# Experimental basis of Special Relativity/Recent Tests of CPT and Lorentz Invariance

## < Experimental basis of Special Relativity

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The *CPT theorem* is a general property of quantum field theories that states (loosely) that any system must behave the same if one applies the *CPT* transform to it: invert all charges (C, charge conjugation), invert all spatial axes (P, parity inversion), and invert the direction of time (T, time inversion). While one cannot actually do any of that in the real world, one can perform experiments in which particles are replaced by antiparticles (C), one looks at situations in which left and right are interchanged (P), and the particles travel along similar paths but in opposite directions and have opposite spin polarizations (T).

*Lorentz Invariance* is the technical term for the statement that SR is valid. Any violation of CPT invariance implies a violation of Lorentz invariance; theories without Lorentz invariance need not have CPT invariance.

- Kosteleckэ and Mewes, “Signals for Lorentz violation in electrodynamics”, Phys. Rev. D66, 056005 (2002).: A review of various limits, terrestrial and astrophysical.
- Mueller, “Testing Lorentz invariance by the use of vacuum and matter filled cavity resonators”, Phys. Rev. D71, 045004 (2005).: A review article.

### Cavity Experiments:

- Müller, H., P.L. Stanwix, M.E. Tobar, E. Ivanov, P. Wolf, S. Herrmann, A. Senger, E. Kovalchuk, A. Peters, “Relativity tests by complementary rotating Michelson-Morley experiments”,arXiv:0706.2031v1 [physics.class-ph].: By combining results from two interferometers made of different materials, located in different hemispheres, rotating on tables, they are able to put limits on more parameters of the SME than otherwise. They have also improved both the statistics and systematic errors of the individual interferometers.

### Particle-Based Experiments:

- Nguyen, H.H., “CPT results from KTeV”, (2001). arXiv:hep-ex/0112046.: -
- Schwingenheuer, B. et al., “CPT tests in the neutral kaon system”, Phys. Rev. Lett., 74, pg 4376–4379, (1995).: -
- Gurzadyan et al., “Probing the Light Speed Anisotropy with respect to the Cosmic Microwave Background Radiation Dipole”, Mod. Phys. Lett., 2005, v.20, pg 19. arXiv:astro-ph/0410742.: -
- Hughes, V.W., Grosse Perdekamp, M., Kawall, D., Liu, W., Jungmann, K., and zu Pulitz, G., “Test of CPT and Lorentz Invariance from Muonium Spectroscopy”, Phys. Rev. Lett., 87, 111804-1-4, (2001). arxiv:hep-ex/0106103.: -
- Bluhm, R., Kosteleckэ, V.A., and Lane, C.D.,”CPT and Lorentz tests with muons”, Phys. Rev. Lett., 84, pg 1098–1101, (2000). arXiv:hep-ph/9912451.: -
- Carey, R.M. et al., “New Measurement of the Anomalous Magnetic Moment of the Positive Muon”, Phys. Rev. Lett., 82, pg 1632–1635, (1999).: -
- R. Grieser, R. Klein, G. Huber, S. Dickopf, I. Klaft, P. Knobloch, P. Merz, F. Albrecht, M. Grieser, D. Habs, D. Schwalm and T. Kaehl, “A test of special relativity with stored lithium ions”, Appl. Phys. B59, no. 2, pg 127 (1994).Klein et al., Zeitschrift fuer Physik A 342, pg 455 (1992).Saathoff, G., Karpuk, S., Eisenbarth, U., Huber, G., Krohn, S., Horta, R.M., Reinhardt, S., Schwalm, D., Wolf, A., and Gwinner, G., “Improved Test of Time Dilation in Special Relativity”, Phys. Rev. Lett., 91, 190403, (2003).G. Saathoff, S. Reinhardt, H. Buhr, L.A. Carlson, D. Schwalm, A. Wolf, S. Karpuk, C. Novotny, G. Huber, and G. Gwinner, Can. J. Phys./Rev. can. phys. 83(4): pg 425–434 (2005)(Saathof's Ph.D. thesis, 2002) http://www.mpi-hd.mpg.de/ato/homes/saathoff/diss-saathoff.pdf(Reinhardt's Ph.D. thesis, 2005) http://archiv.ub.uni-heidelberg.de/volltextserver/volltexte/2005/5934/pdf/doktorarbeit_sreinhardt.pdf: This is an incredibly clever experiment using
^{7}Li^{+}ions in a storage ring, synchronizing a single laser to a 2-level transition via Doppler shifts in both directions. The fractional accuracy in frequency is 10^{−9}, and the limit on deviation from the relativistic formula is 2.2Ч10^{−7}for speeds a substantial fraction of c. - Lane, C.D., “Probing Lorentz violation with Doppler-shift experiments”. arXiv:hep-ph/0505130.: -
- Mittleman, R.K., Ioannou, I.I., Dehmelt, H.G., and Russell, N., “Bound on CPT and Lorentz symmetry with a trapped electron”, Phys. Rev. Lett., 83, pg 2116–2119, (1999).: -
- Gabrielse, G., Khabbaz, A., Hall, D.S., Heimann, C., Kalinowsky, H., and Jhe, W., “Precision mass spectroscopy of the antiproton and proton using simultaneously trapped particles”, Phys. Rev. Lett., 82, pg 3198–3201, (1999).: -
- Dehmelt, H.G., Mittleman, R.K., van Dyck Jr, R.S., and Schwinberg, P., “Past electron positron g-2 experiments yielded sharpest bound on CPT violation”, Phys. Rev. Lett., 83, pg 4694–4696, (1999). arXiv:hep-ph/9906262.: -
- Auerbach et al. (LSND Collaboration), “Test of Lorentz violation in Anti-ν
_{μ}→ Anti-ν_{e}oscillations”. Phys. Rev. D 72, 076004 (2005).: These neutrino oscillations display no significant sidereal variation.

