ScienceWeek

THEORETICAL PHYSICS: ON LORENTZ INVARIANCE

Notes by ScienceWeek

In this context, the term "Lorentz frame" refers to any of the family of inertial coordinate systems, with 3 space coordinates and 1 time coordinate, used in the special theory of relativity. Each frame is in uniform motion with respect to all the other Lorentz frames, and the interval between any two events is the same in all frames.

In this context, the term "Lorentz transformation" refers to any of the family of linear mathematical transformations used in the special theory of relativity to relate the space and time variables of different Lorentz frames.

In this context, the term "Lorentz invariance" refers to the property, possessed by the laws of physics and by certain physical quantities, of being the same in any Lorentz frame, and thus unchanged by a Lorentz transformation.

The following points are made by Maxim Pospelov and Michael Romalis (Physics Today 2004 July):

1) The null result of the celebrated 1887 Michelson-Morley experiment was surprising and difficult to explain in terms of then prevalent physics concepts. It required a fundamental change in the notions of space and time and was finally explained, almost 20 years later, by Albert Einstein's special theory of relativity.

2) Special relativity postulates that all laws of physics are invariant under Lorentz transformations, which include ordinary rotations and changes in the velocity of a reference frame. Subsequently, quantum field theories all incorporated Lorentz invariance in their basic structure. General relativity includes the invariance through Einstein's equivalence principle, which implies that any experiment conducted in a small, freely falling laboratory is invariant under Lorentz transformations. That result is known as "local Lorentz invariance".

3) Experimental techniques introduced throughout the 20th century led to continued improvements in tests of special relativity. For example, 25 years ago, Alain Brillet and John L. Hall used a helium-neon laser mounted on a rotary platform to improve the accuracy of the Michelson-Morley experiment by a factor of 4000. In addition to the Michelson-Morley experiments that look for an anisotropy in the speed of light, two other types of experiments have constrained deviations from special relativity. Kennedy-Thorndike experiments search for a dependence of the speed of light on the lab's velocity relative to a preferred frame, and Ives-Stilwell experiments test special relativistic time dilation.

4) In 1960, Vernon Hughes and coworkers and, independently, Ron Drever conducted a different kind of Lorentz invariance test.(1) They measured the nuclear spin precession frequency in lithium-7 and looked for changes in frequency or linewidth as the direction of the magnetic field rotated, together with Earth, relative to a galactic reference frame. Such measurements, known as Hughes-Drever experiments, have been interpreted, for example, in terms of a possible difference between the speed of light and the limiting velocity of massive particles.(2)

5) Theorists and experimentalists in disciplines ranging from atomic physics to cosmology have been increasingly interested in tests of Lorentz invariance. The high sensitivity of experimental tests combined with recent advances in their theoretical interpretation allows one to probe ultrashort distance scales well beyond the reach of conventional particle-collider experiments. In fact, both the best experiments and astrophysical observations can indirectly probe distance scales as short as the Planck length (~ 10^(-35) m). Experiments that probe such short scales can constrain quantum gravity scenarios.(3-5)

References (abridged):

1. V. W. Hughes, H. G. Robinson, V. Beltran-Lopez, Phys. Rev. Lett. 4, 342 (1960) ; R. W. P. Drever, Phil. Mag. 5, 409 (1960)

2. C. M. Will, Theory and Experiment in Gravitational Physics, Cambridge U. Press, New York (1993)

3. D. Colladay, V. A. Kostelecky, Phys. Rev. D 55, 6760 (1997); Phys. Rev. D 58, 116002 (1998); V. A. Kostelecky, C. D. Lane, Phys. Rev. D 60, 116010 (1999).

4. S. R. Coleman, S. L. Glashow, Phys. Rev. D 59, 116008 (1999)

5. S. M. Carroll, G. B. Field, R. Jackiw, Phys. Rev. D 41, 1231 (1990)

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