Remark on Lehnert’s Revised Quantum Electrodynamics (RQED) as an Alternative to Francesco Celani’s et al. Maxwell–Clifford Equations: With an Outline of Chiral Cosmology Model and its Role to CMNS

2020·0.15 MB·

by  Victor Christianto

J.CondensedMatterNucl.Sci.31(2020)91–102
ResearchArticle
Remark on Lehnert’s Revised Quantum Electrodynamics (RQED) as
an Alternative to Francesco Celani’s et al. Maxwell–Clifford
Equations: With an Outline of Chiral Cosmology Model
and its Role to CMNS
∗
Victor Christianto
MalangInstituteofAgriculture(IPM),Malang,Indonesia
†
Florentin Smarandache
DepartmentofMathematicsandSciences,UniversityofNewMexico,Gallup,USA
‡
Yunita Umniyati
HeadofPhysicsLab,DepartmentofMechatronics,Swiss-GermanUniversity,BSDCity,Indonesia
Abstract
InarecentpaperpublishedinJCMNSin2017,FrancescoCelani,DiTommasoandVassaloarguedthatMaxwellequationsrewritten
inCliffordalgebraaresufficienttodescribetheelectronandalsoultra-densedeuteriumreactionprocessproposedbyHomlidet
al. Apparently, Celanietal. believedthattheirMaxwell–CliffordequationsareanexcellentcandidatetosurpassbothClassical
ElectromagneticandZitterbewegungQM.Meanwhile,inaseriesofpapers,BoLehnertproposedanovelandrevisedversionof
QuantumElectrodynamics(RQED)basedonProcaequations. Therefore, inthispaper, wegaveanoutlineofLehnert’sRQED,
as an alternative framework to Celani et al Zitterbewegung-Classical EM. Moreover, in a rather old paper, Mario Liu described
hydrodynamic Maxwell equations. While he also discussed potential implications of these new approaches to superconductors,
suchadiscussionofelectrodynamicsofsuperconductorsismadeonlyafterTajmar’spaper. (continuedinthenextpage)
⃝c 2020ISCMNS.Allrightsreserved.ISSN 2227-3123
Keywords: Chiralmedium,Chiralgravitationtheory,Electrodynamicsofsuperconductor,Hirschtheory,HydrodynamicsMaxwell
equations,LENR,Londonequations,Maxwellequations,Procaequations,RevisedQED
∗Correspondingauthor.http://researchgate.net/profile/Victor_Christianto,E-mail:[email protected].
†E-mail:fl[email protected].
‡E-mail:[email protected].
⃝c 2020ISCMNS.Allrightsreserved.ISSN 2227-3123
92 V.Christiantoetal./JournalofCondensedMatterNuclearScience31(2020)91–102
(continuedfromthetitlepage)
Therefore, in this paper we present for the first time a derivation of fluidic Maxwell–Proca equations. The name
of fluidic Maxwell–Proca is proposed because the equations were based on modifying Maxwell–Proca and Hirsch’s
theory of electrodynamics of superconductors. It is hoped that this paper may stimulate further investigations and
experimentsinsuperconductorsItmaybeexpectedtohavesomeimpacttocosmologymodelingtoo,forinstancewe
considerahypotheticalargumentthatthephotonmasscanbetheoriginofgravitation. Then,aftercombiningwiththe
so-calledchiralmodificationofMaxwellequations(afterSpröessig),weconsiderchiralMaxwell–Procaequationsas
apossiblealternativeofgravitationtheory. Suchahypothesishasneverconsideredintheliteraturetothebestofour
knowledge. Inthelastsection,wediscusstheplausibleroleofchiralMaxwell–Proca(RQED)inCMNSprocess. Itis
hopedthatthispapermaystimulatefurtherinvestigationsandexperimentsinparticularforelucidatingthephysicsof
LENRandUDDreactionfromclassicalelectromagnetics.
1. Introduction
In a recent paper published in JCMNS in 2017, Francesco Celani, Di Tommaso and Vassalo argued that Maxwell
equationsrewritteninCliffordalgebraaresufficienttodescribetheelectronandalsoultra-densedeuteriumreaction
processproposedbyHomlidetalApparently, Celanietal. believedthattheirMaxwell–Cliffordequationsarequite
excellentcandidatetosurpassbothClassicalElectromagneticstheoryandZitterbewegungQM[1].
