The Voice of Allan Zade
Suppose now this. Both observers prefer to conduct another experiment in a different direction and at the same speed of observer-to-continuum relative motion. They chose direction O-C1 for the new experiment. Once again, the first observer makes some disturbance that makes propagation in the continuum. One full circle of that disturbance forms a sphere again and appears as a wave O-C1 for a motionless observer.
In case of motion, that wave becomes distorted again, as well as in the first case. However, at this time, the wave becomes even more distorted than in the first experiment. It appears as wave B-C1 instead of O-C1. That wave goes in the direction O-C1 and meets the second observer at point O3. The wave has location F2-O3 at that particular moment in the medium. The process of interaction between the wave and the observer begins.
During that interaction, both the observer and the wave keep motion in the continuum. After the exact duration of interaction that coincides with the duration of wave emission, the second observer found himself at the point O4, where he meets the last point of the wave passing the observer by the continuum. The process of interaction finishes. The wave has location O4-G3 in the continuum at that particular moment.
Once again, both observers fall under the delusion that they conducted the identical physical experiment, as evidenced by the readings of their instruments, which point in another direction: the detected duration of interaction between the wave and the observer remains constant. However, that delusion comes from the wave distorted by the motion of the first observer. However, both observers maintain this delusion in their minds because they measure only the duration of wave creation and detection, without considering other properties of waves.
Moreover, this delusion involves the idea that in all cases, the observers meet a disturbance with a wavelength equal to the radius of sphere S, and that this wavelength remains constant in all experiments.
Moreover, they do not understand one more aspect of all experiments. Suppose now this. The second observer detects a disturbance according to his delusion at both the beginning and end points of the measurements.
In that case, the second observer starts interaction with a given wave at the point O3. By the given duration, the observer reaches point O4, as was also the case in the previous experiment. The disturbance appears as waves O3-G3 and F3-F4 at that very moment. Both waves are parallel and have the same location (phases) relative to the first point O3 because their phases are the same, as defined by the experiment.
As a result, the second observer does not meet the end of the wave. He meets the wave at a point where another phase exists, rather than at 360 degrees. That happens because, in this case, the wave covers the distance F3-F4 during the experiment. Its tail (point F3) has a different location relative to point O4 (the tail point of the distorted wave). As a result, the second observer detects only part of the wave instead of the full wave through its interaction with that wave. In other words, he detects a wave with a greater wavelength than expected. Therefore, he detects wavelength changes in the case of no relative motion with the first observer. All physical experiments disprove that point of view. Thus, the second observer meets a distorted wave despite his delusion.
It is also possible to describe the general law of wave distortion:
there, E is the speed of disturbance regarding a given medium, V is the speed of the observer regarding the medium, and W is the “speed” of the distorted wave.
That is a vector equation. Its application to Figure 1 gives three results for the three described experiments. The third experiment appeared as (O-C1) = (OB) + (B-C1). The second experiment appears as (O-C2) = (OB) + (B-C2). The first experiment appears as (O-C2) = (O-C2) + 0.
Zero value in the first case means this. Disturbance starts and finishes at the same point. Therefore, there is no distance between the start and the end points of emission in the case of an observer to a medium static location. In all cases, the “speed” of the distorted wave appears as the third component of that equation. That is the speed of disturbance that the observer detects in his reference frame as “a true wave”. Despite this, the physical disturbance in the continuum maintains the full speed of disturbance-to-medium relative motion, as explained above. However, the motion of the observer distorts that wave (making it shorter in the explained cases).
There is one more case here. It is also possible for the observers to experiment in the OC direction. In that case, equation 1 becomes a “classical” equation for speed addition.
Therefore, there is no exception to that way of wave propagation and distortion.
Suppose now this. There is a third observer who has a different direction of motion and a different speed. He starts observation at the same point as the second observer, O3, but proceeds in the direction of O3-OY. In that case, he also interacts physically with the distorted wave (represented by the blue line). However, after the exact duration of motion, he meets the blue wave at the point OY (instead of O4, as seen by the second observer).
In that particular case, the third observer detects only half of the blue wavelength interacting with his measuring instruments for the same duration. As a result, he detects a longer wavelength of a given disturbance (or its lower frequency). Therefore, he detects the Doppler Effect, which appears only in one condition: when an observer has some relative motion with respect to another observer who is making a disturbance.