Can special relativity be transformed into a coherent theory?

The common sense analysis of the M-M experiment

Or how to change the century-long-overdue relativistic paradigm which is still constricting the evolution of physics

I said earlier that one of the reasons for my preferring Asimov's description of the Michelson-Morley experiment was what I believe to have been a “slip of the tongue” on the part of that author. Now is a good time to reveal it.

By and large, Asimov's description of the experiment is right at the end of his book (Asimov's new guide to science is almost 1000 pages long). A summary of the main points of the experiment, however, is presented on page 350. And in that summary I read the following:

If the earth is moving through a motionless ether, Albert Michelson had reasoned [before conducting the experiment], then a beam of light sent in the direction of its motion and reflected back should travel a shorter distance than one sent out at right angles and reflected back. (My italics.)

Michelson's initial reasoning was clearly the common sense reasoning. Need I explain why? No, I don't think so. This reasoning is so common that just about anyone should easily arrive at the same conclusion. After analysing the experiment mathematically, however, the conventional conclusion was that exactly the opposite is the case! Why? What could possibly change the initial reasoning so dramatically? Asimov says nothing about that in his book, and (as far as I know) neither does anybody else. Of course, the relativists will immediately remind you of certain assumptions (the laws of physics in inertial frames of reference, principle of relativity applied, etc.), but a solid line of reasoning proving that those assumptions are warranted and indispensable... I have never seen anywhere. And that's not all. Even with those assumptions employed, I challenge any physicist to prove that the conventional mathematical analysis is superior to the common sense analysis. Come on, you physicists out there, show me the error in the common sense reasoning below.

• The experiment was designed to establish if there is a frame of reference at absolute rest (call it ether, call it space, call it what you will).
• The initial assumption was that there is such a frame of reference.
• Therefore, all measurements involved should be performed relative to that assumption.

Now, in the case where the beam of light was sent out in a direction perpendicular to that of the earth's motion, the conventional analysis does measure the distance travelled by the light relative to that assumed frame of reference. (“In the time it takes light to reach the mirror the motion of the earth has carried the mirror from...”, remember?) In the parallel case, however, the distance travelled by the beam of light is not measured relative to the assumed frame of reference—even though the same reasoning should categorically be employed. (That's simply because in the time it takes light to reach that mirror, the motion of the earth has carried it from its original point—relative to the assumed frame of reference at absolute rest—to another point, relative to the assumed frame of reference at absolute rest!) A visual description of the common sense reasoning in the Michelson-Morley experiment is shown in the animation below.

In natural language, then, the common sense analysis of the parallel journey says: In the time it takes light to travel from its source to the mirror at its velocity c plus earth's velocity v, the mirror has moved in space a certain distance—which I shall denote z. The distance travelled by the light in the first leg of the parallel journey is, therefore, in mathematical language: (d+z)/(c+v). In the return leg, on the other hand, in the time it takes light to travel back from the mirror to the source the motion of the earth has carried the source a certain distance in space in the direction of the earth's motion. Mathematically this leg of the journey is expressed thus: (d-z)/(c-v). A visual depiction of this common sense analysis of the parallel journey completed by the light is shown in the animation below.

Now, the total time taken by the light to complete the journey in the direction parallel to the earth's direction of motion is:

So how does the common sense result compare to the conventional result of the parallel case? Let's put them side by side and see:

Now we can extract the final conclusion in the common sense analysis of the Michelson-Morley experiment by comparing the two results above. And since I am only interested in a qualitative analysis of the experiment I can easily derive the final conclusion I have been seeking:

Thus, if there is a need of me to say this, for any value of v greater than zero the time taken by the light to cover the distance from its source to the mirror and back is shorter than the time taken by the light to complete the perpendicular journey! And, of course, this conclusion is exactly the same to Michelson's original one (the one put forward by the common sense), and is the exact opposite of the conventional conclusion. Surprised? You shouldn't be. When between the rational analysis of a phenomenon and its formal (mathematical) interpretation there are conditions (assumptions) imposed by the dogma, chances are that the general sense will no longer be common and that the common will no longer make sense. The history of physics is littered with such examples, and more often than not one idea is replaced by its exact opposite.