Inthemeantime,itisknownthatconventionalelectromagnetictheorybasedonMaxwell’sequationsandquantum
mechanics has been successful in its applications in numerous problems in physics, and has sometimes manifested
itselfinagoodagreementwithexperiments. Nevertheless,asalreadystatedbyFeynman,thereareunsolvedproblems
leading to difficulties with Maxwell’s equations that are not removed by and not directly associated with quantum
mechanics [17–20]. Therefore QED, which is an extension of Maxwell’s equations, also becomes subject to the
typicalshortcomingsofelectromagneticinitsconventionalform. ThisreasoningmakesawayforRevisedQuantum
ElectrodynamicsasproposedbyBoLehnert[17–19].
Meanwhile, according to J.E. Hirsch, from theoutset of superconductivityresearch it wasassumed thatno elec-
trostatic fields could exist inside superconductors and this assumption was incorporated into conventional London
electrodynamics[23]HirschsuggeststhattherearedifficultieswiththetwoLondonequations. Tosummarize, Lon-
don’s equations together with Maxwell’s equations lead to unphysical predictions [22] Hirsch also proposes a new
modelforelectrodynamicsforsuperconductors[22–23].
Inthisregard,inaratheroldpaper,MarioLiudescribedahydrodynamicMaxwellequations[25]. Whilehealso
discussedpotentialimplicationsofthesenewapproachestosuperconductors,suchadiscussionofelectrodynamicsof
superconductorsismadeonlyafterTajmar’spaper. Therefore,inthispaperwepresentforthefirsttimeaderivation
offluidicMaxwell–Proca–Hirschequations. ThenameofMaxwell–Proca–Hirschisproposedbecausetheequations
werebasedonmodifyingMaxwell–ProcaandHirsch’stheoryofelectrodynamicsofsuperconductor. Therefore, the
aimofthepresentpaperistoproposeaversionoffluidicMaxwell–Procamodelforelectrodynamicsofsuperconductor,
alongwithanoutlineofachiralcosmologymodel.
Thismaybeexpectedtohavesomeimpacttocosmologymodelingtoo,whichwillbediscussedinthelastsection.
Itishopedthatthispapermaystimulatefurtherinvestigationsandexperimentsinparticularforfractalsuperconductor.
2. Lehnert’sRevisedQuantumElectrodynamics
InaseriesofpapersBoLehnertproposedanovelandrevisedversionofQuantumElectrodynamics,whichherefers
toasRQED.Histheoryisbasedonthehypothesisofanonzeroelectricchargedensityinthevacuum,anditisbased
V.Christiantoetal./JournalofCondensedMatterNuclearScience31(2020)91–102 93
onProca-typefieldequations([20],p. 23):
( )
1 ∂2
−∇2 A =µ J , µ=1,2,3,4, (1)
c2∂t2 µ 0 µ
where
( )
iφ
A = A, (2)
µ c
withAandϕstandingforthemagneticvectorpotentialandtheelectrostaticpotentialinthree-space. Inthreedimen-
sions,wegot([20],p. 23):
curlB ε ∂E
=ε (divE)C+ 0 , (3)
µ 0 ∂t
0
∂B
curlE =− , (4)
∂t
B =curlA, divB =0, (5)
∂A
E =−∇φ− , (6)
∂t
ρ¯
divE = . (7)
ε
0
These equations differ from the conventional form with a nonzero electric field divergence equation (7) and by the
additionalspace–chargecurrentdensityinadditiontodisplacementcurrentatEq. (3). Theextendedfieldequations
(3)–(7)areeasilyfoundalsotobecomeinvarianttoagaugetransformation([20],p. 23).
Themaincharacteristicnewfeaturesofthepresenttheorycanbesummarizedasfollows([20],p. 24):
(a) Thehypothesisofanonzeroelectricfielddivergenceinthevacuumintroducesanadditionaldegreeoffreedom,
leading to new physical phenomena. The associated nonzero electric charge density thereby acts somewhat
likeahiddenvariable.
(b) Thisalsoabolishesthesymmetrybetweentheelectricandmagneticfields,andthenthefieldequationsobtain
thecharacterofintrinsiclinearsymmetrybreaking.
(c) ThetheoryisbothLorentzandgaugeinvariant.