- Note, however, that the LSND results have been a puzzle for several years, as they appear to be inconsistent with other experiments. Just recently they were directly contradicted by the Mini-BooNE results from Fermilab (May 2007, no reference yet).

- Kosteleckэ and Mewes, “Lorentz violation and short-baseline neutrino experiments”, Phys. Rev. D70, 076002 (2004).: Using the published results of the Liquid Scintillator Neutrino Detector (LSND) experiment, an estimated nonzero value (3 ±1)Ч10
^{−19}GeV for a combination of coefficients for Lorentz violation is obtained. This lies in the range expected for effects originating from the Planck scale in an underlying unified theory.

- Note, however, that the LSND results have been a puzzle for several years, as they appear to be inconsistent with other experiments. Just recently they were directly contradicted by the Mini-BooNE results from Fermilab (May 2007, no reference yet).

### Clock-comparison experiments:

- Walsworth, Bear, Humphrey, Mattison, Phillips, Stoner, and Vessot, “New Clock Comparison Searches for Lorentz and CPT Violation”, arxiv:physics/0007063 (2000).Bear, D., Stoner, R.E., Walsworth, R.L., Kosteleckэ, V.A., and Lane, C.D., “Limit on Lorentz and CPT violation of the neutron using a two-species noble-gas maser”, Phys. Rev. Lett., 85, pg 5038–5041, (2000). arXiv:physics/0007049.Bear, D., Stoner, R.E., Walsworth, R.L., Kosteleckэ, V.A., and Lane, C.D., “Erratum: Limit on Lorentz and CPT Violation of the Neutron Using a Two-Species Noble-Gas Maser”, Phys. Rev. Lett., 89, 209902, (2002).Cane, Bear, Phillips, Rosen, Smallwood, Stoner, and Walsworth, “Bound on Lorentz and CPT Violating Boost Effects for the Neutron”, Phys. Rev. Lett. 93, 230801 (2004).: Search for sidereal variation in the frequency difference between co-located
^{129}Xe and^{3}He Zeeman masers sets the most stringent limits to date on leading order Lorentz and CPT violation. By locating the two masers in the same enclosure they eliminate many systematic errors, and are looking at variations at the level of 100 nHz (10^{−7}Hz !). - Kosteleckэ, V.A., and Lane, C.D., “Constraints on Lorentz violation from clock-comparison experiments”, Phys. Rev. D, 60, 116010, (1999). arXiv:hep-ph/9908504.: -
- Bertolami, O., and Rosa, J.G., “New bounds on cubic Lorentz-violating terms in the fermionic dispersion relation”, Phys. Rev. D, 71, 097901. arXiv:hep-ph/0412289.: -
- Berglund, C.J. et al., “New Limits on Local Lorentz Invariance from Hg and Cs Magnetometers”, Phys. Rev. Lett., 75, 1879, (1995).: -
- Phillips, D.F., Humphrey, M.A., Mattison, E.M., Stoner, R.E., Vessot, R.F.C., and Walsworth, R.L., “Limit on Lorentz and CPT violation of the proton using a hydrogen maser”, Phys. Rev. D, 63, 111101, (2001). arXiv:physics/0008230.Humphrey et al., “Testing CPT and Lorentz Symmetry with Hydrogen Masers”, Phys. Rev. A68, 063807 (2003). arXiv:physics/0103068.: -

