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 QED Tunneling – an alternative to the Schrodinger Equation?The similarity of QED tunneling to the Schrodinger equation refutes the Hartman effect that suggest photons at superluminal velocity are created in the gap between double prisms with extensions made to nearfield heat transfer and the Casimir force
The Hartman effect [1] shows the time for evanescent waves to tunnel between double prisms tends to a constant for large gaps. Since the time to cross large gaps is the same as for short gaps, the Hartman effect suggests the photons have crossed the gap with superluminal velocity. However, Winful [2] argued nonpropagating evanescent waves are virtual photons that do not propagate across the gap into the outside world. Since the velocity of evanescent 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 evanescent wave energy until the barrier may be breached, the Hartman effect may be explained by the time for the incident photon energy to accumulate to the barrier height, i.e., the same time for light to cross large gaps has nothing to do with the photons crossing the gap at velocities exceeding the speed of light. Because of this, Winful argued the Hartman effect is completely explained without the need for superluminal velocities. Problem The problem with Winful’s argument of the time delay for the energy of evanescent waves to accumulate prior to breaching the barrier is the fact nonpropagating evanescent waves cannot cross the gap into the outside world even if the stored EM energy can breach the barrier. QED Tunneling In an alternative to the Schrodinger equation, QED tunneling resolves the problem of nonpropagating evanescent waves not being able to cross the gap of the double prism. QED stands for quantum electrodynamics. QED creates real photons from the EM evanescent energy accumulated in the gap that are capable of propagating to the outside world. Although the mathematics of QED is complex, the physics may be readily understood. Simply put, QED creates photons upon supplying EM energy to a QED cavity, i.e., for a cavity with sides d, QED creates photons having wavelength 2d. In the double prism, the gap d is a QED cavity corresponding to a barrier having Planck energy E_{B} = hc/2d, where h is Planck’s constant and c the speed of light. Now, an incident photon with wavelength W has Planck energy E = hc/W. If E < E_{B} , the incident photon cannot breach the barrier. However, the barrier may be breached from the accumulated EM energy of a number N of incident photons. Saturation requires the number N of incident photons, N = E_{B}/E = W/2d > 1. See http://www.prlog.org/ Extensions Like the Schrodinger equation, QED tunneling is fundamental physics applicable to diverse applications including nearfield radiative heat transfer and the ZPE or thermal Casimir force. Nearfield Radiative Heat Transfer The SB equation gives the thermal BB radiative power transferred between the surfaces of bodies provided the gap d between the surfaces is greater than the halfwavelength W/2 of the BB radiation emission, i.e., d > W/2. SB stands for StefanBoltzmann and BB for blackbody. But like the double prism, nearfield heat transfer is based on gaps d < < W/2. Currently, BB radiation is thought [3] to cross nanoscale gaps by tunneling of evanescent waves. Indeed, Maxwell solutions [3] show evanescent waves enhance the heat transfer above that given by the SB equation by 34 orders of magnitude. However, QM precludes the atoms in gap surfaces from having the heat capacity necessary to allow surface temperatures to fluctuate. QM stands for quantum mechanics. Because of this, Maxwell solutions of heat transfer by evanescent waves cannot satisfy the FDT, and therefore are of questionable validity. FDT stands for the fluctuation dissipation theorem. 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 naturally supply the EM energy needed by QED to create standing wave photons that tunnel across the gap as shown in the thumbnail. Unlike the Maxwell solutions, the QED heat transfer based solely on QM does not exceed that given by the SB equation, but offers the advantage of tuning BB radiation to the peak sensitivity of photovoltaic cells. See http://www.prlog.org/ Thermal Casimir Recently, the thermal Casimir force in the gap between neutral surfaces at ambient temperature was measured [4] at Yale and at 4.2 K in tests [5] at Grenoble. The thermal Casimir force differs from that based on the zero point energy or ZPE. In 1948, Casimir made the controversial extension of the ZPE of quantum mechanics for molecules to the field. Later, Lifshitz in 1955 predicted the existence of the thermal Casimir force. Like Casimir, Lifshitz did not consider charge creation upon bringing neutral surfaces close to each other. Since 1948, Casimir experiments including MEMS and semiconductors in photolithography show charge is created upon bringing otherwise neutral surfaces close together contrary to Casimir and Lifshitz theories. Consistent with observations of charge, the ZPE Casimir and thermal Casimir forces are explained [6] by the QED induced electrostatic force. Like the Hartman effect and nearfield heat transfer, QED photons created in the gap charge the neutral plates by the photoelectric effect to produce the ZPE and thermal Casimir forces. See http://www.prlog.org/ Conclusions 1. QED tunneling offers an alternative to Schrodinger’ 2. 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 does not overcome the fact that evanescent waves cannot propagate EM energy into the outside world. 3. QED by converting the stored EM energy of evanescent waves to QED photons that propagate across the gap to the outside world supports Winful’s argument that the Hartman effect has nothing to do with superluminality. 4. In the nearfield, QED tunneling does not increase heat transfer beyond that given by the SB equation, but offers the advantage of tuning BB radiation to the peak sensitivity of photovoltaic cells. 5. The ZPE and thermal Casimir forces are superseded by the QED induced electrostatic force that creates charge upon bringing neutral surfaces close together. References [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: [3] A. Narayanaswamy, et al., “Breakdown of the Planck blackbody radiation law at nanoscale gaps,” Appl Phys A, vol. 96, pp. 357 (2009). [4] A.O. Sushkov, et al., “Observation of the thermal Casimir force,” Nature Physics, vol. 7, pp. 230 (2011). [5] J. Laurent, et al., “Casimir force measurements in AuAu and AuSi cavities at low temperature,” [6] T. Prevenslik, “The QED Induced Electrostatic Force,“ at http://www.nanoqwd.org , 2012. End
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