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Foundations of Classical Electrodynamics, Equivalence Principle, and Cosmic Interactions

Foundations of Classical Electrodynamics, Equivalence Principle, and Cosmic Interactions. Wei-Tou Ni Center for Gravitation and Cosmology (CGC), Department of Physics, National Tsing Hua U.

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Foundations of Classical Electrodynamics, Equivalence Principle, and Cosmic Interactions

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  1. Foundations of Classical Electrodynamics, Equivalence Principle, and Cosmic Interactions Wei-Tou Ni Center for Gravitation and Cosmology (CGC), Department of Physics, National Tsing Hua U. Precision Tests and Cosmic Interactions WTNi

  2. A chapter for the book "Electromagnetism" (ISBN 979-953-307-400-8) by INTECH (open access), to be published February, 2012 [arXiv:1109.5501] Precision Tests and Cosmic Interactions WTNi

  3. Outline • Introduction • Photon mass constraints • Quantum corrections – quantum corrections • Parametrized Post-Maxwell (PPM) electrodynamics • Electromagnetic wave propagation • Measuring the parameters of the PPM electrodynamics • Electrodynamics in curved spacetime and EEP • Empirical tests of electromagnetism and the χ-g framework • Pseudoscalar-photon interaction and the cosmic pol. rotation • Discussion and outlook Precision Tests and Cosmic Interactions WTNi

  4. An example of Accuracy Measure-ment of Light Velocity in History Precision Tests and Cosmic Interactions WTNi

  5. List of experiments measuring the limiting velocity of neutrinos Next talk, Bo-Qiang Ma will discuss theoretical Aspects Precision Tests and Cosmic Interactions WTNi

  6. Introduction – Maxwell Equations and Lorentz Force Law (I)馬克士威方程式與羅倫茲力 (Jackson) (法拉第定律) (無磁單極) (庫倫定律) (安培-馬克士威定律) Precision Tests and Cosmic Interactions WTNi

  7. Introduction – Maxwell Equations and Lorentz Force Law (II)馬克士威方程式與羅倫茲力 • Charges (and currents)  produce E and B fields  influence the Motion of charges Maxwell Equations Lorentz Force Law (連續方程式-電荷守恆) (羅倫茲力) 電荷和電流產生電場和磁場；電場和磁場影響電荷的運動 Precision Tests and Cosmic Interactions WTNi

  8. Introduction – Maxwell Equations and Lorentz Force Law (III)馬克士威方程式與羅倫茲力 • 法拉第定律和無磁單極定律相當於電場和磁場可以由標量勢和向量勢A表示： • 4-vector potential A  (, A) • Second-rank, antisymmetric field-strength tensor F =∂A -∂A • Electric field E [≡ (E1, E2, E3) ≡ (F01, F02, F03)] and magnetic induction B [≡ (B1, B2, B3) ≡ (F32, F13, F21)] • Electromagnetic field Lagrangian density LEM = (1/8π)[E2-B2]. Precision Tests and Cosmic Interactions WTNi

  9. Lagrangian density LEMSfor a system of charged particles in Gaussian units • LEMS=LEM+LEM-P+LP =-(1/(16π))[(1/2)ηikηjl-(1/2)ηilηkj]FijFkl -Akjk-ΣI mI[(dsI)/(dt)]δ(x-xI), • LEMS整个電荷系統拉格朗日 • LEM 電磁場拉格朗日 • LEM-P電磁場-粒子相互作用拉格朗日 • LP粒子拉格朗日 Precision Tests and Cosmic Interactions WTNi

  10. Test of Coulomb’s Law 1/r2+ • Cavendish 1772 ||  0.02 • Maxwell 1879||  5  10-5 • Plimpton and Lawton ||  2  10-9 • Williams, Faller, and Hill 1971  = (2.7  3.1)10-16 4MHz 10kV p 1.5 m  12.1 in  Precision Tests and Cosmic Interactions WTNi

  11. Proca (1936-8) Lagrangian density and mass of photon • LProca = (mphoton2c2/8πħ2)(AkAk) • the Coulomb law is modified to have the electric potential A0 = q(e-μr/r) • where q is the charge of the source particle, r is the distance to the source particle, and μ (≡mphotonc/ħ) gives the inverse range of the interaction Precision Tests and Cosmic Interactions WTNi

  12. Constraints on the mass of photon If cosmic scale magnetic field is discovered, the constraint on the interaction range may become bigger or comparable to Hubble distance (of the order of radius of curvature of our observable universe). If this happens, the concept of photon mass may lose significance amid gravity coupling or curvature coupling of photons. Precision Tests and Cosmic Interactions WTNi

