"In Diagram 2, (lower diagram) the blue point represents the observer, and the arrow represents the observer's velocity vector. When the observer is stationary, the x,y-grid appears yellow and the y-axis appears as a black vertical line. Increasing the observer's velocity to the right shifts the colors and the aberration of light distorts the grid. When the observer looks forward (right on the grid), points appear green, blue, and violet (blueshift) and grid lines appear farther apart. If the observer looks backward (left on the grid), then points appear red (redshift) and lines appear closer together. Note, the grid itself has not changed, but its appearance for the observer has. The main point in the Doppler Effect is to individualize each wave out sourcing the central point and expanding the wave given do to circulatory vibrations at a certain focal point.

Understanding relativistic Doppler effect requires understanding the Doppler effect, time dilation, and the aberration of light. As a simple analogy, consider two people playing catch. Imagine that a stationary pitcher tosses one ball each second (1 Hz) at one meter per second to a catcher who is standing one meter away. The stationary catcher will receive one ball per second (1 Hz). Then the catcher walks away from the pitcher at 0.5 meters per second and catches a ball every 2 seconds (0.5 Hz). Finally, the catcher walks towards the pitcher at 0.5 meters per second and catches three balls every two seconds (1.5 Hz). The same would be true if the pitcher moved toward or away from the catcher. By analogy, the relativistic Doppler effect shifts the frequency of light as the emitter or observer moves toward or away from the other.

Diagram 1 (upper diagram) shows an emitter traveling to the right, whereas Diagram 2 shows the observer traveling right. While the color shift appears similar, the aberration of light is opposite. To understand this effect, again imagine two people playing catch. If the pitcher is moving to the right and the catcher is standing still, then the pitcher must aim behind the catcher. Otherwise the ball will pass the catcher on the right. Also, the catcher must turn in front of the pitcher, or the ball will hit on the catcher's left. Conversely, if the pitcher is stationary and the catcher is moving to the right, then the pitcher must aim in front of the catcher. Otherwise, the ball will pass the catcher on the left. Also, the catcher must turn to the back of the pitcher, or the ball will hit on the catcher's right. The degree to which the pitcher and catcher must turn to the right or left depends on two things: 1) the instantaneous angle between the pitcher-catcher line and the runner's velocity vector, and 2) the pitcher-catcher velocity relative to the speed of the ball. By analogy, the aberration of light depends on: 1) the instantaneous angle between the emitter-observer line and the relative velocity vector, and 2) the emitter-observer velocity relative to the speed of light."

Hi Lloyd,

I brought this over from http://en.wikipedia.org/wiki/Relativistic_Doppler_Effect . I was actually working on a similar baseball analogy when I saw that they had used one much the same the other day. The diagrams show the red and blue shifts per the degrees surrounding an emitter and receiver. The de Broglie wavelength of particles also undergoes shifts due to the Doppler Effect. There is also the matter of information being carried by way of EM radiation which should be considered, which is best explained by the differences of gravitational time dilation and acceleration time dilation. With time dilation due to gravitation, only the clock near the massive gravitational body appears to slow, as can be seen equally by two observers, one within the gravitational well, and one at a higher altitude. Unlike time dilation due to acceleration, the observer near the slower moving clock within the well does not see the higher altitude clock to be running slower also, but sees it to be faster as it is. This is seemingly due to the Doppler shift of information by way of EM radiation within an accelerated frame. The sequencing of information within various EM waves is also prone to red and blue shifts, which correspond to temporal dilation as with the fact that the accelerated clock is actually running slower, yet the clock at rest appears to run slower to the observer within the accelerated frame. This is due to the Doppler shift of the information whereby one observer sees another. I associate this effect similar to the frequency shift of a police radar gun as it catches me speeding all the time.....lmao. If the reflected information was critical to the sequencing of a clock within the visible range, and the velocity was great enough, then I assume there would be related effects by way of the change in position of the accelerated frame from the moment of the emitted radiation to the moment of reception. I think there's an animation on the net somewhere of cars and a light beam bouncing back and forth which goes into all this.

Where I see us heading is the deepest possible subject matter, Lloyd. I am working on my thoughts of how to approach such, but in short, it is how a system is set against itself to give internal definition to all. We take for granted the various forms of motion e.g. linear, angular, spin, vibration, etc, but from the philosophical perspective of a universe, I'm uncertain that any characteristic is wasted, as I would philosophically consider the system to collapse if not fully efficient. I see all things as necessary to something whereby the entire system is self sufficient. There seem to be prerequisites to existence, whereby the universe fills this efficiently. Not to go too deeply into the philosophical, but consider what we've been scientifically discussing. If we can use a linear system of light waves as an absolute ruler with wavelengths as discrete intervals along a distance whereby establishing the relational absolute motions of the angular confined systems (matter) thus uniting RM and QM, then we must also consider the manifestation of the light wave by way of these systems as with an electron emitting photons, radioactive decay, etc. In a sense, the angular localized FS establishes by way of timing the non local linear expression (EM radiation) whereby it will later define distance against, which further defines the timing within the localized system, etc, etc. I can't exactly put my finger on it, but its the depths at which the human knowledge system can go IMHO, as not only understanding the mechanics of the system, but also understanding how the mechanics are crucial to the conservation of existence, and how the various aspects of the mechanics are played against each other where the system gives definition to itself. It's the simple old thought that you can't have a state without the opposing state defining it. In this case, it takes the many states of motion and their ability to produce the other states to create the encompassing self defining system, or at least that's where my mind is leading me.

As to the not so deep applications, I think it would be beneficial to produce a unified objective Classic Mechanical treatment to all of the subjective and often misinterpreted aspects of QM and RM. This is why I am trying to relate the states of motion of both disciplines to mere gear analogies with work conservation and such as with the mechanical advantage aspects. Classical mechanics is a more natural system to our thought process, and I feel it does have the advantage over the others, if we merely find the applications which encompass them all within one methodology.

P.S. I had caught the comments, but it probably is more productive to post them in a post of their own as you did per others following the conversation. I also only work down south on occasion. I actually travel all over the U.S. and have been as far as the Virgin Islands working. I've worked in or traveled through the majority of the states. I'll be headed to Wyoming soon. I've made that trip probably ten times and hate it every time. The only trip I hate worse is California.....