There were actually three major categories of paradoxes, or ‘difficulties,’ concerning the relationships between light and matter that confronted Einstein and the rest of the scientific community in 1905: one was theoretical, one experimental, and one mathematical. We shall now briefly describe and discuss each category.
1. Theoretical Difficulties: There was, of course, the mythical concept of ether, which distorted most theories and the analysis of many experiments. For example, many light experiments were analyzed in terms of whether the hypothetically stationary ether was partially or completely dragged along by the motion of matter through it. Maxwell even theorized that light was a disturbance of the stationary ether.
All physical theories (including electrodynamics and optics) were based on and explained by the concepts of mechanics. For example, the velocities of all material objects were considered to be relative quantities depending upon the material frames of reference with respect to which they were measured. (Rohrlich, p. 52) But Maxwell’s velocity of light at c was a constant quantity, rather than a relative quantity that depended upon its motion.
“Elementary reasoning according to
Newtonian mechanics requires that if the speed of light is c as measured
in a particular reference frame then it cannot also be the same number c
relative to a different frame.” (
2. Experimental Difficulties: The velocity of light from a star appeared to have the same value when it was received by a telescope on Earth, regardless of the orbital motion of that reference frame toward or away from the star. This was the paradoxical conclusion of Bradley’s 1728 aberration of starlight experiment, and of Arago’s 1810 focus of a lens experiment. It was also a conclusion of Fizeau’s 1851 moving water experiment when starlight was used as a light source to measure its velocity in two different directions of the moving water. (see Chapter 7) These conclusions were not consistent with the Newtonian measurements of velocity in different reference frames. (see Figure 7.1A) How could a light ray contact the Earth at the same velocity c regardless of the Earth’s different velocities v relative to the light ray? (see Lindley, p. 55) We shall explain this paradox in Chapter 22E.
In the 1887 Michelson and Morley experiment, light appeared to have the same velocity in all directions regardless of the rotational velocity of the Earth or its orbital velocity of 30 km/s around the Sun. The results of this experiment added several more paradoxes: Why was the motion of the Earth not added to the velocity of light? How could light travel a greater distance in the direction of the Earth’s motion without a greater time interval being detected? How could Michelson’s experiment fail to detect the motion of the Earth through space? (see Feynman, 1963, p. 15-2; Chapters 9 – 12)
3. Mathematical Difficulties: The mathematical difficulties that Einstein imagined to exist are described in detail throughout this Chapter 19 and later chapters.
 In Chapters 22, 23 and later chapters we will explain why many of the concepts of matter and mechanics (including frames of reference, coordinates, transformation equations, Galilean Relativity, and the classical addition of velocities) are not applicable to the transmission velocity of light.
 What material reference frame could the velocity of light at c be measured relative to? The only one appeared to be the theoretical reference frame of stationary ether. (Rohrlich, p. 52)
 In Chapter 21 we will explain the reasons for this paradoxical false assumption.