  13. Quantum corrections to classical electrodynamics Heisenberg-Euler Lagrangian Precision Tests and Cosmic Interactions WTNi

  14. Born-Infeld Electrodynamics Precision Tests and Cosmic Interactions WTNi

  15. Parametrized Post-Maxwell (PPM) Lagrangian density (4 parameters: ξ, η1, η2, η3) • LPPM = (1/8π){(E2-B2)+ξΦ(E∙B) +Bc-2[η1(E2-B2)2 +4η2(E∙B)2+2η3(E2-B2)(E∙B)]} • LPPM = (1/(32π)){-2FklFkl -ξΦF*klFkl +Bc-2 [η1(FklFkl)2+η2(F*klFkl)2+η3(FklFkl)(F*ijFij)]} (manifestly Lorentz invariant form) • Dual electomagnetic field F*ij≡ (1/2)eijkl Fkl Precision Tests and Cosmic Interactions WTNi

  16. Unified theory of nonlinear electrodynamics and gravityA. Torres-Gomez, K. Krasnov, & C. Scarinci PRD 83, 025023 (2011) • A class of unified theories of electromagnetism and gravity with Lagrangian of the BF type (F: Curvature of the connection 1-form A (), with a potential for the B () field (Lie-algebra valued 2-form), the gauge group is U(2) (complexified). • Given a choice of the potential function the theory is a deformation of (complex) general relativity and electromagnetism. Precision Tests and Cosmic Interactions WTNi

  17. Generalized Uncertainty Principle, Blackhole Entropy and modified Newton’s law (Pisin’s talk & Bernard Carr’s talk) • When applying it to the entropic interpretation, we demonstrate that the resulting gravity force law does include sub-leading order correction terms that depend on h-bar. • Such deviation from the classical Newton's law may serve as a probe to the validity of the entropic gravity postulate. • Modified force law Precision Tests and Cosmic Interactions WTNi

  18. Equations for nonlinear electrodynamics (1) Precision Tests and Cosmic Interactions WTNi

  19. Equations for nonlinear electrodynamics (2) Precision Tests and Cosmic Interactions WTNi

  20. Electromagnetic wave propagation in PPM electrodynamics Precision Tests and Cosmic Interactions WTNi

  21. Precision Tests and Cosmic Interactions WTNi

  22. Precision Tests and Cosmic Interactions WTNi

  23. Birefringence or no Birefringnce Precision Tests and Cosmic Interactions WTNi

  24. Measuring the parameters of the PPM electrodynamics • Δn = n║ - n┴ = 4.0 x 10-24 (Bext/1T)2 Precision Tests and Cosmic Interactions WTNi

  25. Measuring the parameters of the PPM electrodynamics • Let’s choose z-axis to be in the propagation direction, x-axis in the Eext direction and y-axis in the Bext direction, i.e., k = (0, 0, k), Eext = (E, 0, 0) and Bext = (0, B, 0). • n± = 1 + (η1+η2)(E2+B2-EB)Bc-2± [(η1-η2)2(E2+B2-EB)2+η32(E2-B2)]1/2 Bc-2. • (i) E=B as in the strong microwave cavity, the indices of refraction for light is • n± = 1 + (η1+η2)B2Bc-2±(η1-η2)B2Bc-2, with birefringence Δn given by Δn = 2(η1-η2)B2Bc-2; • (ii) E=0, B≠0, the indices of refraction for light is n± = 1 + (η1+η2)B2Bc-2±[(η1-η2)2+η32]1/2B2Bc-2, Δn = 2[(η1-η2)2+η32]1/2B2Bc-2. Precision Tests and Cosmic Interactions WTNi

  26. Measuring the parameters of the PPM electrodynamics Precision Tests and Cosmic Interactions WTNi

  27. Lab Experiment:Principle of Experiment Precision Tests and Cosmic Interactions WTNi

  28. Apparatus and Finesse Measurement Precision Tests and Cosmic Interactions WTNi

  29. Suspension and Analyzer’s Extinction ratio Precision Tests and Cosmic Interactions WTNi

  30. Injection Optical Bench Precision Tests and Cosmic Interactions WTNi

  31. Vacuum Chamber and Magnet Precision Tests and Cosmic Interactions WTNi

  32. Current Optical Experiments LNL Ferrara Precision Tests and Cosmic Interactions WTNi

  33. PVLAS Precision Tests and Cosmic Interactions WTNi

  34. Comparisons on the N2 magnetic birefringence measurement PVLAS 2004 Q&A 2009 BMV2011 Precision Tests and Cosmic Interactions WTNi

  35. (Pseudo)scalar field: WEP & EEP with EM field (Pseudo)scalar-Photon Interaction Modified Maxwell Equations  Polarization Rotation in EM Propagaton (Classical effect) Constraints from CMB polarization observation  later in this talk Precision Tests and Cosmic Interactions WTNi

