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AN APPLICATION OF SOUND WAVES TO THE RELATIVISTIC DEFINITION OF SIMULTANEITY


Geryllax Vu

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According to the relativistic definition of simultaneity, if two spatially separated events occur such that the light waves generated by these two events arrive at the midpoint of the line adjoining them, at the same time, then these two events are considered simultaneous. However, if these two events occur in still air, then any sound waves that might also be generated may not arrive at this midpoint, at the same time. The events occur at the endpoints of their adjoining line and form a tandem, of length L, where all the discrete points on the line remain at a fixed distance of separation, whether the tandem is in motion, or at rest. If this tandem (material object) is moving at a constant velocity v along a line parallel to the line adjoining them, through still air, then the sound waves generated by the events at the endpoints will not arrive at the midpoint simultaneously. The speed and direction of the tandem relative to the still air may then be mathematically determined using a modified formula from the Michelson-Morley experiment, in which the value of c is switched from the speed of light, to the speed of sound. With the light flash signaling the departure time of the sound wave, and using clocks to measure the arrival time of the sound wave, then the time interval t along with all the other variable values are available from within the tandem reference frame (the air molecules pass freely through the porous conceptual walls of the reference frame). This methodology of using sound waves to investigate the motion of a material object, combined with the Doppler Effect, calls into question the classical principle of relativity by allowing the determination of relative motion completely from within a single reference frame which is stationary or in motion.

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