The	cNon	Exclusion	Principle	and	the	vastly	different	internal	electron	and muon	center	of	charge	vacuum	fluctuation	geometry Dr.	James	H.	Wilson Jove	Sciences,	Inc. 3834	Vista	Azul,	San	Clemente,	CA	92672 PACS:	14.60.Cd;	12.20-m;03.65.Ud;03.65-w; Key	Words:	QED,	ultraviolet	divergences,	photon	propagator,	electron's	Center	of Charge	(CoC)	shell,	Zitterbewegung,	static	point	electron,	the	electron's	internal harmonic	oscillator,	the	Dirac	velocity	operator,	the	electron	as	a	stable	fluctuation in	the	vacuum,	hydrogen	atom,	entangled	electron/proton	radius	puzzle Abstract The	electronic	and	muonic	hydrogen	energy	levels	are	calculated	very	accurately [1]	in	Quantum	Electrodynamics	(QED)	by	coupling	the	Dirac	Equation	four	vector (c ,mc2)	current	covariantly	with	the	external	electromagnetic	(EM)	field	four vector	in	QED's	Interactive	Representation	(IR).	The	c -Non	Exclusion	Principle(c -NEP)	states	that,	if	one	accepts	c as	the	electron/muon	velocity	operator because	of	the	very	accurate	hydrogen	energy	levels	calculated,	the	one	must	also accept	the	resulting	electron/muon	internal	spatial	and	time	coordinate	operators (ISaTCO)	derived	directly	from	c without	any	assumptions.	This	paper	does	not change	any	of	the	accurate	QED	calculations	of	hydrogen's	energy	levels,	given	the simplistic	model	of	the	proton	used	in	these	calculations	[1].	The	Proton	Radius Puzzle	[2,	3]	may	indicate	that	new	physics	is	necessary	beyond	the	Standard	Model (SM),	and	this	paper	describes	the	bizarre,	and	very different,	situation	when	the electron	and	muon	are	located	"inside"	the	spatially	extended	proton	with	their Centers	of	Charge	(CoCs)	orbiting	the	proton	at	the	speed	of	light	in	S	energy	states. The	electron/muon	center	of	charge	(CoC)	is	a	structureless	point	that	vibrates rapidly	in	its	inseparable,	non-random	vacuum	whose	geometry	and	time	structure are	defined	by	the	electron/muon	ISaTCO	discrete	geometry.	The	electron/muon self	mass	becomes	finite	in	a	natural	way	due	to	the	ISaTCOs	cutting	off	high	virtual photon	energies	in	the	photon	propagator.	The	Dirac-Maxwell-Wilson	(DMW) Equations	are	derived	from	the	ISaTCO	for	the	EM	fields	of	an	electron/muon,	and the	electron/muon	"look"	like	point	particles	in	far	field	scattering	experiments	in the	same	way	the	electric	field	from	a	sphere	with	evenly	distributed	charge	"e" "looks"	like	a	point	with	the	same	charge	in	the	far	field	(Gauss	Law).	The electron's/muon's	three	fluctuating	CoC	internal	spatial	coordinate	operators	have eight	possible	eigenvalues	[4,	5,	6]	that	fall	on	a	spherical	shell	centered	on	the electron's	CoM	with	radius	in	the	rest	frame.	The	electron/muon	internal	time α α α α α α 2 operator	is	discrete,	describes	the	rapid	virtual	electron/positron	pair	production and	annihilation.	The	ISaTCO	together	create	a	current	that	produce	spin	and magnetic	moment	operators,	and	the	electron	and	muon	no	longer	have	"intrinsic" properties	since	the	ISaTCO	kinematics	define	spin	and	magnetic	moment properties. 1.0	Introduction The	Proton	Radius	Puzzle	is	qualitatively	described	well	in	Bernauer's	and	Pohl's Scientific	American	article	[7]	"You	Would	Be	Forgiven	for	Assuming	that	We Understand	the	Proton",	which	is	very	similar	to	the	quantitative	analyses	given	in this	paper,	especially	the	differences	in	the	electron	and	muon	internal	spatial	and time	coordinate	operators	(ISaTCO)	when	they	are	located	inside	the	spatially extended	proton	in	hydro	gen	(see	Figure	1). From	this	point	on	the	word	electron will	mean	any	charged	lepton,	as	the	ISatCO	development	is	the	same.	However,	the spatial	extent	and	period	of	their	CoC	fluctuations	is	inversely	proportional	to	their mass	the	electron,	muon,	and	tau	particle	will	have	significantly	different	EM	fields when	they	are	inside	the	spatially	extended	proton. The	electron's	magnetic	moment	and	spin	are	easily	derived	from	their	ISaTCOs' "discrete	internal	current",	and	the	electron	is	not	a	"structureless"	point	particle with	"intrinsic"	properties,	as	it	appears	in	the	far	field..	If	one	accepts	c as	the velocity	operator	in	the	four	current	used	in	QED	due	to	the	accurate	calculations that	result,	then	one	must	accept	he	electron	internal	structure	that	is	derived directly	from	the	Dirac	Equation's	velocity	operator,	c .	This	is	called	the	c -Non Exclusion	Principle	(c -NEP),	and	violating	this	principle	is	totally	illogical.	The hydrogen	atom	is	selected	to	illustrate	the	electron's	bizarre	properties	because	it	is α α α α 3 stable	and	the	electron's	internal	structure	is	not	destroyed. All	the	recent	models of	the	extended	electron	with	a	point	charge	that	follows	a	continuous	path,	such	as a	helical	curve	[see	8	for	references],	are	incorrect,	because	the	electron's	internal space	and	time	co-ordinates	are	discrete,	as	the	ISaTCO	are	derived	directly	from the	Dirac	Equation.	All	the	previous	analyses	of	Zitterbewegung	(ZBW)	are	not correct	[see	9	for	references],	because	one	does	not	need	to	make	additional,	ad	hoc assumptions	about	the	electron's	internal	structure	beyond	how	the	Dirac	Equation describes	it	with	its	velocity	operator	c . There	is	a	misconception	that	the	Dirac	Equation	is	a	single	particle	equation,	and that	ZBW	discovered	by	Schrodinger	[10]	is	a	non-relativistic	concept	that	is	not incorporated	in	QED.	In	terms	of	Quantum	Field	theory	(QFT),	the	electron	is	its	CoC and	well	defined	vacuum	fluctuation	that	oscillates	rapidly	creating	the	electron	EM field	(see	references	in	Schwartz	[11]),	and	this	paper	will	derive	the	ISaTCOs	based on	the	c -NEP	only	without	ad	hoc	assumptions.	Accepting	the	physical	description of	the	electron's	internal	structure	resulting	from	its	velocity	operator,	c ,	cannot be	refuted	without	refuting	the	very	accurate	predictions	of	QED.	The	QED	solution of	the	electron	internal	"discrete	position	and	time	distribution"	in	hydrogen	shows (see	Figure	1)	that	the	electron	has	non	zero	probability	to	be	located	inside	the spatially	extended	proton.	The	energy	levels	in	hydrogen	are	very	accurately calculated	by	QED	by	importing	the	Dirac	Equation	four	vector	(c ,mc2)	covariantly in	QED's	Interactive	Representation	(IR).	Although	the	QED	calculations	are	highly accurate,	the	physical	description	of	the	electron's	ISaTCO	described	by	the	Dirac α α α α 4 Equation	have	been	completely	missed. In	their	section	on	the	"Physical	Origin	of the	Lamb	Shift",	Eides	et	al.	[1]	state	that	"The	finite	radius	of	the	electron generates	a	correction	to	the	Coulomb	potential...",	and	then	gives	the	equation	for this	correction.	The	QED	"finite	radius"	described	[1]	is	the	ISaTCO	radius.	Eides	et al.	