**"Exploring the Full Range of Classical Electrodynamics: from Applied Physics to General Relativity"**

**4th GIF Workshop**

**October 19 - 24, 2014**

Jerusalem College of Technology, Israel

**Program and Materials**

**Topics discussed**

Deep analysis of wave propagation in dissipative media

Geometry of light propagation

Potential practical importance of non-standard effects in the geometry of light propagating through dispersive, anisotropic and resonant media or media embedded in curved spacetime

Two experiments testing Einstein's Clock Hypothesis were presented and discussed.

Extension of the gauge idea in order to accommodate effects on charge and parity transformation

*Sunday, October 19, 2014*

**19:00-22:00**: Reception. Greeting of the Rector, Prof. Kenneth J. Hochberg

*Monday, October 20, 2014*

**9:00- 9:30****:** Registration

**9:30-10:00****:** Opening Ceremony.

**10:00-11:00****:** Friedrich Wilhelm Hehl, University of Cologne, “Kummer tensor”

**11:15-12:15****:** Claus Laemmerzahl, ZARM, University of Bremen, “On the measurement of the gravitomagnetic clock effect”

**12:15-13:30****:** Lunch

**13:30-14:30**: Yakov Itin, JCT and Hebrew University, “Wave propagation in electromagnetic systems with a linear response”

**14:45-15:45****:** Yaakov Friedman (with E. Yudkin), JCT, “Pulse Propagation in Single Resonant Media and Time Spectrum”

**16:00-17:00****:** Volker Perlick (with C. Laemmerzahl and Y. Itin), ZARM, University of Bremen, “On a Finsler-type modification of the Coulomb law”

**17:15-18:15****:** Tzvi Scarr (with Y. Friedman), JCT, “Relativistic Rotations”

*Tuesday, October 21, 2014*

**9:30-10:30:** Friedrich Wilhelm Hehl, University of Cologne, “A theory of the skewon field: between electrodynamics and gravitation”

**10:45-11:45:** Uziel Sandler, JCT, “Lagrangian Fuzzy Dynamics of Physical and Non-Physical Systems”

**12:00-13:00:** Yaakov Friedman, JCT, “Testing Einstein’s Clock Hypothesis at PETRAIII”

**13:00-14:15:** Lunch

**14:15-15:15:** Shlomo Engelberg, JCT, “Critical Thresholds in Euler-Poisson Equations”

**15:30-16:30:** Alberto Favaro, Oldenburg University, “Electromagnetic Media with Two Light Cones”

**16:45-17:45:** Ezra Yudkin (with Y. Friedman) , JCT, “Testing Einstein’s time dilation and the Clock Hypothesis”

*Wednesday, **October 22, 2014*

Excursion

*Thursday, **October 23, 2014*

**9:30-10:30****:** Wei-Tou Ni, National Tsing Hua University (NTHU), Hsinchu, Taiwan

"On axion, dilaton and skewon modifications in cosmic wave propagation"

**10:45-11:45****:** Yakov Itin, JCT and Hebrew University, “Skewon modification of light cone”

**12:00-13:00****:** Martin Land, Hadassah College, “Pair production in classical electrodynamics”

**13:00-14:15****:** Lunch

**14:15-15:15: **Eduardo Guendelman, Ben Gurion University, “Scalar gauge fields, coupling electromagnetism to global charge, dynamical charges and confinement”

Abstract

Presentation Part1 Part2

Video

**15:30-16:30****:** Roee Steiner, Ben Gurion University, Israel "Dynamical Couplings in Gauge Theories and Relation to Confinement Mechanisms"

**16:45-17:45****:** David Hai Gootwiling (with Y. Friedman), JCT, “Self-dual electromagnetic tensor and the pre-potential”

**Friedrich Wilhelm Hehl, **University of Cologne and University of Missouri, Columbia

Title: A theory of the skewon field: between electrodynamics and gravitation

Abstract: In classical electrodynamics, we assume a local and linear

constitutive law for the vacuum. The constitutive tensor encompasses

36 permittivity/permeability functions characterizing the

electromagnetic properties of the vacuum. These 36 functions can be

grouped into 20+15+1 functions. Thereof, 20 functions finally yield

a dilaton field and the metric of spacetime, 1 function represents the

axion field, and 15 functions the (traceless) skewon field S. In this

lecture, we discuss some of the properties of the skewon field, such as

its electromagnetic energy density, its possible coupling to

Einstein-Cartan gravity, and its corresponding gravitational energy.

