First Part of Talk

1. Important new applications of Proper-time Relativistic Quantum Theory for Electrical Engineers and Physicists: interested in Nano/Atomic scale electrical and optical information processing with individual electrons and photons. S.K.Kurtz Prof Emeritus Electrical Engineering Penn State University

2. Using the new Proper-time Relativistic Quantum Theory (PtRQT for short) we derive: A new De Broglie wave/particle relation l = ( h/ (mo u) where u = v/SQRT[1-(v/c)^2] and demonstrate its intimate connection to: A reduced Compton wavelength l/2p = ( h/2p) /(mo u) which goes smoothly over to l/2p = ( h/2p) /(mo c) as u ->c . This is the reduced Compton wavelength .. From these results we show that as the velocity u increases towards c, i.e. u = dx/dt-> c, that the new reduced De Broglie relation l/2p -> l/2p = a ao - where a is the fine structure constant e^2 c mo / 2h and ao is the Bohr radius 4p eo(h/2p)^2 / (mo e^2) First Part of Talk

3. Second Part of Talk Setting the PtRQM De Broglie wavelength l = ( h / (mo u) equal to the circumference of the Borh orbit r(n) = n ao in atomic hydrogen, (which I will discuss) and taking n=1 we get l-> (2 p a0) a from which we see that the Bohr orbit ao of the hydrogen atom has been decreased from 0.053 nm to 1/137 x .053 nm ~ 0.0004 nm = 0.4 pico m ! This new reduced De Broglie wavelength of the electron l/2p is now also equal to a ao = ( h/2p) / (mo c) the electron’s reduced Compton wave length which is less than the Compton wavelength l = h/mo c by a factor of 2p. Next we show that the Fine Structure Constant a can be expressed as a simple ratio of the impedance of free space Zo = SQRT(mo/eo) over twice the quantized (Von Klitzung) resistance Rk = h/e^2 of the electron a = Zo /( 2 Rk)

4. The fine structure constant a is customarily written as a = (e^2) c mo /2h But c = 1/Sqrt(mo eo) so c mo =Sqrt[mo/eo] which is the impedance of free space Zo So a fine structure a = [(e^2)/2h] Zo which gives a = Z0 / (2h/e^2) = Zo/2 Rk QED Fine structure constant as a ratio the impedance of free space and the Von Klitzung quantum of resistance

5. Where DG = e^2/(2 h) = the change in conductance for a single electron And Go = SQRT(eo/m0)= the conductance of free space Giving a= DG /4 Go the fine structure constant Fine Structure Constant as a ratio of Conductances a = DG/4 Go

6. C = eo (l Compton/2p) = eoaao L= mo (l Compton/2p) = moaao R= h/e^2 w* = 1/Sqrt[LC] = c/(l Compton/2p) Frequency n = 1.6 x 10^20 cycles/sec Resonance Energy E = 0.8775 Mev Atomic scale Quantization and Series and parallel Resonances from quantized L,C and R of the electron

7. ao = 53 pm = 4peo (h/2p)^2/(mo e^2) a = Zo/2 Rk = Sqrt(mo/eo)/2 (h/e^2) Is a ao = (h/2p)/( mo c) the reduced Compton wavelength ? Proof: e^2 ‘s cancel to leave the product aoa = • eoSqrt(mo/eo) [4p ( h/2p)^2/2h] 1/mo= • 1/c x h/2p x 1/mo = (h/2p)/(mo c) • QED Proof that Pt-RQM reduced comptoN wavelength = Alpha FS x Bohr Radius

8. Fine Structure constant a = Zo/ (2Rk) Where Rk =25,812.807449 (86) Ohms = h/e^2 And Zo = 376.7303134031346177 Ohms = SQRT(m0/eo) Giving a = 137.03599910400862 Quote from: Cameron: Photon Match to a Single Free Electron Aperion 17, p198 (2010)

9. In this part of the talk we turn to Photon impedance Matching to a single Free Electron by plotting the electric and magnetic wave impedances calculated as multiples r of the reduced Compton wave length of the electron as a function of the fine structure constant of the electron. They are found to cross over at r= 0.707 a RMS value of the reduced Compton wave length. Third Part of Talk

10. Cameron vol 17 p194 2010 Brookhaven [10] Malcolm.H.McGregor, The Power of Alpha,World Scientific (2007)p307 “The fine structure constant as a coupling constant in quantum chromodynamics.”

