Abstract
We study the flight time fluctuations in an anisotropic medium inspired by a cosmic string with an effective fluctuating refractive index caused by fluctuating vacuum electric fields, which are analogous to the lightcone fluctuations due to fluctuating spacetime metric when gravity is quantized. The medium can be realized as a metamaterial that mimics a cosmic string in the sense of transformation optics. For a probe light close to the analogue string, the flight time variance is ν times that in a normal homogeneous and isotropic medium, where ν is a parameter characterizing the deficit angle of the spacetime of a cosmic string. The parameter ν, which is always greater than unity for a real cosmic string, is determined by the dielectric properties of the metamaterial for an analogue string. Therefore, the flight time fluctuations of a probe light can be manipulated by changing the electric permittivity and magnetic permeability of the analogue medium. We argue that it seems possible to fabricate a metamaterial that mimics a cosmic string with a large ν in laboratory so that a currently observable flight time variance might be achieved.
Highlights
Quantization of fundamental interactions such as electromagnetic, weak and strong interactions, has achieved great success, on one hand, but on the other hand, quantization of gravity, the fundamental interaction known to the mankind the earliest, still remains elusive
A direct result of lightcone fluctuations is that the flight time of a probe light signal from its source to a detector spreads about the classical value in both directions [14,15,16,17,18,19,20]
The flight time of a probe light fluctuates due to a fluctuating effective refractive index when the medium is subjected to a fluctuating background field, which is analogous to the lightcone fluctuation when gravity is quantized
Summary
Quantization of fundamental interactions such as electromagnetic, weak and strong interactions, has achieved great success, on one hand, but on the other hand, quantization of gravity, the fundamental interaction known to the mankind the earliest, still remains elusive. The flight time of a probe light fluctuates due to a fluctuating effective refractive index when the medium is subjected to a fluctuating background field, which is analogous to the lightcone fluctuation when gravity is quantized. We study the flight time fluctuation of certain probe light pulses that arises from a fluctuating refractive index due to electromagnetic vacuum fluctuations in an anisotropic medium that mimics a cosmic string in terms of the classical propagation of light. Such a medium can be realized as a metamaterial in experiment.
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