(d) Thevelocityoflightisnolongerascalarquantity,butisrepresentedbyavelocityvectorofthemodulusc.
(e) Additionalresults: LehnertisalsoabletoderivethemassofZbosonandHiggs-likeboson[21]. Thesewould
paveanalternativewaytonewphysicsbeyondtheStandardModel.
NowitshouldbeclearthatLehnert’sRQEDisagoodalternativetheorytoQM/QED,andthereforeitisalsointeresting
toaskwhetherthistheorycanalsoexplainsomephenomenarelatedtoLENRandUDDreactionproposedbyHomlid
(asarguedbyCelanietal.) [1].
ItshouldbenotedtoothatProcaequationscanbeconsideredasanextensionofMaxwellequations,andtheyhave
beenderivedinvariousways. ItcanbeshownthatProcaequationscanbederivedfromfirstprinciples,andalsothat
ProcaequationsmayhavealinkwiththeKlein–Gordonequation[6,7].
OnepersistentquestionconcerningtheseProcaequationsishowtomeasurethemassofthephoton. Thisquestion
hasbeendiscussedinlengthybyTuetal. [12]. Accordingtotheirreport, therearevariousmethodstoestimatethe
94 V.Christiantoetal./JournalofCondensedMatterNuclearScience31(2020)91–102
Table1. Upperboundonthedispersionofthespeedoflightindifferentrangesoftheelectromagneticspectrum,andthe
correspondinglimitsonthephotonmass([12],p.94).
Author(year) Typeofmeasurement Limitsonmγ(g)
Rossetal.(1937) Radiowavestransmissionoverland 5.9×10−42
MandelstamandPapalexi(1944) Radiowavestransmissionoversea 5.0×10−43
Al’pertetal.(1941) Radiowavestransmissionoversea 2.5×10−43
Florman(1955) Radio-waveinterferometer 5.7×10−42
Lovelletal.(1964) Pulsarobservationsonflourflarestars 1.6×10−42
Frome(1958) Radio-waveinterferometer 4.3×10−40
Warneretal.(1969) ObservationsonCrabNebulapulsar 5.2×10−41
Brownetal.(1973) Shortpulsesradiation 1.4×10−33
Bayetal.(1972) Pulsaremission 3.0×10−46
Schaefer(1999) Gammaraybursts 4.2×10−44
Gammaraybursts 6.1×10−39
upper bound limits of photon mass. In Table 1, some of upper bound limits of photon mass based on dispersion of
speedoflightaresummarized.
FromTable1andalsofromotherresultsasreportedin[12],itseemsthatwecanexpectthatsomedayphotonmass
canbeobservedwithinexperimentalbounds.
3. Hirsch’sProposedRevisionofLondon’sEquations
According to J.E. Hirsch, from the outset of superconductivity research it was assumed that no electrostatic fields
could exist inside superconductors and this assumption was incorporated into conventional London electrodynamics
[22]HirschsuggeststhattherearedifficultieswiththetwoLondonequations. ThereforeheconcludesthatLondon’s
equationstogetherwithMaxwell’sequationsleadtounphysicalpredictions[1]Howeverhestillusesfour-vectorsJ
andAaccordingtoMaxwell’sequations:
4π
(cid:3)2A=− J (8)
c
and
c
J −J =− (A−A ). (9)
0 2 0
4πλ
L
ThereforeHirschproposesanewfundamentalequationforelectrodynamicsforsuperconductorsasfollows[22]
1
(cid:3)2(A−A )= (A−A ), (10a)
0 λ2 0
L
whereLondonpenetrationdepthλ isdefinedasfollows[23]:
L
1 4πnse2
= , (10b)
λ2 mec2
L
alsod’Alembertianoperatorisdefinedas[22]:
1 ∂2
(cid:3)2 =∇2− . (10c)
c2∂2
t
V.Christiantoetal./JournalofCondensedMatterNuclearScience31(2020)91–102 95
Thenheproposesthefollowingequations[22]:
1
(cid:3)2(F −F )= (F −F ) (11)
0 2 0
λ
L
and
1
(cid:3)2(J −J )= (J −J ), (12)
0 2 0
λ
L
⇀ ⇀ ⇀
where F is the usual electromagnetic field tensor and F is the field tensor with entries E and 0 from E and B,
0
respectively,whenexpressedinthereferenceframeatrestwithrespecttotheions.
