Basic Concepts in Physics: From the Cosmos to Quarks

385 Pages·2014·6.19 MB·English

by  Masud Chaichian

Undergraduate Lecture Notes in Physics
Masud Chaichian
Hugo Perez Rojas
Anca Tureanu
Basic Concepts
in Physics
From the Cosmos to Quarks
Undergraduate Lecture Notes in Physics
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M. Chaichian H. Perez Rojas A. Tureanu
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Basic Concepts in Physics
From the Cosmos to Quarks
123
M.Chaichian A.Tureanu
UniversityofHelsinki UniversityofHelsinki
DepartmentofPhysics DepartmentofPhysics
Helsinki Helsinki
Finland Finland
H.PerezRojas
ICIMAF
DepartmentofTheoreticalPhysics
LaHabana
Cuba
ISBN978-3-642-19597-6 ISBN978-3-642-19598-3(eBook)
DOI10.1007/978-3-642-19598-3
SpringerHeidelbergNewYorkDordrechtLondon
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Preface
Thisbookistheoutcomeofmanylectures,seminars,andcolloquiatheauthorshave
givenondifferentoccasionstodifferentaudiencesinseveralcountriesoveralong
periodof time and the experienceand feedbackobtained fromthem. With a wide
range of readers in mind, some topics have been presented in twofold form, both
descriptivelyandmoreformally.
Thisbookisintendednotonlyforfirsttosecondyearundergraduatestudents,as
acomplementtospecializedtextbooksbutalsoforphysicsteachersandstudentsin
highschools.Atthesametime,itisaddressedtoresearchersandscientistsinother
fields,includingengineersandgeneralreadersinterestedinacquiringanoverview
ofmodernphysics.Aminimalmathematicalbackground,uptoelementarycalculus,
matrixalgebraandvectoranalysis,isrequired.However,mathematicaltechnicali-
tieshavenotbeenstressed,andlongcalculationshavebeenavoided.Thebasicand
most important ideas have been presented with a view to introducing the physi-
cal conceptsin a pedagogicalway. Since some specific topics of modernphysics,
particularlythoserelatedtoquantumtheory,areanimportantingredientofstudent
coursesnowadays,thefirstfivechaptersonclassicalphysicsarepresentedkeeping
inmindtheirconnectiontomodernphysicswheneverpossible.
In most chapters, historical facts are included. Several themes are discussed
whicharesometimesomittedinbasiccoursesonphysics.Forinstance,therelation
betweenentropyandinformation,exchangeenergyandferromagnetism,supercon-
ductivity and the relation between phase transitions and spontaneous symmetry
breaking,chirality,thefundamentalC,P,andT invariances,paradoxesofquantum
theory,theproblemofmeasurementinquantummechanics,quantumstatisticsand
specific heat in solids, quantum Hall effect, graphene, general relativity and cos-
mology, CP violation, Casimir and Aharonov–Bohm effects, causality, unitarity,
spontaneoussymmetry breaking and the Standard Model, inflation, baryogenesis,
andnucleosynthesis,endingwithachapterontherelationshipbetweenphysicsand
life,includingbiologicalchiralsymmetrybreaking.
Tonon-specializedreadersitisrecommendedtobypass,atleastonafirstread-
ing, the mathematical content of sections and subsections 1.8, 1.9, 2.5, 3.11, 4.5,
6.7,6.8.1,7.3,7.4.1,8.2,10.3,and10.5.
Duringthepreparationofthisbooktheauthorshavebenefitedgreatlyfromdis-
cussions with many of their colleagues and students, to whom we are indebted.
v
vi Preface
ItisapleasuretoexpressourgratitudeinparticulartoCristianArmendariz-Picon,
AlexanderD.Dolgov,JosefKluson,VladimirM.Mostepanenko,MarkkuOksanen,
Roberto Sussmann, and Ruibin Zhang for their stimulating suggestions and com-
ments, while our special thanks go to Tiberiu Harko, Peter Prešnajder and Daniel
Radu,towhomwearemostgratefulfortheirvaluableadviceinimprovinganinitial
versionofthemanuscript.
Helsinki,Finland MasudChaichian
LaHabana,Cuba HugoPerezRojas
Helsinki,Finland AncaTureanu
March2013
Contents
1 GravitationandNewton’sLaws ............................................ 1
1.1 FromPythagorastotheMiddleAges................................ 2
1.2 Copernicus,Kepler,andGalileo ..................................... 6
1.3 NewtonandModernScience......................................... 13
1.4 Newton’sLaws........................................................ 15
1.4.1 Newton’sFirstLaw ......................................... 15
1.4.2 Newton’sSecondLaw ...................................... 15
1.4.3 PlanetaryMotioninNewton’sTheory..................... 24
1.4.4 Newton’sThirdLaw ........................................ 26
1.5 ConservationLaws.................................................... 27
1.5.1 ConservationofLinearMomentum........................ 28
1.5.2 ConservationofAngularMomentum...................... 29
1.5.3 ConservationofEnergy..................................... 31
1.6 DegreesofFreedom .................................................. 35
1.7 InertialandNon-inertialSystems.................................... 36
1.8 ThePrincipleofLeastAction........................................ 40
1.9 HamiltonEquations................................................... 43
Literature....................................................................... 45
2 Entropy,StatisticalPhysics,andInformation............................. 47
2.1 ThermodynamicApproach........................................... 48
2.1.1 FirstLawofThermodynamics.............................. 49
2.1.2 SecondLawofThermodynamics .......................... 49
2.1.3 ThirdLawofThermodynamics ............................ 51
2.1.4 ThermodynamicPotentials ................................. 51
2.2 StatisticalApproach .................................................. 52
2.3 EntropyandStatisticalPhysics....................................... 58
2.4 TemperatureandChemicalPotential ................................ 60
2.5 StatisticalMechanics ................................................. 60
2.5.1 CanonicalEnsemble ........................................ 62
2.5.2 MaxwellDistribution ....................................... 68
2.5.3 GrandCanonicalEnsemble................................. 70
2.6 EntropyandInformation ............................................. 70
vii
viii Contents
2.7 Maxwell’sDemonandPerpetuumMobile .......................... 72
