Table Of ContentEXAMPLES OF LEPTONIC MONOPOLE
TRACKS ON X-RAY PHOTOGRAPHIC FILMS
Characteristic monopole tracks in caterpillar form. We have hundreds,
even thousands of such tracks.
Two pairs of tracks obtained from an element, the image of which is
reflected in a germanium mirror. Unlike light symmetry, we see that the
symmetry is not left–right : each element of the pair is identical with the
(cid:1)
other but rotated through 180 , as predicted by theory.
A monopole track at the Earth’s North Pole. Theory predicted these
tracks because of the possibility of conversion of neutrinos to monopoles
causedbytheactionofsolarmagneticfieldsonneutrinos.Manysuchtracks
were observed.
VOLUME ONEHUNDREDAND EIGHTY-NINE
A
DVANCES IN
IMAGING AND
ELECTRON PHYSICS
The Leptonic Magnetic Monopole
Theory and Experiments
GEORGES LOCHAK
Fondation Louis de Broglie
23 rue Marsoulan
F-75012 Paris, France
HARALD STUMPF
Institute of Theoretical Physics
University of T€ubingen
D-72076 T€ubingen, Germany
EDITOR-IN-CHIEF
PETER W. HAWKES
CEMES-CNRS, Toulouse, France
AMSTERDAM(cid:129)BOSTON(cid:129)HEIDELBERG(cid:129)LONDON
NEWYORK(cid:129)OXFORD(cid:129)PARIS(cid:129)SANDIEGO
SANFRANCISCO(cid:129)SINGAPORE(cid:129)SYDNEY(cid:129)TOKYO
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This volume is dedicated to Louis de Broglie and Werner Heisenberg,
both winners of the Nobel Prize, by their former students, Georges
Lochak and Harald Stumpf
PREFACE
Mostvolumesinthisseriescontainseveralchaptersonavarietyofsubjectsin
thegeneralareaofimagingandelectronphysics.Occasionally,however,an
entirevolumeisdevotedtoasinglesubjectortoaspecifictheme,andthisis
the case here. The authors have the distinction of being former students of
Louis de Broglie and Werner Heisenberg, to whom they have dedicated
theirbook,andhavespentmanyyearswrestlingwiththeoutstandingques-
tions of quantum mechanics. In particular, they have examined the thorny
problem of the magnetic monopole and they present here their arguments
and conclusions on this difficult topic.
The bookis dividedinto twolarge parts. The first, by GeorgesLochak,
presentsthetheoryoftheleptonicmonopole,amasslessparticlewithspin½
thattravelsatthespeedoflight.Thesecondpart,byHaraldStumpf,setsout
fromthesuggestionthatsuchleptonicmonopolescanbecreatedduringdis-
charges in fluids. This suggestion is pursued in great detail, with extensive
theoretical background.
I have no doubt that this full presentation of ideas that depart from the
mainstreamofthinkingintheoreticalphysicswillkeepinterestinthesubject
alive and readers will surely be grateful to the authors for spelling out their
ideassofully.Itakethisopportunitytoacknowledgetheinvaluablecontri-
butionofMadameMorénasoftheFondationLouisdeBroglieintheprep-
aration of Georges Lochak’s material and of Michael Ruder, who has dealt
with many queries concerning Profesor Stumpf’s text.
Peter Hawkes
j
ix
FOREWORD
The Past and Future of
Magnetic Monopoles
G. Lochak
Contents
1. ABriefHistoryofElectricityandMagnetism xi
2. TheFathersoftheMagneticMonopole xiii
2.1 Maxwell(1873) xiii
2.2 PierreCurie(1894) xv
2.3 Poincaré(1896) xviii
2.4 Dirac(1931) xviii
3. SomeIntroductoryWordsAbouttheLeptonicMonopole xx
4. CharacteristicsoftheTheory xxii
1. A BRIEF HISTORY OF ELECTRICITY AND MAGNETISM
The observation of electricity and magnetism began in ancient times. It is
attributed to the Greeks and the Chinese.
Around 600 B.C., Thales noticed that amber had the ability to attract
light bodies when rubbed with a cat skin. But the Greeks also knew about
magnets, whose name is magnes in Greek. And thus, since amber is called
elektron,theypasseddowntousnotonlythebeginningofthestudyofelec-
tromagnetism, but also the etymology.
TheChinesedidnotknowaboutelectricity,buttheyknewaboutmag-
nets:probablyboththeyandtheGreeksfoundmagnetitemines(i.e.,amag-
netic iron oxide). But the Chinese also discovered the Earth’s magnetism.
They invented the compass (1000 B.C.), and merchant ships brought it to
the rest of the world.
Nevertheless,theobservationofthingsandtheuseofthemwasnotyeta
science, which is the explanation of the behavior of things and their inclusion in
animageoftheworld.TheGreekshaddonethisinastronomy,butnotinelec-
tricity and magnetism.
j
xi
xii G.Lochak
The science of electricity and magnetism started with André-Marie
Amp(cid:1)ere, and was developed by James Clerk Maxwell, who considered
Amp(cid:1)ere the greatest physicist since Isaac Newton. But then Amp(cid:1)ere
lost that distinction when Einstein declared that the greatest was
actually Maxwell. And Maxwell lost that title to Einstein. Records
are fragile!