Inthemeantime,itisknownthatProcaequationscanalsobeusedtodescribeelectrodynamicsofsuperconductors,
see [25–33]. The difference between Proca and Maxwell equations is that Maxwell equations and Lagrangian are
basedonthehypothesisthatthephotonhaszeromass,buttheProca’sLagrangianisobtainedbyaddingmasstermto
Maxwell’sLagrangian[33]Therefore,theProcaequationcanbewrittenasfollows[33]:
4π
∂ Fµν +m2A = Jν, (13a)
µ γ ν c
where m = ω is the inverse of the Compton wavelength associated with photon mass [38]. (Note: ‘omega’ is
γ c
the angular frequency = 2πf, where f is the frequency, the definition of omega involves the “reduced” Compton
wavelength,correspondingwiththereducedPlanckconstant}). Itisalsoclearthatintheparticularcaseofm = 0,
thenthatequationreducestotheMaxwellequation. Intermsofthevectorpotentials,Eq. (13a)canbewrittenas[33]:
4π
((cid:3)+m )A = J . (13b)
γ µ c µ
Similarly, according to Kruglov [31] the Proca equation for a free particle processing the mass m can be written as
follows:
∂ φ (x)+m2φ (x)=0. (14)
ν µν µ
Now, the similarity between Eqs. (8) and (13b) are remarkable with the exception that Eq. (8) is in quadratic form.
ThereforeweproposetoconsideramodifiedformofHirsch’smodelasfollows:
1
((cid:3)2−m2)(F −F )= (F −F ) (15a)
γ 0 λ2 0
L
and
1
((cid:3)2−m2)(J −J )= (J −J ). (15b)
γ 0 2 0
λ
L
TherelevanceoftheproposednewequationsinlieuofEqs. (11)–(14)shouldbeverifiedbyexperimentswithsuper-
conductors[37]. Forconvenience,theEqs. (15a)–(15b)canbegivenaname: Maxwell–Proca–Hirschequations.
96 V.Christiantoetal./JournalofCondensedMatterNuclearScience31(2020)91–102
4. FluidicMaxwell–ProcaEquations
In this regard, in a rather old paper, Mario Liu described a hydrodynamic Maxwell equations [24] While he also
discussedthepotentialimplicationsofthesenewapproachestosuperconductors,suchadiscussionofelectrodynamics
ofsuperconductorsismadeonlyafterTajmar’spaper.Therefore,inthissectionwepresentforthefirsttimeaderivation
offluidicMaxwell–Proca–Hirschequations.
AccordingtoBlackledge,Procaequationscanbewrittenasfollows[7]:
ρ
∇·E⃗ = −κ2ϕ, (16)
ε
0
∇·B⃗ =0, (17)
∂B⃗
∇×E⃗ =− , (18)
∂t
∂E⃗
∇×B⃗ =µ j+ε µ +κ2A⃗, (19)
0 0 0 ∂t
where(withoutassumingPlanckconstant,}=1):
∂A⃗
∇ϕ=− −E⃗, (20)
∂t
B⃗ =∇×A⃗, (21)
mc
κ= 0. (22)
}
Therefore,byusingthedefinitionsinEqs. (16)–(19),andbycomparingwithhydrodynamicMaxwellequationsofLiu
([24],Eq. (2)),nowwecanarriveatfluidicMaxwell–Procaequations,asfollows:
ρ
∇·E⃗ = −κ2ϕ, (23)
ε
0
∇·B⃗ =0, (24)
( )
B˙ =−∇×E−∇× βˆ∇×H , (25)
0
ε µ E˙ =∇×B−µ j−κ2A−(σˆE +ρ v+γˆ∇T)−∇×(aˆ∇×E ), (26)
0 0 0 0 e 0
where:
∂A⃗
∇ϕ=− −E⃗, (27)
∂t
B⃗ =∇×A⃗, (28)
mc
κ= 0. (29)
}
V.Christiantoetal./JournalofCondensedMatterNuclearScience31(2020)91–102 97
Since according to Blackledge, the Proca equations can be viewed as a unified wavefield model of electromagnetic
phenomena [7], therefore we can also regard the fluidic Maxwell–Proca equations as a unified wavefield model for
electrodynamicsofsuperconductor.