So the common sense analysis of the Michelson-Morley experiment leads to a completely different conclusion than the conventional analysis employed by the establishment since 1887. Nonetheless, the two different approaches have something in common: They both conclude that there ought to be a difference between the times taken by the light to complete the two return journeys. The experiment, however, did not detect the difference predicted. Now, we have seen how the conventional establishment dealt with that most unexpected result. Through the propositions of people like Lorentz and Fitzgerald, and with the theoretical contributions of others, the undesirable result of the Michelson-Morley experiment was assimilated in the conventional understanding by being "explained-away" by the special theory of relativity. One might argue (quite rightly) that the undesirable result of the MM experiment was assimilated and “explained away” by the Lorentz-Fitzgerald proposition, but that argument would be unacceptable to the conventional establishment. “Sure”, they would say, “the proposition that objects in motion contract in the direction of their motion by an amount proportional to the motion's rate does, somehow, explain the findings of Michelson and Morley—but that is not enough”. “Why not?”, you might dare to ask. “Because the Lorentz-Fitzgerald proposition does not eliminate the classic idea of a luminiferous ether. The special theory of relativity does that, and that's ultimately what the result of the M-M experiment tells us ”. Hmmm... At this point I shall resist the temptation to contest the validity of the last remark, and I shall proceed instead to explain the result of the M-M experiment by using the common sense version of the Lorentz-Fitzgerald method.

The Lorentz-Fitzgerald contraction could be seen as a desperate and unwarranted act, whose sole reason for creation was to provide some explanation for the inconvenient result of the M-M experiment. Now, to provide an explanation for the negative result of the M-M experiment I will also put forward a proposition. A proposition much more plausible than the conventional Lorentz-Fitzgerald contraction, I should say. And I say that simply because the common sense proposition I will use to explain the result of the M-M experiment is not only able to do that; it is also logically coherent—and, therefore, mentally comprehensible.

The common sense proposition says that all objects in motion extend (in the direction of their motion) and contract (in the direction at right angles to the direction of motion) by an amount determined by their intrinsic velocity.

I believe that some of you have expected to eventually see my proposing that objects in motion extend in the direction of motion, rather than contract, for that proposition was certainly “on the cards”. After all, how better to resolve a line of reasoning that ultimately led to a conclusion diametrically contradictory to the conventional one. But how many of you have anticipated the other half of my proposition—that objects in motion do also contract (along the direction perpendicular to that of motion)? Not many, I'm sure. I am quite firm in my belief, however, that there is an absolute necessity for a two-fold extension-contraction process to explain the result of the M-M experiment in a logically consistent, and physically sensible, manner. In fact one of my many arguments against the special theory of relativity is concerned with the purported manner in which the contraction experienced by objects in motion takes place. After all, what physical object could contract (by an amount that, theoretically, could be anywhere from near zero to 99.9999999999999999999999% infinite) in one direction without experiencing an automatic extension along its perpendicular axis? How could a material object of this Universe, which has contracted in the direction of its motion from its length of (say) many kilometres to a fraction of a millimetre, and which has consequently suffered an increase in its density that is very close to infinite, remain unchanged in shape along the axis perpendicular to the direction of its motion? The special theory of relativity is silent on this issue, and so are the works of Lorentz, Fitzgerald, and others who concerned themselves with writing about the conventional understanding over the years. But if the professed contraction is a real phenomenon, as it is asserted, then the physical changes I've just mentioned should definitely come into play. It is primarily for these reasons that my common sense proposition had to consist of a two-fold transformational process.

That is all I need to say about my common sense analysis of the M-M experiment, as far as I'm concerned. Naturally, my next step is concerned with a review of the special theory of relativity from the perspective created by this analysis. It is time to see if the "fruits" of my labour are tastier than those offered by the conventional establishment, and, indeed, if they are also easier to digest.

The Michelson-Morley experiment

Or how the current dark ages in physics have been drawn by the flawed conventional analysis of that infamous experiment

The Michelson-Morley experiment was conducted in 1887 with the definitive scope of detecting the (rather ill-thought) concept of ether wind. But the experiment was more apt at establishing if there are such things as absolute motion and absolute space, in fact. For those with a limited knowledge of the main aspects related to the experiment the paragraphs below may be helpful.

Physics theories of the late 19th century postulated that, just as water waves must have a medium to move across (water), and audible sound waves require a medium to move through (such as air or water), so also light waves require a medium, the "luminiferous aether". Because light can travel through a vacuum, it was assumed that the vacuum must contain the medium of light. Because the speed of light is so great, designing an experiment to detect the presence and properties of this aether took considerable ingenuity.