F.W.H., Yu.N. Obukhov, G.F. Rubilar, M. Blagojevi\'c, Phys. Lett. A

347 (2005) 14-24

**Shlomo Engelberg**, JCT, Israel (joint work with Eitan Tadmor of the University of Maryland and Hailiang Liu of Iowa State University)

Title: Critical Thresholds in Euler-Poisson Equations

Abstract: In this talk, we discuss the finite-time breakdown of solutions in

various forms of the Euler-Poisson equations. We show that this breakdown

occurs only when the initial conditions cross a *critical threshold*. This type of behavior is most easily observed in the Burgers' equation:

\begin{displaymath}

u_t + u u_x =0.

\end{displaymath}

It is well known that the solutions of this equation break down in finite time unless $u_x(x,0) > 0$ for all $x$. We show that in a variety of cases, a similar critical thresholds exists.

**Alberto Favaro**, Oldenburg University, Germany

Title: Electromagnetic Media with Two Light Cones

Abstract: Electromagnetic media such that the Fresnel surface, governing wave propagation, is the union of two distinct light cones, play a role both in materials science and in spacetime physics. In the former discipline, the crystals endowed with this property are well-studied, as the double cone geometry corresponds to a simple type of birefringence. In the latter context, the nonlinear model of vacuum by Heisenberg and Euler, as well as the general theory due to Plebanski, yield a Fresnel surface, whose significance must be restricted to high-frequency electromagnetic waves, that is the union of two distinct light cones [1].

Not every pair of Lorentzian metrics can arise via the double cone geometry. For instance, there exists no local and linear medium such that the Fresnel surface includes the metrics g1=diag(-1,1,1,1) and g2=diag(-1,2,2,2). We determine the necessary and sufficient conditions for two Lorentzian metrics to proceed from a local and linear medium. Our requirements are very similar to the algebraic Rainich conditions, which lie at the heart of the “already unified field theory” for gravity and electrodynamics [2].

The findings are applied to Chromium Sesquioxide cr2o3, whose Fresnel surface is demon-strated to be the union of two light cones. Two novel 4-dimensional scalars *M*12 and *M*21 are extracted from the optical metrics of this crystal. We calculate *M*12 and *M*21 at a temperature of 298.65K from experimental data. The axion field, another spacetime scalar of Chromium Sesquioxide, was measured in 2008 [3].

References

[1] Y. Obukhov and G. Rubilar. Fresnel analysis of wave propagation in nonlinear Electrodynamics. *Phys. Rev. D*, 66(2):024042, 2002.

[2] C. Misner and J. Wheeler. Classical Physics as Geometry. *Ann. Phys. (NY)*, 2(6):525-603,

1957.

[3] F. Hehl, Y. Obukhov, J. Rivera, and H. Schmid. Relativistic nature of a magnetoelectric

modulus of cr2o3 crystals: a four dimensional pseudoscalar and its measurement. *Phys. Rev. A*, 77:022106, 2008.

**Yaakov Friedman**, JCT, Israel (joint work with Ezra Yudkin)

Title: Pulse Propagation in Single Resonant Media and Time Spectrum

Abstract: We obtain a new formula for the time spectrum of a single resonant media. We show that the fundamental equations for electromagnetic pulse propagation in a single resonant media, described by Burnham and R. Y. Chiao, have an additional solution to the one described there which is used for the calculation of time spectra. Such time spectra are a basic tool in Mossbauer spectroscopy based on synchrotron radiation. We show that the improved solution fits the experimental data from NFS spectra obtained at PETRA III.