Now, having defined fluidic Maxwell–Proca equations, we are ready to write fluidic Maxwell–Proca equations
usingthesamedefinition,asfollows:
1
((cid:3)2 −κ2)(F −F )= (F −F ) (30)
α 0 2 0
λ
L
and
1
((cid:3)2 −κ2)(J −J )= (J −J ), (31)
α 0 2 0
λ
L
where
1 ∂α2
(cid:3)2 =∇α2− . (32)
α c2∂α2
t
Asfarasweknow,theabovefluidicMaxwell–Procaequationshaveneverbeenpresentedelsewherebefore. Provided
theaboveequationscanbeverifiedwithexperiments,theycanbeusedtodescribeelectrodynamicsofsuperconductors.
Asalastnote,itseemsinterestingtoremarkherethatKruglov[31]hasderivedasquare-rootofProcaequations
asapossiblemodelforhadronmassspectrum, thereforeperhapsEqs. (30)–(32)maybefactorized tootofindouta
modelforhadronmasses. However,weleavethisproblemforfutureinvestigations.
5. TowardsChiralCosmologyModel
TheMaxwell–ProcaelectrodynamicscorrespondingtoafinitephotonmasscausesasubstantialchangeoftheMaxwell
stresstensorand, undercertaincircumstances, maycausetheelectromagneticstressestoacteffectivelyas“negative
pressure.” In a recent paper, Ryutov, Budker, Flambaum [34] suggest that such a negative pressure imitates gravita-
tionalpull,andmayproduceaneffectsimilartogravitation.Inthemeantime,thereareotherpapersbyLongo,Shamir,
etc. discussing observations indicating handedness of spiral galaxies, which seem to suggest chiral medium at large
scale. However,sofarthereisnoderivationofMaxwell–Procaequationsinchiralmedium
Inarecentpaper,Ryutov,Budker,FlambaumsuggestthatMaxwell–Procaequationsmayinduceanegativepres-
sureimitatesgravitationalpull,andmayproduceeffectsimilartogravitation[34]
Inthemeantime,thereareotherpapersbyLongo,Shamiretal. discussingobservationsindicatinghandednessof
spiralgalaxies,whichseemtosuggestchiralmediumatlargescale. AsShamirreported:
“Amorphologicalfeatureofspiralgalaxiesthatcanbeeasilyidentifiedbythehumaneyeisthehandedness—
somespiralgalaxiesspinclockwise,whileotherspiralgalaxiesrotatecounterclockwise.Previousstudiessug-
gestlarge-scaleasymmetrybetweenthenumberofgalaxiesthatrotateclockwiseandthenumberofgalaxies
thatrotatecounterclockwise,andalarge-scalecorrelationbetweenthegalaxyhandednessandothercharac-
teristicscanindicateanasymmetryatacosmologicalscale”[40].
However,sofarthereisnoderivationofMaxwell–Procaequationsinachiralmedium. Therefore,inspiredbyRyutov
etalpaper,inthispaper,wepresentforthefirsttimeapossibilitytoextendMaxwell–Proca-typeequationstochiral
medium,whichmaybeabletoexplainoriginofhandednessofspiralgalaxiesasreportedbyLongoetal. [39,40].
Thepresentpaperisintendedtobeafollow-uppaperofourprecedingpaper,reviewingShpenkov’sinterpretation
ofclassicalwaveequationanditsroletoexplainperiodictableofelementsandotherphenomena[38].
98 V.Christiantoetal./JournalofCondensedMatterNuclearScience31(2020)91–102
6. Maxwell–ProcaEquationsinChiralMedium
ProcaequationscanbeconsideredasanextensionofMaxwellequations,andtheyhavebeenderivedinvariousways.
ItcanbeshownthatProcaequationscanbederivedfromfirstprinciples[6],andalsothatProcaequationsmayhave
linkwithKlein–Gordonequation[7].
It should be noted that the relations between flux densities and the electric and magnetic fields depend on the
material. Itiswellknown,forinstance,thatallorganicmaterialscontaincarbonandrealizeinthiswaysomekindof
opticalactivity. Therefore,LordKelvinintroducedthenotionofthechiralitymeasureofamedium. Thiscoefficient
expressestheopticalactivityoftheunderlyingmaterial. Thecorrespondentconstitutivelawsarethefollowing[35]:
√
D =εE+εβ E (Drude–Born–Feodorovlaws), (33)
√
B =µH +µβ H, (34)
wheree=E(t,x)istheelectricpermittivity,j =p(t,x)isthemagneticpermeabilityandthecoefficientβ describes
thechiralitymeasureofthematerial[35].
