Abstract
To use atomic clocks for the in situ determination of differences in the gravitational potential of the Earth’s gravity field was proposed for the first time by Bjerhammar (1985), Vermeer (1983), taking up Einstein’s postulation that two atomic clocks will tick at different rates due to different gravity potential values at different locations. However, this concept has not been demonstrated so far due to limitations in comparing clock frequency at ≤10−18 relative accuracy between two distant locations. Recently, a frequency transfer was demonstrated below 10-18 relative accuracy over a distance of ca. 920 km using an optical fibre (Predehl et al. 2012), with only one optical clock placed at one end of the optical fibre and a H-maser at the other end. In Švehla and Rothacher (2005b) it was proposed to use atomic clocks in space to measure the gravitational potential along an orbit, to measure together with GNSS, both position and gravity in a purely geometrical way. Here we provide the physical background to relativistic geodesy that is not given in Bjerhammar (1985) and, based on this, provide a geometrical representation of gravity and its relation to orbital motion and reference frames for time. We also show that in special cases, it is possible to measure absolute gravity potential values using quantum mechanics, which opens up new possibilities for the use of state-of-the-art optical clocks. Beyond the Standard Model in theoretical physics based on four fundamental forces, gravitation is still separated from the electromagnetic, strong nuclear, and weak nuclear interactions that are successfully related by the quantum field theory at the level of atomic, particle and high energy physics. On the other hand, general relativity brilliantly describes all observed phenomena related to gravitation in our Solar System and at galactic and cosmological scales. However, general relativity is fundamentally incomplete, because it does not include quantum effects. A unified theory relating all four known interactions will represent a step towards the unification of all fundamental forces of nature. Here we show that circular perturbations could provide an interesting representation between quantum mechanics and orbit mechanics. We try to establish an equivalence between the orbit mechanics based on circular perturbations and basic principles of quantum mechanics. We show that gravity at quantum level and at celestial level can be represented with the same property as light, i.e., gravity and light can be represented as oscillating at the equivalent rate and thus propagate at the same rate. In the essence of every orbit one could consider a wave represented by matter and time that could be modelled or represented by two geometrical rotations. We try to represent gravitational potential by two geometrical counter-rotations, with the rotation of spherical harmonic coefficients as generating functions. This dualistic concept is similar to the electromagnetic force where electricity and magnetism are elements of the same phenomenon orthogonal to each other. Following the general relativity, any form of energy that couples with spacetime creates differential geometrical forms that can describe gravity. Thus, gravitation can be considered purely as a geometrical property. However, our geometrical representation using two counter-oscillations (bi-circular orbits) can be considered as describing gravitation from the scalar point of view at the quantum as well as at the celestial level. Thus it gives geometrical and scalar properties of gravitation at the same time. This is similar to the concept of a magnetic field generated on top of an existing electric field, or similar to the concept of matter and antimatter in particle physics, where antimatter is described as material composed of antiparticles with the same mass as particles, but with opposite charge (leptons, baryons). Following recent results from the Planck mission (Planck Collaboration et al. 2013), there is strong evidence that 26.8% of the mass-energy of the Universe is made of non-baryonic dark matter particles, which should be described by the Standard Model.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abramowitz M, Stegun IA (1965) Handbook of mathematical functions: with formulas, graphs, and mathematical tables. J Geophys Res 92:1287–1294
