The Unity of Science

391 Pages·2021·29.701 MB·English

by  David Bensimon

The Unity of Science

The Unity of Science
David Bensimon
First edition published 2022
by CRC Press
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© 2022 David Bensimon
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Library of Congress Cataloging-in-Publication Data
Names: Bensimon, David, author.
Title: The unity of science / David Bensimon.
Description: Boca Raton : Taylor and Francis, 2021. | Includes
bibliographical references and index.
Identifiers: LCCN 2021035071 (print) | LCCN 2021035072 (ebook) | ISBN
9781032112404 (hardback) | ISBN 9781032112411 (paperback) | ISBN
9781003218999 (ebook)
Subjects: LCSH: Science--Philosophy. | Science.
Classification: LCC Q175 .B458 2021 (print) | LCC Q175 (ebook) | DDC
501--dc23
LC record available at https://lccn.loc.gov/2021035071
LC ebook record available at https://lccn.loc.gov/2021035072
ISBN: 9781032112404 (hbk)
ISBN: 9781032112411 (pbk)
ISBN: 9781003218999 (ebk)
DOI: 10.1201/9781003218999
Typeset in Nimbus font
by KnowledgeWorks Global Ltd.
Dedication
Tothefutureenlightenmentofmygrand-children.

Contents
Preface.....................................................................................................................xiii
Acknowledgements..................................................................................................xv
Chapter1 TheUnityofScience......................................................................1
1.1 Introduction...........................................................................1
1.2 TheInventionofMathematics.............................................3
Chapter2 ClassicalMechanics.....................................................................11
2.1 (cid:95)Newton’sLawsofMotion...............................................11
2.2 (cid:95)Newton’sLawofGravitation.........................................16
2.2.1 GravitationalPotentialandEnergyConservation....18
Chapter3 Electromagnetism........................................................................21
3.1 (cid:95) Electrostatics..................................................................21
3.1.1 (cid:95) Coulomb’sLaw...................................................22
3.1.2 ApplicationsofCoulomb’sLaw..............................25
3.1.2.1 Lightning.................................................25
3.1.2.2 TheFieldofaDipole...............................26
3.1.2.3 Piezo-Electricity......................................28
3.1.3 (cid:95) Gauss’sTheorem.................................................29
3.1.4 ApplicationsofGauss’stheorem.............................31
3.1.4.1 TheCapacitor..........................................31
3.1.4.2 MeasuringtheChargeoftheElectron.....32
3.1.4.3 TheElectrostaticLens.............................33
3.1.5 SolvingPoisson’sEquation.....................................34
3.1.5.1 TheMethodofImages.............................35
3.1.6 ElectricFieldinMatter:Dielectrics.........................37
3.2 (cid:95)Magnetostatics.................................................................39
3.2.1 (cid:95) Volta’sBatteryandOhm’sLaw..........................39
3.2.2 (cid:95)Electrostatics,MagnetostaticsandRelativity:
theLorentzForce.....................................................43
3.2.3 ApplicationsoftheLorentzForce...........................45
3.2.3.1 AuroraBorealis.......................................45
3.2.3.2 TheParticleAccelerator..........................47
3.2.3.3 ThePenningtrap......................................49
3.2.4 (cid:95) Ampe`re’sLaw.....................................................49
vii
viii Contents
3.2.5 ApplicationsofAmpe`re’sLaw................................51
3.2.5.1 MagneticFieldofaCurrentSegment.....51
3.2.5.2 MagneticFieldofaCurrentLoop...........52
3.2.5.3 TheSolenoid............................................53
3.2.5.4 D’Arsonval’sGalvanometer....................55
3.2.6 Magnetic Fields in Matter: Permeability and
PermanentMagnets..................................................55
3.3 (cid:95)ElectromagneticInduction.............................................57
3.3.1 (cid:95) Faraday’sLaw.....................................................57
3.3.2 ApplicationsofFaraday’sLaw................................60
3.3.2.1 Inductance................................................60
3.3.2.2 TheElectricTransformer.........................60
3.3.2.3 Electric Motor and Alternating Cur-
rent(AC)Generator.................................61
3.3.2.4 ElectronicCircuits...................................62
