Chapter 6

 

ELECTROMAGNETISM, THE VELOCITIES OF LIGHT, & ETHER

 

During the 19th century:  electrostatics[1] paved the way for the discovery of electromagnetism (EM); Maxwell wrote his famous equations for electromagnetic waves and the transmission velocity of light at c; the wave theory of light triumphed over Newton’s particle theory.  In 1676, Römer discovered that light has a finite velocity, and then during the mid-19th century it was discovered that light has different velocities relative to different media.  Also during the 19th century, the imaginary material medium of stationary ether in space was invented in an attempt to explain and support the wave theory of light.

 

A.  Electromagnetism

The phenomena of electricity and magnetism were known even to the ancient Greeks.  Electricity was associated with lightening, and with shocks from a metal doorknob or from certain types of ‘electric’ eels. Magnetism was originally confined to tricks performed with a magnetic iron ore called ‘loadstone.’  Later, a magnetic iron pointer was used in a ship’s compass to determine the direction of north.  Down through the ages electricity and magnetism were thought to be entirely separate phenomena. 

During the mid-1730s, French scientist Charles du Fay (1698 – 1739) discovered that there are two kinds of electricity, that opposite kinds attract each other and that similar kinds repel each other.  Today, we would call these two kinds of electricity a positive charge and a negative charge.  (Gribbin, 2002, p. 287)

The Greeks were the first to notice that when amber is rubbed with a cloth, the two objects thereafter attract each other. [2] During the mid-18th century, American scientist Benjamin Franklin (1706 – 1790) empirically described this phenomenon as being the result of two different electrical charges, the positive charge on the amber and a negative charge on the cloth. [3]  (Holton, 1973, p. 396)  The modern atomic explanation for the electrostatic effect of rubbing amber is as follows.  Ordinary atoms are neutrally charged:  the positively charged nucleus balances the negatively charged electrons.  When the cloth rubs the amber, the friction causes some of the amber’s negatively charged electrons to be transferred to cloth’s neutral atoms.  The result is negative ions on the cloth and positive ions on the amber. [4] (Id., p. 398)

By 1750, English scientist John Mitchell (1724 – 1793) had “discovered that the force of repulsion between two like magnetic poles obeys an inverse square law,” similar to the strength of the force of gravity of two masses with respect to their distance apart.  (Gribbin, 2002, p. 288)  But few people paid any attention.  Finally, in 1780, French scientist Charles Coulomb (1736 – 1806) performed torsion balance experiments that convincingly demonstrated that both electric forces and magnetic forces conform to such an inverse square law.  This is now called Coulomb’s Law (Id.), which states:

“that the force which a stationary charge q1 exerts upon a stationary charge q2 is directly proportional to the magnitudes of the charges [and] inversely proportional to the square of the distance between them…”[5]  (French, p. 231)

 

In the year 1800, Italian scientist Alessandro Volta (1745 – 1827) invented the battery, which consisted of a negatively charged rod (cathode) and a positively charged rod (anode) in a diluted acidic solution.  (Holton, 1973, pp. 412 – 413)  In 1807, British chemist Humphrey Davy used the current emanating from a battery to separate the molecules of potash and soda into their component elements, potassium and sodium (a process called ‘electrolysis’).  (Id., p. 412)  At this point, experiments with electricity began to increase more rapidly.[6]

Then in 1820, largely by chance, Danish scientist Hans Christian Oersted (1777-1851) discovered a connection between the two phenomena of electricity and magnetism.  During one of his lectures, he noticed that a magnetic needle oriented toward north was deflected 90° when an electric current (an electric charge in motion) flowed along a wire that was parallel to the needle.  This was the first example in history where a force “did not act along a line connecting the sources of the force.”  (Holton, 1973, p. 416)  Oersted named this puzzling interaction ‘electromagnetism.’[7]  (Gamow, 1961, pp. 135 – 136) 

When English physicist Michael Faraday (1791-1867) learned of Oersted’s experiments and observations in 1821, he soon theorized that electricity might be induced from a magnet.[8]  He repeated Oersted’s experiment.  Thereafter, from the results of his many experiments, including the visual pattern of iron filings which surround the two poles of a magnet (Figure 6.1A), Faraday deduced that an electric current produces an infinite number of circular magnetic ‘lines of force’ around it that are perpendicular to the direction of the current.[9]  He illustrated these lines of force by drawing arrows on a piece of paper in the direction of such magnetic force (Figure 6.1B) and called all of these lines together a ‘magnetic field.’  Faraday also used arrows to illustrate other electric and magnetic lines of force such as attraction, repulsion and various types of currents.  (Figures 6.1C and 6.1D)  Finally, in 1831, after much trial and error, Faraday moved a permanent magnet through a closed loop of wire (a coil) and induced a moving electric charge or ‘current’ in the wire. [10] (Gondhalekar, p. 134; Holton, 1973, pp. 417 – 420; Gamow, 1961, pp. 143 – 146)  During his long career as a scientist, Faraday discovered a great deal of the empirical foundation for the laws of electrodynamics.[11]  Many theories and much experimentation with electromagnetism, electricity and electrodynamics followed these revolutionary discoveries.[12]

Beginning in about 1850, Scottish mathematical physicist James Clerk Maxwell (1831 – 1879) began studying electromagnetism, and particularly Faraday’s papers on the subject.  He analyzed Faraday’s lines of force with the aid of mechanical and mathematical models, and Faraday’s analogies to physical processes.  However, unlike Faraday, Maxwell was also a first rate mathematician. 

Maxwell realized that Faraday’s lines of force not only had magnitudes but vectors (directions of forces) as well, and so he analyzed them as velocity vectors.  (Cropper, pp. 160 – 161)  Like Faraday, Maxwell also used arrows to illustrate electric and magnetic forces, but he gave his arrows names, such as ‘convergence,’ ‘divergence,’ and ‘curl’ depending upon their directions.  (Figure 6.2A)  He varied the lengths of his arrows in order to illustrate their magnitudes, and (like Faraday) he also referred to them as ‘fields.’[13]

In 1855 and 1856, Maxwell published his first paper on electromagnetism, entitled “On Faraday’s Lines of Force.”[14] (Maxwell’s Papers, Vol. I, pp. 155 – 229)  In this paper, Maxwell gave mathematical form to Faraday’s concepts.  He also described most of his own previously discovered phenomena of electricity, magnetism and electromagnetism in numerous mathematical equations.[15]  (Figure 6.3A)  In the process, Maxwell drew analogies between his fields of force and the flow of fluids.  For each type of vector he assigned a different bold letter:  A, B, E, H, and J.[16]  (Cropper, pp. 161 – 162)  Maxwell also: 

“extended Faraday’s induction theory—that …a changing magnetic field creates an electric field—to the reciprocal statement, that a changing electric field generates a magnetic field.  Here is the unification of electric and magnetic fields in the ‘electromagnetic field.’”  (Schwinger, p. 13) 