Earth travels a tremendous distance in its orbit around the sun, at a speed of around 30 km/s or over 108,000 km per hour. The sun itself is travelling about the Galactic Center at even greater speeds, and there are other motions at higher levels of the structure of the universe. Since the Earth is in motion, it was expected that the flow of aether across the Earth should produce a detectable "aether wind". Although it would be possible, in theory, for the Earth's motion to match that of the aether at one moment in time, it was not possible for the Earth to remain at rest with respect to the aether at all times, because of the variation in both the direction and the speed of the motion.

At any given point on the Earth's surface, the magnitude and direction of the wind would vary with time of day and season. By analysing the return speed of light in different directions at various different times, it was thought to be possible to measure the motion of the Earth relative to the aether.

Michelson had a solution to the problem of how to construct a device sufficiently accurate to detect aether flow. The device he designed, later known as an interferometer, sent a single source of white light through a half-silvered mirror that was used to split it into two beams travelling at right angles to one another. After leaving the splitter, the beams travelled out to the ends of long arms where they were reflected back into the middle on small mirrors. They then recombined on the far side of the splitter in an eyepiece, producing a pattern of constructive and destructive interference based on the spent time to transit the arms. If the Earth is traveling through an ether medium, a beam reflecting back and forth parallel to the flow of ether would take longer than a beam reflecting perpendicular to the ether because the time gained from traveling downwind is less than that lost traveling upwind. The result would be a delay in one of the light beams that could be detected when the beams were recombined through interference. Any slight change in the spent time would then be observed as a shift in the positions of the interference fringes.

The paragraphs above are from Wikipedia, where you can also find a detailed conventional analysis of the experiment. In what follows I will also use a conventional analysis of the Michelson-Morley experiment, written by Isaac Asimov. The reason I'm using that particular description is two-fold: Firstly, because Asimov's description is better suited to my purpose (which is looking for absolute space and motion); secondly, because in Asimov's description I found a beautiful “slip of tongue” about how common sense has been stripped of its sense by a silly assumption, a dogmatic view, and a terrible mathematical translation. Before getting to that, however, I want to show you below an animation with a basic image of the interferometer used in the experiment. (My interferometer may look different than Michelson's, but it nevertheless contains all the relevant features of the original interferometer. In the animation below S is the source of light, the two M are the two mirrors, and the two d represent the lengths of the interferometer's arms. The rest of the animation is pretty much self explanatory, so I'll say no more about that.)

In analysing the experiment we shall assess individually the two paths travelled by the beams of light. Thus, in the case where light is sent out in the direction of earth's motion, from the source S to the mirror M over the distance d, the light travels at its velocity c + the velocity of the earth v. This is the first leg of the journey, and mathematically this is expressed thus: d / (c + v). The second leg of this (parallel) journey takes place from the mirror M back to the source S, over the distance d. In this case, however, the light travels at its velocity c minus earth's velocity v. Mathematically this second leg of the journey is expressed thus: d / (c – v). In Asimov's words, from this point on:

The total time for the round trip is:

Combining the terms algebraically, we get:

Now suppose that the light-beam is sent out to a mirror at the same distance in a direction at right angles to the earth's motion through the ether. The beam of light is aimed from S (the source) to M (the mirror) over the distance d. However, during the time it takes the light to reach the mirror, the earth's motion has carried the mirror from M to M ', so that the actual path travelled by the light beam is from S to M '.

This distance we call x, and the distance from M to M ' we call y (see diagram above). While the light is moving the distance x at its velocity c, the mirror is moving the distance y at the velocity of the earth's motion v. Since both the light and the mirror arrive at M ' simultaneously, the distances travelled must be exactly proportional to the respective velocities. Therefore:

Now we can solve for the value of x by use of the Pythagorean theorem... In the right triangle S M M ' then, substituting vx/c for y:

The light is reflected from the mirror at M ' to the source, which meanwhile has travelled on to S '. Since the distance S ' S '' is equal to S S ', the distance M ' S '' is equal to x. The total path travelled by the light beam is therefore:

The time taken by the light beam to cover this distance at its velocity c is:

How does this compare with the time that light takes for the round trip in the direction of the earth's motion? Let us divide the time in the parallel case by the time in the perpendicular case...:

Now any number divided by its square root gives the same square root as a quotient... So the last equation simplifies to:

This expression can be further simplified if we multiply both the numerator and the denominator [like below]:

And there you are. That is the ratio of the time that light should take to travel in the direction of the earth's motion as compared with the time it should take in the direction perpendicular to the earth's motion. For any value of v greater than zero, the [last] expression above is greater than 1. Therefore, if the earth is moving through a motionless ether, it should take longer for light to travel in the direction of the earth's motion than in the perpendicular direction. (In fact, the parallel motion should take the maximum time and the perpendicular motion the minimum time.) Michelson and Morley set up their experiment to try to detect the directional difference in the travel time of light. By trying their beam of light in all directions, and measuring the time of return by their incredibly delicate interferometer, they felt they ought to get differences in apparent velocity...