Now,itmaybesaidthat,despitethecontributionsfrommanyothersin
these fields, the science of electricity and magnetism owes its fundamental
ideas to three men: Amp(cid:1)ere, Maxwell, and Michael Faraday. Consider the
following points:
1. Starting from experiments of Oersted and others, Amp(cid:1)ere and Faraday
gathered electricity and magnetism in a single doctrine that claims that:
a. An electric current produces magnetism (Amp(cid:1)ere).
b. A variation of magnetism produces electricity (Faraday).
These twostatements are notreciprocal becauseinthefirst case,the
electric current may be static, while in the second case, magnetism
must vary.
2. The next discovery was the notion of field, born in the same years. The
idea appeared in two steps:
a. At first, Amp(cid:1)ere’s and Faraday’s attention was drawn to the lines of
magnetic or electric forces. Amp(cid:1)ere based his “Electrodynamics“
on the interactions between small elements of currents and intro-
ducedavector,knowninFrenchasthedirectrice,whichtodayiscalled
the magnetic field.
Faradayobservedfiguresdrawnbyironfilingsscatteredonasheetof
paperaboveamagnet.Heinterpretedthemaslinesofforceandthen
as lines of field, a concept that is now taught in every textbook.
b. The second step is due to Faraday alone.He introduced theentirely
new idea that an electric or a magnetic force acts owing to a new
property of the surrounding space: the electromagnetic field.
This idea required a new type of mathematics that was capable of gath-
eringelectricandmagneticpropertiesinanewimageoftheworld.Thiswas
theachievementofMaxwell’sequations,whichareengravedintothepan-
theonof science and are theobject of universal admiration,as expressed by
Ludwig Boltzmann in his Treatise of Electromagnetism, quoting a verse of
Foreword xiii
Goethe’sFaust:“WareseinGottderdiesenZeilenschrieb?”(Wasitagodwho
wrote down these signs?)1.
Thus, beside the empty world inherited from Democritus, filled with
material points obeying Newton’s laws of mechanics, appeared another
physical world: a resurgence of the world of Anaxagoras, filled with fields.
Maxwell’s equations became the counterpart of Newton’s mechanics. But
these contradictory worlds were destined to concur as follows:
(cid:129) In1905,theEinsteinphotonbroughtthecorpusclesbackintothetheoryof
light,fromwhichtheyhadbeenexpelledbythewavetheoryofMaxwell,
ChristiaanHuygens,and Augustin-JeanFresnel.Einsteinprovedthatthe
still-mysteriousphotoelectriceffectwasaconsequenceofhishypothesis.
(cid:129) Conversely,in1923,LouisdeBrogliediscoveredthatmaterialcorpuscles
havewaveproperties.Hegavethefirstformulasformatterwaves,inter-
pretedthespectrumofNielsBohr’satomintermsofstationaryelectron
waves, and predicted the diffraction of electrons. Matter and Light, the
titleofoneofhisbooks,becamethesymbolofthenewquantumworld:
wave-particle dualism.
2. THE FATHERS OF THE MAGNETIC MONOPOLE
2.1 Maxwell (1873)
We have already noted the absence of symmetry between the Amp(cid:1)ere and
Faradaylaws,whichfavorselectricity,sincewecancreatemagnetismwitha
stationaryelectriccurrent(theelectromagnet),whereasweneedavariation
ofmagnetismtocreateanelectriccurrent(Faraday’sinduction).Thisasym-
metryoccursbecausewecanproduceanelectriccurrent,butnotamagnetic
current.
1 ConcerningMaxwell’sequations,thereisaninterestingstory.WhenFaradayannouncedhislawof
induction,nobodybelievedinitbecause,unlikeAmp(cid:1)ere’slaw,itwasnotbetweentime-independent
physicalquantities,butratherincludedthetimevariationofamagneticfield.Thiswascomplete
nonsense:howcouldthevariationofafieldproduceaneffect?Ittookalongtimebeforetheyoung
MaxwellbroughtthelawsofAmp(cid:1)ere,Faraday,andCoulombintoasetofequations,andhe
discoveredthatsomethingwasinconsistent,notinFaraday’slawbutinAmp(cid:1)ere’slawdnamely,that
atermdependingontimewasmissing.Hecreatedthisterm(thedisplacementcurrent),andhis
equationsbecamethecelebratedMaxwellequations,whichledtotheelectromagnetictheoryof
lightand,later,toradiowaves.Thesecondresultofthisstorywillbediscussedelsewhereinthis
book:muchlater,in1934,LouisdeBrogliepublishedtheequationofthephoton,consideredasthe
fusionoftwoDiracparticles,andhederivedfromquantummechanicstheMaxwellequations
withoutaddinganydisplacementcurrent,whichappearsautomaticallyasaconsequenceof
relativisticsymmetry.
xiv G.Lochak
Nevertheless,in1785,Charles-Augustin deCoulombmeasured hislaw
offorcein1=r2,notonlyforelectricchargesbutformagneticchargeseven
though he possessed only what he called “electric poles “ (small, charged
objects), but no “magnetic poles.” So he used long magnetic wires, whose
extremities could not interact, as Maxwell explained in his Treatise on Elec-
tricity and Magnetism.
