Einstein's physics [electronic resource] : atoms, quanta, and relativity - derived, explained, and appraised / Ta-Pei Cheng

Author:: Cheng, Ta-Pei
Published:: Oxford : Oxford University Press, 2013.
Physical Description:: 1 online resource : illustrations

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Machine generated contents note: pt. I ATOMIC NATURE OF MATTER -- 1.Molecular size from classical fluids -- 1.1.Two relations of molecular size and the Avogadro number -- 1.2.The relation for the effective viscosity -- 1.2.1.The equation of motion for a viscous fluid -- 1.2.2.Viscosity and heat loss in a fluid -- 1.2.3.Volume fraction in terms of molecular dimensions -- 1.3.The relation for the diffusion coefficient -- 1.3.1.Osmotic force -- 1.3.2.Frictional drag force---the Stokes law -- 1.4.SuppMat: Basics of fluid mechanics -- 1.4.1.The equation of continuity -- 1.4.2.The Euler equation for an ideal fluid -- 1.5.SuppMat: Calculating the effective viscosity -- 1.5.1.The induced velocity field v' -- 1.5.2.The induced pressure field p' -- 1.5.3.Heat dissipation in a fluid with suspended particles -- 1.6.SuppMat: The Stokes formula for the viscous force -- 2.The Brownian motion -- 2.1.Diffusion and Brownian motion -- 2.1.1.Einstein's statistical derivation of the diffusion equation -- 2.1.2.The solution of the diffusion equation and the mean-square displacement -- 2.2.Fluctuations of a particle system -- 2.2.1.Random walk -- 2.2.2.Brownian motion as a random walk -- 2.3.The Einstein--Smoluchowski relation -- 2.3.1.Fluctuation and dissipation -- 2.3.2.Mean-square displacement and molecular dimensions -- 2.4.Perrin's experimental verification -- pt. II QUANTUM THEORY -- 3.Blackbody radiation: From Kirchhoff to Planck -- 3.1.Radiation as a collection of oscillators -- 3.1.1.Fourier components of radiation obey harmonic oscillator equations -- 3.2.Thermodynamics of blackbody radiation -- 3.2.1.Radiation energy density is a universal function -- 3.2.2.The Stefan--Boltzmann law -- 3.2.3.Wien's displacement law -- 3.2.4.Planck's distribution proposed -- 3.3.Planck's investigation of cavity oscillator entropy -- 3.3.1.Relating the oscillator energy to the radiation density -- 3.3.2.The mean entropy of an oscillator -- 3.4.Planck's statistical analysis leading to energy quantization -- 3.4.1.Calculating the complexion of Planck's distribution -- 3.4.2.Planck's constant and Boltzmann's constant -- 3.4.3.Planck's energy quantization proposal---a summary -- 3.5.SuppMat: Radiation oscillator energy and frequency -- 3.5.1.The ratio of the oscillator energy and frequency is an adiabatic invariant -- 3.5.2.The thermodynamic derivation of the relation between radiation pressure and energy density -- 4.Einstein's proposal of light quanta -- 4.1.The equipartition theorem and the Rayleigh--Jeans law -- 4.1.1.Einstein's derivation of the Rayleigh--Jeans law -- 4.1.2.The history of the Rayleigh--Jeans law and "Planck's fortunate failure" -- 4.1.3.An excursion to Rayleigh's calculation of the density of wave states -- 4.2.Radiation entropy and complexion a la Einstein -- 4.2.1.The entropy and complexion of radiation in the Wien limit -- 4.2.2.The entropy and complexion of an ideal gas -- 4.2.3.Radiation as a gas of light quanta -- 4.2.4.Photons as quanta of radiation -- 4.3.The photoelectric effect -- 4.4.SuppMat: The equipartition theorem -- 5.Quantum theory of specific heat -- 5.1.The quantum postulate: Einstein vs. Planck -- 5.1.1.Einstein's derivation of Planck's distribution -- 5.2.Specific heat and the equipartition theorem -- 5.2.1.The study of heat capacity in the pre-quantum era -- 5.2.2.Einstein's quantum insight -- 5.3.The Einstein solid---a quantum prediction -- 