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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
FIRST PART OF TALK
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 =o (h/2p)^2 / (mo e^2)

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==o) over twice the quantized
(Von Klitzung) resistance Rk = h/e^2 of the electron
a = Zo /( 2 Rk)
FINE STRUCTURE CONSTANT AS A RATIO THE IMPEDANCE OF
FREE SPACE AND THE VON KLITZUNG QUANTUM OF RESISTANCE
The fine structure constant a is customarily
written as a = (e^2) c mo /2h
 But c = 1/Sqrt(mo =o) so c mo =Sqrt[mo==o]
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 OF CONDUCTANCES
a = DG/4 Go

Where
DG = e^2/(2 h) = the change in conductance for a
single electron

And

Giving
Go = SQRT(=o/m0)= the conductance of free space
a = DG /4 Go the fine structure constant
ATOMIC SCALE QUANTIZATION AND SERIES AND PARALLEL RESONANCES
FROM QUANTIZED L,C AND R OF THE ELECTRON
C = =o (l Compton/2p) = =o a ao
 L= mo (l Compton/2p) = mo a ao
 R= h/e^2

w* = 1/Sqrt[LC] = c/(l Compton/2p)
 Frequency = = 1.6 x 10^20 cycles/sec
 Resonance Energy E = 0.8775 Mev

PROOF THAT PT-RQM REDUCED COMPTON WAVELENGTH = ALPHA FS X BOHR RADIUS
ao = 53 pm = 4p =o (h/2p)^2/(mo e^2)
a = Zo/2 Rk = Sqrt(mo==o)/2 (h/e^2)
Is a ao = (h/2p)/( mo c) the reduced
Compton wavelength ?
Proof:
e^2 ‘s cancel to leave the product ao a =
=o Sqrt(mo==o) [4p ( h/2p)^2/2h] 1/mo=
1/c
x h/2p x 1/mo = (h/2p)=(mo c)
QED
Fine Structure constant
a = Zo/ (2Rk)
Where
Rk =25,812.807449 (86) Ohms = h/e^2
And
Zo = 376.7303134031346177 Ohms = SQRT(m===o)
Giving
a = 137.03599910400862
Quote from: Cameron: Photon Match to a Single Free Electron Aperion 17, p198
(2010)
THIRD PART OF TALK

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.
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.”
ELECTRIC AND MAGNETIC WAVE IMPEDANCE OF A FREE ELECTRON : APERION VOL 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
OUTLINE OF TALK CON’T

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
nanocircuits where 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.
NEAR FIELD ELECTRIC AND MAGNETIC WAVE IMPEDANCES AS A FUNCTION OF SCALE PARAMETER R
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
LIGHT AS BOTH A WAVE AND A PARTICLE SIMULTANEOUSLY:
NATURE COMMUNICATIONS MARCH 2ND_2015
Note the Go used here is the G per electron spin = DG = e^2/2h used in earlier slides
ATOMIC SCALE CAPACITANCE OF ATOMS PHYS REV VOL 74 , 2006
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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.
I = G V G= DG /per electron= (2 e^2 /h) M where M(E) = u(E- =) and u is the
Heavyside function
2D-Electron Gas Nina Leonhard SS210
IMPORTANT LENGTH SCALES, NINA LEONHARD: CONDUCTANCCE QUANTIZATION AND
LANDAUER FORMULA SS210
CONDUCTANCE QUANTIZATION IN TRANSISTOR ; NINA LEONHARD SS2010
CONCLUSIONS
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 CON’T

We have demonstrated that this leads to
important new physics where the reduced De
Broglie wavelenth l=2p = hbar/mo u=>
smoothly over to the reduced Compton
wavelength l=2p = hbar/mo c at v/c =
1/SQRT[2] = .707 WITHOUT THE PARTICLE
MASS CHANGING (ie mo stays mo).
CONCLUSIONS CONTINUED
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
C = =o (l Compton/2p) = =o a ao
 L= mo (l Compton/2p) = mo a ao
 R= h/e^2
 and a Parallel Resonance
 w* = 1/Sqrt[LC] = c/(l Compton/2p)
 Frequency = = 1.6 x 10^20 cycles/sec
 Resonance Energy E = 0.8775 Mev

Original De Broglie relationship using Lorentz
transformation of special Relativity
 l =p=h/mv