They found no differences at all in the velocity of light with changing direction! To put it another way, the velocity of light was always equal to c, regardless of the motion of the source—a clear contradiction of the Newtonian laws of motion. In attempting to measure the absolute motion of the earth, Michelson and Morley had thus managed to cast doubt not only on the existence of the ether, but on the whole concept of absolute rest and absolute motion, and upon the very basis of the Newtonian system of the universe. (I. Asimov—Asimov's new guide to science, pp. 811-814)

The results of the experiment generated a subsequent linear reasoning and theoretical development which eventually reached a climax with Einstein's creation of the relativistic philosophy. Thus, following the path opened by the Michelson-Morley experiment, in 1893...

...the Irish physicist George Francis FitzGerald came up with a novel explanation to account for the negative results of the M-M experiment. He suggested that all matter contracts in the direction of its motion and that the amount of contraction increases with the rate of motion. According to this interpretation, the interferometer is always shortened in the direction of the earth's “true” motion by an amount that exactly compensates for the difference in distance that the light beam has to travel. Moreover, all possible measuring devices, including human sense organs, would be “foreshortened” in just the same way, so that the foreshortening could, in no possible way, be measured.

Then:

The Dutch physicist Hendrik Antoon Lorentz soon carried FitzGerald's idea one step further. Thinkink about cathode rays, on which Lorentz was working at the time, he reasoned that if the charge of a charged particle were compressed into a smaller volume, the mass of the particle should increase. Therefore, a flying particle foreshortened in the direction of its travel by the FitzGerald contraction would have to increase in mass.

Until, finally:

Einstein introduced a second important idea in his special theory of relativity: that the speed of light in a vacuum never varies, regardless of the motion of its source. In Newton's view of the universe, a light beam from a source moving toward an observer should seem to travel more quickly than one from a source moving in any other direction. In Einstein's view, this would not seem to happen, and from that assumption he was able to derive the Lorentz-FitzGerald equations. He showed that the increase of mass with velocity, which Lorentz had applied only to charged particles, can be applied to all objects of any sort. Einstein reasoned further that increases in velocity would not only foreshorten length and increase mass but also slow the pace of time; in other words, clocks would slow down along with the shortening of the yardsticks. (I. Asimov—Asimov's new guide to science, pp. 352-357)

And there it is—the theoretical development following the Michelson-Morley experiment. According to the conventional establishment, the road from the Michelson-Morley experiment to the creation of relativity was a natural and sensible progression that culminated with Einstein's vision. The special theory of relativity became one of the most precious jewels in the crown of physics, and as such it has been reigning absolutely now for just over a century. Most conventional physicists, who are die-hard relativists, no longer question the special theory of relativity—in spite of its many apparent vagaries. But, in the last four or five years, a small number of conventional physicists have found the need (and courage) to question the absolute validity of Einstein's first theory of relativity. One of them, Lee Smolin, believes for instance that the special theory of relativity needs to be changed, somehow, (although he doesn't seem to know how exactly that could be done, or what exactly needs to be changed). However, the cold fact is that physicists like Lee Smolin are so very few at this point in time that the special theory of relativity should still enjoy its absolute status for quite a while yet.

The special theory of relativity has been—nevertheless—opposed by many people since its inception, and that reality is still manifest today. The conventional physicists may scream all they want about the “irrefutable” validity of the theory; the fact is that more and more people are no longer fascinated by the bombastic picture painted by relativists. Instead, they are increasingly asking: “What on earth are you saying, Messrs. Physicists?” To which, of course, the relativists of today can only reply with the same arguments and the same mental pictures used by the relativists at the very beginning of the twentieth century. Not much has changed in the relativity saga, with the exception of some new “patching up” being required. For instance, Einstein assumed that the known velocity of light could never be superseded. That assumption had to hold, for otherwise things could be sent backwards in time. But the fact of the matter is that the speed of light has been superseded (and in the worst of all possible scenarios, in the form of an undeniable signal)! So, our relativists had no choice but to “patch up” the theory, somehow. In the end no one is quite sure if that particular hole in the special theory of relativity has been “patched-up”, although you can bet your last dollar that no relativist would accept that the “hole” is still there for all to see! In fact, no one is quite sure how relativists could claim that other “holes” in the special theory of relativity (in the form of the twin and the clock paradoxes) do not exist. I will come back to these issues a little later. Next, however, we'll reassess the Michelson-Morley experiment from the “common sense” perspective.

