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Novel Relativity Theories of Synthetic Aperture Radar
Published in Maged Marghany, Automatic Detection Algorithms of Oil Spill in Radar Images, 2019
This formula simply articulates that SAR can assign a time to a distant event by sending a microwave signal to the objects and backscatter and averaging the (proper) times of sending and receiving. Nonetheless, the concept of delineating hypersurfaces of simultaneity in terms of ‘SAR time’ has rarely been applied to noninertial satellite orbit or to non-flat spacetimes. This is perhaps due to Bondi’s claim [133] that “how a clock reacts to acceleration is utterly dependent on how the clock is constructed”. Consistent with Dolby [134] the postulation that ‘proper times’ will show identically as a function of acceleration or as a function of gravitational fields, which is a simple principle of general relativity, without which proper time would have no physical meaning. There is, therefore, no purpose to use ‘radar time’ to speed up SAR or to warp space-times. Since SAR time can be described short of any remark of coordinates it is, by construction, independent of our choice of coordinates. In this case, radar time or SAR time is single-valued, corresponds to proper time on the SAR path, and is invariant as a function of ‘time-reversal’—that is, under reversal of the sign of the SAR’s proper time [134].
The Sagnac effect and the role of simultaneity in relativity theory
Published in Journal of Modern Optics, 2021
Gianfranco Spavieri, George T. Gillies, Espen Gaarder Haug
For motion on the x−y plane, let the inertial frame be instantaneously co-moving with a point on the rim of the rotating disk and be the laboratory inertial frame where the centre of the disk is stationary. Let us assume that, at , the origin O of is at and y = r, instantaneously coinciding with the origin O of S in the direction of motion. The relation implies , or the curvilinear transformation between frame and , equivalent to the transformation between S and for infinitesimal variations. Absolute synchronization and simultaneity can be achieved with no problem by external synchronization of clocks of frame with clocks of frame . The proper time τ of the clock (or measuring apparatus) can be taken to be, , and to first order in v/c. Let us consider a signal propagating at the local speed along in the rotating frame. Then, as also remarked by several authors, the relation between the local speed u in and the local speed in on the rotating disk, is given by the Galilean composition of velocities , because .
Light propagation and local speed in the linear Sagnac effect
Published in Journal of Modern Optics, 2019
Gianfranco Spavieri, George T. Gillies, Espen Gaarder Haug, Arturo Sanchez
We assume that the conveyor arm AB is much larger than the radius r of the pulley, specifically, , as derived in Appendix. In this case, the circular Sagnac effect of Figure 2(a) is essentially completely linearized by the equivalent system of Figure 2(b). At the time , clock C, being fixed to the moving conveyor belt, moves from frame S to frame after being accelerated and acquiring the velocity u relative to S, in the negligibly short time (as shown in Appendix). This way, starting from the time , clock C will be co-moving with O of frame . In the meantime, the light pulse reflected at B is now moving toward C ≡ O in the upper part of the conveyor belt and the physical situation is the same as described in our Gedankenexperiment. The length of the conveyor belt (the ‘ground’ path) is and the sequence of path sections, covered by the light pulse in its round trip, starts from C ≡ O to reach B and then, after reflection, from B back to C ≡ CO. The round-trip proper time , taken by the light pulse to cover the round-trip ground path of the conveyor belt and measured by the single clock C, is known and must correspond to the sum of the proper time interval measured by C ≡O when in the lower part of the conveyor belt, plus the proper time interval measured by C ≡ CO when in the upper part. Depending on the type of synchronization adopted and its interpretation, the sequence of time intervals displayed by the measuring device (clock C), following the progression of the light pulse in its round trip, is the following.