Now,sincewewanttoobtainMaxwell–Procaequationsinchiralmedium,thenEq. (28)shouldbereplacedwith
Eq. (34). Butsuchahypotheticalassertionshouldbeinvestigatedinmoredetailed.
SinceaccordingtoBlackledge,theProcaequationscanbeviewedasaunifiedwavefieldmodelofelectromagnetic
phenomena[7],thenwecanalsoregardtheMaxwell–Procaequationsinchiralmediumasafurthergeneralizationof
hisunifiedwavefieldpicture.
7. PlausibleRoleofChiralSuperconductorModeltoLENR/CMNS
AccordingtoR.M.Kiehn,chiralityalreadyarisesinelectromagneticequations,i.e. Maxwellequations[41]:
“From a topological viewpoint, Maxwell’s electrodynamics indicates that the concept of Chirality is to be
associated with a third rank tensor density of Topological Spin induced by the interaction of the four vector
potentials{A,φ}andthefieldexcitations(D,H).ThedistinctconceptofHelicityistobeassociatedwiththe
third rank tensor field of Topological Torsion induced by the interaction of the 4 vector potentials and field
intensities(E,B)...
In the electromagnetic situation, the constitutive map is often considered to be (within a factor) a linear
mappingbetweentwosixdimensionalvectorspaces. Assuchtheconstitutivemapcanhavebotharight-or
aleft-handedrepresentation,implyingthattherearetwotopologicallyequivalentstatesthatarenotsmoothly
equivalentabouttheidentity”.
Therefore,herewewillreviewsomemodelsofchiralityinsuperconductorsandothercontexts,inhopethatwemay
elucidatethechiralityoriginofspiralingwaveasconsideredbyCelanietal.forexplainingUDDreaction(cf.Homlid).
Here,wesummarizesomereportsonchiralityasobservedinexperiments:
(a) F.Qinetal. reported“Superconductivityinachiralnanotube”[42]. Theirabstractgoesasfollows: “Chiral-
ity of materials are known to affect optical, magnetic and electric properties, causing a variety of nontrivial
phenomenasuchascirculardichiroismforchiralmolecules,magneticSkyrmionsinchiralmagnetsandnon-
reciprocal carrier transport in chiral conductors. On the other hand, effect of chirality on superconducting
transport has not been known. Here we report the nonreciprocity of superconductivity—unambiguous evi-
dence of superconductivity reflecting chiral structure in which the forward and backward supercurrent flows
arenotequivalentbecauseofinversionsymmetrybreaking.Suchsuperconductivityisrealizedviaionicgating
V.Christiantoetal./JournalofCondensedMatterNuclearScience31(2020)91–102 99
inindividualchiralnanotubesoftungstendisulfide. Thenonreciprocalsignalissignificantlyenhancedinthe
superconductingstate,beingassociatedwithunprecedentedquantumLittle-Parksoscillationsoriginatingfrom
theinterferenceofsupercurrentalongthecircumferenceofthenanotube. Thepresentresultsindicatethatthe
nonreciprocityisaviableapproachtowardthesuperconductorswithchiralornoncentrosymmetricstructures”.
Inotherwords,chiralitymayplayasignificantroleinelectromagneticcharacterofsuperconductors.
(b) Inotherpaper,Kungetal. reported: “Usingpolarization-resolvedresonantRamanspectroscopy,weexplore
collective spin excitations of the chiral surface states in a three dimensional topological insulator, Bi Se .
2 3
We observe a sharp peak at 150 meV in the pseudovector A2 symmetry channel of the Raman spectra. By
comparing the data with calculations, we identify this peak as the transverse collective spin mode of surface
Diracfermions. Thismode,unlikeaDiracplasmonorasurfaceplasmoninthechargesectorofexcitations,is
analogoustoaspinwaveinapartiallypolarizedFermiliquid,withspin-orbitcouplingplayingtheroleofan
effectivemagneticfield”[43]. Whatwewouldemphasizehereisthatthecollectivespinmodemayalterthe
Diracfermions,seealso[44].
