1.4  The Relativity of Light
Evidently the word “light” is being used to signify two different things on the first and fourth days [of creation].
-Not evidently.  Light doesn’t depend on its source…. Sun , stars . candles, light bulbs, or the divine. Light is light is light.

...if light consists of material corpuscles, then according to Galilean relativity there should be an inertial reference frame with respect to which light is at rest in a vacuum, whereas in fact we never observe light in a vacuum to be at rest, nor even noticeably slow, with respect to any inertial reference frame.
- A frame in which aether is flowing at c opposite to a light beam would zero net speed in the absolute reference frame, like a boat moving upstream in a river current that matches its still-water motor speed. .
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..we find that light propagates best through regions (vacuum) in which there is no detectable material with a definite rest frame..
- If best means fastest, then the Sagnac exp.  results has the co-rotating beam moving at c + v in a definite rest frame – the lab.

...and again we cannot conceive of light at rest in any inertial frame.
- A frame in which aether is flowing at c opposite to a light beam is conceivable.

...numerous experiments showed that light propagates at the same speed in all directions relative to the source, just as we would expect for streams of inertial corpuscles.
-Numerous, but not all. Exceptions are the Fizeau confirmation of Fresnel drag, Sagnac, Ruyong Wang and Dufour & Prunier.

Hence some of the attributes of light seemed to unequivocally support an emission theory,
- Sagnac rules out emission theory.
....if we apply a Galilean transformation to these coordinates, the wave equation is not satisfied with respect to the transformed coordinates.
- An indication that aether motion in an absolute frame must be included.

...the wave equation could actually be relativistic, just like the dynamic behavior of inertial particles, provided we are willing to consider a transformation of the space and time coordinates that differs from the Galilean transformation.
- No need for this if aether motion is included in the analysis.
But a valid transformation has to agree with all physical experiments, like the Sagnac X, not just tests that obey the wave equation!

None of this conflicts with the observed behavior of light, because the motion of light is observed to be both linear and isotropic with respect to inertial coordinate systems.
- Inertia is not isotropic when aether is in motion.  Note that  v != 0 in Sagnac’s lab or rotor frame.

The fact that light is not at rest with respect to any system of inertial coordinates does not conflict with the principle of relativity if we agree that light is not a material object.
- An aether flow of c counter to a light beam direction of c is a rest frame for light.
Light obeys E = mc^2,  so photons have mass.
...two relatively moving systems of inertial coordinates are related to each other by Galilean transformations, so that the composition of co-linear speeds is simply additive. ...we aren't free to impose this assumption on the class of inertial coordinate systems, because they are fully determined by the requirement for inertia to be homogeneous and isotropic.
- Which it isn’t, in general.

Toward the end of the nineteenth century, more precise observations revealed that is not quite correct. It was found that the speed of object C in terms of inertial rest frame coordinates of A is not v + u, but rather (v+u)/(1+uv/c^2), where c is the speed of light in a vacuum.
- Lab frame must be used, not an IFR.  
What are the precise observation references for (v+u)/(1+uv/c^2)?  
The empirical correspondence between inertial isotropy and lightspeed isotropy can be illustrated by a simple experiment.  Three objects, A, B, and C, at rest with respect to each other ....etc.
 -If done on the Earth with sufficient precision, the light flashes westward would be faster than eastward.. even on Earth this shows light anisotropy  due to a westbound aether wind.
The experiment is meaningless without a specification of the aether’s velocity. Speed and direction.

...we also find that if the light is emitted at the same time and place from an object D that is moving with respect to B, the light's speed is still isotropic with respect to B's inertial rest frame. Now, this might seem to suggest that light is a disturbance in a material medium in which the objects A,B,C just happen to be at rest, but this is ruled out by the fact that it applies regardless of the state of (uniform) motion of those objects. 
- The gap in logic again, is that the motion of the underlying aether is not considered.   Would not the flight path of a plane be affected by the wind, the motion of the medium in which the plane is flying?

...with respect to the original x,t coordinate system, the speeds of the cannon-balls from D are not given by simply adding (or subtracting) the speed of the cannon-balls with respect to D's rest frame to (or from) the speed of D with respect to the x,t coordinates. 
- They must include the aether flow as seen in the lab frame.

...although the speed of light is isotropic with respect to any inertial spacetime coordinates,
- The speed of light is isotropic with respect to any FR at rest in the aether, or the lab frame, with the aether flow subtracted or compensated for.

The relationship between the frequency (and energy) of the light with respect to the rest frame of the emitting body and the frequency (and energy) of the light with respect to the rest frame of the receiving body does depend on the relative velocity between those two massive bodies.
- Sagnac showed that aether motion must be included, with respect to the lab frame.

Incidentally, notice that we can rule out the possibility of object B and D dragging the light medium along with them, because they are moving through the same region of space at the same time, and they can't both be dragging the same medium in opposite directions.
-But the natural motion of the aether in the absolute lab frame can be dragging B and D.

...in the case of light we're unable to identify any definite material medium, so the medium has no definite rest frame.
- SagX identifies a causal aether  and a unique reference frame, the ECEF or lab frame.
...Lorentz began with the absolute ether frame coordinates t and x, in terms of which every event can be assigned a unique space-time position (t,x), and then he considered a system moving with the velocity v in the positive x direction. 
- So Lorentz is using a fixed aether frame. V is the relative speed of the second system to the aether.  But Sagnac results are inconsistent with this model (fixed aether).

...he [Lorenz] tentatively proposed an additional transformation that must be applied to x",t" in order to give coordinates in terms of which Maxwell's equations apply in their standard form.
- Maxwell's equations will apply in their standard form if the first frame is the lab frame.
Lorentz was dissatisfied with the proliferation of hypotheses that he had made in order to arrive at this theory.
- Understandable; he had crossed over to rationalism by removing the connection to reality (experiments) that the scientific method requires.