PHYSICS 798G - SPECIAL TOPICS IN EXPERIMENTAL GRAVITATION 15 MARCH 2007 ________________________________________________________________________________________________________ 1 Experimental Tests of Local Lorentz Invariance Michael C. Scholten Atomic, Molecular, and Optical Group. Department of Physics, University of Maryland Physics 798G (Submitted March 15, 2007) Lorentz invariance, fundamental to Relativity and the Standard Model, has been thoroughly investigated both theoretically and experimentally in the past 15 years. This investigation, motivated in large by attempts to unify gravity with the Standard Model through quantum gravity, has led to strict constraints on the nature and size of a violation. A historical perspective of Lorentz’s work, a brief discussion of the theoretical framework, and a discussion of high-precision tests and their results are presented. I. INTRODUCTION In the late 19th century, Albert Michelson and Edward Morley performed the most famous measurement of zero in the history of physics1. The prevailing theory of the day supposed a medium for light propagation, called “luminiferous ether,” in a similar sense to how sound needs air to propagate. Michelson and Morley recognized that the Earth should be subject to “ether winds” that changed according to the rotation of the Earth on its axis and around the Sun. The speed of light moving with or against this wind would be different, so this should be measurable. Michelson created an interferometer by sending a source of white light through a half-silvered mirror, then allowing the two beams to travel some distance along perpendicular arms, which were then reflected back along their paths and recombined on the far side of the splitter in an eyepiece. This formed an interference pattern, which was related to the length of the arms, or the speed of light in each arm. Since the arms were perpendicular, the “ether wind” should have a different effect on the light in each arm, causing a shift in the interference fringes. By mounting the interferometer on a marble table floating in a vat of mercury, Michelson and Morley calculated their experimental sensitivity would allow them to measure a shift of 1/100th of a fringe. The shift was expected to be four-tenths of a fringe if the ether was stationary with respect to the Sun. They saw a shift consistent with zero. Michelson and Morley reported their results in an 1887 American Journal of Physics article2, stating, “The relative velocity of the earth and the ether is probably less than one sixth the earth’s orbital velocity, and certainly less than one-fourth.” Stokes then presented a theory that supposed the ether was at rest on the earth’s surface, which required a velocity potential. Michelson and Morley went on to say, “If now it were legitimate to conclude from the present work that the ether is at rest with regard to the earth’s surface, according to Lorentz there could not be a velocity potential, and his own theory also fails.” Hendrik Lorentz3 continued to search for an explanation of the Michelson-Morley experiment. In 1892 he proposed the idea that bodies contract in the direction of motion; length contraction. He also introduced the idea of local time, which described the relativity of simultaneity between reference frames in relative motion, and time dilation. Lorentz published in 1905 what Henri Poincaré called the “Lorentz transformations.” Paul Langevin said of this publication4, “It is the great merit of H. A. Lorentz to have seen that the fundamental equations of electromagnetism admit a group of transformations which enables them to have the same form when one passes from one frame of reference to another; this new transformation has the most profound implications for the transformations of space and time.” The Lorentz transformations removed contradictions between electromagnetism and classical mechanics regarding the transformation of fields, and they were the mathematical foundation of Einstein’s Special Relativity. In fact, “Until the first World War, Lorentz's and Einstein's theories were regarded as different forms of the same idea, but Lorentz, having priority and being a more established figure speaking a more familiar language, was credited with it.”5 While the Standard Model and General Relativity are Lorentz covariant (invariant under Lorentz transformations), they are incompatible with each other. A number of theories attempting to incorporate gravity with the three forces of the Standard Model may contain hidden or small corrections that violate Lorentz invariance and CPT symmetry6. Over the last fifteen years, Alan Kostelecky7 has developed the Standard Model Extension (SME), which is a modification of thePHYSICS 798G - SPECIAL TOPICS IN EXPERIMENTAL GRAVITATION 15 MARCH 2007 ________________________________________________________________________________________________________ 2 Standard Model of particle physics and Einstein’s theory of General Relativity. This theory provides a quantitative description of Lorentz and CPT violations by developing a set of coefficients that can be experimentally restricted, thus ruling out theoretical models that make predictions concerning the size of these violations. In a way, the physics world has come full circle since Michelson and Morley’s 1887 experiment. Physicists today are essentially searching for evidence of an “ether wind,” for evidence of a preferred reference frame. They continue to measure zero to greater and greater precision, setting constraints on the coefficients in the SME, and restricting the size of Lorentz and CPT violations. These experiments cover the full field of physics, from neutrino oscillations to proton-antiproton mass measurements to atomic physics. II. THEORETICAL BACKGROUND Lorentz transformations consist of rotations and boosts (changes in velocity). There are three rotations, one around each spatial direction,