11. Electric and Magnetic wave impedance of a free electron : Aperionvol 17 p195 (2010) Peter Cameron Brookhaven Nat lab Lambda_e = reduced De Broglie wavelength, r= near field scale factor, for r=1 Lamda_e -> reduced Lambda Compton.wavelength ~ 1 pico m

12. In the final section of this talk we discuss the quantization of the the Circuit parameters C capacitance, L inductance and R resistance and their application using the Landuauer Formula and its extension by Buttiker to the recent developments in atomic scale circuit design of nanocircuitswhere ohms law, Kirchoffs law and the other familiar laws of cirucit design can be applied down to the level of individual electrons and photons in can be impedance matched using nanowires, carbon nanotubes and metastructures, atomic silicon transitors etc. Outline of talk con’t

13. Near field Electric and magnetic Wave impedances as a function of scale parameter R

14. Quote from Peter Cameron Brookhaven Nat Lab. in Aperion 17, 193-200 (2010) *Also Compare to CQM expressons for Masses of muon, proton, Neutron etc. in terms of Fine structure constant

15. Light as both a wave and a Particle simultaneously: Nature communications March 2nd_2015

16. Note the Go used here is the G per electron spin = DG = e^2/2h used in earlier slides

17. Neutral Atoms Behave Much Like Classical Spherical Capacitors James C. Ellenbogen∗ Nanosystems Group, The MITRE Corporation, McLean, Virginia 22102, USA (The scaling of the capacitance with radius is explored in detail for neutral atoms, and it is found that they behave much like macroscopic spherical capacitors. The quantum capacitances of atoms scale as a linear function of the mean radii of their highest occupied orbitals. The slopes of the linear scaling lines include a dimensionless constant of proportionality κ that is somewhat analogous to a dielectric constant, but for individual atoms. The slope and κ assume discrete values Neutral Atoms Behave Much Like Classical Spherical Capacitors characteristic of elements in different regions of the periodic table. These observations provide a different, electrostatics-based way of understanding the periodic behavior of the elements. Atomic Scale Capacitance of Atoms Phys Rev Vol 74 , 2006

19. I = G V G= DG /per electron= (2 e^2 /h) M where M(E) = u(E- e) and u is the Heavyside function

22. 2D-Electron Gas Nina Leonhard SS210

23. Important Length Scales, Nina Leonhard: ConductancceQuantizAtion and Landauer Formula ss210

24. Conductance Quantization in Transistor ; Nina Leonhard SS2010

29. We have demonstrated that the Proper Time Relativistic Quantum Mechanics developed at Howard University over three decades leads to a new and powerful form of De Brgolies Wave/Particle relation l = h/( mo u) where u = dx/dt and v/Sqrt[1-(v/c)^2] and b=Sqrt[c^2+u^2] Conclusions

30. We have demonstrated that this leads to important new physics where the reduced De Broglie wavelenthl/2p = hbar/mo u-> smoothly over to the reduced Compton wavelength l/2p = hbar/mo cat v/c = 1/SQRT[2] = .707 WITHOUT THE PARTICLE MASS CHANGING (ie mo stays mo). Conclusions con’t

31. Next taking 2pl deBroglie = n ao (ao =53 pm, and n=principle quantum number n=1 for ground state)we have shown that when the new reduced De Broglie wavelength goes down to the reduced Compton wavelength, the electron radius goes down to a ao = r* = .386 pm where a is the fine structure constant ! This leads us atomic scale quantized relations for the electrical circuit parameters R, L and C namely (next slide) Conclusions continued

32. C = eo (l Compton/2p) = eoaao L= mo (l Compton/2p) = moaao R= h/e^2 and a Parallel Resonance w* = 1/Sqrt[LC] = c/(l Compton/2p) Frequency n = 1.6 x 10^20 cycles/sec Resonance Energy E = 0.8775 Mev Conclusions Continued

33. Original De Broglie relationship using Lorentz transformation of special Relativity l / p = h / m v