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Ta-Pei Cheng Talk Based on … Ta-Pei Cheng talk based on … Oxford Univ Press (2013) Einstein’s Physics Atoms, Quanta, and Relativity --- Derived, Explained, and Appraised Albert Einstein 1. Atomic Nature of Matter 1879 – 1955 2. Quantum Theory The book 3. Special Relativity explains his physics 4. General Relativity in equations 5. Walking in Einstein’s Steps Today’s talk 1. The quantum postulate: Planck vs Einstein provides w/o math details 2. Einstein & quantum mechanics some highlight 3. Relativity: Lorentz vs Einstein historical context 4. The geometric theory of gravitation & influence 5. Modern gauge theory and unification 3 Einstein, like Planck, arrived at the quantum hypothesis thru the study of BBR Blackbody Radiation cavity radiation = rad in thermal equilibrium ∞ ∞ 2nd law ν u(uT(T) =) =∫ ρρ(T(T,ν,ν)d)νdν KirchhoffTo find the (1860) u(T) and ρ ( T, ) functions:densities u ( T ) and ρ ( T ,ν) 0∫0 Stefan (1878) Boltzmann (1884) law: u(T ) = aT 4 = universal functions rep intrinsic property of radiation Thermodynamics + Maxwell EM (radiation pressure = u/3 ) electromagnetic radiation = a collection of oscillators u = E 2, B 2 ~ oscillator energy kx 2 oscillating energy ~ frequency : Their ratio of is an adiabatic invariant 3 What is the f function? ρ (T ,ν ) =ν f (ν / T ) Wien’s displacement law (1893) Wien’s distribution (1896) : ρ ( T , ν ) = αν 3 e − βν / T fitted data well…. until IR αν 3 ρ(T,ν ) = eβν /T −1 4 αν 3 ρ(T,ν ) = Blackbody Radiation Planck (1900): e βν / T − 1 3 2 U = (c 8/ πν )ρ and dS = dU /T → entropy S ε = nh ν n = 2,1,0 ,... Einstein’s 1905 proposal of light quanta was not a direct follow-up of Planck’s 10 5 Einstein’s 1905 proposal of light quanta ε =hν 3 2 Einstein used Planck’s calculation U = (c 8/ πν )ρ and 1 invoked the equipartition theorem of stat mech U = 2 kT to derive the Rayleigh-Jeans law: ρ = 8πc−3kT ν2 noted its solid theoretical foundation ∞ showing BBR = clear challengebut to classical physics u = ρdν = ∞ poor accounting of the data, notably the problem of ultraviolet catastrophe ∫ 0 Rayleigh-Jeans = the low frequency limit of the successful Planck’s distribution new physics The high frequency limit ( Wien’s distribution )ρ = αν 3e−βν /T Einstein undertook a statistical study of (BBR) wien : instead of W, calculate ∆S due to volume change (BBR) wien ~ ideal gas → (BBR) wien = a gas of light quanta with energy of ε = nh ν Einstein arrived at energy quantization independently ---- cited Planck only in 2 places A year later……Einstein gave a new derivation of Planck’s distribution 6 Einstein’s discoveries in quantum theory (1900) Planck: ε = hν is only Einstein’s(1913) Bohr’s photon quantum idea was jumps strongly describe resisted a formal relation by absorptionthe physics andcommunity emission for of manyphotons years (1905) Einstein: the quantum idea must (1916–17)because Einstein it conflicted construct with athe microscopic known represent new physics theoryevidence of radiation–matterfor the wave nature interaction: of light Millikan, Planck, … proposed photoelectric effect as test (A and B coeff ); The central novelty and beyond BBR : Q theory of specific heat (1907) lasting feature is the introduction of probability in quantum dynamics General acceptance of the photon idea h as conversion factor particle ↔ wave Only after Compton scattering (1924) (1924–25) Bose-Einstein statistics Einstein stated for the 1 st time : & condensation quanta carried by point-like particles “point of view of Newtonian emission theory ” Photon carries energy + momentum p = h / λ 15 7 Einstein & Quantum Mechanics Modern quantum mechanics : states = vectors in Hilbert space (superposition) His discoveries in quantum theory: observables = operators (commutation relations) Wave/particle nature of light, Classical radiation field quantum jumps etc. can all be = collection of oscillators elegantly accounted for in the framework of Quantum radiation field quantum field theory = collection of quantum oscillators E = (n + 1 )hν • A firm mathematical foundation for Einstein’s photon idea n 2 • Quantum jumps naturally accounted for by ladder operators ˆ ˆ ˆ ⇒ particle [a− , a+ ] = hν , a± n ~ n ±1 behavior QFT description broadens the picture of interactions not only can alter motion, but also allows for emission and absorption of radiation → creation and annihilation of particles Alas, Einstein never accepted this neat resolution Beautiful resolution of wave-particle duality as he never accepted ikx in radiation energy fluctuation wave ~ ˆea the new framework of QM 8 Einstein & QM: The debate with Bohr Orthodox interpretation of QM (Niels Bohr & co): the attributes of a physical object (position, momentum, spin, etc.) can be assigned only when they have been measured. Local realist viewpoint