[puppypower (OP)]

Let me set up this topic with a practical example. Say we start with a train that is stationary and sounds it horn. Everyone, from any angle, will hear the same pitch. Next, we have a same train moving along a track. It again sounds it's horn. Because of the velocity and direction of motion and the resultant Doppler shift, anyone standing in front of the train, will hear a higher pitch; blue shift. Anyone standing behind the train will hear a lower pitch; red shift. While anyone standing aside the train will hear no change of pitch; original wave.

Although this makes sense and can demonstrated, once the sound waves leave the train, and propagate outward without any further train motion induction, do the spherical sound waves from the horn, forever remain egg shaped, because of the motion?  In other words, if we step backward, forward or away perpendicular, the ratios of pitch change stay the same; egg wave.

Next, how do these egg shaped waves impact wave addition when they encounter spherical waves, that are not egg shaped? Can the egg waves add to the spherical waves to give a false positive for motion, via the composite wave? If not, is the egg wave more of a multi-reference induced illusion? Or is there another explanation?

The title is Doppler Shift and Entropy. I included the concept of entropy, since this can be used as a way to address the final question. When entropy increases. energy is absorbed. This would be analogous to a red shift, since the transformed wave has less energy value than the original wave. Things are spreading out into a more open state of higher entropy; train moves away.

The blue shift would mean gaining energy, due to the lowering of entropy, and the release of energy. This is added to the observed wave. Things are getting closer into a state of lower entropy lie water becoming ice; exothermic. These equal and opposite affects should be a wash since energy cannot be destroyed.

One reference will experience lower entropy and the other reference will experience higher entropy, without any net change of free energy, This zero change of entropy should not allow any net change during wave addition. Change will imply creating or destroying energy using egg wave addition.

The question comes back do the egg shaped waves implicit of Doppler shift adding to circular waves where there is no motion, to form a false positive of motion. Is this observed, or does entropy normalization rule so this is not observed? 

I like thinking outside the box and I thought everyone would like to experience outside the box  starting at the front door. One does not have to leave the box but can open the front door and look out to see it is nice place to be.

[Bored chemist]

Or is there another explanation?

Apparently, but it isn't a scientific explanation.

The blue shift would mean gaining energy, due to the lowering of entropy,

No, it's not.
I can prove that, but you wouldn't listen.

[puppypower (OP)]

Let me change the scenario slightly to make it easier to perceive. We have two observers separated by a distance. One source of sound is attached to a moving object. I will add a second source, which is stationary, between the two observers. When the moving sound wave source is adjacent to the stationary source, this will trigger both sources to bing.

We have two source and two waves. The moving source wave will show red and blue shift; egg shaped wave, to each respective reference. While the stationary source has a spherical wave. Since they are close, if they wave add the composite wave will a rounder wave implicit of less velocity for the moving source and finite velocity for the stationary source. 

Since the two sources ping at the same time, which one is moving and which one is stationary if   but can only hear the composite sound? Will they both appear to be moving? We will need a second sense to clear this up.

An interesting addendum is to lower the pressure of the air in the above experiment to simulate the expansion of space. This will make the sound waves slow down, since the wave propagate faster in higher density mediums. The speed of sound increases as we go from gas, to liquid to solid for the same material. Since the velocity of the moving source is now a larger fraction of the slower speed of sound, in the expanded medium, the red and blue shifts will appear stronger than they were before we dropped the pressure. The egg appears longer.

The aether theory is not accepted as the medium of light transmission. However, it is interesting how the red shift of sound waves increases with expanded space. The main point was the red shift connected to multiple wave sources, both stationary and moving, wave add and can make motion and lack of motion, ambiguous

I did use entropy arguments to suggest a way to work around these problems. Let me do a scenario for Bored Chemist so he can see where I was heading. Say we have a cylinder of pressured liquid propane. We open the valve to expand the liquid into a gas. This expansion will cause the tank and the gas to cool. Since the state liquid has lower entropy, than the gas state for any material, the cooling; IR red shift, is connected to an entropy increase.

Say we have a star that is generating high pressures due to immense gravity. It gives off surface materials that go from higher to lower pressure; from star to space. This increases material entropy, at the same time, these material are giving off electron emissions. The entropic cooling will red shift thermal emissions, if the electron transitions are connected black body radiation; heat. Stars are classified by heat based radiation.

[Bored chemist]

egg shaped wave,

From what point of view is the wave "egg shaped".

I did use entropy arguments to suggest a way to work around these problems.

No
You wrote the word "entropy" and pretended that it was anything to do with what you are describing.
It isn't.

The aether theory is not accepted as the medium of light transmission

Because it's wrong.
Why introduce it?

Let me do a scenario for Bored Chemist so he can see where I was heading.

Thank you for clarifying that you were heading into word salad.
Though, to be honest, I had guessed.