5.4.The Debye solid and phonons -- 5.4.1.Specific heat of a Debye solid -- 5.4.2.Thermal quanta vs. radiation quanta -- 6.Waves, particles, and quantum jumps -- 6.1.Wave--particle duality -- 6.1.1.Fluctuation theory (Einstein 1904) -- 6.1.2.Energy fluctuation of radiation (Einstein 1909a) -- 6.2.Bohr's atom---another great triumph of the quantum postulate -- 6.2.1.Spectroscopy: Balmer and Rydberg -- 6.2.2.Atomic structure: Thomson and Rutherford -- 6.2.3.Bohr's quantum model and the hydrogen spectrum -- 6.3.Einstein's A and B coefficients -- 6.3.1.Probability introduced in quantum dynamics -- 6.3.2.Stimulated emission and the idea of the laser -- 6.4.Looking ahead to quantum field theory -- 6.4.1.Oscillators in matrix mechanics -- 6.4.2.Quantum jumps: From emission and absorption of radiation to creation and annihilation of particles -- 6.4.3.Resolving the riddle of wave--particle duality in radiation fluctuation -- 6.5.SuppMat: Fluctuations of a wave system -- 7.Bose--Einstein statistics and condensation -- 7.1.The photon and the Compton effect -- 7.2.Towards Bose--Einstein statistics -- 7.2.1.Boltzmann statistics -- 7.2.2.Bose's counting of photon states -- 7.2.3.Einstein's elaboration of Bose's counting statistics -- 7.3.Quantum mechanics and identical particles -- 7.3.1.Wave mechanics: de Broglie--Einstein--Schrodinger -- 7.3.2.Identical particles are truly identical in quantum mechanics -- 7.3.3.Spin and statistics -- 7.3.4.The physical implications of symmetrization -- 7.4.Bose--Einstein condensation -- 7.4.1.Condensate occupancy calculated -- 7.4.2.The condensation temperature -- 7.4.3.Laboratory observation of Bose--Einstein condensation -- 7.5.SuppMat: Radiation pressure due to a gas of photons -- 7.6.SuppMat: Planck's original analysis in view of Bose--Einstein statistics -- 7.7.SuppMat: The role of particle indistinguishability in Bose--Einstein condensation -- 8.Local reality and the Einstein--Bohr debate -- 8.1.Quantum mechanical basics---superposition and probability -- 8.2.The Copenhagen interpretation -- 8.2.1.The Copenhagen vs. the local realist interpretations -- 8.3.EPR paradox: Entanglement and nonlocality -- 8.3.1.The post-EPR era and Bell's inequality -- 8.3.2.Local reality vs. quantum mechanics---the experimental outcome -- 8.4.SuppMat: Quantum mechanical calculation of spin correlations -- 8.4.1.Quantum mechanical calculation of spin average values -- 8.4.2.Spin correlation in one direction -- 8.4.3.Spin correlation in two directions -- pt. III SPECIAL RELATIVITY -- 9.Prelude to special relativity -- 9.1.Relativity as a coordinate symmetry -- 9.1.1.Inertial frames of reference and Newtonian relativity -- 9.2.Maxwell's equations -- 9.2.1.The electromagnetic wave equation -- 9.2.2.Aether as the medium for electromagnetic wave propagation -- 9.3.Experiments and theories prior to special relativity -- 9.3.1.Stellar aberration and Fizeau's experiment -- 9.3.2.Lorentz's corresponding states and local time -- 9.3.3.The Michelson--Morley experiment -- 9.3.4.Length contraction and the Lorentz transformation -- 9.3.5.Poincare and special relativity -- 9.4.Reconstructing Einstein's motivation -- 9.4.1.The magnet and conductor thought experiment -- 9.4.2.From "no absolute time" to the complete theory in five weeks -- 9.4.3.Influence of prior investigators in physics and philosophy -- 9.5.SuppMat: Lorentz transformation a la Lorentz -- 9.5.1.Maxwell's equations are not Galilean covariant -- 9.5.2.Lorentz's local time and noncovariance at O(v2/c2) -- 9.5.3.Maxwell's equations are Lorentz covariant -- 10.The new kinematics and E = mc2 -- 10.1.The new kinematics -- 10.1.1.Einstein's two postulates -- 10.1.2.The new conception of time and the derivation