### Astrophysical tests:

- Ellis, J.R., Farakos, K., Mavromatos, N.E., Mitsou, V.A., and Nanopoulos, D.V., “Astrophysical probes of the constancy of the velocity of light”, Astrophys. J., 535, 139–151, (2000).arXiv:astro-ph/9907340.: -
- Ellis, J.R., Mavromatos, N.E., Nanopoulos, D.V., and Sakharov, A.S., “Quantum-gravity analysis of gamma-ray bursts using wavelets”, Astron. Astrophys., 402, 409–424, (2003).arXiv:astro-ph/0210124.: -
- Biller, S.D., Breslin, A.C., Buckley, J., Catanese, M., Carson, M., Carter-Lewis, D.A., Cawley, M.F., Fegan, D.J., Finley, J.P., Gaidos, J.A., Hillas, A.M., Krennrich, F., Lamb, R.C., Lessard, R., Masterson, C., McEnery, J.E., McKernan, B., Moriarty, P., Quinn, J., Rose, H.J., Samuelson, F., Sembroski, G., Skelton, P., and Weekes, T.C., “Limits to quantum gravity effects from observations of TeV flares in active galaxies”, Phys. Rev. Lett., 83, 2108–2111, (1999). arXiv:gr-qc/9810044.: -
- Boggs, S.E., Wunderer, C.B., Hurley, K., and Coburn, W., “Testing Lorentz Non-Invariance with GRB021206”, (2003). arXiv:astro-ph/0310307.: -
- Ellis et al., “Robust Limits on Lorentz Violation from Gamma-Ray Bursts”, arXiv:astro-ph/0510172 (2005).: If the speed of light has an energy dependence c(E) ~ c
_{0}(1 −E/M), a limit on M is obtained: M > 0.9Ч10^{16}GeV/c^{2}. - Kosteleckэ and Mewes, “Cosmological Constraints on Lorentz Violation in Electrodynamics”, Phys. Rev. Lett., 87, no. 25, 251304 (2001).: Certain coefficients for Lorentz violation are bounded to less than 3Ч10
^{−32}.

### Vacuum Cerenkov radiation:

- Lehnert, R., and Potting, R., “The Cerenkov effect in Lorentz-violating vacua”, Phys. Rev. D, 70, 125010, (2004). arXiv:hep-ph/0408285 .Lehnert, R., and Potting, R., “Vacuum Cerenkov radiation”, Phys. Rev. Lett., 93, 110402, (2004). arXiv:hep-ph/0406128.: -
- Coleman, S.R., and Glashow, S.L., “Cosmic ray and neutrino tests of special relativity”, Phys. Lett. B, 405, 249-252, (1997). http://arXiv.org/abs/hep-ph/9703240.Coleman, S.R., and Glashow, S.L., “Evading the GZK cosmic-ray cutoff”, (1998). arXiv:hep-ph/9808446.Coleman, S.R., and Glashow, S.L., “High-energy tests of Lorentz invariance”, Phys. Rev. D, 59, 116008, (1999). arXiv:hep-ph/9812418.: -
- Greisen, K., “End to the cosmic ray spectrum?”, Phys. Rev. Lett., 16, pg 748–750, (1966).Zatsepin, G.T., and Kuzmin, V.A., “Upper limit of the spectrum of cosmic rays”, J. Exp. Theor. Phys. Lett., 4, pg 78–80, (1966).: The original GZT papers.