The phase is not dependent on the thickness of the tunneling barrier, therefore when the barrier is thick enough "it appears to violate relativity."
So Steinberg points out the momentum (frequency) becomes imaginary and that's why time is negative and it is NOT just an artifact of using a non-relativistic wave function (Schroedinger).
Steinberg did his Ph.D. under Raymond Ciao! Wow.
The propagation really is faster than light ...but the integrated energy (amplitude squared) is smaller because of the barrier and therefore no signal is transmitted faster than light....
Therefore it is nonlocal as a "post-selected" system.
So using Feynman's transitional amplitude that Basil J. Hiley points out is the same as the Weak value - aka the conditional expectation value - the "imaginary negative frequency momentum" indeed is superluminal with a negative time aka "backaction"!!
the standing wave sees a higher local density than if there was no interference but when the standing wave is in the barrier the density is very low (as the imaginary momentum with no back or forward propagation).
"Bohmian trajectories can't cross - ONLY the front part gets transmitted - that comes immediately from Bohm - it agrees nicely with that intuition."
That's where you get the big Quantum Potential - the particles slow down before they even enter in the barrier....but instead you calculate just how long they spend inside the barrier only.
you don't spend any "real" time in the barrier and that's why the group delay is so short...with the imaginary part of the standing wave being superluminal.
the dwell time in the cavity becomes less than the cavity length divided by the speed of light.
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