[1]	go	on	to	state:	"the	finite	size	of	the	electron	(caused)	by	the	QED	radiative corrections	leads	to	a	shift	of	hydrogen	energy	levels". It	is	c that	causes	the "finite	electron	radius	to	Eides	et	al.	[1]	refer,	not	QED's	perturbation	calculations.. This	article	should	not	be	controversial	because	the	c -NEP	cannot	be	refuted logically. QED's	covariant	perturbation	theory	accurately	calculates	hydrogen energy	levels,	but	misses	the	physical	picture	of	the	electron	completely. QFT correctly	addresses	the	vacuum	fluctuations	in	general	[11],	but	does	not	derive	the electron's	ISaTCO	with	a	point	CoC	located	on	a	spherical	shell	in	the	rest	frame	and an	oblate	spheroidal	shell	in	non	rest	frames.	QED	predicts	the	exact	electron propagator,	but	QED	fails	to	cut	off	the	high	energy	virtual	photons	at	the	CoC	shell defined	by	the	ISaTCO,	and	the	electron	self	energy	becomes	infinite	in	a	natural way.	This	paper	will	derive	the	correct	photon	propagator	defined	by	the	electron's ISaTCO,	without	ad	hoc	assumptions	like	Renormalization,	Tree	Theory,	etc..	The electron	described	by	the	Dirac	Equation	and	the	ISaTCO	is	never	one	particle.	It	is	a three,	or	five,	or	seven,	or....	2n-1...	particle	model,	with	a	point	electron	located	at its	CoC	in	the	presence	of	a	virtual	electron/positron	pair,	whose	positron annihilates	the	original	electron	leaving	behind	the	electron	from	the	virtual	pair. There	can	be	any	number	of	virtual	pairs	present,	but	there	is	1/137.04	less	likely	to be	two	sets	of	virtual	electron	pairs	than	one,	and	(1/137.04)2 less	likely	to	have α α 5 three	sets	of	electron/positron	pairs	than	one,	etc..	This	virtual	pair	production	and annihilation	occurs	as	vacuum	fluctuations	on	a	very	rapid	time	scale	of	~	1.4	10-21 sec.	for	the	electron,	and	approximately	207	times	more	rapidly	for	the	muon. In	this	paper	the	Dirac-Maxwell-Wilson	(DMW)	Equations	are	derived	for	the electric	and	magnetic	fields	of	an	electron	in	the	hydrogen	atom,	and	the	impact	of the	electron's	CoC	vacuum	fluctuations	is	shown	to	be	negligible	a	few	Compton wavelengths	from	the	electron's	Center	of	Mass	(CoM).	The	electron	appears	as	a "structureless	point	particle"	in	the	far	field,	as	observed	in	the	electron/proton scattering	experiments	used	to	probe	the	proton's	internal	structure	(see	[12]	for further	references).	Trying	to	observe	the	electron's	vacuum	fluctuations	structure externally	with	high	energy	photons	would	destroy	the	electron,	creating	other particles	from	the	inelastic	interactions..	It	is	fortunate	that	the	electron	is	stable	in hydrogen	and	that	it	is	actually	located	"inside"	the	proton	in	the	S-Level	energy states	some	of	the	time,	or	the	impact	of	electron's	vacuum	fluctuations	would	not be	measured	in	hydrogen.	If	the	electron	were	located	only	at	its	Bohr	orbit,	the impact	of	the	electron's	vacuum	fluctuations	on	hydrogen	energy	levels	would	never be	observed.	In	addressing	the	electron/muon	"Proton	Radius	Puzzle"	this	paper will	show	how	significantly	different	the	electron	and	muon	EM	fields	are	when	the electron	and	muon	CoMs	are	located	"inside"	the	proton,	due	to	the	highly	different spatial	and	time	extent	of	their	vacuum	fluctuation	geometries.	The	spatially extended	proton,	with	the	electron	and	muon	CoCs	traveling	at	the	speed	of	light around	their	CoMs	"inside"	the	proton,	is	a	bizarre	picture,	but	is	predicted 6 accurately	by	QED	and	QFT. The	muon	CoC	is	~	207	times	closer	to	the	proton's center	when	the	electron	and	muon	CoMs	are	located	inside	the	proton.	This	bizarre situation	is	absolutely	confirmed	by	QED's	very	accurate	estimates	of	the	hydrogen and	muon	energy	levels	[1],	but	is	shows	the	need	for	a	much	more	accurate	model of	the	proton's	internal	structure. In	[9]	Pohl	and	Bernauer	state:"	If	the	muon	is 200	times	closer	to	the	proton,	it	should	also	be	spending	considerably	more	time inside	the	proton	(indeed,	the	probability	is	increased	by	a	factor	of	2003	,	or	8 million).	Thus,	in	turn	changes	the	Lamb	shift	of	the	atom	by	2	percent	–	a	relatively huge	amount	that	should	be	easy	to	spot."	If	the	proton	radius	is	scaled	up	to	0.5	cm. (about	half	the	size	of	a	pea),	the	muon	CoC	would	be	approximately	6	m.	from	the proton's	CoM	at	the	origin,	while	the	electron's	CoC	would	be	over	1200	m. from	the proton's	CoM	at	the	origin.	In	both	cases	the	extended	proton	is	well	"within"	the electron	or	muon	CoC	shell,	and	the	proton's	quarks	experience	significantly different	electromagnetic	(EM)	field	fluctuations	from	induced	the	electron	or	muon. Even	though	this	situation	is	chaotic,	QED	calculates	the	electron	and	muon interactions	with	their	c vacuum	fluctuations	very	accurately	in	estimating	the resulting	hydrogen	energy	levels.	QED	does	not	predict	the	electron	and	muonic proton	radius	differences	accurately.	The	latest measurements	by	Pohl	et	al.	[2,	3] for	the	proton	radius	for	muonic	and	electronic	hydrogen	are	approximately	0.84	fm and	0.87	fm	respectively. The	proton	is	not	a	central	force	in	the	near	field	due	to three	quarks	exchanging	gluons	inside	a	very	complex	proton	spatial	structure,	and the	2S1/2	–	2P1/2	hydrogen	energy	levels	would	likely	not	be	degenerate	at	the	Dirac Equation	level	for	a	more	accurate	model	of	the	proton. α 7 There	are	no	classical	analogs	to	the	electron	position	probability	distributions	in the	hydrogen	atom. The	electron	velocity	operator	c defines	its	CoC	vacuum fluctuations,	and	has	eigenvalues	+/c.	Negative	energies	and	virtual electron/positron	pair	production	occur	within	the	electron	internal	structure defined	by	the	ISaTCO	in	highly	non	classical	terms.	This	paper	will	stress	that	you cannot	separate	the	electron	or	muon	CoC	from	their	ISaTCO	defined	vacuum fluctuations. In	the	next	section	the	time	dependence	and	geometrical	distribution	of	electron discrete	ISaTCO	will	be	derived	in	the	Heisenberg	Representation	following	Sakurai [13]	and	the	author's	three	previous	papers	[4,	5,	6].	The	following	two	states cannot	be	differentiated: 1. The	electron	or	muon	are	structureless	point	particles	with	"intrinsic"	spin and	magnetic	moments,	and	infinite	self-energy	when	viewed	from	the	far field. 2. The	specific	electron	and	muon	ISaTCO	generate	a	current	distributed	on	a spherical	shell	of	a	specific	radius	in	the	rest	frame,	and,	by	Gauss'	Law,	one cannot	differentiate	this	case	from	a	static	point	particle	in	the	far	field. 3. Hu	states	[14]:	"It	is	a	general	belief	that	the	electron	is	a	point-like	particle	with almost	no	measurable	dimensions,	and	that	the	electron	does	not	possess	any	subconstituent.	