 

            In 1856, Maxwell sent a copy of his ‘Lines of Force’ paper, which contained his electromagnetic field equations, to Faraday for his review.  Faraday’s written response included a comment with respect to “the time of magnetic action.”[17]  (Cropper, p. 162)  This comment seemed to be a revelation for Maxwell.  If there was a time interval between the emission and action of the magnetic force, then during this interval the force must be traveling through the theoretical ether in empty space.  (Id., pp. 162 – 163)

            Thereafter, Maxwell devised a fanciful mechanical vortex model of the elastic ether to aid in his analysis of electromagnetic fields traveling through the medium of the hypothetical ether.  (Figure 6.2B)  Maxwell then devised an analogy “between the medium [of ether] through which electric and magnetic forces were transmitted…and” his complicated vortex model of the ether.  (Id., p. 163)  As a result of this analogy and other lengthy analysis, Maxwell finally concluded that electric fields and magnetic fields must be disturbances of the elastic ether that were transmitted through the medium of the ether in the form of transverse undulations or electromagnetic waves.[18]  According to Maxwell, “the electric field and the magnetic field are perpendicular to one another and to the direction of…propagation.”[19]  (see Purcell, p. 334; Figure 6.2C) 

In 1861 and 1862, Maxwell published his second paper on electromagnetism, entitled “On Physical Lines of Force,” which described all of the above conclusions and contained a somewhat different set of field equations for electromagnetic waves transmitting through the ether in a vacuum.[20]  (Maxwell’s Papers, Vol. I, pp. 451 – 515; Figure 6.3B)  “In writing his equations, Maxwell had to use electrostatic units for electric fields, and electromagnetic units for magnetic fields.”  (Gamow, 1961, p. 156)  Maxwell expressed the constant ratio between such units by the symbol c in his equations, which also theoretically represented the speed at which his electromagnetic waves moved.[21]  (Griffin, p. 432) 

Maxwell then performed calculations to determine the value of c, and thus the speed of his electromagnetic wave disturbances through the ether.  (Id.; Cropper, p. 164)  Maxwell’s calculations asserted that:  “one electromagnetic unit is equal to 3 x 1010 electrostatic units.”  (Gamow, 1961, p. 156)  Amazingly, this constant ratio of c was very similar to the velocity of light that Fizeau had determined in 1849, and to a speed that Weber and Kohlrausch had calculated for another electromagnetism experiment in 1856.[22]  (Born, p. 165; Cropper, p. 164; Purcell, p. 334) 

Maxwell analyzed all of these seemingly unrelated coincidences, and ultimately concluded that:

“The velocity of transverse undulations in our hypothetical medium, calculated from the electro-magnetic experiments of MM. Kohlrausch and Weber, agrees so exactly with the velocity of light calculated from the optical experiments of M. Fizeau, that we can scarcely avoid the inference that light consists of the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.”  (Maxwell’s Papers, Vol. I [Purcell, p. 334]; Cropper, p. 164)

 

“This velocity is so nearly that of light that it seems we have strong reason to conclude that light itself (including radiant heat and other radiations, if any) is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws.”  (Maxwell’s Papers, Vol. I [Griffin, p. 432])

 

In other words, prior to 1865, Maxwell conjectured that light was an electromagnetic disturbance of the material ether which transmits at velocity c in the form of transverse undulations (or waves) of ether as such disturbance propagates through the medium of stationary ether.[23] After many confirming experiments, these conjectures ultimately resulted in a unification of the realms of electromagnetism and optics.[24]  (Cropper, p. 164; Gamow, 1961, p. 156; Bergmann, p. 17)

            Sobel described Maxwell’s theory for the constant transmission velocity of light relative to its medium of the ether in a very clear and succinct manner.

“The ether can be thought of as a frame of reference relative to which the speed of light is given.  For example, when we say that sound travels at 344 meters per second, we mean that the wave moves at that speed relative to the air, and when we say that light travels at 300,000 kilometers per second, we mean this speed relative to the ether.  Air is the medium of sound; ether is the medium of light.”  (Sobel, p. 200)

 

Thus, Maxwell’s theory and equations for electromagnetic waves assert that when light and other forms of EM radiation come into existence in the medium of ether (actually the vacuum of empty space), all of their waves instantly propagate in all possible directions at the same constant transmission speed or velocity of c (300,00 km/s) relative to the medium of ether (again, actually the vacuum of empty space because we now know that ether does not exist). [25] (see Figure 6.11; Bergmann, pp. 16, 17, 27; Rohrlich, p. 50) 

In 1865, Maxwell wrote another paper, which was entitled:  “A Dynamical Theory of the Electromagnetic Field.”  (Maxwell’s Papers, Vol. I, pp. 526 – 597)  Maxwell explained the title of his 1865 paper, as follows:

“The theory I propose may…be called a theory of the Electromagnetic Field, because it has to do with the space in the neighborhood of the electric or magnetic bodies, and it may be called a Dynamical theory, because it assumes that in that space there is matter in motion, by which the observed electromagnetic phenomena [light] are produced.”  (Id., p. 527)

 

The ‘matter in motion’ in space that Maxwell was describing “was, as before in his Lines of Force papers, the ether.” [26] (Cropper, p. 165)  For Maxwell and many others of his era, “electricity and magnetism were [merely] aspects of matter—just stresses in the aether.”[27] (Smolin, p. 38)  Thus, as long as someone believes in a material substance called ‘ether,’ Maxwell’s electromagnetic theory of light may be described as ‘Dynamical;’ the result of applied forces.[28] 

We now know that when chemical, atomic, electrodynamic or other forms of energy are applied to atoms their energy state increases, some of their particles may become excited, and the atoms may emit excited photons (radiation) in the visible region of the radiation spectrum.   (see Figure 6.9A)  This process is called the “generation’ or ‘emission’ of light.  (Halliday, p. 890)  In 1865, Maxwell understandably misinterpreted this process to be a ‘disturbance’ that was created in the hypothetical stationary ether, and that ether in a disturbed form was constantly transmitted as electromagnetic waves (light) in all possible directions at the velocity of c (300,000 km/s) relative to the stationary medium of ether.[29]  We shall call this constant transmission velocity of light at c relative to its hypothetical medium of ether, the ‘transmission velocity of light’ in a vacuum.

