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Register a new userExperimental constraints on the second clock effect
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We set observational constraints on the second clock effect, predicted by Weyl unified field theory, by investigating recent data on the dilated lifetime of muons accelerated by a magnetic field. These data were obtained in an experiment carried out in CERN aiming at measuring the anomalous magnetic moment of the muon. In our analysis we employ the definition of invariant proper time proposed by V. Perlick, which seems to be the appropriate notion to be worked out in the context of Weyl space-time.
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The main theoretical aspects of gravitomagnetism are reviewed. It is shown that the gravitomagnetic precession of a gyroscope is intimately connected with the special temporal structure around a rotating mass that is revealed by the gravitomagnetic clock effect. This remarkable effect, which involves the difference in the proper periods of a standard clock in prograde and retrograde circular geodesic orbits around a rotating mass, is discussed in detail. The implications of this effect for the notion of ``inertial dragging in the general theory of relativity are presented. The theory of the clock effect is developed within the PPN framework and the possibility of measuring it via spaceborne clocks is examined.
As a consequence of gravitomagnetism, which is a fundamental weak-field prediction of general relativity and ubiquitous in gravitational phenomena, clocks show a difference in their proper periods when moving along identical orbits in opposite directions about a spinning mass. This time shift is induced by the rotation of the source and may be used to verify the existence of the terrestrial gravitomagnetic field by means of orbiting clocks. A possible mission scenario is outlined with emphasis given to some of the major difficulties which inevitably arise in connection with such a venture.
The difference in the proper azimuthal periods of revolution of two standard clocks in direct and retrograde orbits about a central rotating mass is proportional to J/Mc^2, where J and M are, respectively, the proper angular momentum and mass of the source. In connection with this gravitomagnetic clock effect, we explore the possibility of using spaceborne standard clocks for detecting the gravitomagnetic field of the Earth. It is shown that this approach to the measurement of the gravitomagnetic field is, in a certain sense, theoretically equivalent to the Gravity Probe-B concept.
We investigate how stable circular orbits around a main compact object appear depending on the presence of a second one by using the Majumudar--Papapetrou dihole spacetime, which consists of the two extremal Reissner--Nordstr om black holes with different masses. While the parameter range of the separation of the two objects is divided due to the appearance of stable circular orbits, this division depends on its mass ratio. We show that the mass ratio range separates into four parts, and we find three critical values as the boundaries.
We consider the relativistic tidal effects on frequency shift of clock-comparison experiments. The relativistic formulation for frequency shift and time transfer is derived in the gravitational field of a tidal, axisymmetric, and rotating Earth. With the help of Love numbers describing the tidal response of solid Earth, we formulize the mathematical connection between tidal effects from the ground-based clock-comparison experiments and the local gravity tides from the gravimeters, which in turn provides us an approach to eliminate tidal influences on clock comparison with the local gravity tides data. Moreover, we develop a method of the perturbed Kepler orbit to determine relativistic effects of clock comparison for space missions, which allows more precise calculations comparing to the conventional method of unperturbed Kepler orbit. With this perturbed method, it can give the perturbation of relativistic effects due to the orbital changes under the influences of tidal forces, Earths oblateness etc. In addition, as the applications of our results, we simulate tidal effects in frequency shift for the clock comparison on the ground and also give some estimates for TianQin mission and GPS.
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