This	belief	is	largely	based	on	the	results	of	Møller	and	Bhabha scattering,	obtained	from	many	experiments	performed	in	the	last	twenty	years	at PETRA	(Positron-Electron	Tandem	Ring	Accelerator	Facility	at	DESY	laboratory	in Hamburg),	PEP(The	Positron-Electron	Project,	a	collaborative	effort	of	SLAC	and α 8 Lawrence	Berkeley	Laboratory),	TRISTAN	(The	e+eCollider	at	National	Laboratory for	High	Energy	Physics,	KEK	in	Japan),	and	LEP	(The	Large	Electron	Positron Collider	at	CERN).	In	the	experiments	conducted	at	PEP	in	the	tests	of	leptonic substructure,	Bender	et	al.	stated,	"experimentally	there	is	no	indication	that	the electron	has	structure	[composite	of	more	fundamental	particles].	Lower	limits	for cutoff	parameters	are	in	the	100-200	GeV	range,	corresponding	to	an	electron	size of	less	than	10-16	cm.	Therefore,	if	the	electron	is	a	composite	particle	its constituents	are	strongly	bound,	giving	the	electron	the	observed	point-like	quality at	experimentally	accessible	energies	(67).	As	a	matter	of	fact	the	results	obtained from	the	scattering	experiments	have	been	a	"no-go"	sign	to	any	attempt	of	the	so called	largeelectron	theories,	where	the	size	of	the	electron	was	in	an	order	of	its Compton	wavelength." These	far	field	electron	scattering	experiments	in	the	far	field	are	meaningless	for the	ISaTCO	internal	structure	of	the	electron.	In	fact,	stating	that	the	electron	is	a structureless	point	particle	with	"intrinsic"	properties	violates	the	c -NEP,	and	one cannot	accept	c in	the	QED	four	current,	and	reject	the	direct	derivation	of	the ISaTCO	from	c as	the	Dirac	Equation	velocity	operator. The	analysis	of	the electron	and	muon	physical	pictures	when	inside	the	proton	in	hydrogen	implies much	work	needs	to	be	done	in	deriving	a	more	accurate	model	of	the	proton structure	to	develop	a	QED	solution	with	this	improved	proton	model. A	recent	paper	[15]	models	the	strong	force	distribution	of	the	proton,	and	a	similar analysis	is	needed	for	the	EM	distribution	within	the	proton	structure	to	include	the α α α 9 three	charged	quarks.	The	newly	proposed	Electron-Ion	Collider	(EIC)	is	being	built to	probe	the	proton	internal	structure	with	beams	of	electrons	(see https://doi.org/10.17226/25171	for	a	complete	description	of	the	EIC),	and	the June	2019	Scientific	American	article	"The	Deepest	Recesses	of	the	Atom"	for	the basic	physics	behind	the	need	for	the	EIC. According	to	these	references	there	are	~ 1080	protons	and	neutrons,	and	an	equal	number	of	electrons,	in	the	universe,	but we	don't	yet	know	where	the	proton	gets	its	mass	or	spin.	While	the	proton	consists of	three	quarks	and	gluons	and	their	virtual	anti	particles,	the	three	quarks'	total mass	is	much	lighter	than	the	proton,	accounting	for	~	"2	percent"	of	the	proton mass	and	less	than	"30%	of	the	proton's	spin"	according	to	these	EIC	references. One	point	of	this	article	is	that	the	electron	and	muon	in	hydrogen	already	probe	the internal	structure	of	the	spatially	extended	proton's	complex	internal	structure	for	S energy	levels,	and	electronic	hydrogen	is	absolutely	stable. If	and	when	the	EIC	is finally	built	and	producing	data	in	2030,	perhaps	more	can	be	done	to	probe	the proton	internal	structure.	In	the	mean	time,	with	the	theory	developed	in	this	article and	an	improved	proton	model,	QED	can	be	used	to	address	the	Proton	Radius Puzzle.	The	author	feels	strongly	that	the	EIC	will	be	valuable,	but	the	electron model	of	a	structureless	point	particle	with	intrinsic	properties	is	certainly inaccurate	for	the	electron	and	muon	in	hydrogen	where	their	NR-VFGs	are	an inseparable	part	of	the	particle	and	are	always	present. If	a	tau	particle	version	of	hydrogen	could	be	produced	it	could	also	exhibit	unique TNR-VFG	inside	the	proton	when	its	CoC	is	17.7	times	closer	to	the	proton's	center 10 than	the	muon's	CoC.	Perhaps,	a	third	value	of	the	proton	radius	could	be	measured from	various	S-P	level	transitions	in	the	same	way	that	the	muonic	and	electronic hydrogen	unique	proton	radii	are	measured. 2.0	Geometrical	properties	of	vacuum	fluctuations	that	the	electron	and	muon exhibit	within	the	hydrogen	atom Although	"electron"	is	used	in	the	rest	of	this	paper,	the	equations	apply	equally	to the	muon	by	changing	the	mass.	The	Dirac	Equation	CoC	velocity	operator,	c ,	must be	accepted	as	is,	even	though	far	from	the	classical	picture	of	continuous time	and space	CoM	dynamics	due	to	the	c NEP	discussed	in	the	previous	section.	Even though	c is	a	4	x	4	complex	matrix	representing	the	electron's	velocity,	and	goes against	one's	classical	intuition,	one	must	accept	the	electron	CoC	with	its	very	well defined	vacuum	fluctuations	defined	by	the	Dirac	Equation.	The	electron	position ICOs	are	derived	directly	from	c ,	and	are	discrete	and	relativistic,	while	externally the	electron's	CoM	is	consistent	with	classical	mechanics. The	electron	or	muon	CoC vibrating	rapidly	internal	to	the	CoC	shell	have	a	very	short	range	impact,	and appears	to	be	a	point	particle	with	intrinsic	properties	in	the	far	field,	as	exists	in	the electron/proton	scattering	experiments.	Within	the	hydrogen	atom	the	electron's internal,	discrete	geometrical	CoC	structure	is	measured	in	a	very	stable	fashion	by the	proton,	and	the	electron's	ICO	operators	create	an	unusual	EM	environment when	the	electron	CoM	is	near	or	"inside"	the	proton,	as	allowed	by	the	QED predicted	position	probabilities	in	hydrogen's	S	energy	levels	depicted	in	Figure	1. A.	The	Electron's	CoC	position	operator	defining	its	deterministic	vacuum fluctuation	geometry α α α α 11 Let	us	start	with	the	expression	for	the	electron's	CoC	ICO	from	Sakarai	[13	(p	116)]. Bold	symbols	will	signify	3-D	vectors	in	this	paper,	while	scalars	are	given	by	non bold	symbols.	In	the	Heisenberg	representation (1) where (2) and (3) The	center	of	mass	coordinate	xCoM	is	given	by (4) and	the	Heisenberg	representation	of	the	CoC	coordinates,	where	operators	are	time independent,	is	given	by: (5) Now	let for	an	electron's	CoM	moving	in	the	z	direction. A straightforward	calculation	inserting	Equation	(3)	into	(5),	and	using	standard	anti commutation	rules	yields: (6) where k	with	k	=	0,	1,	2,	3	are	the	normal	DE	4x4	complex	matrices,	and	should	not be	confused	with	the	Special	Relativity	(SR)	"gamma"	factor .	In	the	electron's	rest frame	(pCoM	=	p	=	0),	and	dropping	the	CoM	momentum	superscript	for	p	for simplicity	for	the	remainder	of	the	paper,	we	obtain 2 /2 1 1 1( ) (0) ( / 2)( (0) ) DiH tk k k D k k D Dx t x c p H t ic cp H H eα −− − −= + + − hh 2 DH c mcβ= ⋅ +pα 1 2/ ( )D DH H E p − = CoM 2 1( ) (0)k k k Dx t x c p H t −= + CoM 1 1( 0) ( 0) ( / 2)( )CoCk k k k D Dx t x t ic cp H Hα − −= = = + −h ( )CoM 3 p=p k CoC CoM 3 2 3 3 3 3( ) ( / 2 )x p x mc E γ− = h γ γ 12 (7) (p3)	is	the	electron's	intrinsic	coordinate	in	the	direction	of	the	motion	of	its center	of	mass	motion .	