Maxwell’s electromagnetic theory of light “contained twenty equations in twenty unknowns.  (Miller, p. 87)  However, it was very difficult to determine exactly what some of Maxwell’s ideas really were.  In 1870, German physicist Hermann von Helmholtz (1821 – 1894) took it upon himself to put “some order into this situation,” and he began combining and simplifying Maxwell’s electromagnetic field equations.  English scientist Oliver Heavyside (1850 – 1925) arrived at a similar set of simplified equations at about the same time.  (Id.)  By 1890, Hertz had further simplified Maxwell’s electromagnetic equations down to only four for electrodynamics.  (Id., p. 12; see Figure 6.3A)  In 1892, Dutch physicist H. A. Lorentz further worked on Hertz’s modified equations, and put all of Maxwell’s equations substantially in their modern form for both a moving charge (a ‘current’) and for “radiation in the absence of charges” (light).  (Id., pp. 24 – 25)  These final eight equations were first described by Max Abraham in 1902 as the “Maxwell-Lorentz field equations.”[30]  (Id., p. 24; see Figure 6.3)

Let us now summarize the major aspects of Maxwell’s concepts of light as they are described or implied in Part VI (entitled “Electromagnetic Theory of Light”) of Maxwell’s 1865 paper.  (see Maxwell’s Papers, Vol. I, pp. 577 – 588)

1.  Light was characterized by Maxwell as an electromagnetic disturbance of the hypothetical substance of ether.

2.  Light is manifested as two mutually perpendicular electromagnetic fields (waves or vibrations) which transmit transversely to each other and to their direction of propagation.

3.  Light propagates through the elastic medium of ether or a vacuum at the constant velocity of c.

4.  Maxwell computed the value of c to be 3 x 1010 meters per second,[31] which was very close to the experimentally determined magnitude of propagating light.

5.  Maxwell always referred to the constant velocity of light in the abstract or with respect to its medium of a vacuum, rather than relative to material bodies.[32]

In 1873, Maxwell discussed and explained all of his theories of electromagnetism in a two-volume work entitled, “A Treatise on Electromagnetism.”  Maxwell died in 1879 at the same age (48) as his mother and as a result of the same disease (abdominal cancer).  (Cropper, pp. 155 – 156)

 

B.  What is the difference between electromagnetism (EM), electricity, electrodynamics and electromagnetic waves (radiation)?

 

            Both phenomena of electricity and electromagnetic waves have electric fields and magnetic fields associated with them, both are energy phenomena, both can travel at or almost at the same speed (c), and both represent different manifestations of a more general phenomenon of nature:  electromagnetism.  However, this is where the empirical similarities cease or get fuzzy.

            Electricity can be divided into two broad categories:  electrostatics and electrodynamics.  Electrostatics involves electric charges at rest, the forces between them, and the electric fields associated with such charges and forces.  (Oxford Physics Dictionary, p. 147)  Whereas, electrodyamics involves electric charges in motion (now called electric currents) which usually flow through or toward an opaque conductor, the forces created by electric fields and magnetic fields, and the relationships between the above.[33]  (Id., p. 138)  Such relationships include power (measured in watts), rate of flow (measured in amps), potential (measured in volts), and resistance (measured in ohms).  All problems of electrodynamics can be reduced to problems of electrostatics. (see Miller, p. 275) 

            On the other hand, electromagnetic waves or radiation (including visible light) involves the generation and emission of electromagnetic fields or waves of photons from a material source, the transmission of such fields or waves through the vacuum of empty space or another medium[34] at a definite velocity, with electric and magnetic fields oscillating perpendicularly toward each other and toward their linear direction of propagation.[35]  (see Oxford Dictionary of Physics, p. 140)  None of the above-described special or empirical characteristics of electricity apply to phenomena of electromagnetic waves (radiation), including induction of a current by relative motion, power, potential, charge, current, conductors, forces, or resistance.  Instead, the various different phenomena of electromagnetic waves (including visible light radiation) have their own special or empirical characteristics, including wavelength, frequency, instantaneous constant velocity, reflection, refraction, the index of refraction, dispersion, diffraction, diffusion, interference, and absorption.[36]

            Why do we draw the above distinctions between the ‘electrodynamics’ of electricity and the ‘electromagnetic waves’ of EM radiation (light)?  Because Einstein, throughout his Special Theory, constantly commingled such EM phenomena with material concepts and referred to such different EM phenomena as if they all were the same thing.  For example, Einstein appeared to generalize the concept of ‘induction’ of a current by means of relative motion so that ‘electrodynamics’ could be defined as any relationship between EM and matter.[37]  He attempted to prove his impossible concepts for the velocities of light with mechanical concepts that are only applicable to electrodynamics or matter, such as inertial motions, frames of reference, clocks, rigid rods, coordinates and kinematics.  Then he referred to concepts of light, such as the Doppler Effect of light and the aberration of starlight, as electrodynamic applications of his Special Theory.  Einstein also referred to concepts of electricity (i.e. electromagnetic mass, which is actually just an EM resistance) as if it was a ponderable material mass of atoms; all in an attempt to convince the reader that his ad hoc mathematical Special Theory might have some empirical merit.[38]

 

C.  Light and its constant transmission velocity of c in a vacuum.

During the 17th century, Newton had hypothesized that light was composed of particles or ‘corpuscles,’ whereas Descartes, Robert Hooke (1635 – 1703), and Dutch scientist Christiaan Huygens (1629 – 1695) had conjectured that light was formed of impulses or waves that traveled through an invisible medium in space called ‘ether.’  (Holton, 1873, pp. 384, 386)  Newton’s particle theory of light carried the day for over a century, due largely to Newton’s great prestige.  (Id., p. 391) 

Then in 1801, English scientist Thomas Young (1773-1829) revived the wave theory of light.  He proposed that vibrating (or oscillating) waves of light are continuously created at a material light source and that they radiate out from the light source in all possible directions in the form of continually propagating spheres.[39]  (Figures 6.4A and 6.4B)  Young also asserted that each sphere has exactly the same state of oscillation, called ‘phase.’  In other words, the light waves in each sphere all oscillate in phase, vis. at any instant every light wave in a sphere is at an identical crest, or at an identical trough.[40] (Born, p. 98; see Figure 6.4C)

At first Young’s wave theory was greatly criticized.  But gradually it began to explain phenomena that could not be explained by Newton’s particle theory.  By 1817, both Young and his colleague French scientist Augustin Fresnel (1788 – 1827) had given a complete explanation of the phenomena of the interference of light and of the polarization of light based on the wave theory.[41]  (EB, 1969, Vol. 13, p. 748c)  Newton’s particle theory of light could not explain these phenomena.  Then in 1853, French physicist Jean Foucault (1819 – 1868), using the wave theory of light, demonstrated that the velocity of light in water was less than in air, whereas the particle theory predicted just the opposite.  (Goldberg, p. 84)  By this time the wave theory had begun to overwhelm Newton’s particle theory of light.[42]

Maxwell’s equations and his ‘electromagnetic wave theory’ of light were consistent with the philosophy of Descartes, Huygens and Young who preceded him.  On the other hand, during early 1905 Einstein theorized that light is propagated as ‘quanta,’ or mass-less particles of light energy (later called ‘photons’).[43]  (Holton, 1973, pp. 438 – 441)  Einstein’s particle theory resulted in a paradoxical ‘wave-particle duality’ of light.[44]  Which theory of light is correct?  How can we make a choice?  Dingle described this dichotomy and the resulting paradox:

“Of the nature of light we have the most contradictory evidence.  In some phenomena, such as interference and diffraction, it seems impossible to conceive of it as other than a wave motion in a medium; in others, such as the photo-electric effect, we can conceive of it only as concentrated in particles.  Though we have devised mathematical formulae capable of describing both these sets of phenomena, we have not succeeded in framing a verbal description of light that will give us a uniquely clear mental picture of what it is or of how it operates.”  (Dingle, 1961, p.12)

 

So we ask the questions:  Does a choice between waves and particles even have to be made?  Could not rays of light be composed of continuous wave trains of photons that become fields of incident and reflected energy?  Photons generated, emitted and propagated in the form of a wave train could explain both the phenomena of interference, polarization and diffraction, as well as the photoelectric effect.  It would be consistent with the known fact that the higher the frequency of EM waves, the greater the energy they transmit.  More wave trains of photons (packets of energy) per unit of distance propagated should exhibit greater energy.  A wave train of photons would also help to explain the phenomenon of refraction, the index of refraction and the mysterious results of Fizeau’s 1851 light experiment, which we shall discuss in the next chapter.[45]

Galileo believed that light might have a finite transmission velocity, and in 1607 he attempted to discover this velocity.  However, his experiment with two men each holding lanterns at a distance of 3 kilometers was too crude for any definitive results.  (Hoffmann, 1983, pp. 43, 44)  On the other hand, Descartes believed that light traveled at an infinite velocity from its source over a distance to an observer.  In other words, that light propagated over any distance instantaneously.  (Goldberg, p. 433) 

In 1676, Danish astronomer Olaus Römer (1644-1710) deduced from different time intervals between his observations of each succeeding eclipse of Jupiter’s moon Io that light must have a finite velocity.  (see Figures 6.5 and 6.6)  It was known that the Earth was moving at different speeds and over different distances toward or away from Jupiter during their solar orbits, and Römer deduced that this resulted in different distances and time intervals which Jovian light must travel at a finite velocity relative to the linearly moving Earth.  (Figure 6.6)  Acting on Römer’s data and other available data for distances, Huygens soon calculated the finite velocity of light through empty space to be about 220,000 km/s.  (Holton, 1973, pp. 387 – 388)  Strangely enough, Römer’s published findings were largely ignored for over half a century.[46]  (Hoffmann, 1983, pp. 44, 45; Gondhalekar, p. 125) 

When Römer and Huygens were measuring the finite velocity of light from the eclipse of Io to the Earth, they must have intuitively realized that the beginning of such eclipse did not occur simultaneously with their observation of it many minutes later.  On the contrary, they must have realized that they were actually observing such eclipse many minutes after it began, and that the time of their observation was equal to the time interval delay for light from Io to travel the distance to the Earth at such finite velocity.  What they did not realize, however, was that this time interval delay phenomenon of light would (about 3 centuries later) become important for the precise measurements of moving bodies on Earth.[47]

In 1728, English astronomer James Bradley (1693 – 1762) empirically confirmed Römer’s conclusions that the velocity of light is finite.  By using a method now called the ‘aberration of light’ (Figure 7.1), Bradley deduced and demonstrated that the ratio of the solar orbital speed of the Earth (approximately 30 km/s) to the velocity of starlight is about 1:10,000.  Based on this information, Bradley then calculated that the transmission velocity of light in the vacuum of empty space was approximately 303,000 km/s.  (Hoffmann, 1983, pp. 46-49)  This was an amazingly close approximation.

In 1849, French scientist Armond Fizeau, using a mechanical method, found roughly the same value for the velocity of light in air as Bradley (about 315,000 km/s).  A few years later in 1862, Foucault estimated the velocity of light relative to the medium of air to be about 298,000 km/s using a rotating mirror method.  (Maxwell’s Papers, Vol. I, p. 580; EB, 1969, Vol. 13, p. 1130a)  The exact transmission velocity of light in a vacuum (in vacuo) is now determined by current technology to be 299,792.458 km/s.[48]  (Halliday, p. 892)  In fact, the ‘meter’ is now defined “as the distance that light travels in a vacuum in 1/299,792,458 of a second.”  (Purcell, p. 473)  Yet, for the sake of simplicity, throughout this book we shall refer to the velocity of light in the vacuum of empty space as 300,000 km/s.  This unique and constant transmission velocity of light in vacuo is referred to as ‘c,’ and because it does not vary, it is an inherent property of light in vacuo.[49]

 

D. Different transmission velocities of light in material media.

Empirically, light also has different and slower transmission velocities relative to transparent media other than a vacuum, such as air, water, glass, or diamond.  (see Chart 6.7A and Figure 6.8)  There appears to be a direct correlation between the atomic particle density of the particular material medium and the transmission velocity of any color of light relative to it.  (Chart 6.7A)  In clear air at sea level, light transmits only slightly slower than in the near vacuum of empty space.  In the denser medium of pure water, light transmits at only about three-fourths of its velocity in air (its specific velocity also depends upon its wavelength or color).  In the somewhat denser medium of glass, light transmits at only about two-thirds of its velocity in air (again its specific velocity depends upon the wavelength or color of the light).  (Goldberg, p. 86; Halliday, p. 893)

“The mechanism responsible for the propagation of light in matter is scattering (in effect, absorption and reemission of the scattered light).”  (Halliday, p. 893)  But this theoretical process of a photon of light colliding with an atomic particle (i.e. an electron) of matter (the photon then being absorbed and reemitted) cannot be instantaneous.  Empirically, it takes a longer time interval for a photon to propagate through a material medium (in proportion to its density) than through the same distance in empty space.  For example, water (H2O) is more densely packed with molecules and atomic particles than air, which contains fewer free atoms (i.e. oxygen, hydrogen) and molecules (i.e. CO2) per volume. Therefore, it follows that each photon takes a longer time interval to be absorbed by a greater quantity of densely packed atomic particles of water and then reemitted, than with respect to air.  It is suggested by the author that this is the basic reason why photons empirically transmit slower in stationary water (226,000 km/s) than in stationary air (about 299,700 km/s).  Stated a different way:  in water “the distance over which the original light is absorbed and reemitted is of the order of micrometers, and in air it is of the order of millimeters.”[50]  (Halliday, p. 893)

The following is a more specific explanation for the above suggested phenomenon:  If a continuous light ray is a wave train of photons, then the greater the frequency of the waves of such wave train (the shorter the wavelengths) the greater the number of photons passing through the specific number of molecules, atoms and subatomic particles (electrons) of a particular material medium.  Therefore, the more photons that must be absorbed and reemitted by a specific number of electrons during a given period of time, and the slower will be the transmission of such wave train of photons through such material medium.  Likewise, if each of the atoms of the particular material medium has a greater number of electrons, then the slower will be the transmission (absorption and reemission) of a certain number of photons through this denser field of electrons.