On space and motion

Some of my confrontations from 2008-2010

My work on the nature of light and colours--Part 2

My work on the nature of light and colours

My analysis of Newton's theory of light and colours

My analysis of Goethe's work on light and colours

Goethe's edge spectra

If the slit of the spectral apparatus is extremely widened or if a broad white strip is observed against black paper through a prism, as described by Goethe in the Didactic Part of his Theory of Color, the edge spectrum shown in Fig. 7a will be perceived. Goethe explains these edge spectra as being the shift of the objects from their real position caused by the effect of the prism. According to Goethe, the image is not shifted completely as if it in fact resisted the shift. As a result, a ”secondary image” is produced which slightly precedes the actual image. If the bright rectangle is viewed through a prism, it is shifted to the left by refraction, and the bright secondary image is superposed on the dark paper. Goethe propounds that bright on dark produces blue which changes into violet if the effect of the dark increases. On the right edge, the image of the dark surface shifts over the remaining bright ”principal image”. Dark on bright produces yellow which, according to Goethe, accounts for the yellow seam. Where the effect of the dark increases, yellow changes into red.

From the physico-optical viewpoint, it is an untenable interpretation that edge spectra should be caused by principal and secondary images and their resistance to displacement. In the case of a wide slit, the edge spectra can be demonstrated to result from the overlap of monochrome slit images, as illustrated in Fig. 7b. For greater clarity, the slit images of the individual colors are shown in a vertical arrangement. On the right, (starting from 1), the red edge spectrum is very obvious because both red and yellow are fully represented here. On the left in the illustration, the blue edge spectrum is visible (at 1’ and 2’). At the position marked with 4, all colors are present and produce white. 

Extraordinary observations were made by Goethe on the ”negative slit” (Fig. 8a): Unlike the experiment described above, a broad black strip is viewed against a white background through the prism. An unusual ”reversed spectrum” is observed here, displaying the respective complementary colors of the previously described edge spectrum. The formation of this ”reversed spectrum” can be demonstrated in Fig. 8b. Starting at the top, a dark field should be drawn in the middle between the strips of the same color. The background at 0 and 0’ – previously black – is now white because all colors are present here. The previously white center at 4 is now black due to the lack of any color. On the left, the sequence of colors towards the edge is red (3’), reddish yellow (2’) and yellow (1’), and on the right violet (3), blue (2) and bluish green (1). Goethe lists the following ”elements” between white and white, from right to left: blue, bluish red, black, reddish yellow, yellow (Theory of Colors; Didactic Part § 246), corresponding to the positions marked here with 2, 3, 4, 2’, 1’. If the normal slit or the white strip becomes increasingly narrow, the standard prismatic spectrum is gradually obtained, with green instead of white in the middle. If the ”negative slit” or the black strip becomes increasingly narrow, the red and violet spectral ends overlap at position 4 to form purple, the complementary color of green, as can be seen in the illustration. As a result, the following color sequence is obtained with a thin black strip or negative slit: white, yellow, orange, red, purple, violet, blue, bluish green, white.

This excerpt is from an article written for a magazine published for the famous Carl Zeiss Company. Its authors are: Prof. Lutz Wenke (Dean of the Faculty of Physics and Astronomy at the Friedrich Schiller University in Jena), Dr. Friedrich Zollner, Manfred Tettweiler (both from the Institute of Applied Optics) and Hans-Joachim Teske (Manager of the Astronomical Instruments business unit at Carl Zeiss). There are a few interesting points you must have noticed in the “demonstration” above. Firstly, the orientation of the prism is not mentioned, and the sentence which was probably meant to reveal that orientation (“If the bright rectangle is viewed through a prism, it is shifted to the left by refraction...”) is still not clear enough. In any event, we know the orientation necessary to produce the colours observed: The prism has to be oriented with its refractive angle (vertex) pointing to the observer’s left. Secondly, the spectral colours do not extend for the whole width of the white strip. This is rather odd and, in any case, it’s an ad hoc decision. Thirdly, I’m sure you have noticed how convoluted the ‘explanation’ is (especially for the so-called “negative spectrum”), considering how simply it could have been shown where the observed colours originate. Fourthly, the “demonstrations” illustrated in the figures make no sense, when the orientation of the prism is taken into consideration—for in figures 7b and 8b the spectral colours are depicted to run at a 90 degree angle to the normal way of refraction!