Bjerhammar A (1985) On a relativistic geodesy. J Geodesy 59:207–220. https://doi.org/10.1007/BF02520327
Braxmaier C, Dittus H, Foulon B et al (2012) Astrodynamical space test of relativity using optical devices I (ASTROD I)—a class-M fundamental physics mission proposal for cosmic vision 2015–2025: 2010 update. Exp Astron 34:181–201. https://doi.org/10.1007/s10686-011-9281-y
Cacciapuoti L, Salomon C (2009) Space clocks and fundamental tests: the ACES experiment. Eur Phys J Spec Top 172:57–68. https://doi.org/10.1140/epjst/e2009-01041-7
Ciufolini I, Pavlis EC (2004) A confirmation of the general relativistic prediction of the Lense-Thirring effect. Nature 431:958–960. https://doi.org/10.1038/nature03007
de Broglie L (1924) Recherches sur la théorie des quanta (Researches on the quantum theory), Thesis (Paris). Ann Phys (Paris) 3:22 (1925)
Debs JE, Robins NP, Close JD (2013) Measuring mass in seconds. Science 339:532–533. https://doi.org/10.1126/science.1232923
Droste S, Ozimek F, Udem T et al (2013) Optical-frequency transfer over a single-span 1840 km fiber link. Phys Rev Lett 111:110801. https://doi.org/10.1103/PhysRevLett.111.110801
Einstein A (1905) Zur elektrodynamik bewegter körper. Ann Phys 322:891–921. https://doi.org/10.1002/andp.19053221004
Einstein A (1916) Die grundlage der allgemeinen relativitätstheorie. Ann Phys 354:769–822. https://doi.org/10.1002/andp.19163540702
Kopeikin SM (2003) The post-Newtonian treatment of the VLBI experiment on September 8, 2002. Phys Lett A 312(11):147–157. https://doi.org/10.1016/s0375-9601(03)00613-3
Lan S-Y, Kuan P-C, Estey B et al (2013) A clock directly linking time to a particle’s mass. Science 339:554–557. https://doi.org/10.1126/science.1230767
Montenbruck O, Gill E (2000) Satellite orbits: models, methods, and applications. Springer
Moritz H (1993) Geometry, relativity, geodesy. Wichmann, Karlsruhe
Muller H, Peters A, Chu S (2010) A precision measurement of the gravitational redshift by the interference of matter waves. Nature 463:926–929. https://doi.org/10.1038/nature08776
Planck Collaboration, Ade PAR, Aghanim N et al (2013) Planck 2013 results. XVI. Cosmological parameters
Pound RV, Rebka GA (1959) Gravitational red-shift in nuclear resonance. Phys Rev Lett 3:439–441. https://doi.org/10.1103/PhysRevLett.3.439
Predehl K, Grosche G, Raupach SMF et al (2012) A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place. Science 336:441–444. https://doi.org/10.1126/science.1218442
Rummel R (2006) Physical geodesy. Lecture notes. TU München, Germany
Scientific Collaboration LIGO, Collaboration Virgo, Abbott BP, Abbott R et al (2016) Observation of gravitational waves from a binary black hole merger. Phys Rev Lett 116:061102. https://doi.org/10.1103/PhysRevLett.116.061102
Solarić N, Solarić M, Švehla D (2012) Nove revolucionarne mogućnosti u geodeziji koje pružaju otkrića za koja su dobivene Nobelove nagrade za fiziku 2005. i 1997. godine. Geodetski list 66(89):1–19
Švehla D, Rothacher M (2005b) Kinematic precise orbit determination for gravity field determination. In: A window on the future of geodesy. International association of geodesy symposia, vol 128. Springer, Berlin, pp 181–188. https://doi.org/10.1007/3-540-27432-4_32
Vermeer M (1983) Chronometric levelling. Rep Finnish Geodet Inst 83:1–7
Vessot RFC, Levine MW, Mattison EM et al (1980) Test of relativistic gravitation with a space-borne hydrogen maser. Phys Rev Lett 45:2081. https://doi.org/10.1103/PhysRevLett.45.2081
Wolf P, Bordé CJ, Clairon A et al (2009) Quantum physics exploring gravity in the outer solar system: the SAGAS project. Exp Astron 23:651–687. https://doi.org/10.1007/s10686-008-9118-5
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Svehla, D. (2018). Geometrical Representation of Gravity. In: Geometrical Theory of Satellite Orbits and Gravity Field . Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-76873-1_29
Download citation
DOI: https://doi.org/10.1007/978-3-319-76873-1_29
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-76872-4
Online ISBN: 978-3-319-76873-1
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)