Title: Testing Einstein’s Clock Hypothesis at PETRA III

Abstract: We present the results of our experiment at PETRA III in November 2013 and discuss the open problems which arose in understanding the results.

**David Hai Gootvilig**, JCT, Israel (joint work with Yaakov Friedman)

Title: Self-dual electromagnetic tensor and the pre-potential

Abstract: We define the Hodge dual operator on the standard representation of the Lie algebra of the Lorentz group on Minkowski space. For any EM field tensor, we associate a self-dual tensor. We show that outside of the sources of the field, a self-dual 4-potential can be defined.

For an arbitrary observer, we find a constant, depending only on the null-displacement between the observer and the source of the field, which is invariant under the self-dual representation of the Lorentz group. This invariant is used to define the pre-potential of the EM field. We show that the pre-potential of a point charge in arbitrary motion produces the correct field and that outside of the sources, the pre-potential is always self-dual.

Maxwell's equations for the pre-potential are derived. The gauge freedom of the pre-potential is described. We find conditions on the current density for the existence of a pre-potential.

Examples for the relation between the pre-potential, the 4-current and the field are presented in the following cases: a charged infinite rod, a charged infinite plate, and the current through an infinite solenoid.

**Eduardo Guendelman**, Ben Gurion University, Israel

Title: Scalar gauge fields.

Abstract: In this talk, we give a variation of the gauge procedure which employs a scalar gauge field, B(x), in addition to the usual vector gauge field Au(x). We study this variation of the usual gauge procedure in the context of a complex scalar matter field 0(x) with a U(1) symmetry. We will focus primarily on the case when 0(x) develops a vacuum expectation value via spontaneous symmetry breaking. We find that under these conditions, the scalar gauge field mixes with the Goldstone boson that arises from the breaking of a global symmetry. Some other interesting features of this scalar gauge model are: (i) The new gauge procedure gives rise to terms which violate C and CP symmetries. This may have applications in cosmology or for CP violation in particle physics; (ii) the existence of mass terms in the Lagrangian which respect the new extended gauge symmetry. Thus, one can have gauge field mass terms even in the absence of the usual Higgs mechanism; (iii) the emergence of a sine-Gordon potential for the scalar gauge field; (iv) a natural, axion-like suppression of the interaction strength of the scalar gauge boson.

**Yakov Itin**, JCT and Hebrew University, Israel

First Talk: Optic tensor and skewon covector

Second Talk: Skewon modification of light cone

**Claus Laemmerzahl**, ZARM, University of Bremen, Germany

Title: On the measurement of the gravitomagnetic clock effect

Abstract: On the level of orbits of satellites, the gravitomagnetic field of a rotating gravitating body such as the Earth manifests itself in the precession of the orbital plane (Lense-Thirring effect) or in the precession of the spin of a spinning top (Schiff effect). Here we discuss the question whether and how this gravitomagnetic field can also be measured using clocks on orbiting satellites. Two clocks on counter-rotating equatorial circular orbits around the Earth show a difference of about s per revolution. However, the measurability of this effect depends on the accuracy and stability of the clocks used as well as on the precise knowledge of the satellites orbits.

It is shown that with present technology, it is possible in principle to measure this gravitomagnetic clock effect with satellites on arbitrary orbits. In particular, we analyze whether the gravitomagnetic clock effect has an impact on the clocks on the Galileo satellites. Such a measurement would constitute another important Solar System test of

Einstein's General Relativity.