  36. Galileo’s experiment on inclined plane(Contemporary painting ofGiuseppe Bezzuoli)Galileo Equivalence Principle: Universality of free-fall trajectories Precision Tests and Cosmic Interactions WTNi

  37. GP-B and Rotational EP Precision Tests and Cosmic Interactions WTNi

  38. Einstein Equivalence Principle • EEP:(Einstein Elevator): Local physics is that of Special relativity • Study the relationship of Galileo Equivalence Principle and EEP in a Relativistic Framework: framework --- A general phenomenological framework for studying the coupling of gravity to electromagnetism • The photon sector of many frameworks are included: e.g., SME – Standard Model Extension SMS – Standard Model Supplement Precision Tests and Cosmic Interactions WTNi

  39. Electromagnetism：Charged particles and photons Special Relativity framework (Pseudo)scalar-Photon Interaction Galileo EP constrainsto： Precision Tests and Cosmic Interactions WTNi

  40. Various terms in the Lagrangian(W-T Ni, Reports on Progress in Physics, 2010 /also in arXiv) Precision Tests and Cosmic Interactions WTNi

  41. Empirical Constraints: No Birefringence Precision Tests and Cosmic Interactions WTNi

  42. Empirical Constraints from Unpolarized EP Experiment: constraint on Dilaton for EM: φ = 1 ± 10^(-10) Cho and Kim, Hierarchy Problem, Dilatonic Fifth, and Origin of Mass, ArXiv0708.2590v1 (4+3)-dim unification with G=SU(2), L<44 μm (Kapner et al., PRL 2007) L<10 μm (Li, Ni, and Pulido Paton, ArXiv0708.2590v1 Lamb shift in Hydrogen and Muonium gr-qc Precision Tests and Cosmic Interactions WTNi

  43. Emprirical constraints: H  g (One Metric) Precision Tests and Cosmic Interactions WTNi

  44. Constraint on axion: φ < 0.1Solar-system 1973 (φ < 10^10) • Metric Theories of Gravity • General Relativity • Einstein Equivalence Principle recovered • For a recent exposition of this, see Hehl & Obukhov ArXiv:0705.3422v1 Precision Tests and Cosmic Interactions WTNi

  45. Change of Polarization due to Cosmic Propagation • The effect ofφis to change the phase of two different circular polarizations of electromagnetic-wave propagation in gravitation field and gives polarization rotation for linearly polarized light.[6-8] • Polarization observations of radio galaxies put a limit ofΔφ≤1 over cosmological distance.[9-14] • Further observations to test and measureΔφ to 10-6 is promising. • The natural coupling strength φ is of order 1. However, the isotropy of our observable universe to 10-5 may leads to a change (ξ)Δφ of φ over cosmological distance scale 10-5 smaller. Hence, observations to test and measureΔφ to 10-6are needed. Precision Tests and Cosmic Interactions WTNi

  46. The angle between the direction of linear polarization in the UV and the direction of the UV axis for RG at z > 2. The angle predicted by the scattering model is 90^o • The advantage of the test using the optical/UV polarization over that using the radio one is that it is based on a physical prediction of the orientation of the polarization due to scattering, which is lacking in the radio case, • and that it does not require a correction for the Faraday rotation, which is considerable in the radio but negligible in the optical/UV. Precision Tests and Cosmic Interactions WTNi

  47. Precision Tests and Cosmic Interactions WTNi

  48. Constraints on cosmic polarization rotation from CMB polarization observationsAll consistent with null detection at 2 σ level[See Ni, RPP 73, 056901 (2010) for detailed references] Precision Tests and Cosmic Interactions WTNi

  49. CMB Polarization Observation • In 2002, DASI microwave interferometer observed the polarization of the cosmic background. • With the pseudoscalar-photon interaction , the polarization anisotropy is shifted relative to the temperature anisotropy. • In 2003, WMAP found that the polarization and temperature are correlated to 10σ. This gives a constraint of 10-1 rad or 6 degrees of the cosmic polarization rotation angle Δφ. Precision Tests and Cosmic Interactions WTNi

  50. CMB Polarization Observation • In 2005, the DASI results were extended (Leitch et al.) and observed by CBI (Readhead et al.) and CAPMAP (Barkats et al.) • In 2006, BOOMERANG CMB Polarization • DASI, CBI, and BOOMERANG detections of Temperature-polarization cross correllation • QuaD • Planck Surveyor was launched last year with better polarization-temperature measurement sensitivity. Sensitivity to cosmic polarization rotation Δφ of 10-2-10-3 expected. Precision Tests and Cosmic Interactions WTNi

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