Maxwell gave a central place to Coulomb’s law not only for electricity,
but also for magnetism. Magnetic poles are described at the beginning of
volume 2 of his Treatise, which shows that electric and magnetic charges
havethesamephysicaldimensionsandarethusexpressedinthesameunits.
But neither in the electric case nor in the magnetic case are particles men-
tionedinthesensethatwenowunderstandthem(aslocalizedmicroobjects).
Theexperimentaldiscoveryoftheelectronasaparticledthefruitofnumer-
ous worksdwas announced by J. J. Thomson in 1897. A first theory came
fromHendrikLorentzatthistime,butthetruetheorycamelater,withthe
Dirac equation in 1928.
TheMaxwellpoleswereonlyaroughdraft,butMaxwellwasthefirstto
understand that vectors representing electricity and magnetism are of a dif-
ferentnature.Thefirstisapolarvector,ofthesamekindasavelocity,while
the second is an axial vector of the same kind as a rotation axis.
Despitesomeanalogies,electricityandmagnetismarefundamentallydif-
ferent; this difference appears in their symmetry properties. The image of a
magnetic field in a mirror perpendicular to it is the field itself, while the
image of an electric field perpendicular to a mirror is inverted. That is,
theimageisthemirrorimageoftheobject.Conversely,theimageofamag-
neticfieldparalleltoamirrorisparalleltothefield,butinverted,whilethe
image of an electric field parallel to a mirror is the field itself.
In other words, there is no exact analogy between electricity and mag-
netism, contrary to what is often claimed and to the analogy falsely attrib-
uted to Maxwell’s equations. These errors arise because polar and axial
vectorsarerepresentedbythesamesymbols.Maxwellknewthis,andPierre
Curie tried to impose different notations for these reasons, but in vain.
Through the discovery (quickly forgotten!) of the difference between
polar and axial vectors, Maxwell was the second (after Louis Pasteur) to
approach the fundamental property of enantiomorphism, or chirality; i.e., the
difference between left and right, such as the left and right hands. Chiral
comes from the Greek kheir (hand).
Actually, Pasteur was the first to discover this phenomenon in another
field, not in electromagnetism but in crystallography. He discovered that
Foreword xv
therearetwokindsofcrystalsoftartaricacid:leftandright.Eachofthemis
not its own mirror image, but the image of the other in a mirror, like two
hands.WhenPasteurmadethisdiscovery,hewasstillastudentattheEcole
Normale Supérieure. In a state of great excitement, he immediately went
out of the room where he worked, declaring with enthusiasm in the corri-
dor, “The Universe is not symmetric to itself !” He was immediately con-
vinced of the universal character of his result. And when he said that to
his old master, Jean-Baptiste Biot, the latter replied: “I am moved to tears
by what you are telling me !”
ThisdiscoverylayattheoriginofthebiologicalachievementsofPasteur,
anditmustberememberedthatafewyearsbeforetheselineswerewritten,a
Nobel Prize was awarded to William Knowles, Ryoji Noyori and Barry
Sharpless for a discovery of great importance for medicine: the chiral cata-
lysts,abletoseparateleftandrightsyntheticmolecules.Awholegeneration
remembersthedramaofamildlysedativemedicine,thalidomide,prescribed
to pregnant women, who gave birth to children without arms or legs as a
result of the drug. The reason for this was that the synthetic molecules
were a mixture of left and right molecules, one group of which (and only
one)beingteratogenic.Andweshallseewhatfollowedfromthediscovery
ofchiralityinphysics:ithappenedthatbetaradioactivityischiraltoo,andit
introduces enantiomorphism just like tartaric acid and magnetism.
Inmyopinion,itmaybeassertedthatPasteurandMaxwell,intwodif-
ferent fields of science, discovered in enantiomorphism one of the most
importantresultsofthe19thcentury.Thefollowingstepwasthediscovery,
byLeeandYang,in1956,ofthe“non-conservationofparity”(asomewhat
barbaric name for chirality) of weak interactions. This was the last physical
discovery to change our physical image of the world. But between Pasteur
andMaxwellandthisdiscovery,therewereseveralgreatcontributors:Pierre
Curie, Henri Poincaré, and Paul Dirac.
2.2 Pierre Curie (1894)
PierreCuriewasoneofthegreatsuccessorstoMaxwellinthefieldofelec-
tromagnetism. He knew even better than Maxwell the difference between
electricityandmagnetism,andheprovedthatthisdifferenceisofageomet-
ric natureandconcernsgeneralsymmetry laws. Hepublishedapapertitled
“On the Symmetry of Physical Phenomena, the Symmetry of Electric and
MagneticFields,”whichwasthefirstgeneralpaperonasubjectthatwould
dominate physics in the 20th century.