(c) Karimi et al. studied deviation from Larmor’s theorem, their abstract begins as follows: “Larmor’s theorem
holdsformagneticsystemsthatareinvariantunderspinrotation. Inthepresenceofspin–orbitcouplingthis
invarianceislostandLarmor’stheoremisbroken:forsystemsofinteractingelectrons,thisgivesrisetoasubtle
interplaybetweenthespin-orbitcouplingactingonindividualsingle-particlestatesandCoulombmany-body
efects”[45]. WhatwewouldemphasizehereispossibleobservationofCoulombmany-bodyeffects,andthis
seemstoattractconsiderableinterestsrecently,seealso([45],parta).
8. ConcludingRemarks
Inaseriesofpapers,BoLehnertproposedanovelandrevisedversionofQuantumElectrodynamics(RQED)basedon
Procaequations.WesubmitaviewpointthatLehnert’sRQEDisagoodalternativetheorytoQM/QED,andthereforeit
isalsointerestingtoask: CanthistheoryalsoexplainsomephenomenarelatedtoLENRandUDDreactionofHomlid
(asarguedbyCelanietal)? Whilewedonotpretendtoholdalltheanswersinthisregard,wejustgaveanoutlineto
Procaequationstoelectrodynamicsofsuperconductors,thentochiralitymodel.
Nonetheless, one of our aims with the present paper is to propose a combined version of London–Proca–Hirsch
model for electrodynamics of superconductor. Considering that Proca equations may be used to explain electrody-
namics in superconductor, the proposed fluidic London–Proca equations may be able to describe electromagnetic of
superconductors. It is hoped that this paper may stimulate further investigations and experiments in particular for
superconductor. Itmaybeexpectedtohavesomeimpacttocosmologymodelingtoo.
AnotherpurposeistosubmitanewmodelofgravitationbasedonarecentpaperbyRyutov,Budker,Flambaum,who
suggest that Maxwell–Proca equations may induce a negative pressure imitates gravitational pull, and may produce
effect similar to gravitation. In the meantime, there are other papers by Longo, Shamir etc. discussing observations
indicatinghandednessofspiralgalaxies,whichseemtosuggestchiralmediumatlargescale.
However, so far there is no derivation of Maxwell–Proca equations in chiral medium. In this paper, we propose
Maxwell–Proca-typeequationsinchiralmedium,whichmayalsoexplain(albeithypothetically)originofhandedness
ofspiralgalaxiesasreportedbyM.Longoetal.
ItmaybeexpectedthatonecandescribehandednessofspiralgalaxiesbychiralMaxwell–Procaequations. This
wouldneedmoreinvestigations,boththeoreticallyandempirically
This paper is partly intended to stimulate further investigations and experiments of LENR inspired by classical
electrodynamics,asacontinuationwithourpreviousreport.
100 V.Christiantoetal./JournalofCondensedMatterNuclearScience31(2020)91–102
9. Postscript
It shall be noted that the present paper is not intended to be a complete description of physics of LENR and UDD
reaction(Homlidetal.). Nonetheless,wecanremarkonthreethings:
(1) AlthoughusuallyProcaequationsareconsiderednotgaugeinvariant,thereforesomeresearcherstriedtoderive
agaugeinvariantmassiveversionofMaxwellequations,arecentexperimentsuggestU(1)gaugeinvarianceof
Procaequations,see[46].
(2) Since Proca equations can be related to electromagnetic Klein–Gordon equation, and from Klein–Gordon
equationonecanderivehydrinostatesofhydrogenatom,thenonecanalsoexpecttoderiveultradensehydro-
genandhydrinostatesfromProcaequation. Thisbringsustoaconsistentpictureofhydrogen,seealsoMills
etal. [47–50].
(3) Chiralityeffectofhydrino/UDDmaybeobservedinexperimentsinthenearfuture.
Acknowledgments
Special thanks to George Shpenkov for sending his papers and books. Discussions with Volodymyr Krasnoholovets
and Robert Neil Boyd are gratefully appreciated. Nonetheless, the ideas presented here are our sole responsibility.
Oneoftheseauthors(VC)dedicatesthispapertoJesusChristwhoalwaysguideshimthroughallvalleyofdarkness
(Psalms23). HeistheGoodShepherd.
References
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