This is truly a very strange “demonstration” and I wonder how many physicists, apart from these authors, are accepting it. There could be, however, a possibility that I may have misunderstood something in the “demonstrations” above, and in that case I would love to hear from those who could clarify the situation. On the other hand, I (and I have reasons to believe that you, too) can explain the colours observed much, much easier.

The second example I want to give you is from a paper written by David Seamon, titled “Goethe’s way of science as a phenomenology of nature”.

To understand Goethe’s style of looking and seeing, I want to focus on the prism experiments in part two of Theory of Color. These easy-to-do exercises are a helpful way to introduce students to phenomenological looking because a phenomenon is present—the appearance of color in a prism—which, on one hand, most people are unfamiliar with yet which, on the other hand, can be readily examined, described, and verified through sustained work with the prisms. Table 1 indicates the kind of questions one should keep in mind in doing these experiments and, for that matter, all Goethean science. 

Participants are asked to begin by simply looking through the prism, seeking to become more and more familiar with what is seen. They record their observations in words and colored drawings. Ideally, the experiments are done by a group of four or five, so that participants can report their observations to each other and bring forth descriptive claims—e.g., “I see a halo of color around all objects” or “I notice that there only seem to be colors along edges of objects.” Other participants can then confirm or reject these observations in their own looking and seeing. Gradually, the group moves toward a consensus as to exactly how, where, and in what manner colors appear.

This process of looking is slow and requires continual presentation, corroboration, recognition of error, and correction. Eventually, however, group members can establish a thorough picture of what their experience of color through the prism is and end with a set of descriptive generalizations like those in table 2.

SEEING AND UNDERSTANDING BROADER PATTERNS

The general exercise of looking through the prism just described is excellent for introducing students to the effort, care, and persistence required to produce accurate phenomenological description, but Goethe’s aim is considerably larger: to discover a theory of color that arises from the colors themselves through our growing awareness and understanding of them.

Here, we move into a stage of looking and seeing that explores the wholeness of color by describing in what ways the colors arrange themselves in relationship to each other and to the edge of light and darkness that, as discovered in the experiment just described, seems to be a prerequisite for any color to arise at all.

To identify such patterns and relationships, Goethe presents a series of experiments using a set of cards with black and white patterns that are to be viewed carefully through the prism and results accurately recorded. Examples of these cards are illustrated in table 3 and instructions for the use of three of these cards is provided in tables 4 and 5.

The value of the cards in these experiments is that they provide a simple way to direct the appearance of color and, thereby, provide a more manageable and dependable context for looking and describing. Rather than seeing color along any edge, participants are now all looking at the same edge displaced in the same way so they can be certain that they will see the same appearance of colors.

In regard to card A, for example, we begin with the white area above the black and, through the prism, look at the white-black horizontal edge in the middle of the card. If the image that we see is displaced by the prism below the actual card, then at the edge we see the darker colors of blue above violet (see drawing 1). If we turn the card upside down so that black is above white, we now see something quite different—a set of lighter edge colors that, from top down, are red-orange and yellow (see drawing 2).

As drawings 3 and 4 indicate, the experiments with cards B and C are perhaps the most intriguing because they generate two colors not as regularly seen as in the dominant spectra of yellow-orange-red and blue-indigo-violet. As one moves card B farther away toward arm’s length, there is a point at which the yellow and blue edges merge, and a vivid green appears horizontally so that the original white rectangle is now a band of rainbow (drawing 3). For card C, a similar point is reached where the red and violet edges merge to create a brilliant magenta (drawing 4)

The first thing you might have realised is that from what we have discussed thus far you can explain why the colours in the drawings 1 and 2 are observed. You might have also established—without looking through a prism or reading the instructions—that the colours in those drawings are observed only when the prism is oriented with the vertex pointing down. In fact, you might have realised that, in principle, you could predict what colours would be observed by looking through a prism at all six cards in table 3—even though we haven’t yet discussed the colours observed in experiments like those depicted in drawings 3 and 4. The new colours seen in those drawings (green and magenta) are the products of a mixture of certain spectral colours, as indeed it is explained. But the most important thing you have probably realised is the simplicity with which you can predict and explain the origins of the colours observed in Goethean experiments. You might thing that this explanation is accommodated by common sense and that—therefore—it is rather conspicuous. You might also think that it follows directly from Newton’s reply to Lucas and, on that basis alone, that physicists would have embraced it a long time ago. You might indeed think about all this, but you would be wrong. As you have seen in the first example I gave you earlier, and as it will become evident from the next two examples written by physicists, the explanation that can best predict and describe the observations of Goethean prismatic experiments is not part of the defensive arsenal of the scientific community. 