The empirical ratio between the velocity of a particular light ray through a vacuum at c and the velocity of such light ray at v through a particular transparent material medium is called the ‘index of refraction,’[51] or n, of such particular light ray (and its specific wavelength) relative to a particular material medium (and its particular atomic particle density).[52]  (see Halliday, p. 905; Chart 6.7B)  Therefore, n = c/v.[53]  (Id.)  The velocities and indexes shown on Figure 6.7 have been obtained using monochromatic light [54] (vis. yellow sodium light) which has only one color, and thus only one wavelength (589 nm). Other colors of light have different wavelengths, as do other types of EM radiation.  (see Figure 6.9)  White light is basically a combination of all colors or wavelengths of the visible EM spectrum.  

It follows from the above concepts that the transmission velocity of a particular wavelength of light relative to a particular stationary material medium does not vary (it is invariant).[55]  Therefore, such constant transmission velocity may be considered to be an inherent property of such particular light wavelength through such particular material medium.

Let us now discuss the related phenomena of refraction and dispersion.  Empirically, when a light ray with a specific wavelength propagates through the medium of the air (or a vacuum) and then obliquely enters the surface of a different material medium (i.e. water), it appears to bend or refract.  For example, when a pencil is placed at an angle in a glass of water, light from it is refracted and the pencil appears broken at the water line.  The word ‘refraction’ comes from the Latin word for ‘broken’ or ‘fractured.’   This phenomenon occurs for all EM waves.  “If the speed is smaller in the second medium, the ray is bent toward the normal to the interface, as one would expect when light passes from a rare to a dense medium; if the speed is greater in the second medium, the ray is bent away from the normal.”[56]  (Holton, 1973, p. 387; see Figure 6.7C)

What happens when a coherent ray of white sunlight propagates through the air at almost c, and then propagates through a clear glass prism?  If the light ray enters the surface of the prism in a direction perpendicular to the surface of the glass (called ‘the normal’), then it will continue to propagate as a coherent light ray in the same direction through the clear glass prism, albeit at a slower velocity of approximately 197,000 km/s.[57]  (Figure 6.7D)

            On the other hand, if such light ray enters the surface of the glass prism at an angle (say 60 degrees) relative to the surface, then its component colors (wavelengths) will refract at different angles relative to the normal and visibly change their direction of propagation.  The empirical result will be a dispersal of the component wavelengths into a rainbow-like effect of colors.  (see Figure 6.7D)  The longer the wavelength of a particular color (i.e. red) the less its frequency through the prism, the faster its velocity of transmission, and the less its angle of refraction.  The shorter the wavelength of a particular color (i.e. blue) the greater its frequency through the prism, the slower its velocity of transmission, and the greater its angle of refraction.  The above process is called ‘dispersion.’  (Goldberg, p. 87; Halliday, pp. 892, 893, 904, 905)

What causes different transmission velocities of different colors (wavelengths) of light relative to different material media?  The answer is a combination of the wavelength (or frequency) of the particular light rays and the atomic particle density of the particular material medium through which such light rays propagate.  In effect, each color or wavelength of light that passes through a particular material medium creates a separate index of refraction with respect to such material medium. 

Why do these empirical refraction and dispersion effects occur?  Let us now attempt to answer this question by describing what may happen on the quantum level.  When white light composed of many wave trains of photons (each with a different color or wavelength) enters the surface of a prism at an angle, the longer component waves of photons (i.e. red light) with less frequent waves encounter fewer atomic particles (i.e. electrons) than shorter more frequent waves of photons (i.e. blue light).  Thus, where fewer red light photons encounter fewer electrons over a certain distance, it takes less time for such red light photons to be absorbed and re-emitted over that certain distance.  The result is a faster velocity for such red light photons, and thus a lesser angle of refraction from the previous rectilinear path of the original white light through the air at almost c.  (see Figure 6.7D)

            On the other hand, the shorter component waves of photons (i.e. blue light) with more frequent waves encounter more atomic particles (i.e. electrons) than the longer less frequent waves of photons (i.e. red light).  Thus, where a greater number of blue light photons encounter more electrons over a certain distance, it takes more time for such blue light photons to be absorbed and re-emitted over that certain distance.  The result is a slower velocity for such blue light photons, and thus a greater angle of refraction from the previous rectilinear path of the original white light through the air at almost c.  (see Figure 6.7D)

            From the above discussion we can deduce the following.  The angle of refraction indicates the total magnitude of slowing down of photons with a certain frequency as compared to their usual rectilinear path at c through a perfect vacuum.[58]  In effect, Fermat’s 17th century conjecture was not correct:  light does not necessarily chose a path of least time.  Its path is sometimes determined by other factors.  It may also be concluded that each electromagnetic wave contains the same number of photons (regardless of its length), because it is the frequency of such waves of photons that is associated with their magnitude of refraction and with their energy content.

  A clear and concise summary of many of the concepts discussed in Sections A and C of this chapter is set forth in Memo 6.10.

 

E.  The stationary ether theory.

            When Young revived Descartes’ impulse or wave theory of light in the early 19th century, along with it came Descartes’ 1638 conjecture that light waves are carried or supported through space by a material substance called ‘ether.’[59] Water waves can be interpreted to be a disturbance of the material substance of water that forms and supports them.  Likewise, sound waves may be interpreted to be a disturbance of the material substance of air that forms and supports them.  If light waves are a disturbance of the medium through which they propagate, as was theorized by Maxwell and others, then how could this medium be empty space? Empty space is not a material substance; it is nothing.  What then would be disturbed and what would form and support the light waves?  (Goldberg, p. 82)  Because of this perceived necessity of a material medium for the formation, support and propagation of light waves, the scientists of the 19th century merely postulated the existence of luminiferous (light bearing) ether. [60] (Hoffmann, 1983, p. 56)

            Over the centuries, many types of aether were imagined by scientists to explain various phenomena.[61]  As explained by Maxwell:

“The only aether which has survived is that which was invented by Huygens to explain the propagation of light.  The evidence for the existence of the luminiferous aether has accumulated as additional phenomena of light and other radiations have been discovered; and the properties of this medium, as deduced from the phenomena of light, have been found to be precisely those required to explain electromagnetic phenomena.”[62]  (Maxwell’s Papers, Vol. II, Ether, p. 764)

 

Maxwell further conjectured that “light is not a substance but a process going on in a substance,” possibly “an electrical disturbance,” but in any case the process is a “vibration.”[63]  (Id., pp. 765, 766)  Despite all of these assumptions, conjectures, deductions, inventions, and the devout belief that they engendered for over a century, ‘aether’ eventually turned out to be nothing more than a creative myth invented to explain non-existent imagined problems.[64]

            What would be the amazing properties of this hypothetical substance called ‘ether’?  It must fill all of space as far as astronomers and their telescopes can observe light.  It must be “capable of transmitting energy.”  (Maxwell’s Papers, Vol. II, Ether, p. 767)  It must be rigid, because a priori it must support the extremely high frequency of light over great distances.  It must possess “elasticity similar to that of a solid body” (Id.), in order to account for the phenomenon of polarization.  It must be enormously strong in order to transmit light waves for vast distances at the velocity of light.  It must be intangible (have no mass), because how else could the planets and the moon pass through it as if it were not even there.[65]  (Goldberg, p. 84, 85; Holton, 1973, pp. 393 - 394) 

Finally, if ether is not affected by the celestial bodies moving through it, then it must be at rest in Newton’s absolute space.  Because it suited one of his early 19th century theories, Fresnel even postulated that the ether was stationary in space.  (Lorentz, 1921, p. 793)  A priori, ether also had to be absolutely at rest, because otherwise Maxwell’s constant velocity of light at c might vary from place to place.  Such were the fanciful speculations of 19th century scientists.