Literature....................................................................... 78
3 ElectromagnetismandMaxwell’sEquations.............................. 81
3.1 Coulomb’sLaw ....................................................... 84
3.2 ElectrostaticandGravitationalFields................................ 86
3.3 Conductors,Semiconductors,andInsulators........................ 87
3.4 MagneticFields....................................................... 88
3.5 MagneticFlux......................................................... 89
3.6 Maxwell’sEquations.................................................. 91
3.6.1 Gauss’sLawforElectricFields ............................ 91
3.6.2 Gauss’sLawforMagnetism................................ 92
3.6.3 Faraday’sLaw............................................... 94
3.6.4 Ampère–MaxwellLaw...................................... 95
3.7 LorentzForce ......................................................... 96
3.8 FieldsinaMedium ................................................... 99
3.9 MagneticProperties...................................................102
3.9.1 Diamagnetism...............................................103
3.9.2 Paramagnetism ..............................................103
3.9.3 Ferromagnetism.............................................103
3.9.4 Ferrimagnetism, Antiferromagnetism,
andMagneticFrustration ...................................105
3.9.5 SpinIcesandMonopoles...................................106
3.10 PhaseTransitions .....................................................106
3.11 SpontaneousSymmetryBreaking....................................107
3.12 Superconductivity.....................................................109
3.13 MeissnerEffect:TypeIandIISuperconductors ....................110
Literature.......................................................................111
4 ElectromagneticWaves ......................................................113
4.1 WavesinaMediumandinÆther....................................114
4.2 ElectromagneticWavesandMaxwell’sEquations..................115
4.2.1 WavePropagation...........................................117
4.2.2 Coherence ...................................................118
4.3 GenerationofElectromagneticWaves...............................119
4.3.1 Retardedpotentials..........................................119
4.3.2 Mechanismsgeneratingelectromagneticwaves...........120
4.4 WaveProperties.......................................................121
4.4.1 Interference..................................................121
4.4.2 Diffraction...................................................124
4.4.3 Polarization..................................................128
4.4.4 SpectralComposition.......................................130
4.5 FourierSeriesandIntegrals ..........................................133
4.6 ReflectionandRefraction.............................................135
4.7 DispersionofLight ...................................................137
Contents ix
4.8 BlackBodyRadiation ................................................138
Literature.......................................................................141
5 SpecialTheoryofRelativity.................................................143
5.1 PostulatesofSpecialRelativity ......................................143
5.2 LorentzTransformations .............................................147
5.3 LightConeandCausality.............................................150
5.4 ContractionofLengths ...............................................152
5.5 TimeDilation:ProperTime..........................................153
5.6 AdditionofVelocities.................................................156
5.7 RelativisticFour-Vectors .............................................156
5.8 ElectrodynamicsinRelativisticallyCovariantFormalism..........158
5.9 EnergyandMomentum...............................................161
5.10 Photons................................................................162
5.11 Neutrinos..............................................................163
5.12 TachyonsandSuperluminalSignals .................................164
Literature.......................................................................166
6 AtomsandQuantumTheory................................................167
6.1 MotionofaParticle...................................................167
6.2 EvolutionoftheConceptofAtom...................................170
6.3 Rutherford’sExperiment .............................................170
6.4 Bohr’sAtom...........................................................171
6.5 Schrödinger’sEquation...............................................174
6.6 WaveFunction ........................................................177
6.7 OperatorsandStatesinQuantumMechanics........................184
6.8 QuantumHarmonicOscillator .......................................188
6.8.1 Schrödinger’sEquationfortheHarmonicOscillator......189
6.8.2 LadderOperators............................................191
6.9 EmissionandAbsorptionofRadiation ..............................193
6.10 StimulatedEmissionandLasers .....................................194
6.11 TunnelEffect..........................................................194
6.12 IndistinguishabilityandPauli’sPrinciple............................195
6.13 ExchangeInteraction .................................................197
6.14 ExchangeEnergyandFerromagnetism..............................198
6.15 DistributionofElectronsintheAtom................................199
6.16 QuantumMeasurement...............................................200
6.16.1 UandREvolutionProcedures .............................201
6.16.2 OnTheoryandObservableQuantities.....................202
6.17 ParadoxesinQuantumMechanics...................................203
6.17.1 DeBroglie’sParadox .......................................203
6.17.2 Schrödinger’sCatParadox..................................204
6.17.3 TowardtheEPRParadox ...................................205
6.17.4 AHiddenVariableModelandBell’sTheorem............207