W.-T. Ni ???

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Foundations of Classical Electrodynamics and
Optical Experiments to Measurethe Parameters of
the PPM (Parametrized Post-Maxewellian)
Electrodynamics ?????????(arXiv 1109.5501)

• W.-T. Ni ???
• Department of Physics,
• National Tsing Hua University
• weitou_at_gmail.com

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Outline

• Introduction Maxwell equations and Lorentz
  force law
• 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 ?-g
  framework
• Pseudoscalar-photon interaction and the cosmic
  pol. rotation
• Discussion and outlook

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Introduction Maxwell Equations and Lorentz
Force Law (I)????????????
(Jackson)
(?????)
(????)
(????)
(??-??????)
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Introduction Maxwell Equations and Lorentz
Force Law (II)????????????
(?????-????)
(????)

• Charges (and currents) ? produce E and B fields ?
  influence the Motion of charges
• Maxwell Equations
  Lorentz Force Law

????????????????????????
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Introduction Maxwell Equations and Lorentz
Force Law (III)????????????

• ???????????????????????????????A??
• 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
  (1/8p)E2-B2.

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Lagrangian density LEMS for a system of charged
particles in Gaussian units

• LEMSLEMLEM-PLP
• -(1/(16p))(1/2)?ik?jl-(1/2)?il?kjFij
  Fkl
• -Akjk-SI mI(dsI)/(dt)d(x-xI)
  ,
• LEMS ??????????
• LEM ???????
• LEM-P ???-??????????
• LP ??????

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Test of Coulombs 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 ?
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Proca (1936-8) Lagrangian density and mass of
photon

• LProca (mphoton2c2/8ph2)(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/h) gives the inverse range of the
  interaction

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Constraints on the mass of photon
Williams, Faller Hill (1971) Lab Test mphoton 10-14 eV ( 2 10-47 g) µ-1 2 107 m
Davis, Goldhaber Nieto (1975) Pioneer 10 Jupitor flyby mphoton 4 10-16 eV ( 7 10-49 g) µ-1 5 108 m
Ryutov (2007) Solar wind magnetic field mphoton 10-18 eV ( 2 10-51 g) µ-1 2 1011 m
Chibisov (1976) galactic sized fields mphoton 2 10-27 eV ( 4 10-60 g) µ-1 1020 m
A good Reference Goldhaber, A. S. Nieto, M. M.
(2010). Photon and Graviton Mass Limits. Review
of Modern Physics, Vol.82, No.1, (January-March
2010), pp. 939-979
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Quantum corrections to classical electrodynamics
Heisenberg-Euler Lagrangian

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Born-Infeld Electrodynamics
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Parametrized Post-Maxwell (PPM) Lagrangian
density (4 parameters ?, ?1, ?2, ?3)

• LPPM (1/8p)(E2-B2)?F(EB)
• Bc-2?1(E2-B2)2 4?2(EB)22?3(E2-B2)(
  EB)
• LPPM (1/(32p))-2FklFkl -?FFklFkl
• Bc-2 ?1(FklFkl)2?2(FklFkl)2?3(Fk
  lFkl)(FijFij)
• (manifestly Lorentz invariant form)
• Dual electomagnetic field Fij (1/2)eijkl Fkl

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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.

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Equations for nonlinear electrodynamics (1)
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Equations for nonlinear electrodynamics (2)
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Electromagnetic wave propagation in PPM
electrodynamics
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Birefringence or no Birefringnce
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Measuring the parameters of the PPM
electrodynamics

• ?n n - n- 4.0 x 10-24 (Bext/1T)2

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Measuring the parameters of the PPM
electrodynamics

• Lets 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 (?1?2)(E2B2-EB)Bc-2
  (?1-?2)2(E2B2-EB)2?32(E2-B2)1/2 Bc-2.
• (i) EB as in the strong microwave cavity, the
  indices of refraction for
• light is
• n 1 (?1?2)B2Bc-2(?1-?2)
  B2Bc-2,
• with birefringence ?n given by
• ?n
  2(?1-?2)B2Bc-2
• (ii) E0, B?0, the indices of refraction for
  light is
• n 1 (?1?2)B2Bc-2(?1-?2)
  2?321/2B2Bc-2,
• ?n
  2(?1-?2)2?321/2B2Bc-2.

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Measuring the parameters of the PPM
electrodynamics
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Lab ExperimentPrinciple of Experiment
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Apparatus and Finesse Measurement
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Suspension and Analyzers Extinction ratio
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Injection Optical Bench
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Vacuum Chamber and Magnet
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???????Finesse(???/??????????????)
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Current Optical Experiments
LNL Ferrara
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PVLAS
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Rotation and ellipticity sensitivity comparisons
using ellipsometers with optical path multipliers
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PVLAS Ferrara on 3 competing experiments (I)

• Q A in Taiwan They have the mirrors of the FP
  installed in two distant vacuum chambers
  suspended with attenators of ambient vibrations
  of the type developed for interferometric
  gravitational wave detectors. The separation of
  the two optical halves seems to limit the
  sensitivity of their apparatus. The finesse is
  below 105
• OSQAR at CERN uses a LHC dipole magnet 15 m long
  that can reach a 9 T field. The ellipsometer will
  exploit a FP to maximize the number of
  reflections and a novel optical techique to
  modulate the MBV effect. Since it is not feasible
  to set the LHC magnet in rotation and a
  modulation of the LHC magnet field intensity
  could be achieved only at very low frequency, the
  experiment foresees to modulate the polarization
  of the light entering the ellipsometer by setting
  in rotation the polarization plane.