The	Dirac	Equation	defines	a	CoC	momentum operator	naturally	as	mc ,	and	the	internal	space/time	structure	of	the	electron	is quantized	or	discrete	[4,	5,	6]. The	role	of multiplying	the	rest	mass	m	in	Equation	(2)	accounts	for	interaction with	the	negative	electron	energy	states,	and	it	will	appear	again	in	the	definition	of spin	angular	momentum. The	Dirac	Equation's	electron	coordinate	operator	magnitude	in	the	direction	of motion	is	contracted	by	the	square	of	the	SR	contraction	factor since = (8) where	the	SR	contraction	factor	of	a	rigid	body	is	given	by =	1/	(1	–	(v3/c)2)1/2. The	symbol	" "	=	vCoM/c	is	used	in	this	paper	for	both	the	SR	velocity	factor	and	the fourth	gamma	matrix, 4,	but	the	equations	make	it	clear	where	the	scalar	or	the 4x4	complex	matrix	are	used.	The	electron	described	by	the	Dirac	Equation	includes the	ICO	vacuum	fluctuations,	and	is	far	from	a	structureless	point	particle,	and contraction	of	the	electron's	CoC	current	shell	for	CoM	momentum	along	the	z-axis is	non	zero	in	directions	perpendicular	to	the	electron's	CoM	motion.	A CoC CoM 3 3 3( 0) ( 0) ( / 2 )x p x p mc γ= − = = h CoC 3x 3  p=p k α β γ CoC CoM 3 2 3 3 3 3( ) ( ) / 2x p x p mc E− = h 2/ 2mcγh γ β γ ( )3 p=p k 13 straight	forward	calculation	for	k	=1	from	Equation	(5)	with yields	(the	k	=2 coordinate	is	similar) (9) Thus,	in	the	perpendicular	directions	to	the	electron's	CoM	motion,	the	ICO	not	only contracts	in	magnitude,	but	also	has	an	additional	term related	to the	electron	spin in	the	perpendicular	direction. A	simple	calculation yields (10a) = /2mc for p = p3k (10b) Therefore,	the	coordinates	of	its	CoC	current	shell	are	contracted	by	the	exact	SR contraction	of	1/ in	the	direction	perpendicular	to	the	electron's	CoM	motion,	and are	caused	by	the	nature	of	the	non	random	vacuum	fluctuations. The	Dirac	Equation	predicts	that	the	magnitude	of	the	electron's	ICOs will	contract to	a	point	particle	as with	an	ellipsoidal	or	oblate	spheroid	shape,	where	the ellipsoid's	semi	minor	axis	is	in	the	direction	of	the	electron's	CoM	motion. The Harmonic	Oscillator	nature	of	the	CoC	intrinsic	coordinates	is	now	clear: = = (11a) and	their	two	time	derivatives =	c and =	0 (11b) 3  p=p k CoC CoM 2 CoM 2 1 3 1 3 3 2 1( ) ( ) / 2x p x p c E p c mcγ⎡ ⎤− = Σ +⎣ ⎦h 3 2( / 2)( / )c p c E Σh 2(( / 2) )Σh CoC CoM 1 3 1 3( ) ( ) ( / 2) ( )x p x p c E p− = h ! γ γ 3v c→ ( )CoCk kX pΔ ( ) ( ) CoC CoM k k k kx p x p− 2 2/ 2 (Σxp )k kc E c mcγ⎡ ⎤+⎣ ⎦h ( ) CoC k kX p • Δ kα ( ) CoC k kX p •• Δ 2( )[ ( )]CoCo k kX pω= − Δ 14 Thus,	the	Dirac	Equation	predicts	directly	that	the	electron's	CoC	coordinate operators, ,	form	three	independent	sets	of one	dimensional	Harmonic Oscillators	for	any	arbitrary	CoM momentum p,	and	this	is	caused	by	the	nature	of the	ZBW	vacuum	fluctuations. These	electron	CoC	not	only	oscillates	at	a	very	rapid rate	of =	2E/ ,	but	there	are	only	eight	discrete	ICO	eigenvalues,	+/- /2E(p) , in	the	two	directions	perpendicular	to	the	CoM	motion	and	+/- //2E(p) 2	in	the direction	of	COM	motion. In	the	electron's	rest	frame,	the	CoC	ICO	eigenvalues	are =	+/- /2mc	for	k	=	1,	2,	3. The	Dirac	Equation	does	not	reveal	why these	internal	coordinates	are	discrete,	or	why	the	restoring	Harmonic	Oscillator potential	exists (12) where	the	restoring	"spring	constant"	K	=	4mE2(p)/ 2.	The	electron	vacuum fluctuations	producing	the	ICOs	defined	above	are	the	cause	of	this	internal	electron harmonic	oscillator	restoring	force,	and	the	Dirac	Equation	predicts	the	electron's CoC's	chaotic	rapidly	oscillating	motion	that	creates	a	current	over	time.	The discrete	vacuum	fluctuations	energy	levels	of	the	electron	are	deduced	from	the electron	coordinate	harmonic	oscillator	are	given	by En	=	(n	+	1/2) =	(2n	+	1)	E(p) (13) where	the	ground	state	energy	E0	=	E(p),	and	the	energy	of	the	excited	states	are	E1 =	3E(p),	E2	=	5E(p),	etc.. Thus,	the	Dirac	Equation	implies	directly	that	the	first ( )CoCk kX pΔ oω h h γ h γ ( 0)CoCk kX pΔ = h 2 2 2 2 2( ( )) (1/ 2) ( ) (1 / ( ))CoC CoCk k k k k kV X p K X p mc p c E pΔ = Δ = − h h oω 15 excited	Harmonic	Oscillator	state	of	the	free	electron	requires	the	absorption	of	a real	photon	with	energy	of	at	least	2E(p)	to	elevate	the	electron	to	an	energy	level	of 3E(p).	This	is	the	nature	of	the	electron's	CoC	's	vacuum	fluctuations.	In	the	electron rest	frame	(p =	0)	a	photon	of	energy	2mc2	is	necessary	to	elevate	the	electron	to	its first	excited	state,	and,	in	QED	or	Dirac's	Hole	Theory	description,	this	is	exactly	the amount	of	energy	necessary	to	raise	the	energy	level	of	a	virtual	negative	energy electron	across	the	"forbidden"	region	of	2mc2.	In	Dirac's	Hole	Theory,	a	positive energy	electron	and	a	positron	(corresponding	to	the	"Hole"	in	the	completely	filled sea	of	negative	energy	electron)	are	produced. An	external	EM	field	is	required	to supply	the	real	photon	of	energy	2mc2,	but	the	electron	CoC vacuum	fluctuations produce	virtual	electron/positron	pairs,	which	are	formed	and	annihilated	quickly to	establish	the	specific	electron	vacuum	fluctuation	geometry	defined	above	for	the electron	in	the	hydrogen	atom.	The	electron's	instantaneous	CoC	position	is	a	single discrete	point	that	is	in	a	rapid	oscillation	about	its	CoM	creating	a	current	over	time with	the	Harmonic	Oscillator	frequency	of =	2E/ ,	and	within	the	hydrogen atom,	for	averaging	times	large	compared	to	its	ZBW	period	of	~	1.4	10-21	sec..	This is	a	very	specific,	non	random	property	of	the	impact	of	the	electron's	CoC	vacuum fluctuations.	The	electron	appears	over	time	as	a	uniform	current,	caused	by	the "spinning"	charge	e	on	the	CoC	shell. The	electron	internal	time	operator	is	also discrete	[5,6],	so	the	current	set	up	by	the	electron's	CoC	quantized	internal	space and	time	position	sequence	only	seems	continuous	when	measured	over	times	long compared	to	the	electron's	non	random	CoC	vacuum	fluctuation	period.	The	above description	of	the	electron	in	hydrogen	is	absolutely	consistent	with	modern	QED oω h 16 calculations	of	hydrogen	energy	levels	[1]	and	QFT	[11],	but	the	above	geometrical distribution	of	the	electron's	CoC	is	missed	completely	in	QED	and	QFT.	No	one	can "picture	the	quantized	nature	of	the	electron	internal	position	and	time	operators discussed	in	this	section	classically. B.	