Abstract
Geodetic Very Long Baseline Interferometry (VLBI) measures the group delay in the barycentric reference frame. As the Earth is orbiting around the Solar system barycentre with the velocity V of 30 km/s, VLBI proves to be a handy tool to detect the subtle effects of the special and general relativity theory with a magnitude of (V∕c)2. The theoretical correction for the second order terms reaches up to 300 ps, and it is implemented in the geodetic VLBI group delay model. The total contribution of the second order terms splits into two effects – the variation of the Earth scale, and the deflection of the apparent position of the radio source. The Robertson-Mansouri-Sexl (RMS) generalization of the Lorenz transformation is used for many modern tests of the special relativity theory. We develop an alteration of the RMS formalism to probe the Lorenz invariance with the geodetic VLBI data. The kinematic approach implies three parameters (as a function of the moving reference frame velocity) and the standard Einstein synchronisation. A generalised relativistic model of geodetic VLBI data includes all three parameters that could be estimated. Though, since the modern laboratory Michelson-Morley and Kennedy-Thorndike experiments are more accurate than VLBI technique, the presented equations may be used to test the VLBI group delay model itself.
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References
Altamimi Z, Rebischung P, Métivier L, Collilieux X (2016) ITRF2014: a new release of the international terrestrial reference frame modeling nonlinear station motions. J Geophys Res Solid Earth 121:6109–6131. https://doi.org/10.1002/2016JB013098
Cole TW (1976) Astronomical tests for the presence of an ether. Mon Not R Astron Soc 175(1):93P–96P. https://doi.org/10.1093/mnras/175.1.93P
Herrmann S, Senger A, Möhle K, Nagel M, Kovalchuk EV, Peters A (2009) Rotating optical cavity experiment testing lorentz invariance at the 10−17 level. Phys Rev D 80:105,011. https://doi.org/10.1103/PhysRevD.80.105011
Kennedy RJ, Thorndike EM (1932) Experimental establishment of the relativity of time. Phys Rev 42:400–418. https://doi.org/10.1103/PhysRev.42.400
Klioner S, Zschocke S, Soffel M, Butkevich A (2012) Testing local Lorentz invariance with high-accuracy astrometric observations. In: The twelfth Marcel Grossmann meeting, pp 1478–1480. https://doi.org/10.1142/9789814374552_0251
Lambert SB, Le Poncin-Lafitte C (2009) Determining the relativistic parameter gamma using very long baseline interferometry. Astron Astrophys 499(1):331–335. https://doi.org/10.1051/0004-6361/200911714
Le Poncin-Lafitte C, Hees A, Lambert S (2016) Lorentz symmetry and very long baseline interferometry. Phys Rev D 94:125,030. https://doi.org/10.1103/PhysRevD.94.125030
Mansouri R, Sexl R (1977a) A test theory of special relativity: I. Simultaneity and clock synchronization. Gen Relativ Gravit 8(7):497–513. https://doi.org/10.1007/BF00762634
Mansouri R, Sexl R (1977b) A test theory of special relativity: III. Second-order tests. Gen Relativ Gravit 8(10):809–814. https://doi.org/10.1007/BF00759585
Michelson A, Morley E (1887) On the relative motion of the earth and the luminiferous ether. Am J Sci 34(203):333–345. https://doi.org/10.2475/ajs.s3-34.203.333
Nothnagel A, Alef W, Amagai J, Andersen PH, Andreeva T, Artz T, Bachmann S, Barache C, Baudry A, Bauernfeind E et al (2015) The IVS data input to ITRF2014. GFZ Data Services, Helmoltz Centre, Potsdam, Germany. https://doi.org/10.5880/GFZ.1.1.2015.002
Petit G, Luzum B (2010) IERS Conventions 2010. IERS Technical Note No. 36
Robertson H (1949) Postulate versus observation in the special theory of relativity. Rev Mod Phys 21:378–382. https://doi.org/10.1103/RevModPhys.21.378
Robertson DS, Carter WE (1984) Relativistic deflection of radio signals in the solar gravitational field measured with VLBI. Nature 310:572–574. https://doi.org/10.1038/310572a0
Shapiro SS, Davis JL, Lebach DE, Gregory JS (2004) Measurement of the solar gravitational deflection of radio waves using geodetic very-long-baseline interferometry data, 1979–1999. Phys Rev Lett 92:121,101. https://doi.org/10.1103/PhysRevLett.92.121101
Smoot GF, Gorenstein MV, Muller RA (1977) Detection of anisotropy in the cosmic blackbody radiation. Phys Rev Lett 39:898–901. https://doi.org/10.1103/PhysRevLett.39.898
Tobar ME, Wolf P, Bize S, Santarelli G, Flambaum V (2010) Testing local lorentz and position invariance and variation of fundamental constants by searching the derivative of the comparison frequency between a cryogenic sapphire oscillator and hydrogen maser. Phys Rev D 81:022,003. https://doi.org/10.1103/PhysRevD.81.022003
Will CM (1992) Clock synchronization and isotropy of the one-way speed of light. Phys Rev D 45:403–411. https://doi.org/10.1103/PhysRevD.45.403
Acknowledgements
The authors thank the anonymous reviewers for their suggestions and comments which helped to improve the manuscript significantly. We acknowledge the IVS and all its components for providing VLBI data (Nothnagel et al. 2015). Hana Krásná works within the Hertha Firnberg position T697-N29, funded by the Austrian Science Fund (FWF). This paper has been published with the permission of the Geoscience Australia CEO.
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Titov, O., Krásná, H. (2018). Testing Special Relativity with Geodetic VLBI. In: Freymueller, J., Sánchez, L. (eds) International Symposium on Advancing Geodesy in a Changing World. International Association of Geodesy Symposia, vol 149. Springer, Cham. https://doi.org/10.1007/1345_2018_48
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DOI: https://doi.org/10.1007/1345_2018_48
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