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A tunnelled wavepacket peak exits early. Why is that not faster-than-light travel?

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Answer: Wavepacket peak shape

Whole pulse crossingA whole pulse crossing the barrier like a compact train is the classical picture, but tunnelling filters and reshapes waves. The outgoing peak can represent a selected part of the incident wave rather than the same tagged object arriving early. That is why peak timing is a dangerous substitute for transit timing.

Wavepacket peak shapeCorrect. The peak is not a tagged particle sprinting through the wall; the barrier can preferentially transmit and reshape parts of a wavepacket. In that case a peak position or group delay is not a clean transit time. An early peak can be a property of filtering, not a message beating light.

Moving barrier edgeA moving barrier edge would be an ordinary experimental change, not the tunnelling paradox. In the standard discussion the barrier is fixed, while the transmitted wave is selected from the incident wave. The surprise comes from wave interference and filtering, not from the wall quietly sliding toward the detector.

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