The	CoC	c Induced	Vacuum	Fluctuation	Contribution	to	the	Lamb	Shift In	a	classical	analysis	of	the	Darwin	term	for	the	non	relativistic	solution	of	the hydrogen	atom,	Sakurai	[9]	derives	the	expression	for	the	"ZBW"	(Sakurai's	term) correction	to	the	potential	from	a	point	proton	to	an	electron	whose	coordinates "fluctuate"	over ,	assuming	a	long	time	average	compared	to sec (14) Sakurai	[9]	states	that	Equation	(14)	above	is	the	classical	derivation	of	the	ZBW term	apart	from	the	"incorrect"	numerical	term	" "	instead	of	the	correct	" " term. However,	if	one	inserts	the	Dirac	Equation's	intrinsic	coordinates,	where ,	the	correct	numerical	factor	of	" "	is	obtained	for	the Darwin	term. The	Dirac	Equation	predicts	the	electron	CoC	vacuum	fluctuation induced "radius2"	of in	the	rest	frame,	and,	in	QFT	terminology,	one can	say	the	SG	vacuum	fluctuations	near	an	electron's	CoC	yields	a	very	specific radius	of	the	fluctuations	that	agrees	exactly	with	the	Darwin	Term. The	Dirac Equation's	ICOs	established	by	the	Dirac	Equation	are	required	to	give	the	correct answer. Eides	et	al. [1]	derive	Equation	(14)	as	the	largest	contribution	to	the Lamb	Shift,	but	only	note	that	it	is	due	to	the	fluctuating	"electron	coordinate", α /mcΔ ≈x h 2110− 2 2 3( ( ) ( )) [ ( ) / 6] ( )V V e δ+Δ − ≈ Δx x x x x 1/ 6 1/ 8 2 2 2 2 2( ) 3 / 4CoC m c aΔ = =R h 1/ 8 2 2 2 23 / 4a m c≡ h 17 without	mentioning	ZBW	or	the	Dirac	Equation	from	which	the	fluctuations originate. C.	The	electron's	magnetic	moment The	intrinsic	magnetic	moment	of	the	electron	in	the	hydrogen	atom	in	the	rest frame	is	generated	by	the	Dirac	Equation's electron's	vacuum	fluctuations	as	a localized	current	distribution,	but	with	c as	the	CoC	velocity	operator,	and	is defined	as: mCoC	=	1/2[ (15) mCoC	is	proportional	to times	the	normal	expression	for	electron	spin.	If	S	= is	the	spin	operator,	then	L	+ S	is	the	constant	of	the	motion. In	the Dirac	Equation	mass	is	given	by m	to	account	for	positive	and	negative	energies, and	likewise S	accounts	for	positive	and	negative	energies	for	electron	spin.	The fact	that	the	non-relativistic	solution	of	the	hydrogen	atom	using	the	Dirac	Equation always	uses ,	and	not ,	supports	this	concept. Equation	3.243 in	Sakurai	[13]	shows	that	the	electron	helicity	is	constant	only	if	there	is	no external	electric	field,	but	the	electron	can	never	escape	its	own	self	electric	field. Thus,	the	Dirac	Equation	implies	that	the	electron	g-factor	is	not	exactly	2,	without referring	to	QED. QED	is	an	excellent	and	efficient	way	to	calculate	the	deviation	of the	g-factor	from	2,	and	the	author	is	not	proposing	a	second	method	to	calculate	it. The	physical	cause	of	the	electron	anomalous	magnetic	moment	is	the	interaction with	its	own	electric	field,	proven	by	Sakurai's	result	[13]	in	his	Equation	3.243,	but he	couldn't	deduce	the	physical	cause	without	the	theory	developed	here. α 3 ( )] / 2 ( )CoCd x e m⊗ =∫ x J Σβh 3 ( )] / 2 ( )CoCd x e m⊗ =∫ x J Σβh β ( / 2 )e m Σβh β β β ( / 2 )e m Σβh ( / 2 )e m Σh 18 3.0	The	Dirac-Maxwell	–Wilson	Equations If	one	accepts	that	c is	the	velocity	operator	for	the	electron's	CoC	velocity,	then the	Dirac-Maxwell-Wilson	DMW	Equations follow	directly.	The	electron's	CoC motion	is	chaotic	due	to	electron's	non	random	vacuum	fluctuations,	and	discrete	in time due	to	the	same vacuum	fluctuations	in	the	hydrogen	atom	[5,6]. The	Dirac	Equation	EM	field	operators	are	developed	for	the	electron's	rest	frame	to describe	the	non-relativistic	EM	field	with	vacuum	fluctuation,	since	the	CoM	for	the electron	in	the	hydrogen	atom	is	a	continuous	average	of	the	CoC	motion.	The	DMW Equations	can	be	extended	to	non	rest	frames	using	Equations	(5)	through (10a/10b),	but	this	is	unnecessary	for	the	electron	or	muon	in	hydrogen. For	any	observation	point	(x,	y,	z)	the	free	electron's	scalar	potential	will	have,	with equal	probability,	one	of	the	eight	possible	values (16) The	"k"	index	always	refers	to	one	of	eight	electron/muon	ICO	eigenvalues,	and	the "prime	index"	is	the	integration	variable	over	the	Dirac	Equation's	CoC	charge density.	The	unprimed	indices	are	for	the	observation	point.	The	4x4	identity	matrix I	will	not	be	shown	although	it	will	understood	to	multiply	all	expressions	for	the electron's	scalar potential	electric	field.	It	is	easy	to	show	that (17) kα 2 2 3 2 2 0.5 0 0 0 ( , , , , , ) sin ( ( ) / ( 2 cos( ))CoC rk k k k kr a d d r dr e a ar π π θ φ θ φ φ θ θ δ ∞ ′Φ = −Δ + − Θ∫ ∫ ∫ r R I) r cos( ) [sin cos sin cos sin sin sin sin cos cos ]rk k k k k kθ φ θ φ θ φ θ φ θ θΘ = + + 19 The	integration	over	the	quantized	angular	coordinates	is	not	trivial	like	it	was	for the	smooth	ICOs	in	a	previous	article	[4].	As	stated	in	the	previous	section,	the	Dirac Equation's	ICOs	are	analogous	to	the	quantized	spin	angular	momentum	operators in	Dirac's	theory,	where	the	quantization	about	the	"z-axis"	is	valid	no	matter	where one	chooses	this	axis	for	the	electron	in	the	hydrogen	atom. In	fact,	the	geometry	of the	eight,	equally	probable	Dirac	Equation	ICOs	naturally	defines	two	spin	states depending	on	the	sign	of in	Equation	(17).	For	example,	if	one	arbitrarily assigns	the	ICO	eigenvalue as	k=1,	the	ICO	eigenvalue as	k=2,	the	ICO	eigenvalue as k=3,	and	the	Dirac	Equation	ICO	eigenvalue as	k=4,	then the	k	=	1,2,3,4	ICO	eigenvalues	geometrically	are	arbitrarily	called	"spin	up"	in	this paper. A	little	geometry	shows	that =+	(1/3)0.5	and	that =+	(2/3)0.5	for k=1,2,3,4.	Using	the	term	"spin	down"	to	describe	the	ICOs	with	negative	"z coordinate",	the	k=5,6,7,8	terms	still	have =+	(2/3)0.5,	but	have =- (1/3)0.5. Even	though	the	CoC	shell	is	spherical	in	the	electron's	rest	frame,	the quantization	of	the	ICOs	defined	by	the	ZBW	vacuum	fluctuations	resulting	from	the Dirac	Equation	make	it	easier	to	use	Cartesian	coordinates. The	distance	between any	Dirac	Equation	ICO	eigenvalue	and	the	field	observation	point	(x,	y,	z,)	given	in Equation	(1)	are	defined	for	"spin	up"	and	"spin	down"	as	Equation	(18): (18) cos kθ ( / 2 , / 2 , / 2 )mc mc mch h h ( / 2 , / 2 , / 2 )mc mc mc−h h h (! /2mc ,−! /2mc ,! /2mc) (−! /2mc ,−! /2mc ,! /2mc) cos kθ sin kθ sin kθ cos kθ 2 2 0.5 2 2 0.52 cos( )) ( ( / )[sin cos 2 cos sin sin 2 sin / cos ])rk k ka ar a r mc θ φ φ θ φ θ θ+ − Θ = + − + + −(r r h 20 where	the	"+/-"	in	front	of	the term	represents	spin	up	(k=1,2,3,4)and	spin down	(k=5,6,7,8),	respectively. Also, =	+	1/ for	k=	1,	4,	5,	and	8	and	-1/ for	k	=	2,	3,	6,	7,	while =	+	1/ for	k=	1,	2,	5,	6	and	–	1/ for	k	=	3,	4, 7,	8.	For	example	the	k	=	1	distance	is: (19) where	r2 =	x2	+	y2	+	z2,	a2	is	a	constant	in	the	rest	frame,	and	sign	preceding	x,	y,	and z	in	Equation	(15)	are	given	by	the	above	definitions	in	deriving	Equation	(19)	from (18).	