of the Lorentz transformation -- 10.1.3.Relativity of simultaneity, time dilation, and length contraction -- 10.2.The new velocity addition rule -- 10.2.1.The invariant spacetime interval -- 10.2.2.Adding velocities but keeping light speed constant -- 10.3.Maxwell's equations are Lorentz covariant -- 10.3.1.The Lorentz transformation of electromagnetic fields -- 10.3.2.The Lorentz transformation of radiation energy -- 10.4.The Lorentz force law -- 10.5.The equivalence of inertia and energy -- 10.5.1.Work--energy theorem in relativity -- 10.5.2.The E = mc2 paper three months later -- 10.6.SuppMat: Relativistic wave motion -- 10.6.1.The Fresnel formula from the velocity addition rule -- 10.6.2.The Doppler effect and aberration of light -- 10.6.3.Derivation of the radiation energy transformation -- 10.7.SuppMat: Relativistic momentum and force -- 11.Geometric formulation of relativity -- 11.1.Minkowski spacetime -- 11.1.1.Rotation in 3D space---a review -- 11.1.2.The Lorentz transformation as a rotation in 4D spacetime -- 11.2.Tensors in a flat spacetime -- 11.2.1.Tensor contraction and the metric -- 11.2.2.Minkowski spacetime is pseudo-Euclidean -- 11.2.3.Relativistic velocity, momentum, and energy -- 11.2.4.The electromagnetic field tensor -- 11.2.5.The energy--momentum--stress tensor for a field system -- 11.3.The spacetime diagram -- 11.3.1.Basic features and invariant regions -- 11.3.2.Lorentz transformation in the spacetime diagram -- 11.4.The geometric formulation---a summary -- pt. IV GENERAL RELATIVITY -- 12.Towards a general theory of relativity -- 12.1.Einstein's motivations for general relativity -- 12.2.The principle of equivalence between inertia and gravitation -- 12.2.1.The inertia mass vs. the gravitational mass -- 12.2.2."My happiest thought" -- 12.3.Implications of the equivalence principle -- 12.3.1.Bending of a light ray -- 12.3.2.Gravitational redshift -- 12.3.3.Gravitational time dilation -- 12.3.4.Gravity-induced index of refraction in free space -- 12.3.5.Light ray deflection calculated -- 12.3.6.From the equivalence principle to "gravity as the structure of spacetime" -- 12.4.Elements of Riemannian geometry -- 12.4.1.Gaussian coordinates and the metric tensor -- 12.4.2.Geodesic equation -- 12.4.3.Flatness theorem -- 12.4.4.Curvature -- 13.Curved spacetime as a gravitational field -- 13.1.The equivalence principle requires a metric description of gravity -- 13.1.1.What is a geometric theory? -- 13.1.2.Time dilation as a geometric effect -- 13.1.3.Further arguments for warped spacetime as the gravitational field -- 13.2.General relativity as a field theory of gravitation -- 13.2.1.The geodesic equation as the general relativity equation of motion -- 13.2.2.The Newtonian limit -- 13.3.Tensors in a curved spacetime -- 13.3.1.General coordinate transformations -- and Contents note continued: 13.3.2.Covariant differentiation -- 13.4.The principle of general covariance -- 13.4.1.The principle of minimal substitution -- 13.4.2.Geodesic equation from the special relativity equation of motion -- 14.The Einstein field equation -- 14.1.The Newtonian field equation -- 14.2.Seeking the general relativistic field equation -- 14.3.Curvature tensor and tidal forces -- 14.3.1.Tidal forces---a qualitative discussion -- 14.3.2.Newtonian deviation equation and the equation of geodesic deviation -- 14.3.3.Symmetries and contractions of the curvature tensor -- 14.3.4.The Bianchi identities and the Einstein tensor -- 14.4.The Einstein equation -- 14.4.1.The Newtonian limit for a general source -- 14.4.2.Gravitational waves -- 14.5.The Schwarzschild solution -- 14.5.1.Three classical tests -- 14.5.2.Black holes---the full power and glory of general relativity -- 15.Cosmology -- 15.1.The cosmological principle -- 15.1.1.The Robertson--Walker spacetime -- 15.1.2.The discovery of the expanding universe -- 15.1.3.Big bang cosmology -- 15.2.Time evolution of the universe -- 15.2.1.The FLRW cosmology -- 15.2.2.Mass/energy content of the universe -- 15.3.The cosmological constant -- 15.3.1.Einstein and the static universe -- 15.3.2.The Inflationary epoch -- 15.3.3.The dark energy leading to an accelerating universe -- pt. V WALKING IN EINSTEIN'S STEPS -- 16.Internal symmetry and gauge interactions -- 16.1.Einstein and the symmetry principle -- 16.2.Gauge invariance in classical electromagnetism -- 16.2.1.Electromagnetic potentials and gauge transformation -- 16.2.2.Hamiltonian of a charged particle in an electromagnetic field -- 16.3.Gauge symmetry in quantum mechanics -- 16.3.1.The minimal substitution rule -- 16.3.2.The gauge transformation of wavefunctions -- 16.3.3.The gauge principle -- 16.4.Electromagnetism as a gauge interaction -- 16.4.1.The 4D spacetime formalism recalled -- 16.4.2.The Maxwell Lagrangian density -- 16.4.3.Maxwell equations from gauge and Lorentz symmetries -- 16.5.Gauge theories: A narrative history -- 16.5.1.Einstein's inspiration, Weyl's program, and Fock's discovery -- 16.5.2.Quantum electrodynamics -- 16.5.3.QCD as a prototype Yang--Mills theory -- 16.5.4.Hidden gauge symmetry and the electroweak interaction -- 16.5.5.The Standard Model and beyond -- 17.The Kaluza--Klein theory and extra dimensions -- 17.1.Unification of electrodynamics and gravity -- 17.1.1.Einstein and unified field theory -- 17.1.2.A geometric unification -- 17.1.3.A rapid review of electromagnetic gauge theory -- 17.1.4.A rapid review of general relativistic gravitational theory -- 17.2.General relativity in 5D spacetime -- 17.2.1.Extra spatial dimension and the Kaluza--Klein metric -- 17.2.2."The Kaluza--Klein miracle" -- 17.3.The physics of the Kaluza--Klein spacetime -- 17.3.1.Motivating the Kaluza--Klein metric ansatz -- 17.3.2.Gauge transformation as a 5D coordinate change -- 17.3.3.Compactified extra dimension -- 17.3.4.Quantum fields in a compactified space -- 17.4.Further theoretical developments -- 17.4.1.Lessons from Maxwell's equations -- 17.4.2.Einstein and mathematics -- 17.5.SuppMat: Calculating the 5D tensors -- 17.5.1.The 5D Christoffel symbols -- 17.5.2.The 5D Ricci tensor components -- 17.5.3.From 5D Ricci tensor to 5D Ricci scalar -- pt. VI APPENDICES -- A.Mathematics supplements -- A.1.Vector calculus -- A.1.1.The Kronecker delta and Levi-Civita symbols -- A.1.2.Differential calculus of a vector field -- A.1.3.Vector integral calculus -- A.1.4.Differential equations of Maxwell electrodynamics -- A.2.The Gaussian integral -- A.3.Stirling's approximation -- A.3.1.The integral representation for n! -- A.3.2.Derivation of Stirling's formula -- A.4.Lagrangian multipliers -- A.4.1.The method -- A.4.2.Some examples -- A.5.The Euler--Lagrange equation -- A.5.1.Mechanics of a single particle -- A.5.2.Lagrangian density of a field system -- B.Einstein's papers -- B.1.Einstein's journal articles cited in the text -- B.2.Further reading -- C.Answers to the 21 Einstein questions -- Glossary of symbols and acronyms -- 1.Latin symbols -- 2.Greek symbols -- 3.Acronyms -- 4.Miscellaneous units and symbols.

Summary:

Many regard Albert Einstein as the greatest physicist since Newton. What exactly did he do that is so important in physics? We provide an introduction to his physics at a level accessible to an undergraduate physics student. All equations are worked out in detail from the beginning.

Subject(s):

ISBN:

9780191744488 (ebook)

Note:

Includes index.

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