of reality (Einstein ,…): a physical object has definite attributes whether they have been measured or not. …. QM is an incomplete theory Einstein, Podolsky & Rosen (1935) : A thought experiment highlighting the “spooky action-at-a-distance ” feature: the measurement of one part of an entangled quantum state would instantaneously produce the value of another part, no matter how far the two parts have been separated. the discussion and debate of “EPR paradox” have illuminated some of the fundamental issues related to the meaning of QM Bell’s theorem (1964) : these seemingly philosophical questions could lead to observable results. The experimental vindication of the orthodox interpretation has sharpened our appreciation of the nonlocal features of quantum mechanics. Einstein’s criticism allowed a deeper understanding of the meaning of QM. Nevertheless, the counter-intuitive picture of objective reality as offered by QM still troubles many, leaving one to wonder whether quantum mechanics is ultimately a complete theory. 20 9 12SR 1 Special Relativity Maxwell’s equations: EM wave – c Contradict relativity? 2 inertial frames x’ = x - vt & d/dt’ = d/dt → velocity addition rule u’ = u - v The then-accepted interpretation: Max eqns valid only in the rest-frame of ether Key Q: How should EM be described for sources and observers moving with respect to the ether-frame ? “The electrodynamics of a moving body” Michelson-Morley null result @ O( v2/c 2) length contraction −1 v v2 x ' = x − vt t'=t − v x x ' = γ (x − vt ) t'= γ t − 2 x γ = 1− 2 [ + a math construct ‘local time ’] c 2 c c Lorentz transformation Maxwell ‘covariant’ to all orders (1904) Still in the framework of ether …Applicable only for EM A very different approach by Einstein… 10 Special Relativity Magnet-conductor thought experiment Einstein’sWith very a differentkeen sense approach of aesthetics … in physics Einstein was troubled by • Dichotomy of matter ~ particles , radiation ~ waves → Light quanta • EM singles out 1 particular frame : the ether frame Relativity is a symmetry in physics Case I : moving charge in B (ether frame) Physics unchanged under some transformation Lorentz force (per unit charge) Relativity = same physics in all coordinate frames f = v × B How to reconcile (Galilean) relativity u’ = u - v e with the constancy of c? Case II : changing B induces an E via Resolution: simultaneity is relative Faraday’s law, resulting exactly the Time is not absolute, but frame dependent t’ ≠ t same force, yet such diff descriptions From this 1905 realization to full theory in 5 weeks 10yrs Relation among inertial frames Seeking a more symmetric picture valid in all frames correctly given by Lorentz transformation , with Galilean transformation as low v/c approximation • Dispense with ether All nontrivial results follow from this new conception of time ▪ Invoke the principle of relativity The new kinematics applicable to all physics 25 11 Special Relativity Geometric formulation Even simpler perspective Hermann Minkowski (1907) Essence of SR: time is on an equal footing as space . To bring out this symmetry, unite them in a single math structure, spacetime Emphasizes the invariance of the theory: c → s SR: The arena of physics is the 4D spacetime s2 = −c2t 2 + x2 + y 2 + z 2 = [x][g][x] Einstein was initially not impressed , −1 ct calling it 1 x .. “untilsuperfluous he tried learnedness to formulate” = ()ct x y z = length 2 General relativity (non-inertial frames) 1 y c as the conversion factor 1space z ↔ time = Field theory of gravitation Gravity = structure of spacetime Lorentz-transformation = rotation R ˆ in spacetime SR = flat spacetime metric [g] → all SR features GR = curved spacetime 12 Why does GR principle automatically “ Gravity disappears in a free fall frame ” bring gravity into consideration? How is gravity related to spacetime? The Equivalence Principle (1907) played a key role in the formulation of general theory of relativity starting from Galileo Remarkable empirical observation All objects fall with the same acceleration a ↑ = ↓ g Einstein: “My happiest thought ” EP: Motion in grav field totally independent of accelerated frame = inertial frame w/ gravity properties of the test body, attributable directly to underlying spacetime? EP as the handle of going from SR to GR Einstein proposed in 1912: SR → GR, flat → curved spacetime gravitational field = warped spacetime 30 13 Relativity Equations written in terms of 4-tensors as a coordinate symmetry are automatically relativistic Special relativity flat spacetime Rˆ = spacetime-independent transformation Global symmetry General relativity Must replace ordinary derivative by curved spacetime with moving basis vectors covariant differentiation general coord transf = spacetime dependent [ d
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