Negative group delay for Dirac particles traveling traveling through a potential well

Xi Chen, Chun-Fang Li

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Yue Ban, Xi Chen, Chun-Fang Li

Xi Chen, Chun-Fang Li

The properties of group delay for Dirac particles traveling through a potential well are investigated. A necessary condition is put forward for the group delay to be negative. It is shown that this negative group delay is closely related to its anomalous dependence on the width of the potential well. In order to demonstrate the validity of stationary-phase approach, numerical simulations are made for a Gaussian-shaped temporal wave packet. A restriction to the potential-well's width is obtained that is necessary for the wave packet to remain distortionless in the traveling. Numerical comparison shows that the relativistic group delay is larger than its corresponding nonrelativistic one.

Chun-Fang Li, Qi Wang

Ahmed Albezawi

The observation of negative group delays in anomalously dispersive media—where in the peak of a light pulse appears to exit a medium before it enters—has generated persistent conceptual unease since the foundational experiments of Garrett and McCumber, Steinberg, Kwiat, and Chiao, Nimtz, and Wang, Kuzmich, and Dog?ariu. Standard treatments acknowledge that causality is not violated yet offer no satisfactory account of why, resorting to kinematic arguments about pulse reshaping that leave the physical picture obscure. In this paper we resolve the problem struc?turally, not kinematically, using the framework of Relational Retrocausal QuantumMechanics (RRQM). In RRQM, the photon is not a particle travelling through spaceein time; it is a static spectral object Ψµ(p) ∈ L2(R4, d4p) ⊗ V defined over the fullfour-dimensional momentum manifold. Its spacetime manifestation ψµ(x)—obtained by Fourier transform—is a static interference pattern on R4. What is measured as a “group delay” is the shift in the locus of constructive interference of this static pattern induced by the spectral reshaping operator of the medium. A negative group delay is therefore a negative coordinate of a shifted interference locus, not the transit time ofany object. The question of whether this violates causality is categorically malformed: nothing moves, so nothing moves faster than light.

Yan Wang, Xi Chen, Yue Ban +1 more