E. Hackmann and C. Laemmerzahl: A generalized gravitomagnetic clock effect, arXiv:1406.6232 [gr-qc].

**Martin Land**, Hadassah College, Israel

Title: Pair production in classical electrodynamics

Abstract: We calculate pair production from bremsstrahlung as a classical effect in Stueckelberg electrodynamics. In this framework, O(3,1)-covariant events parameterized by a Poincare-invariant chronological time evolve in an unconstrained 8D phase space, and interact through five gauge fields defined on spacetime and the independent chronological time. We consider a three-stage interaction which according to the laboratory clock appears as (1) the scattering of particle-1 with a heavy nucleus to produce bremsstrahlung, (2) the creation of a particle/antiparticle pair from the radiation component of the bremsstrahlung, (3) annihilation of the antiparticle with particle-2 in the presence of a second heavy nucleus. When parameterized in chronological time, the underlying process develops as (1) the scattering of particle-2 from the second nucleus to backward time evolution with negative energy, (2) the scattering of particle-1 from the first nucleus and release of bremsstrahlung, (3) absorption of bremsstrahlung radiation by particle-2 which returns to forward time evolution with positive energy.

**Volker Perlick**, ZARM, University of Bremen, Germany

Title: Lagrangian Fuzzy Dynamics of Physical and Non-Physical Systems

Abstract: In this talk, we show how to study the evolution of a system, given imprecise knowledge about the state of the system and the dynamics laws. Our approach is based on Fuzzy Set Theory, and it will be shown that the Fuzzy Dynamics of an n-dimensional system is equivalent to Lagrangian (or Hamiltonian) mechanics in an n+1-dimensional space. In some cases, however, the corresponding Lagrangian is more general than the usual one and could depend on the action. In this case, Lagrange's equations gain a non-zero right-hand side proportional to the derivative of the Lagrangian with respect to the action. Examples of such systems are unstable systems, systems with dissipation and systems which can remember their history. Moreover, in certain situations, the Lagrangian could be a set-valued function. The corresponding equations of motion then become differential inclusions instead of differential equations. We will also show that the principal of least action is a consequence of the causality principle and the local topology of the state space and not an independent axiom of classical mechanics.

We emphasize that our adaptation of Lagrangian mechanics does not use or depend on specific properties of the physical system being modeled. Therefore, this Lagrangian approach may be equally applied to non-physical systems. An example of such an application is presented as well.

**Tzvi Scarr**, JCT, Israel (joint work with Yaakov Friedman)

Title: Relativistic Transformation for the Radius of a Rotating Disk

Abstract: Based on the symmetries of a rotating system, we derive the general form of the relativistic spacetime transformations from a rotating system to an inertial one. The explicit form of these transformations is derived rigorously, using only the basic tenets of Special Relativity and the methods of *covariant uniform acceleration*. There are no arbitrary assumptions, as in all previous theories. We show that the speed, with respect to an inertial frame, of a rest point in a rotating system of *any* size does not exceed the speed of light. This implies that special relativity does not impose a limitation on the size of a rotating object. We obtain global relativistic rotations. The *horizon problem* does not arise. We show how to synchronize clocks on a rotating disk, avoiding the *time gap*.

**Roee Steiner**, Ben Gurion University, Israel

Title: Dynamical Couplings in Gauge Theories and Relation to Confinement Mechanisms

Abstract: By using a variation of the gauge procedure which employs a scalar gauge field, B(x), in addition to the usual vector gauge field Au(x), we can couple abelian gauge fields to currents which allow dynamical coupling constants, which could depend, for example, on the local value of a scalar field. In the simplest realization of these models, such theories naturally lead to a confinement of charge inside bags, where the charge current is confined inside Bags via MIT Bag model boundary conditions. Other formulations allow the possibility of gauge invariant formulation of dynamical couplings, for example, time-dependent fine structure constant, without associated confinement mechanisms.

**Ezra Yudkin**, JCT, Israel (joint work with Yaakov Friedman)

Title: Testing Einstein's time dilation and clock hypothesis

Abstract: Einstein's time dilation may be tested by the Transverse Doppler shift. Similarly, the Clock Hypothesis can be tested by a Doppler shift due to acceleration. Mossbauer spectroscopy with a rotating absorber can be used to test such shifts. We explain the need of a Synchrotron Mossbauer Source for such an experiment. We present the results of the HC-1361 experiment performed at ESRF to study the Mossbauer spectra of a rotating absorber, and propose a method to test properly Einstein's time dilation and clock hypothesis.