For	k	=	2	through	8	the	signs	of	the	x,	y,	and	z	terms	in	Equation	(19)	change	as specified	in	Equation	(18)	with	the	specific	values	Thus,	the	electron's	eight	electric field	operators	for	each	of	the	equally	probable	Dirac	Equation	ICO	eigenvalues	are given	by	the	operator ,	where	the	variable	dependencies	are	now	clear and	will	not	be	listed	in	every	equation.	For	k	=1 and (20) where	i,	j,	and	k	are	unit	vectors	in	the	x,	y,	and	z	directions.	For	k	=	2	through	8	the signs	of	the	x,	y,	and	z	terms	in	the	denominator	and	the terms	in	the numerator	of	Equation	(20)	change	as	specified	above.	An	instantaneous measurement	of will	yield	one	of	eight	possible	values	with	equal	probability with	average	value	over	time (21) cosθ cos kφ 2 2 sin kφ 2 2 2 2 0.5 2 2 0.5 12 cos( )) ( ( / )[ ]) ra ar a mc x y z+ − Θ = + − + +(r r h k k= −∇ΦE 1 1= −∇ΦE 2 2 1.5 1 [( / 2 ) (y / 2 ) +(z- / 2 ) ] ( ( / )[ ])e x mc mc mc a mc x y z= − + − + +E i + j k / rh h h h / 2mch kE 8 ave 1 1/ 8 k k k = = = ∑E E 21 Unfortunately,	Equations	(20)	and	(21)	do	not	simplify	into	a	single	simple expression,	but	the	far	field	(r>>	a)	expressions	are	the	expected	ones.	In	the	far field, consistent	with	the	static	point	model. There	are	large	fluctuations	in	the	electron's	electric	field	when	the	electron	or muon	CoM	is	located	at	or	near	r	=	0	"inside"	the	proton.	One	can	easily	see	from Equation	(20)	that	there	would	be	very	small	fluctuations	in	the	electron's	electric field	in	the	hydrogen	atom,	if	the	electron	were	always	located	near	the	Bohr	orbit, which	is	in	the	far	field	of	the	proton	as	discussed	above.	The	solution	to	the	wave function	for	the	hydrogen	atom	depicted	in	Figure	1	clearly	show	that	the	electron and	muon	can	be	located	near	and	at	the	origin	"inside"	the	proton	for	the	S	states. In	this	case	the	electron	and	muon	non	random	vacuum	fluctuations	impact	the proton	in	a	fundamentally	different	way.	They	both	have	the	same	negative	charge oscillating	rapidly	around	the	proton	governed	by	non	random	vacuum	fluctuation geometries,	but	the	muon's	CoC	is	~	207	times	closer	to	the	proton	when	both	have their	CoM	positions	at	the	origin	inside	the	proton. These	electric	field	oscillations back	on	the	proton	from	the	electron	and	muon	when	their	CoM	positions	are	near or	inside	the	proton	are	violent,	chaotic,	and	very	complex.	The	proton	is	comprised of	three	quarks	with	fractional	charges	that	interact	via	the	EM	interaction	by	the exchange	of	photons	and	by	strong	interaction	by	the	exchange	of	gluons	as described	by	Quantum	Chromodynamics	(QCD). It	is	unknown	if	the	proton's	three quarks	exhibit	non	random	vacuum	fluctuations	[15],	but,	considering	the	presence of	the	non	random	vacuum	fluctuation	geometries	for	the	electron	and	muon	in 3 ave /re≈E r 22 hydrogen,	it	is	possible	that	similar	vacuum	fluctuation	geometries	are	present	for the	three	charged	quarks	within	the	proton. The	hydrogen	energy	levels	calculated by	QED	that	compare	accurately	with	theory	use	an	inaccurate	proton	model	when the	electron	or	muon	CoM	is	"inside"	or	near	the	proton's	location.	The	author cannot	yet	prove	that	the	very	different	vacuum	fluctuation	geometries	produced	by the	electron	and	muon	near	the	proton	location	would	cause	a	difference	in	the measured	energy	levels	or	proton	charge	radius,	but	very	different	muon	and electron electric	fields	are	produced	at	the	proton	location	in	the	hydrogen	atom. Although	Equation	(20)	shows	that =0	at	r=0,	the	location	of	the	CoM. The magnitude	of increases	as	~	1/a3	with	increasing	r	near	the	origin.	The electron's	electric	field	magnitude	never	becomes	infinite	near	the	origin	as	it	does in	the	single	static	point	model,	and,	fortunately,	the	proton	"measures"	this	impact accurately	through	the	non	random	vacuum	fluctuations	contribution	to	hydrogen energy	levels. The	Dirac	Equation's	CoC	shell	defines	the	current	operator	as (22) where	c is	the	Dirac	Equation	velocity	operator,	which	is	unique	because	it	is	the same	for	all	eight	ICO	positions.	The	Dirac	Equation's	CoC	and	Equation	(22)	define the	electron's	vector	potential	operator	in	the	rest	frame	by (23) aveE aveE 3 )CoC CoCk keδ ′= −ΔJ (r R α α 2 2 0.5( , , , , , ) / ( 2 cos( ))rk k k kr a e a arθ φ θ φ = + − ΘA α r 23 The	CoC	ICOs	will	not	allow	one	to	simplify	the	Dirac	Equation	velocity	operator	c into	a	diagonal	form,	even	in	the	electron's	rest	frame. There	are	two	current components	suggested	by	the	expectation	value	of	c for	non-relativistic	physical environments.	The	average	value	of	c is	just	a	steady	current	moving	at	the	speed of	the	electron's	CoM	[4,5,	6],	while	there	is	a	rapidly	rotating	current	producing	the point	dipole	moment	in	the	far	field.	Defining we	get i (24a) j (24b) k (24c) for	the	three	components	of	the	k	=1	for	the	electron	magnetic	field	operator . The	k	=	2	through	8	expressions	for are	obtained	in	the	same	way	as	for	the electric	field	by	inserting	the	correct	sign	for	x,	y,	and	z	in	the	denominator	and	the correct	sign	in	front	of in	the	numerator	of	Equations	(24a),	(24b),	and (24c).	Taking	the	time	average does	not	result	in	a	very	simple expression	with	clear	physical	interpretation,	but	the	ICOs	produce	the	most accurate	estimate	of	the	single	electron's	magnetic	field,	assuming	only	that	the Dirac	Equation's	geometric	estimate	of	its	vacuum	fluctuations	is	valid. In	Equations	(20)	and	(24	a,	b,	c) ,	where in	analogy	with [1],	with	the	Dirac	Equation	CoC	velocity	operator	replacing	the	vector	CoM	velocity used	in	Classical	Electrodynamics. Equations	(16)	through	(24)	and	all	the associated	information	in	this	section	define	the	DMW	Equations	for	the	electron	or α α α 1∇⊗1B = A 2 2 1.5 11 3 2[( ( / ) ( / )] / ( ( / )[ ])e y mc z mc a mc x y zα α= − − − + − + +B rh h h 2 2 1.5 12 1 3[( ( / ) ( / )] / ( ( / )[ ])e z mc x mc a mc x y zα α= − − − + − + +B rh h h 2 2 1.5 13 2 1[( ( / ) ( / )] / ( ( / )[ ])e x mc y mc a mc x y zα α= − − − + − + +B rh h h 1B kB / 2mch 8 ave 1 1/ 8 k k k = = = ∑B B ( / )k op kc= ⊗B V E op cα=V 24 muon	within	hydrogen,	which	obey	Maxwell's	Equations	only	in	the	far	field. Currently,	there	is	no	way	to	determine	if	the	DMW	Equations	apply	to	a	free electron	or	muon	due	to	the	very	short	range	non	random	vacuum	fluctuation impact.	All	experiments	done	to	date,	such	as	the	electron/proton	scattering experiments	[12,	14]	are	done	in	the	electron's	far	field	where	the	electron's	NRVFG	has	little	impact.	