In "Beiträge zur Optik" Goethe advises us to look through a glass prism and observe the colour phenomena that appear. It soon becomes evident to the observer that colours appear at distinct borders between dark and bright areas in the field of view. If you vary the geometrical conditions you find that all of the various configurations can be boiled down to four principal spectra: The two border-spectra [red-yellow] and [violet-blue] and the two aperture-spectra [cyan-magenta-yellow] and [red-green-violet].

An essential feature of the world of prismatic colours is a basic symmetry: whenever white and black are interchanged in the pattern, the other colours are interchanged specifically, i.e. yellow is interchanged with violet, purple with green, and cyan with red.

Thus, if the upper half of the picture (in the illustration above) should be additively superimposed upon the lower half, the result would ideally be a full white rectangle. If they were instead superimposed subtractively, i.e. as colour slides, laid upon each other, then the result would be a wholly black rectangle. The two halves are perfectly complementary: They have not a single wavelength in common and together cover the whole range.

Goethe was enthusiastic over the discovery he had made, namely that the complementary relationship among colours, since long well known to the painters, had such an evident foundation in the physics of colour. For that reason he was anxious to stress that all four spectra had to be considered as basis for a true theory of colour –not only the particular one, obtained in case of a narrow aperture, studied by Newton. The physicists of Goethe's time told him that all these phenomena could very well be explained by help of Newton's concept of rays of light, differently refrangible. But Goethe stubbornly maintained that it was not just a question of explanation but of basic principles.

Pondering things over during the years, I think I have come to an understanding of what Goethe was after. He was pointing out a lack, or shall we say imperfection, in Newton's theory, especially as this theory was propagated by Newton's followers and late disciples.

The above was written by the physicist Pehr Sällström. Let us compare our (unconventional) explanation of the colours observed in the picture given with Goethe’s explanation (as described by the named physicist). Before doing that, however, notice that the orientation of the prism is not mentioned. Nevertheless, we don’t need to look through a prism in order to establish the orientation of the prism that will result in the specific colours displayed—we can firmly deduce that the only orientation which will result in the depicted colours is an orientation of the prism pointing with its refractive angle (vertex) to the right. I should also mention here that we’ll ignore some of the spectra that will be generated by the picture above, concentrating only on the spectra discussed. To make our task easier I have numbered the spectra of interest in the figure below, and I have also numbered the sources responsible for those spectra (according to our understanding, of course).

On the right picture I have numbered the four spectra observed, in the order in which they were listed in the article. On the left picture I have correspondingly numbered the sources generating the spectra, as I said before. Now, in the article there isn’t an explanation per se of where the four spectra come from—there is only a rather observational (phenomenological) comment that accompanies the picture. Apart from that comment the author says: “An essential feature of the world of prismatic colours is a basic symmetry: whenever white and black are interchanged in the pattern, the other colours are interchanged specifically, i.e. yellow is interchanged with violet, purple with green, and cyan with red”. These observations are quite useless in understanding the phenomenon—they are similar to learning the multiplication table by heart, where knowing the answer does not mean understanding the principle. (Besides that, Goethe’s enthusiasm for finding a physical basis for “colour-complementarity” is rather mystifying, in my opinion. But that’s another story.)

From our perspective, the spectra observed can be easily explained as being generated by an observation through a prism of four ‘independent’ sources.

Thus, spectrum number 1 in the picture on the right (the red-yellow) is one half of the spectrum generated by the white rectangle 1 in the left picture. The other half of the spectrum generated by the rectangle 1 is formed by a violet-blue combination, which is contributing to the creation of spectrum 3. The orientation of the colours in spectrum 1 points to where the other half is. Spectrum 1 is observed to appear towards the base of the prism, while the other half (the violet-blue combination) is observed to appear towards the vertex of the prism—just like we’ve already established.

Spectrum 2 (the violet-blue) is one half of the full spectrum generated by the white rectangle 2. The other half of that full spectrum is the red-yellow combination, and it can be seen (albeit, less vividly than its counterpart) at the border between the white rectangle 2 and the grey background of the page.

Spectrum 3 (the blue-magenta-yellow) is formed by the violet-blue half of the spectrum generated by the rectangle 1 and the red-yellow half spectrum generated by the white rectangle 3. In effect, the magenta component of spectrum 3 is formed by the mixing of red and violet—the blue and yellow components remaining unaffected. The violet-blue combination of the full spectrum generated by rectangle 3 can be seen at its border with the page itself.