Even though ether was thought to be normally stationary in space, it was also theorized by Stokes, Fresnel and others that locally it might be dragged along by the motion of the Earth through it.  (see D’Abro, 1927, pp. 122 – 123)  Whether ether was totally dragged along, only partially dragged along, or not dragged along at all seemed to depend upon which theory a 19th century scientist was advocating and attempting to arbitrarily justify.  At some point, it was even theorized that stationary ether was a specially privileged and absolute universal reference frame or “coordinate system in which the speed of light is equal to c in all directions.” [66]  (Bergmann, p. 27; Bird, p. 55; Rohrlich, p. 52) 

Maxwell, and even Faraday, ardently believed in the concept of a substance called ‘ether’ absolutely at rest in space.[67]  Faraday referred to it many times in his writings.  Maxwell’s equations describing the laws of electromagnetism and the constant velocity of light at c were assumed to be written with respect to this theoretically stationary substance.  (Cropper, pp. 163 – 165; Purcell, p. 334)  Thus, it was assumed by many scientists that Maxwell’s equations and velocity c must be valid only with respect to the stationary ether. [68] (Resnick, 1968, pp. 16, 17; Rohrlich, p. 52) 

At this juncture, let us now ask the question:  was Maxwell’s assumption of the existence of the hypothetical ether medium necessary for the validity of his theory of light or his electromagnetic wave equations?  The answer is No.  Maxwell’s theory of light and his EM equations have always applied with equal validity relative to other mediums, such as a vacuum, air, water, glass, and diamond.  During the period 1880 to 1905, it was finally realized that ether was just a fictitious medium in space, and that in reality the celestial medium for the transmission of light was nothing more than the vacuum of empty space.  For this reason, the fictitious ether was irrelevant to the validity of Maxwell’s equations.  Since empty space is basically a void of nothing which is not capable of any motion, the medium of empty space can also be considered as ‘stationary’ for purposes of Maxwell’s equations.  Thus, Maxwell’s equations now state that the transmission velocity of light is c relative to the medium of the vacuum of empty space.

After Maxwell’s equations and theories were published in their final Maxwellian form in 1873, questions were posed by various members of the scientific community as to whether such equations might change relative to a body (i.e. the Earth) which was moving with respect to the stationary ether frame?  (Hoffmann, 1983, p. 82)  In other words, did the velocity of light vary from a constant c and become c – v or c + v depending upon its direction of its propagation relative to the direction and magnitude of motion of a material body through the ether?  (Resnick, 1968, p. 16; Bird, pp. 57 - 58)

The conventional wisdom of the latter part of the 19th century asserted that if an electromagnetic experiment could be devised to measure the magnitude of the speed (v) of the Earth through the stationary ether in different directions relative to the velocity (c) of light, v/c, then the absolute speed and direction of the Earth through the reference frame of stationary ether could be determined.[69]  (Hoffmann, 1983, pp. 56, 85, 86; Goldberg, p. 86)  A priori, this hypothetical experiment could also determine the velocity of light relative to the moving Earth and demonstrate the existence of stationary ether. 

            It was also hypothesized by some scientists that if the ether was truly stationary, then the motion of the Earth through it should create an ‘ether wind’ effect.  This ‘ether wind’ effect was theoretically much like the wind sensation that is created when one stands on the bow of a ship that is rapidly moving through stationary air.  (Gamow, 1961, p. 165; Hoffmann, 1983, p. 86)  It was further assumed that a ray of light propagating to and fro in the direction of such ‘ether wind’ would take a longer interval of time to complete its journey than if such light ray propagated perpendicular to such ether wind, and that such difference in time interval could be detected.  This last assumption was based upon the known fact that it takes a boat on Earth longer to travel to and fro with and against a current of water, than to and fro across such current.  (Gamow, 1961, pp. 165 – 166; see Figure 9.3B)

            During the 1870’s, numerous electromagnetic experiments were devised to measure the magnitude of the theoretical ‘ether wind’ (caused by the Earth moving through the stationary ether) as compared to the velocity of light, v/c, and thus to determine the magnitude of the absolute speed of the Earth through the ether.  But all of these first order (first approximation) experiments failed to detect any magnitude for the theoretical ether wind or any absolute speed of the Earth through the ether.  (Hoffmann, 1983, p. 86)  Nevertheless, the scientific community remained collectively convinced that the hypothesis of a stationary material substance in absolute space was a necessary and fundamental law of nature.  (Bergmann, p. 27)

            By 1880, the hypothesis of ether as a preferred or special stationary reference frame in space was firmly entrenched in scientific dogma.[70]  The best way to demonstrate the existence of stationary ether was to somehow determine the absolute speed of the Earth relative to the stationary ether reference frame.  But how?  In 1881, a Russian born American scientist named Albert Michelson would devise an interference of light experiment in order to attempt to answer these questions.  (see Chapter 9)

Throughout the remainder of this treatise we shall discover that the mythical concept of stationary ether has caused serious theoretical misconceptions, anomalies and enigmas for physics that still distort scientific thought in the twenty-first century.



[1] ‘Electrostatics’ is “the study of electric charges at rest, the forces between them…and the electric fields associated with them.”  (Oxford Dictionary of Physics, p. 147)

[2] The word ‘electricity’ is derived from the Latin word ‘electrum,’ which means amber.  (Schwinger, p. 15) 

[3] About 1753, Franklin was also able to collect a small quantity of an electric charge from lightening passing along a kite string.  He then stored it in a Leyden jar, an early form of battery or condenser.  (Gamow, 1961, p. 127)

[4] An ‘ion’ is “an atom…that has either lost [or gained] one or more electrons.”  (Holton, 1973, p. 235)

[5] Coulomb’s Law will be referred to many times throughout this treatise, and especially with regard to quantum physics.

[6] What is electricity?  One description is:  a property of negatively charged electrons and positively charged protons that have a force field associated with them and that can be separated by an expenditure of energy.  (Webster’s Dictionary, p. 436)  Bertrand Russell ambiguously described it as “a way in which things behave…merely a convenient name for certain physical laws.”  (Russell, 1923, pp. 24, 25)

[7] “Electricity and magnetism…are in a sense one and the same phenomenon.”  (Rohrlich, p. 49)

[8] Faraday, like Franklin, Cavendish (1731 – 1810), and many other famous scientists, was almost completely self-taught, and yet he became one of the world’s greatest physicists.