In	the	far	field	the	electron	or	muon	appears	to	be	a	point particle	with	"intrinsic"	properties,	but	this	paper	shows	that	this	point	particle assumption	is	not	true	in	the	hydrogen	atom. To	penetrate	the	electron's	or	muon's CoC	shell	to	measure	the	impact	of	specific	vacuum	fluctuations	for	a	free	particle, the	high	energy	required	will	the	electron	or	muon	decaying	into	other	particles. The	DMW	Equations	are	the	most	accurate	description	of	the	electron	or	muon	in the	hydrogen	atom. The	electron's	Lorentz	Force	operator	is ,	and	from	Equations	(20) and	(24) (25) where and = The	Lorentz	Force	operator	is	a	direct	consequence	of	the	Dirac	Equation's	SG vacuum	fluctuations,	but	the	Dirac	Equation	does	not	specify	the	physical	basis	for the	CoC	dynamics	based	on	continual	virtual	electron/positron	pair	interactions	in the	vacuum	within	the	CoC	shell.	In	deriving	Equation	(25)	the	electric	field	part	of Fk =e(Ek +α ⊗Bk ) Fk =(e 2 /Rk3)(−ΔR k+(i(Σ⊗ΔRk )) ΔRk = (x −εk x! /mc)i+( y −εk y! /mc)j+(z −εkz! /mc)k Rk 3 2 2 3/2 2 2 3/22 cos( )) ( ( / )[ ])r x y zk k k ka ar a mc x y zε ε ε+ − Θ = + − + +(r r h 25 the	Lorentz	Force	is	repulsive,	but	is	overcome	by	the	magnetic	field	ICOs	to	be	a	net restoring	force	directed	toward	the	CoM.	The	second	term	in	Equation	(25)	is	a "tangential"	force	perpendicular	to	the	electron's	ICO	and	spin,	and	the	total	Lorentz Force	operator	ensures	the	electron's	CoC	remains	on	the	CoC	shell	and	is	not	driven inward	toward	the	CoM.	Perhaps	Equation	(25)	can	be	understood	in	QFT	as	sort	of a	"Casmir	effect"	where	the	totality	of	wavelengths	outside	the	CoC	shell	produce	a net	inward	force	against	the	wavelengths	that	are	"cutoff"	at	higher	wavelengths inside	the	electron's	CoC	shell. 4.0	Finite	Electron	Self	Mass	in	Hydrogen Since	the	development	of	the	electron	ICOs	is	absolutely	consistent	with	modern QED	calculations	on	hydrogen	energy	levels	[1],	the	CoC	's	c derived	ICOs	establish a	natural	cut	off	energy	[4,	5,	6]	that	is	consistent	with	the	geometrical	CoC	shell description	of	the	electron	given	in	the	sections	above. The	fully	covariant	QFT estimate	of	electron	self	mass	in	the	rest	frame	was	derived	by Weinberg	[16],	and can	be	calculated	using	the	radius	a	of	the	CoC	shell,	and	is: (26) In	QED	self-mass	is	"logarithmically	divergent,"	and	much	less	divergent	than	the "linear	divergence"	of	Classical	Electrodynamics	or	the	QM	estimate. In	QED	the photon	propagator	is	incorrect,	because	it	is	not	cut	off	by	the	physical	geometrical description	of	the	electron	SG	vacuum	fluctuation	shell.	I	t	is	not	correct	to	say	that the	electron	has	a	finite	radius,	because	the	CoC	derived	from	the	Dirac	Equation	is	a point.	It	is	the	CoC	embedded	in	the	vacuum	fluctuations	in	QFT	terms	that	produce α 0 0(3 / 2 ) ln( / ) (.068679 )m m ca mα π αΔ = =h 26 a	specific	geometrical	extended	shell	on	which	there	is	a	current.	Nothing	in	this article	implies	that	the	electron	has	a	spatially	distributed	charge	distribution	at	a single	time.	The	electron	CoC	vacuum	fluctuations	create	a	vibrating	charge	speed that	creates	a	current	over	time.	The	very	small	QED	derived	self	mass	shown	in Equation	(26)	is	finite,	and	occurs	in	a	natural	fashion	once	the	physical	geometrical description	of	the	electron	a	given	in	this	aper	is	known.	The	Dirac	Equation,	and, therefore	QFT	and	QED	in	the	IR	(which	incorporates	c in	the	four	vector	current), predicts	all	interactions,	including	self interactions,	occur	on	the	CoC	shell. Feynman	self	mass	diagrams	should	have	the	virtual	photon	emission	and absorption	distance	no	closer	than	the	distance	between	adjacent	points	in	the electron's	eight	quantized	ICOs.	Renormalization	and	tree	diagrams	to	overcome QED's	self	mass	ultra	violet	infinities	are	unnecessary	and	ad	hoc.	It's	unfortunate that	one	can't	turn	off	the	electron	charge	to	experimentally	test	the	result	in Equation	(26). 5.0 Conclusions	and	proposed	model	complexity	to	address	the electrodynamic	interaction	between	the	proton	quarks/gluons	and	the electron/muon	CoC	in	hydrogen. The	known	parameters	predicted	by	QED	for	the	hydrogen	atom	are	the	energy levels	and	a	probability	distribution	of	the	electron	and	muon	positions	in	these energy	levels,	as	illustrated	in	Figure	1.	The	electron's	c induced	fluctuations	are fully	incorporated	in	QED,	and	accurate	energy	levels	are	predicted.	The	previous sections	show	that	both	the	electron	and	muon	ICOs	define	these	vacuum α α 27 fluctuations	with	a	specific	geometry	within	the	hydrogen	atom.	These	non	random electron	and	muon	vacuum	fluctuations	are	caused	by	virtual	pair	production	and subsequent	pair	annihilation	at	time	scales	of	a	period	~1.4	10-21	sec.	(and	~	207 times	more	rapid	for	the	muon),	that	is	unimaginably	short	in	duration	The	electron and	muon	position	probability	shown	in	Figure	1	increases	as	the	electron	or	muon position	moves	further	from	the	proton	center,	until	it	peaks	at	the	Bohr	orbit	where the	electron	and	muon	CoC	fluctuations	are	negligible	in	the	proton	far	field,	as shown	by	the	DMW	Equations	(see	Equations	16,	20a,	20b,	and	20c).	The	Proton Radius	Puzzle	probably	indicates	that	a	more	precise	model	of	the	proton	is required	for	the	case	when	the	electron	or	muon	CoM	is	very	near	or	inside	the proton. There	is	no	deterministic	theory,	and	perhaps	there	never	can	be,	due	to	the probabilistic	nature	of	Quantum	Mechanics,	for	the	forces	that	cause	the	electron and	muon	to	move	dynamically	to	satisfy	the	QED	probability	for	positions	in various	energy	states.	QED	does	not	address	the	complex	model	of	the	proton	with three	fractionally	charged	quarks	held	in	place	by	the	strong	force	caused	by	the exchange	of	gluons	against	both	attractive	and	repulsive	EM	forces	between	quarks inside	the	proton. The	position	of	the	quarks	within	the	proton	may	be	perturbed by	the	relatively	weaker	EM	interaction	with	the	electron	and	muon	when	the proton	is	at	times	"inside"	the	CoC	fluctuations	of	a	negative	charge	moving	at	the speed	of	light. 28 The	degeneracy	of	the	hydrogen	atom	energy	levels	in	the	Dirac	Equation	solution	of the	hydrogen	atom	for	the	2S1/2 2P1/2	and	similar	states	with	the	same	energy	level and	total	spin,	but	different	orbital	energy	levels,	is	caused	by	the	assumption	of	a central	force	for	the	proton.	The	author	is	developing	a	model	of	the	proton	with	the three	fractionally	charged	quarks	held	in	place	by	the	strong	force	based	on Shanahan	et	al	[15]	and	its	references,	but	with	the	electron	and	muon	CoC oscillating	around	the	proton	center	at	the	speed	of	light.	For	the	more	probable positions	of	the	electron	and	muon	CoM	further	away	from	the	proton	towards	their Bohr	orbit,	the	impact	of	vacuum	fluctuations	is	minimal	and	the	electron	and	muon seem	like	point,	structureless	particles	(or	CoC	shells)	from	the	far	field	location	of the	proton.	