Winful's argument against superluminality in the Hartman effect is supported by QED

QED converts the stored energy of non-propagating evanescent waves to photons that propagate through double prisms to the outside world thereby supporting Winful’s argument that superluminal velocities do not occur in the Hartman effect
Superluminality suggested by the Hartman effect is refuted by Winful's argument
Superluminality suggested by the Hartman effect is refuted by Winful's argument
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June 16, 2012 - PRLog -- Background

The Hartman effect [1] suggests superluminal velocities as the evanescent tunneling time tends to a constant for large barriers. With evanescent tunneling, the barrier may be the gap between double prisms as shown in the thumbnail. When the prisms are in contact, the light passes straight through, but when there is a gap, the light may either tunnel across or follow the refracted path. Since the time for light to travel across large gaps is found to be the same as for short gaps, the Hartman effect has been interpreted to suggest the photons have crossed the gap with superluminal velocity.

However, Winful [2] argues non-propagating evanescent waves are virtual photons that do not propagate across the gap into the outside world. Since the velocity of non-propagating waves is meaningless, the light in the Hartman effect cannot travel at superluminal velocities, but rather only be delayed. Of course, if the delay in tunneling is interpreted as a transit time then the Hartman effect naturally leads to superluminal velocities.

On the other hand, if the delay in tunneling is the time for storing incident photon energy until the barrier can be breached, the Hartman effect may be explained [3] by the saturation of incident photon energy in the barrier. The delay is then the time for the flux of incident photons to saturate before the barrier is breached. Because of this, Winful claims the Hartman effect is completely explained by the saturation of stored energy without the need for superluminal velocities.  For an overview of the Hartman effect and Winful’s argument, see


The problem with Winful’s argument of the delayed time for stored energy of evanescent waves necessary to breach the barrier is the fact non-propagating evanescent waves cannot propagate irrespective of whether the stored energy can breach the barrier. What this means is tunneling of photons through the double prism gap occurs by a more fundamental mechanism that creates photons from stored energy that are indeed capable of propagating across the gap. Evanescent waves are not this mechanism, but rather are only a way of supplying EM energy of incident photons to the gap. EM stands for electromagnetic.

QED Tunneling

QED provides a way of creating photons from the stored EM energy of evanescent waves stored in the gap. QED stands for quantum electrodynamics. Simply put, QED creates photons if EM energy is supplied to a QED cavity, e.g., for a cavity with sides of X/2, the standing QED photons created have wavelength X.

In the double prism, the gap d is a QED cavity having a resonant wavelength 2d that corresponds to a barrier having Planck energy EB = hc/2d, where h is Planck’s constant and c the speed of light. Now, a single incident photon having wavelength W has Planck energy E = hc/W. Since E < EB , the incident photon cannot breach the barrier. Over time, however, absorbed EM energy from a number of incident photons accumulates in the QED cavity until saturation breaches the barrier. Saturation requires the number N of incident photons, N = EB /E = W/2d > 1.

QED tunneling by the creation of propagating photons supports Winful’s interpretation of the Hartman effect by the saturation time of stored incident photon energy in the barrier. Unlike evanescent photons that cannot propagate across the gap, the QED created photons not only propagate across the gap, but travel beyond into the outside world.  Assuming the Planck energy E of a single incident photon is localized in the QED cavity in time 2d/c, the time t* to create a QED photon from N incident photons is, t* = N*2d/c = W/c.  Consistent with the Hartman effect, the time t* therefore tends to a constant independent of the gap d while depending only on the wavelength W of the incident photons, i.e., for W < 2d, there is no QED cavity effect with the incident photons localizing in the gap in their own time, t* = W/c.


The QED conversion of EM energy from non-propagating evanescent waves to propagating photons that can interact with the outside world need not be limited to the Hartman effect.  In this regard, BB thermal radiation is the source of EM energy in near-field radiative heat transfer across gaps d. BB radiation having wavelengths W >> d is thought to transmit radiation across nanoscale gaps by evanescent waves. Unlike incident photons from an external laser in the double prism, atoms in the surfaces of nanoscale gaps are physically part of the QED cavity, and therefore the surface atoms naturally supply the EM energy needed by QED to create standing wave photons that transfer radiation across the gap. Indeed, QED tunneling in micron gaps may provide a more practical solution in radiative heat transfer than the nanoscale gaps required for evanescent tunneling. See PPT presentation at  NANORAD 2012 “Invalidity of Near Field Heat Transfer,”, 2012.  


1.  Winful’s argument that the delay in tunneling is the time for storing the EM energy from incident photons until the barrier can be breached cannot overcome the fact that evanescent waves cannot propagate the stored energy into the outside world.  

2.  QED by converting the stored EM energy of evanescent waves to QED photons that can propagate across the barrier to the outside world supports Winful’s argument that the Hartman effect has nothing to do with superluminality.

3.  In radiative heat transfer, QED tunneling in micron gaps may offer a practical advantage over evanescent tunneling in nanoscale gaps.


[1] T. E. Hartman "Tunneling of a wave packet," vol. 33,  J. Appl. Phys., pp. 3427 (1962).
[2] H. Winful "Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox," Phys. Rep., vol. 436, pp.1–69 (2006).
[3] H. Winful, “Origin of the Hartman Effect,” p. 47 of [2]
Source:QED Radiations
Tags:Hartman effect, Superluminality, Winful, Evanesent Waves, Qed
Industry:Science, Research
Location:Youngwood - Pennsylvania - United States
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Page Updated Last on: Jun 18, 2012
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