Testing nonlinear vacuum electrodynamics with Michelson interferometry

Abstract

We discuss the theoretical foundations for testing nonlinear vacuum electrodynamics with Michelson interferometry. Apart from some nondegeneracy conditions to be imposed, our discussion applies to all nonlinear electrodynamical theories of the Plebański class, i.e., to all Lagrangians that depend only on the two Lorentz-invariant scalars quadratic in the field strength. The main idea of the experiment proposed here is to use the fact that, according to nonlinear electrodynamics, the phase velocity of light should depend on the strength and on the direction of an electromagnetic background field. There are two possible experimental setups for testing this prediction with Michelson interferometry. The first possibility is to apply a strong electromagnetic field to the beam in one arm of the interferometer and to compare the situation where the field is switched on with the situation where it is switched off. The second possibility is to place the whole interferometer in a strong electromagnetic field and to rotate it. If an electromagnetic field is placed in one arm, the interferometer could have the size of a gravitational wave detector, i.e., an arm length of several hundred meters. If the whole interferometer is placed in an electromagnetic field, one would have to do the experiment with a tabletop interferometer. As an alternative to a traditional Michelson interferometer, one could use a pair of optical resonators that are not bigger than a few centimeters. Then the whole apparatus would be placed in the background field and one would either compare the situation where the field is switched on with the situation where it is switched off or one would rotate the apparatus with the field kept switched on. We derive the theoretical foundations for these types of experiments, in the context of an unspecified nonlinear electrodynamics of the Plebański class, and we discuss their feasibility. A null result of the experiment would place bounds on the parameters of the theory. We specify the general results to some particular theories of the Plebański class; in particular, we give numerical estimates for Born, Born-Infeld and Heisenberg-Euler theories.

Effects of nonlinear vacuum electrodynamics on the polarization plane of light

“…E.g., in Ref. [16] we have seen that with interferometric methods one could find a bound on b 0 in the order of b 0 7 × 10 7 T which corresponds to b 0 7 × 10 11 √ g/ √ cm s in Gaussian units. Assuming that a rotation of the polarization plane by one arcminute could be measured, ∆ϕ ≈ 3 × 10 −4 rad, we would need electric and magnetic fields of…”

“…Earlier studies of the high-frequency limit in nonlinear theories were restricted to the derivation of the eikonal equation from the zeroth order of the generalized Maxwell equations. It is well known that, as a result, one finds that the light rays are the null geodesics of two optical metrics; this was first shown by Novello et al [18] and later, in different representations, by Obukhov and Rubilar [19] and by Schellstede et al [16]. To the best of our knowledge, the transport law of the polarization plane was not yet considered for an arbitrary theory of the Plebański class.…”

On the weak‐field approximation of nonlinear vacuum electrodynamics of the Plebański class

“…Finally, three further remarks should be made: First, the series expansions of the Lagrangian's derivatives L F and L G via (19) do not destroy a present absence of birefringence within the accuracy of the desired order of approximation [27].…”

“…In that case, the definitions and field equations (1), (2), (4 I ), (4 III ), and (10 II ) remain unchanged, while one has to exchange F ab → √ −g F ab , Third, it is possible to use the approximation procedure developed also in terms of the excitation instead of the field strength if one confines oneself to the source-free theory with j m = 0. To go over to the corresponding field equations, one can use the scheme presented in [27]. If this scheme is also used for the approximate field equations, one gets the whole approximation method in terms of the excitation, but one should keep in mind that the potential of the field strength becomes an anti-potential of the excitation.…”

Rapidly rotating pulsar radiation in vacuum nonlinear electrodynamics

“…Vacuum nonlinear electrodynamics effects is an object that piques a great interest in contemporary physics [1][2][3][4]. First of all it is related to the emerging opportunities of experimental research in terrestrial conditions using extreme laser facilities like Extreme Light Infrastructure (ELI) [5][6][7], Helmholtz International Beamline for Extreme Fields (HIBEF) [8].…”