Additional	factors	complicating	this	model	of	the	proton	EM	interaction with	the	electron	and	muon	are: 1. It	is	unknown	if	the	quarks	inside	the	proton	exhibit	their	own	specific vacuum	fluctuations	(see	[15]	for	an	analysis	of	the	Foldy-Darwin	Term) 2. When	the	entire,	spatially	extended	proton	is	"inside"	the	electron	and	muon CoC	oscillations	caused	by	vacuum	fluctuations,	the	EM	interaction	is	the sum	of	three	separate	interactions	with	each	of	the	three	proton	quarks,	or	a complex	four	body	problem. 3. The	electrodynamic	forces	of	the	very	different	muon	and	electron	CoC distances	from	the	origin	need	to	be	estimated	when	the	spatially	extended proton	is	inside	the	muon	and	electron	CoC	shells. The	average	muon attraction	to	the	proton	when	its	CoM	is	at	the	origin	is	~	(207)2 ~4	x104 stronger	than	that	of	the	electron	when	its	CoM	is	at	the	origin.	It	is	not 29 known	what	impact	this	will	have	on	the	average	proton	electromagnetic charge	distribution,	or	"proton	radius". The	fact	that	the	proton	"measures"	the	vacuum	fluctuation	impact	of	the	electron and	muon	within	the	hydrogen	atom	is	a	most	unique	situation.	If	one	attempted	to penetrate	the	electron	or	muon	CoC	shells	at	close	range	with	a	highly	energetic photons	or	charged	particles,	the	inelastic	scattering	debris	of	the	collision	would not	reveal	the	valuable	information	that	the	hydrogen	atom	provides.	It	is	not known	yet	if	impact	of	vacuum	fluctuations	within	the	hydrogen	atom	changes	the proton	charge	radius	significantly	for	muonic	and	electronic	hydrogen,	but calculating	the	QED	estimate	of	the	electron	and	muon	ICOs	with	a	more	accurate proton	model	must	be	completed	to	determine	the	impact	on	the	Proton	Radius Puzzle.	The	electron	and	muon	are	defined	by	the	Dirac	Equation	to	have	discrete position	and	time	ICOs,	and	their	true	digital	nature	is	beyond	our	classical comprehension.	The	DMW	Equations	provide	the	most	accurate	estimate	of	the electron's	or	muon's	EM	fields	in	the	hydrogen	atom. Appendix	A. Test	proposed	for	a	relativistic	entangled	electron/positron	pair exchanging	information	slower	than	instantaneously	through	their	correlated non random	vacuum	phase	fluctuations? Previous	sections	show	that	the	electron	or	muon	eight	ICO	eigenvalues	are	equally likely,	and	the	electron	occupies	both	spin	states	equally	until	an	external	EM	is applied,	resulting	in	the	electron	being	spin	up	or	down	with	equal	probability.	An 30 electron	or	muon	CoC	can	be	in	any	of	the	8	possible	ICO	eigenvalueswith	equal probability, and	does	not	exist	in	one	spin	state	or	the	other,	but	in	both	at	once. Quantum	Entanglement:	Since	c induced	fluctuations	exist	for	an	electron	or muon	in	hydrogen,	one	can	make	a	testable	speculation	[5,	6]	about	the	cause	of Quantum	Entanglement	for	the	special	case	of	the	electron/positron	(or	muon/anti muon)	entangled	pairs.	If	the	positron	is	a	negative	electron	traveling	backward	in time,	its	phase	becomes	"phase	locked"	1800 out	of	phase	with	the	electron	as	the travel	away	from	each	other	in	a	vacuum	that	contains	their	phase	fluctuations. Changes	in	the	electron	or	positron	phase	travel	at	a	speed	of	c2/vCoM,	which	is nearly	instantaneous	for	vCoM	<<	c.	Changing	the	electron	or	positron	spin	reverses their	phase,	which	is	almost	instantaneously	sensed	by	the	other	particle	as	a	phase reversal	through	the	fluctuating	vacuum. Although	this	explanation	for	the	quantum entanglement	for	an	entangled	electron/positron	pair	is	a	speculation,	it	can	be tested.	If	the	electron/positron	pair	traveled	apart	at	a	speed	of	.5c,	the	phase	speed carrying	the	information	between	particles	would	not	be	instantaneous,	but	would be	2c.	Only,	if	the	entangled	electron/positron	pair	was	nearly	at	rest	would	the information	transfer	be	instantaneous.	The	results	in	this	paper	show	the	electron CoC	and	its	vacuum	fluctuation	is	a	single	entity	and	inseparable	from	one	another unless	the	electron	is	destroyed	by	an	external	EM	field.	The	speculation	above asserts	that	an	electron	positron	entangled	pair	may	also	possess	a	very	specific	non random	phase	for	the	entangled	pair.	The	test	proposed	above	is	conceptually straight	forward,	but	the	relatively	high	sped	of	separation	to	measure	non instantaneous	information	exchange	may	be	difficult	to	measure	experimentally α 31 due	to	difficulty	keeping	the	electron/positron	pair	entangled	over	a	large	enough separation	to	measure	the	difference	in	information	velocity	from	instantaneous. References: 1.	M.	L.	Eides,	Grotch,	H.,	and	Shelyuto,	V.,	"Theory	of	Light	Hydrogenlike	Atoms", Phys.	Rept.	342	(2001)	63-261 2.	R.	Pohl,	"The	size	of	the	proton	from	the	Lamb	shift	in	muonic	hydrogen",	Nature July	10,	2010	(updated	2017	by	"Proton	size	issue	215-slides.pdf")	. 3. R.	Pohl	et	al.	[CREMA	Collaboration],	Science	353,	no.	6300,	669	(2016). 4.	J.	H.	Wilson,	"The	Dirac	Electron	Discrete	Internal	Structure	and	Its	Rapidly Oscillating	Charge	Shell",	PHYSICS	ESSAYS	28,	1,	(2015) 5.	J.	H.	Wilson,	"A	Compton	scattering	experiment	to	test	the	shape	of	the	Dirac election's	center	of	charge	oscillating	shell",	PHYSICS	ESSAYS	29,	3,	(2016) 6.	J.	H.	Wilson,	"Measuring	Zitterbewegung	Predicted	by	the	Dirac	Equation	for	a Free	Electron",	PHYSICS	ESSAYS	31,	1,	(2018) 7.	S.	Bruce,	"Maxwell-Like	Equations	for	Free	Dirac	Electrons",	Zeitschrift	fur Naturforschung 73(4),	February	2018 . 8.	D.	Hestenes,	Found.	Phys.	40,	1	(2010) 9 J.	Bernauer	and	Pohl	R.,	"You	Would	Be	Forgiven	for	Assuming	that	We Understand	the	Proton",	Sci.	Am.,	Feb.	2104. 10. E.	Schrödinger,	Sitzungsber	Preuss.	Akad.	Wiss.	Berlin	(Math.	Phys.),	24 (1930),	p.	418. 11.	Schwartz,	Mathew	D.,	Quantum	Field	Theory	and	the	Standard	Model, Cambridge	University	Press,	2014. 12.	S.A.	Bruce,	"The	Schrödinger	Equation	and	Negative	Energies",	Z.	Naturforsch. 2018;	73(12)a:	1129–1135 32 13.	J.	J.	Sakurai,	Advanced	Quantum	Mechanics,	(Addison	Wesley	Publishing Company,	1967)	29. 14	.	Hu,	Q.,	"The	Nature	of	the	Electron",	Physics	Essays	17(4),	January	2006. 15.	Shanahan,	P.	E.	and	W.	Detmold,	'Pressure	Distribution	and	Shear	Forces	inside the	Proton",	Phys.	Rev.	Lett.	122,	072003,	22	February	2019. 16.	.	S. Weinberg,	The	Quantum	Theory	of	Fields,	(Cambridge	University	Press	Vol. I	and	II,	(1995). Figure	1	Caption:	Electron	Position	Probability	Distribution	in	the	Hydrogen	Atom 33 The	Hydrogen	Energy	Levels	are	estimated	very	accurately,	but	the positions	of	the	electron	and	proton	are	not	known	deterministically The	ZBW	fluctuations	only	impact energy	levels	when	the	electron position	is	near/inside	the	proto n	in	the	1S	and	2S	levels If	the	Hydrogen	atom	had	classical	Bohr	orbits, there	would	be	no	Darwin	Term,	and	ZBW	would be	hidden Bohr	Radius	5.25	x	10-11	m