Michimura - Tests of Lorentz Invariance with an Optical Ring Cavity

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Springer Nature Singapore Pte Ltd. 2017

Yuta Michimura Tests of Lorentz Invariance with an Optical Ring Cavity Springer Theses Recognizing Outstanding Ph.D. Research 10.1007/978-981-10-3740-5_1

1. Introduction

Yuta Michimura 1

(1)

Department of Physics, The University of Tokyo, Bunky, Tokyo, Japan

Yuta Michimura

Email:

Special Relativity is based upon two postulates, the special principle of relativity and the principle of the constancy of the speed of light. Starting from these two postulates, Einstein revealed that Lorentz transformation, not Galilean transformation, is the space-time coordinate transformation []. As a consequence, Lorentz invariance underlies all the theories of fundamental interactions, such as the Standard Model of particle physics and General Relativity.

However, theoretical works towards the unification of fundamental interactions, such as string theories or loop quantum gravity, have led to the idea that Lorentz invariance may only be approximate at attainable energies []. We could say that the dipole component of the CMB anisotropy comes from red and blue shifts from our velocity with respect to the CMB rest frame. If the CMB rest frame is the preferred frame, which is denied by Special Relativity, our vision of the Universe will be turned upside down.

There are almost no quantitative predictions at what level we can observe Lorentz violation. For example, Ref. [] suggests Lorentz violation at level, but this number only comes from the ratio between the Planck mass and the electroweak scale. Thus, we should perform experimental searches for Lorentz violations with increasing precision. Even if we could not find any violation within the experimental precision, we can restrict possible new theories.

Here, we test Lorentz invariance by testing the isotropy of the speed of light using an optical ring cavity. Especially, we have tested if the speed of light propagating in one direction and that in the opposite direction are the same. This one-way test cannot be done with usual electromagnetic interferometers or cavities used for previous Michelson-Morley type experiments. This is because usual interferometers or cavities have closed paths for electromagnetic wave and can only measure the average speed of light propagating back and forth.

We have solved this problem by placing a piece of dielectric material along one side of the optical path of a triangular optical ring cavity. If there is a difference between the speed of light propagating in opposite directions, the resonant frequencies for the clockwise direction and the counterclockwise direction will be shifted in opposite signs. Thus, we measured the resonant frequency difference between two counterpropagating directions with double-pass configuration to get the Lorentz violation signal. This double-pass configuration enables a null measurement of the resonant frequency difference. Also, this differential measurement is highly insensitive to environmental disturbances because the effects of cavity length fluctuations are common to both resonances.

This thesis is organized as follows: Chap. concludes the results of this work and gives future prospects of this research.

The author of this thesis tried to make this thesis readable for nonexperts of the Standard Model Extension. Details of the analysis within the frame work of the Standard Model Extension are described in Sect..

We note here that the tests of Lorentz invariance in photons have also been done very precicely with gamma ray astronomy, taking advantage of cosmological distances. From polarization measurements and light-curve measurements of light from gamma ray burts, there are tight constraints on the vacuum birefringence []. However, anisotropy in the speed of light arises from the different kind of Lorentz violation, which is hard to search with gamma ray astronomy.

The author of this thesis designed and developed the experimental apparatus, performed the year-long observation run, and did the data analysis. Nobuyuki Matsumoto helped developing the optics and kept the laser frequency to be locked during the observation run. Matthew Mewes theoretically analyzed the apparatus in the framework of the Standard Model Extension. Masaki Ando provided the idea of making use of double-pass configuration. Noriaki Ohmae, Wataru Kokuyama, and Yoichi Aso gave important advice on optics and noise sources. Kimio Tsubono and Masaki Ando were the supervisors and the leaders of our group. This work has been done at the University of Tokyo.

References

A. Einstein, Zur Elektrodynamik bewegter Krper. Ann. Phys. (Leipzig) , 891 (1905) ADS CrossRef MATH

D. Mattingly, Modern tests of Lorentz invariance. Living Rev. Relat. , 5 (2005) ADS CrossRef MATH

V.A. Kosteleck, N. Russell, Data tables for Lorentz and CPT violation. Rev. Mod. Phys. , 11 (2011); updated version available at arXiv:0801.0287

V.A. Kosteleck, Proceedings of the Sixth Meeting on CPT and Lorentz Symmetry (World Scientific, Singapore, 2014) CrossRef

V.A. Kosteleck, S. Samuel, Spontaneous breaking of Lorentz symmetry in string theory. Phys. Rev. D , 683 (1989) ADS CrossRef

V.A. Kosteleck, R. Potting, CPT and strings. Nucl. Phys. B , 545 (1991) ADS MathSciNet CrossRef MATH

R. Gambini, J. Pullin, Nonstandard optics from quantum space-time. Phys. Rev. D , 124021 (1999) ADS MathSciNet CrossRef

C.H. Lineweaver, L. Tenorio, G.F. Smoot, P. Keegstra, A.J. Banday, P. Lubin, The dipole observed in the COBE DMR four-year data. Astrophys. J. , 38 (1996) ADS CrossRef

D. Colladay, V.A. Kosteleck, Lorentz-violating extension of the standard model. Phys. Rev. D , 116002 (1998) ADS CrossRef

V.A. Kosteleck, M. Mewes, Signals for Lorentz violation in electrodynamics. Phys. Rev. D , 056005 (2002) ADS CrossRef

V.A. Kosteleck, M. Mewes, Constraints on relativity violations from gamma-ray bursts. Phys. Rev. Lett. , 201601 (2013) ADS CrossRef

V. Vasileiou, A. Jacholkowska, F. Piron, J. Bolmont, C. Couturier, J. Granot, F.W. Stecker, J. Cohen-Tanugi, F. Longo, Constraints on Lorentz invariance violation from fermi-large area telescope observations of gamma-ray bursts. Phys. Rev. D , 122001 (2013) ADS CrossRef

A.A. Abdo et al., A limit on the variation of the speed of light arising from quantum gravity effects. Nature , 331 (2009) ADS CrossRef

Springer Nature Singapore Pte Ltd. 2017

Yuta Michimura Tests of Lorentz Invariance with an Optical Ring Cavity Springer Theses Recognizing Outstanding Ph.D. Research 10.1007/978-981-10-3740-5_2

2. Tests of Lorentz Invariance

Yuta Michimura 1

(1)

Department of Physics, The University of Tokyo, Bunky, Tokyo, Japan

Yuta Michimura

Email:

Abstract

Tests of Lorentz invariance have been performed in wide variety of fields since Einsteins special relativity was formulated more than 100 years ago. In this chapter, we will review previous tests of Lorentz invariance, particularly in the field of electrodynamics. Firstly, Sect. describes the purpose and the scope of our experiment.

Keywords

Lorentz invariance Anisotropy One-way speed of light

2.1 Test Theories

In order to compare the precision of various experimental tests of Lorentz invariance, it is useful to introduce Lorentz violating parameters to physical theories. There are various test theories which have their own sets of parameters depending on their assumptions, but Robertsons framework [] has been developed and used not only in the field of electrodynamics but also in other interactions.

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