3.4 (cid:95)Maxwell’sEquations.......................................................66
3.4.1 (cid:95) EnergyConservationandRadiatedPower..........70
3.4.2 ApplicationsofMaxwell’sEquations......................72
3.4.2.1 TheRadiatingDipole..............................72
3.4.2.2 TheDipoleAntenna................................73
3.4.2.3 TheParadoxofAtomicStability.............76
3.4.2.4 TheColoroftheSky...............................76
3.4.2.5 The Doppler-Fizeau Effect and the
ExpansionoftheUniverse.......................78
3.4.2.6 TheDarknessofNight.............................79
3.5 Optics...................................................................................80
3.5.1 ElectromagneticWavesinMatter:Refraction.........81
3.5.2 Fermat’sPrinciple....................................................85
3.5.2.1 GeometricalOptics..................................86
3.5.3 Diffraction................................................................89
3.5.4 DispersionofLightandtheColorsoftheRainbow92
Chapter4 QuantumMechanics...................................................................97
4.1 (cid:95)ThePuzzlesofMatterandRadiation...........................98
4.1.1 (cid:95) Black-BodyRadiation.......................................100
4.1.1.1 TheSunandEarthTemperatures...........103
4.1.1.2 TheUniverseasaPerfectBlack-Body..104
4.1.2 ThePhoto-ElectricEffect.......................................106
4.1.2.1 DigitalCamerasandSolarCells............107
4.1.3 Bohr’sAtomandtheSpectrumofHydrogen........107
4.1.3.1 Particle-WaveDuality............................108
4.1.3.2 The Bohr-Sommerfeld Quantization
Rule........................................................109
4.1.4 AbsorptionandStimulatedEmission....................109
Contents ix
4.2 (cid:95)QuantumMechanicalFormalism................................112
4.2.1 (cid:95) Example:ParticleinaBox................................118
4.3 SimpleQMsystems...........................................................120
4.3.1 TheChiralAmmoniaMolecule.............................120
4.3.1.1 Schro¨dinger’sCat..................................122
4.3.1.2 Bell’sInequalities..................................124
4.3.2 TheAmmoniaMoleculeinanElectricField.........124
4.3.2.1 TheAmmoniaMaser.............................125
4.3.3 TheEnergySpectrumofAromaticMolecules......128
4.3.4 ConductionBandsinSolids...................................129
4.4 (cid:95)Momentum,SpaceandEnergyOperators.................133
4.4.1 (cid:95) HeisenbergUncertaintyPrinciple.....................136
4.5 (cid:95)Schro¨dinger’sEquation................................................137
4.5.1 Particle-WaveDuality:Diffraction.........................137
4.5.2 ParticleInterferenceObservedwithBuckyballs....139
4.5.3 Particle-WaveDuality:Refraction.........................140
4.5.4 TheScanningTunnelingMicroscope....................142
4.5.5 (cid:95) TheCorrespondencePrinciple..........................144
4.6 (cid:95)Dirac’sEquation:AntiparticlesandSpin...................146
4.6.1 SpinandMagneticDipole.....................................149
4.6.2 Antiparticles...........................................................151
4.7 AngularMomentumWavefunction................................153
4.8 (cid:95)TheHydrogenAtomandElectronicOrbitals............155
4.9 (cid:95)ManyElectronSystems................................................157
4.9.1 (cid:95) ThePeriodicTableoftheElements..................158
4.10 TheChemicalBond..........................................................162
4.10.1 VariationalApproachtoMolecularEnergyLevels163
4.10.1.1 Hu¨ckel’sMolecularOrbitalTheory.......166
4.10.2 MolecularRotationalSpectrum.............................168
4.10.3 MolecularVibrationalSpectrum............................169
4.11 TimeIndependentPerturbationTheory........................172
4.11.1 EnergyLevelsinNon-HydrogenAtoms................174
4.11.2 TheStarkEffect.....................................................175
4.11.2.1 QuantumWells......................................175
4.11.2.2 DiatomicMolecules...............................176
4.11.3 TheZeemanEffect.................................................178
4.11.3.1 MagneticResonanceImaging(MRI)....180
4.12 TimeDependentPerturbationTheory...........................181
4.12.1 TransitionsbetweenElectronicEnergyLevels......183
4.12.2 MolecularRotational-VibrationalTransitions.......185
4.12.3 AbsorptionandFluorescenceEmission.................188
4.12.3.1 Super-ResolutionMicroscopy...............191
4.12.3.2 TheLaser...............................................193