment saw the speed‐up that this landscape picture predicts, something the old Bohmian map simply lacked.