[9] This deduction by Faraday explained the paradox of Oersted’s experiment.

[10] This is the basic principle underlying modern electric generators and dynamos.  As fate would have it, American scientist Joseph Henry (1797 – 1878) actually was the first to produce electricity from magnetism around 1830, but Faraday was the first to publish his findings.  (Holton, 1973, p. 418)  Faraday is also credited with inventing the electric motor, and numerous other things related to electromagnetism.

[11] ‘Electrodynamics’ is “the study of electric charges in motion [‘currents’], the forces created by electric and magnetic fields, and the relationship between them.”  (Oxford Dictionary of Physics, p. 138)

[12] For instance, French scientist Andre Ampere (1775-1836) developed the idea of electric current as the motion of electric charges along a wire, surrounded by a circular magnetic field.  German physicist Georg Ohm (1787-1854) discovered that wires formed from different metals had different resistances to electric currents.  (Gamow, 1961, pp. 136, 138)

[13] “Maxwell used the term ‘field’ to describe the physical state of affairs in a region of space that can manifest a certain kind of force:  the gravitational field of the Earth; the electric field of a charge; the magnetic field of an electric current.”  (Schwinger, p. 13)

[14] In writing this paper Maxwell borrowed liberally from the prior work of William Thompson.  (Cropper, p. 161)

[15] In order to attempt to empirically justify his mathematics, Maxwell artificially postulated the physical existence of a fictional ‘displacement current’ in a ‘dielectric’ (a non-conductor of electricity), which a priori cannot occur.  (Dingle, 1972, pp. 130 – 131)

[16] Vector “B was equal to H in a vacuum, but differed from it in a material medium.”  (Cropper, p. 162)  Vector “A was pure Maxwellian speculation,” and he called it ‘vector potential.’  (Id.)  During the late 19th century, Maxwell’s successors wrote Vector A out of Maxwell’s equations, but in 1959 David Bohm brought it back.  (Id.)

[17] Evidently, Faraday “was reminded of his own conjectures, that magnetic (and presumably electric) effects were transmitted in a finite time, not instantaneously.”  (Cropper, p.163)

[18] “Maxwell was accustomed to thinking in terms of mechanics, so apparently for this reason he explained the new EM fields as disturbances or stresses of the hypothetical material medium…ether.”  (Bergmann, pp.17, 27) 

[19] “Technically, this mutually crosswise motion makes the wave a transverse one.”  (Holton, 1973, p. 389)

[20] Maxwell’s symmetrical equation for an electromagnetic field in empty space (Figure 6.3B) implied to him “the possibility of electromagnetic waves.”  (Purcell, p. 331)

[21] The constant velocity c was ‘hidden’ or ‘embedded’ in Maxwell’s equations.  (see Purcell, p. 331)

[22] Fizeau’s velocity of light in air was 314,858,000 meters per second; Weber’s speed was 310,740,000 m/s; Foucault’s “more accurate” velocity of light in 1862 was 298,000,000 m/s.  (Maxwell’s Papers, Vol. 1, pp. 579 – 580)

[23] Such theoretical disturbances of the ether were later characterized as ‘electromagnetic waves.’  The existence of electromagnetic waves was later confirmed in 1888 by the experiments of Heinrich Hertz (1857 – 1894).  (Gamow, 1961, p. 154; Bergmann, p. 17; Rohrlich, p. 50)  Hertz also discovered radio waves and microwaves.  (Cropper, p. 164)

[24] ‘Optics’ is:  “the study of light and the phenomena associated with its generation, transmission and detection.”  (Oxford Dictionary of Physics, pp. 337 – 338)

[25] “Maxwell thought of space itself [or stationary ether] as a medium.”  (Purcell, p. 330)  We shall further discuss this property of light, this constant transmission velocity of light at c relative to the medium of ether (or empty space), in the next section of this chapter, and in Chapters 21 and 22.

[26] Based on the above three quotes from Maxwell during the 1860’s, it becomes obvious that for Maxwell light was not something independent from the ether that was propagating through it; rather, light was the ether itself in a disturbed form.

[27] During this period of the 19th century known as the ‘Mechanical World View,’ electromagnetism was thought of merely as a branch of mechanics.

[28] ‘Dynamics’ is the ‘branch of mechanics concerned with the motion of bodies under the action of forces.”  (Oxford Dictionary of Physics, p. 125)

[29] Electrical disturbances were supposed to propagate as stresses and strains in an all pervasive…medium.”  (Miller, p. 87)

[30] They were basically Maxwell’s electromagnetic equations combined and simplified by Helmholtz, Heavyside, Hertz and Lorentz.  Although Lorentz was the last to work on them, he only had a relatively  minor part in such process, so adding Lorentz’s name to Maxwell’s equations was really a misnomer or false attribution by Max Abraham (during the early twentieth century).  This fact will become important in Chapter 36 when we discuss Einstein’s failed general confirmations of his Special Theory.

[31] This value was “the number of electrostatic units in one electromagnetic unit of electricity, and this, according to our result, should be equal to the velocity of light in air or vacuum.”  (Maxwell, 1865, Maxwell’s Papers, Vol. I, pp. 579 – 580)

[32] Whereas Einstein frequently referred to the constant velocity of light at c relative to linearly moving bodies, which is a completely different and invalid concept.  (see Einstein, Relativity, pp. 22 – 23; Chapters 21 and 22)

[33] Maxwell only used the term ‘electrodynamics’ when he referred to electric currents, not when he referred to light.  (see Maxwell, 1873, Vol. II, pp. 173 – 174)  The Penguin Dictionary of Physics defines ‘electrodynamics’ as the “branch of science that studies the mechanical forces generated between neighboring circuits when carrying electric currents.”  (p. 125)

[34] With visible light this medium must be transparent.

[35] Also, as Maxwell asserted:  “only transversal vibrations can be propagated.”  (Maxwell’s Papers, Vol. I, p. 582)

[36] Again, as previously mentioned:  “the study of light and the phenomena associated with its generation, transmission and detection” is called ‘optics.’  (Oxford Dictionary of Physics, pp. 337 – 338)

[37] For instance, the relationship between the velocity of light at c and the velocity of linearly moving bodies at v.

[38] Unfortunately for physics, Einstein appears to have succeeded handily with these mischaracterizations.

[39] On the other hand, a coherent laser light beam is continuously “emitted in an extremely narrow range of directions.”  (Sobel, p. 181)

[40] “With light…our knowledge is almost entirely inferential.  We can observe no vibration in the source, and we cannot observe light itself at all in any sense.”  (Dingle, 1961, p. 12)  However, recently in Science magazine, scientists have claimed to be able to observe a light wave.

