General Relativistic Two-Body Problem: Theory and Experiment and the Role of Hidden Momentum
Emphasis will be placed on unusual aspects of our derivation, particularly the use of techniques from the more developed realm of QED (quantum electrodynamics). We obtain explicit results for the precession of the spin (rotation) and orbital effects and w
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Abstract Emphasis will be placed on unusual aspects of our derivation, particularly the use of techniques from the more developed realm of QED (quantum electrodynamics). We obtain explicit results for the precession of the spin (rotation) and orbital effects and we discuss the relatively recent (2008) verification of our spin precession result. Unusual features of our orbital precession analysis is the appearance of hidden momentum effects whose origins may be traced to a special relativistic effect.
1 Introduction The work of Schiff [1] in 1960 led to a resurgence of interest in analyzing and measuring the Lense-Thirring effect due to spin (rotation) effects. In particular, Barker and I [2], using a potential which we derived using techniques from QED, obtained the classical motion of a gyroscope in the gravitational field of a much larger mass with a quadrupole moment. Our method of derivation was much shorter and more straightforward than conventional methods especially as we made use of familiar Lagrangian concepts. Also, our results agreed with Schiff except that our equations of orbital motion appeared to be different than those of Schiff (although they both led to the same orbital precession results). Later, we traced this difference to the use of a different choice of coordinates [3], which was not due to the freedom enjoyed by the use of general relativity but due to a special relativistic effect, which we will discuss below in connection with hidden momentum. When the first binary pulsar was discovered [4], we were motivated to extend our results to the two-body domain [5, 6]. However, due to the nature of their system, Hulse and Taylor were unable to observationally verify our results. However, with the discovery of the double pulsar, our results were verified to an accuracy of 13 % [7]. In Sect. 2, we discuss the derivation of our results and their experimental verification. Then, in Sect. 3, we discuss the origin of hidden momentum. R.F. O’Connell (B) Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001, USA e-mail: [email protected] © Springer International Publishing Switzerland 2015 D. Puetzfeld et al. (eds.), Equations of Motion in Relativistic Gravity, Fundamental Theories of Physics 179, DOI 10.1007/978-3-319-18335-0_7
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2 Two-Body Results: Theory and Experimental Verification QED theory generally deals with the electromagnetic interaction of elementary particles whereas gravitation for the most part is confined to macroscopic systems. Thus, we decided to start with the gravitational interaction of two electrons, given by a one-graviton exchange interaction [8]. Next, making use of the universality of the gravitational interaction, we obtain the classical macroscopic result by letting 1 (1) σ → S(1) , 2 1 (2) σ → S(2) , 2
(1)
where σ (1) and σ (2) are the Pauli spin matrices associated with electrons 1 and 2 and where S(1) and S(2) are the classical spin angular momenta of the macroscopic masses m 1 and m 2 . Thus,
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