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PVLAS Ferrara on 3 competing experiments (II)

• According to our experience in this set-up the
  rotation of the polarization will generate a very
  large signal due to the intrinsic birefringence
  of the FP mirrors.
• BMV in Toulouse homodyne, high intensity
  magnetic field, employing pulsed magnets (few
  ms), 40 cm long, that have already reached peak
  intensities in excess of B 15 T, L 0.5 m
  total length, 5 shots/hour. Finesse 105, 10(-7)
  per square root Hertz ellipticity sensitivity.
  For ten times improvement in sensitivity, it
  takes 650 years of continuous datataking.

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Comparisons on the N2 magnetic birefringence
measurement
PVLAS 2004 QA 2009 BMV2011
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(Pseudo)scalar field WEP EEP in EM field
Modified Maxwell Equations ? Polarization
Rotation in EM Propagaton (Classical
effect) Constraints from CMB polarization
observation ? This talk
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Galileos experiment on inclined plane
(Contemporary painting of Giuseppe Bezzuoli)
Galileo Equivalence Principle Universality of
free-fall trajectories
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GP-B and Rotational EP
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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

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ElectromagnetismCharged particles and photons
Special Relativity
framework
Galileo EP constrains to
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Various terms in the Lagrangian(W-T Ni, Reports
on Progress in Physics, next month /also in arXiv)
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Empirical Constraints No Birefringence
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Empirical Constraints from Unpolarized EP
Experiment constraint on Dilaton for EM f 1
10(-10)
Cho and Kim, Hierarchy Problem, Dilatonic Fifth,
and Origin of Mass, ArXiv0708.2590v1 (43)-dim
unification with GSU(2), Llt44 µm (Kapner et
al., PRL 2007)
Llt10 µm (Li, Ni, and Pulido Paton,
ArXiv0708.2590v1
Lamb shift in Hydrogen and
Muonium gr-qc
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Emprirical constraints H ? g (One Metric)
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Constraint on axion f lt 0.1Solar-system 1973 (f
lt 1010)

• Metric Theories of Gravity
• General Relativity
• Einstein Equivalence Principle recovered
• For a recent exposition, see Hehl
• Obukhov ArXiv0705.3422v1

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Change of Polarization due to Cosmic Propagation

• The effect of f is 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 of ?f 1 over cosmological distance.9-14
• Further observations to test and measure ?f to
  10-6 is promising.
• The natural coupling strength f is of order 1.
  However, the isotropy of our observable universe
  to 10-5 may leads to a change (?)?f of f over
  cosmological distance scale 10-5 smaller. Hence,
  observations to test and measure ?f to 10-6 are
  needed.

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The angle between the direction of linear
polarization in the UV and the direction of the
UV axis for RG at z gt 2. The angle predicted by
the scattering model is 90o

• 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.

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Constraints on cosmic polarization rotation from
CMB polarization observationsSee Ni, RPP 73,
056901 (2010) for detailed references
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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 10s. This gives a
  constraint of 10-1 rad or 6 degrees of the cosmic
  polarization rotation angle ?f.

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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 ?f of 10-2-10-3 expected.

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References
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Space contribution to the local polarization
rotation angle -- µS13f,µ?xµ ?f cos ? ?x0.
The time contribution is f,0 ?x0. The total
contribution is (?f cos ? f,0) ?x0. (?x0 gt
0)
Intergrated f(2) - f(1) 1 a point at the
decoupling epoch 2 observation point
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Variations and Fluctuations

• Rotation f(2) - f(1)
• df(2) - df(1) df(2) variations and fluctuations
  at the last scattering surface of the decoupling
  epoch df(1), at present observation point, fixed
• ltdf(2) - df(1)2gt variance of fluctuation
  coupling? 10(-5)2
• The coupling depends on various cosmological
  models

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COSMOLOGICAL MODELS

• PSEUDO-SCALAR COSMOLOGY, e.g., Brans-Dicke theory
  with pseudoscalar-photon coupling
• NEUTRINO NUMBER ASYMMETRY
• BARYON ASYMMETRY
• SOME other kind of CURRENT
• LORENTZ INVARIANCE VIOLATION
• CPT VIOLATION
• DARK ENERGY (PSEUDO)SCALAR COUPLING
• OTHER MODELS

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Constraints on cosmic polarization rotation from
CMB
Newest Brown et al. 11.28.7 8.7 mrad
QuaD 2009
All consistent with null detection and with one
another at 2 s level
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Outlook

• Precision tests of Classical Electrodynamics will
  continue to serve physics community in frontier
  research, in the quantum regime, in gravitation
  and in cosmology
• Thank you for your attention