[41] Young and Fresnel explained polarization by assuming that light waves are transverse to the direction of propagation.  (Holton, 1973, p. 393)  This may have been the source of Maxwell’s similar concept.

[42] The two major empirical criteria for electromagnetic waves of light are:  velocity and periodicy or frequency (from which waves, wavelength, and wave phase can be inferred).

[43] Einstein’s photon theory best explains the photoelectric effect, some anomalous specific heats and fluorescence.  (Holton, 1973, pp. 440, 441, 443)

[44] Largely in an attempt to resolve this paradoxical duality, ad hoc quantum field theories were later invented during the 20th century.  (see Chapter 34)

[45] This suggestion of a ‘wave train of photons’ will be discussed further in Chapters 7, 34, and other chapters.

[46] During a trip to England during the 1680’s, Römer discussed his findings and deductions with Newton.  However, Newton did not adopt Römer’s theory in the Principia, because it was not conclusively confirmed by Bradley until 1728 (the year after Newton’s death).

[47] The application of this distance/time interval delay phenomenon of light for such precise measurements of moving terrestrial bodies was specifically pointed out by Einstein in 1905.  However, as it turns out, such imprecision had been known by physicists for decades, but it had intentionally been ignored by mathematicians for purposes of simplicity.  (see Chapter 25)

[48] “The velocity of light we can measure satisfactorily only as an average velocity over a to-and-fro journey, though, with the assistance of mechanical theory, we can get a rough value for a one-way velocity from observations of Jupiter’s satellites.”  (Dingle, 1961, p. 12)  Also see www.sciam.com and www.physics.nist.gov.

[49] Maxwell’s constant velocity of light at c occurs no matter how little or how great the light’s intensity may be.  The velocity of c also experimentally appears to be the limiting speed for high-energy particles of matter, regardless of how much force or energy is applied in an attempt to make them reach or exceed c. (Chapter 32)

[50] “In effect, the light that we see from the Sun comes to our eyes not directly from the Sun but from the molecules of air a few millimeters in front of our eyes.”  (Halliday, p. 893)

[51] “the index of refraction is a characteristic of the medium that light enters.”  (Sobel, p. 5)

[52] The ‘index of refraction’ is basically a misnomer, because such index is independent of the empirical phenomenon of ‘refraction.’

[53] In effect, the Index of Refraction tells us the relative atomic particle density of each particular material medium with respect to the same color of light.  “It is well known from optics that ‘n’ [the index of refraction] is a function of wavelength.”  (Griffiths, p. 398)  But it is also a function of the density of the particular material medium.

[54] “Monochromatic” means light with one color, and one wavelength.

[55] On the other hand, if a material medium is linearly moving relative to the light wave, it must be considered to be a different medium relative to which light has a different transmission velocity, depending upon the relative velocity between the light ray and the medium.  (see Chapter 7)

[56] It is interesting to note that “French mathematician Pierre de Fermat [1601 – 1665] unified the laws of reflection and refraction by showing that both could be deduced from the postulate that light chooses a path of least time.”  (Sobel, p. 5)

[57] A priori, the component colors of the rainbow that comprise such white ray of sunlight will each propagate at a somewhat different velocity, but empirically this phenomenon cannot generally be perceived due to the coherent nature of the light ray.

[58] This phenomenon is somewhat similar to Newton’s second law of motion where the greater the force applied to change the direction of an inertial motion, the greater the angle of deviation of such motion from the rectilinear.  With light, the greater energy (and time for absorption and re-emission) of more frequent wavelengths of photons takes the place of the greater force.

[59] The concept of ether was first mentioned by the ancient Greeks in an attempt to explain the motions of the Earth and the other planets around the Sun.  (Goldberg, pp. 46, 47)  Descartes’ ‘ether hypothesis’ was also based on his abhorrence of a vacuum and his dislike of the concept of ‘action-at-a-distance’ with no physical contact.  (Maxwell’s Papers, Vol. II, ‘Ether,’ p. 763)  To Descartes, force, heat and light could only be transferred by physical contact, ergo by a physical substance like ether.  [Note:  ‘Ether’ was spelled ‘aether’ during much of the 19th century, and before.]

[60] That light waves could oscillate in empty space, without some material medium which also vibrates, forms and supports the light waves, seemed to be an unthinkable concept to 19th century scientists, even without empirical evidence to substantiate this conviction.  For instance, Heinrich Hertz once stated:  “Take electricity out of the world, and light vanishes; take the luminiferous ether out of the world, and electric and magnetic forces can no longer travel through space.”  (Folsing, p. 159)

[61] “The luminiferous ether lay at the foundation of the structure Maxwell had created.  His accomplishment, in the nineteenth-century view, had been to unify the ethers of light, radiant heat, electricity, and magnetism.”  (Sobel, p. 199)

[62] One piece of ‘evidence’ that convinced Maxwell as to the necessity of ether was his assumption that “air itself…cannot transmit transverse vibrations.”  Only a solid can transmit transverse vibrations, asserted Maxwell.  (Maxwell’s Papers, Vol. II, Ether, p. 768)

[63] Maxwell also conjectured that:  “The process may, however, be an electromagnetic one, and as in this case the electric displacement and the magnetic disturbance are perpendicular to each other.”  (Maxwell’s Papers, Vol. II, Ether, p. 766)

[64] As we shall later demonstrate, this was also the case with Special Relativity and many other mathematical theories.

[65] If it had no mass, it would not be affected by gravity.  These hypothetical properties were “not shared by any known medium.”  (Bergmann, p. 27)

[66] The 19th century concept of stationary ether as an absolute reference frame in space may be considered as a materialization of Newton’s artificial concept of absolute space.

[67] As Maxwell stated:  “Whatever difficulties we may have in forming a consistent idea of the constitution of the aether, there can be no doubt that the interplanetary and interstellar spaces are not empty, but are occupied by a material substance or body, which is certainly the largest, and probably the most uniform body of which we have any knowledge.”  (Maxwell’s Papers, Vol. II, Ether, p. 775)

[68] For example, in the 1890’s, H. A. Lorentz asserted that Maxwell’s equations and the constant velocity of light at c were only theoretically valid for an experiment that was conducted in the stationary ether.  (Hoffmann, p. 82)

[69] This, of course, assumed that the ether was unaffected by the motion of the Earth.  On the other hand, if the Earth dragged the ether (with the light embedded in it) along at the same speed as the Earth, then a priori no variation in the velocity of light could be observed in any direction.  Also, if the ether (with the light embedded in it) was only partially dragged along by the moving Earth, then it was assumed that there should only be a partial variation in the velocity of light in each direction.  (Goldberg, p. 86)

[70] In retrospect, all of these ad hoc assumptions and beliefs concerning ether are ridiculous.  But during the 19th century, the scientific community had convinced itself that they were correct, so they were firmly believed to be true.  The analogy of these ridiculous ether beliefs to similar current beliefs in Special Relativity and other arbitrary mathematical theories is compelling, as we shall see in later chapters.