1 w.-t. ni 倪維斗 department of physics, national tsing hua university [email protected]...

1

W.-T. Ni 倪維斗Department of Physics,

National Tsing Hua [email protected]

Foundations of Classical Electrodynamics

and Optical Experiments to Measure

the Parameters of the PPM (Parametrized Post-Maxewellian)

Electrodynamics 經典電動力學的基礎 (arXiv 1109.5501)

2011.12.12. NTHUFoundations of Classical Electrodynamics and PPM Framework

W-T Ni

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 χ-g framework Pseudoscalar-photon interaction and the cosmic pol.

rotation Discussion and outlook

2011.12.12. NTHUFoundations of Classical Electrodynamics and PPM Framework W-T Ni 2

Introduction – Maxwell Equations and Lorentz Force

Law (I)馬克士威方程式與羅倫茲力

2011.12.12. NTHU Foundations of Classical Electrodynamics and PPM Framework W-T Ni 3

(Jackson)

( 庫倫定律 )

( 法拉第定律 )

( 安培 - 馬克士威定律 )

( 無磁單極 )


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


Law (II)馬克士威方程式與羅倫茲力

( 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


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].

Lagrangian density LEMS for 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


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


12.1 in

1.5 m

4MHz 10kV p

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


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

Quantum corrections to classical electrodynamics


Heisenberg-Euler Lagrangian

Born-Infeld Electrodynamics


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


Unified theory of nonlinear

electrodynamics and gravity

A. 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.


Equations for nonlinear electrodynamics (1)


Equations for nonlinear electrodynamics (2)


Electromagnetic wave propagation

in PPM electrodynamics

2011.12.12. NTHU Foundations of Classical Electrodynamics and PPM Framework W-T Ni16

Birefringence or no Birefringnce


Measuring the parameters of the PPM electrodynamics Δn = n║ - n┴ = 4.0 x 10-24 (Bext/1T)2


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+η3

2(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.


Measuring the parameters of the PPM electrodynamics


Measuring the parameters of the PPM electrodynamics


Lab Experiment:Principle of Experiment


Apparatus and Finesse Measurement


Suspension and Analyzer’s Extinction

ratio


Injection Optical Bench


Vacuum Chamber and Magnet

目前出光狀態與 Finesse( 將耗散 / 投影損失視為反射率較差的表現 )


Current Optical Experiments

2011.12.12. NTHU

Foundations of Classical Electrodynamics and PPM Framework W-T Ni 30

LNLFerrara

PVLAS


Rotation and ellipticity sensitivity comparisons using ellipsometers

with optical path multipliers


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 10^5

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.


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 10^5, 10^(-7) per square root Hertz ellipticity sensitivity. For ten times improvement in sensitivity, it takes 650 years of continuous datataking.


Comparisons on the N2 magnetic birefringence

measurement


PVLAS 2004Q&A 2009BMV2011

(Pseudo)scalar field: WEP & EEP in EM field

Foundations of Classical Electrodynamics and PPM Framework W-T Ni 362011.12.12. NTHU

(Pseudo)scalar-Photon Interaction

Modified Maxwell Equations Polarization Rotation in EM Propagaton

(Classical effect)Constraints from CMB polarization observation This talk


Galileo’s experiment on inclined plane (Contemporary painting of Giuseppe Bezzuoli)

Galileo Equivalence Principle: Universality of free-fall trajectories

GP-B and Rotational EP



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 g


Electromagnetism ：Charged particles and

photons

)()()16

1( 2/1

II

IIk

kklijijkl

I xxdt

dsmgjAFFL

]21

21

[)( 2/1 ijklkjiljlikijkl ggggg ψ

Special Relativity

g framework

Galileo EP constrains to ：

)()()16

1( 2/1

II

IIk

kklijjlikjl

I xxdt

dsmgjAFFL

ηη

(Pseudo)scalar-Photon Interaction

Various terms in the Lagrangian

(W-T Ni, Reports on Progress in Physics, next month /also in arXiv)



Empirical Constraints: No Birefringence


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


Emprirical constraints: H g (One Metric)


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, see Hehl & Obukhov ArXiv:0705.3422v1


Change of Polarization due to Cosmic Propagation

The effect of φ 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 Δφ ≤ 1 over cosmological distance.[9-14]

Further observations to test and measure Δφ 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 measure Δφ to 10-6 are needed.

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.

Constraints on cosmic polarization rotation from CMB polarization

observations[See Ni, RPP 73, 056901 (2010) for detailed references]



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.


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.


References


Space contribution to the local polarization rotation angle -- [μΣ13φ,μΔxμ] = |▽φ| cos θ Δx0. The time contribution is φ,0 Δx0. The total contribution is (|▽φ| cos θ + φ,0) Δx0. (Δx0 > 0)

Intergrated:φ(2) - φ(1)φ(2) - φ(1)

1: a point at the 1: a point at the decoupling epochdecoupling epoch

2: observation 2: observation pointpoint


Variations and Fluctuations

Rotation φ(2) - φ(1)Rotation φ(2) - φ(1) δδφ(2) - φ(2) - δδφ(1): φ(1): δδφ(2) variations and φ(2) variations and

fluctuations at the last scattering fluctuations at the last scattering surface of the decoupling epoch; surface of the decoupling epoch; δδφ(1), φ(1), at present observation point, fixedat present observation point, fixed

<[<[δδφ(2) - φ(2) - δδφ(1)]^2> variance of φ(1)]^2> variance of fluctuation ~ [couplingfluctuation ~ [couplingξ × 10^(-5)]^2 × 10^(-5)]^2

The coupling depends on various The coupling depends on various cosmological modelscosmological models


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


Constraints on cosmic polarization rotation from

CMB

All consistent with null detection and with one another at 2 σ level

Newest : Brown et al. 11.2±8.7 ±8.7 mrad QuaD 2009

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


1 w.-t. ni 倪維斗 department of physics, national tsing hua university [email protected]...

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