Spectrum 4 (the red-green-violet) is the full spectrum generated by the narrow white rectangle 4. The green component of that spectrum is the result of the mix of its yellow and blue components. Spectrum 4 displays three colours (red-green-violet) only if the observation is conducted from a distance greater than approx. 20cm. If you look at spectrum 4 from a smaller distance you will see the yellow and blue components instead.

This is my explanation for those so-called four spectra. Compare it with Goethe’s, or with the one offered by the physicists from whom I gave you the first example, and judge for yourself. I know that my explanation can account for all possible subjective prismatic experiments, and that it can also predict what colours will be seen in all circumstances. This explanation is so accurate and comprehensive that I will therefore call it, henceforth, the law of colour-display in subjective prismatic experiments. In the last example I want to show you we will apply the law of colour-display to some more complicated shapes. Then in the next chapter I’ll continue to test the law and I will also showwhere the spectral colours originate and how they come into observation.

The final example I want to show you comes from an article titled “Exploratory Experimentation: Goethe, Land, and Color Theory” which appeared in Physics Today in July 2002.

Goethe's experimental procedure comprised two stages: an analytic one that moved from complex appearances through simpler ones to a first principle, and a synthetic stage that moved in reverse order, showing how more complex appearances are related to the first principle. The analytic stage is illustrated by a set of experiments with black-and-white images. Figure 2 shows how a few of the images Goethe used look when viewed through a prism with its refracting angle held downward. The general law determined by Goethe was that colored fringes arose at black-white borders parallel to the prism's axis: yellow and red when the white was below the black, blue and violet when it was above, as shown in the prism view of Figure 2e. For Goethe, these fringes constituted an elementary appearance of prismatic color from which all others could be derived. For example, Goethe's experiments with black and white rectangles showed that the Newtonian and complementary spectra (see the prism views of Figures 2c and d) were generated when the colored fringes from two closely spaced black-white boundaries encountered each other: The yellow and blue fringes mixed to produce green; the red and violet produced magenta. For Goethe, therefore, the Newtonian and complementary spectra were compound phenomena that could be derived from the law of colored fringes.

The synthetic stage of Goethe's investigation is illustrated by his experiments on the colored fringes that appear when gray and colored images on various backgrounds are viewed through a prism. Figure 3 shows how part of one of Goethe's diagrams (see the cover of this issue), from Theory of Colors, looks through a prism with its refracting angle held downward. Experiments with squares in different shades of gray against white and black backgrounds showed that the intensity of the colored fringes increased with the lightness contrast at the boundary. More complex phenomena were seen using colored squares, which exhibited fringes with new colors not seen in the previous experiments. Goethe argued, quite plausibly, that those new colors were due to the mixing of the elementary fringe colors with the colors of the squares themselves. Goethe regarded that mixing the true explanation of Newton's observation that a red square, viewed through a prism against a black background, appears displaced slightly higher than a blue one, as seen in the upper right of Figure 3. Whereas Newton had adduced this observation to prove that different colors of light have different refrangibilities—the first proposition of his Opticks—Goethe saw it as merely a special case of the more general law of colored fringes.

Goethe's analytic investigations proceeded from the complex to the simple. Shown are five black-and-white images selected from a series studied by Goethe, viewed with the naked eye (top, adapted from Contributions to Optics, ref. 1) and through a prism with its refracting angle held downward (bottom). The up-down sequence of all the colors is reversed if the refracting angle is held upward. (a) An irregular arrangement of black and white exhibited colored fringes with no apparent order. (b) The colors generated by a simpler checkerboard pattern were periodic and exhibited regular changes as the checkerboard was rotated, but were still too complicated to be expressed in a law. (c) The colored fringes generated by a white rectangle depended on the width of the rectangle and its distance from the prism. A very narrow rectangle, or one at a great distance, exhibited a spectrum with just three colors. Wider rectangles, such as the one shown, displayed fringes whose colors--red, yellow, green, blue, and violet--were consistent with those of the Newtonian spectrum. (d) A black rectangle on a white background exhibited a spectrum—blue, violet, magenta, red, and yellow—complementary to that of (c). The complementary spectrum's central magenta, called "pure red" by Goethe, is not in the Newtonian spectrum. (e) The boundaries of wider rectangles acted as isolated black-white contrasts, displaying red and yellow fringes when the black was above, blue and violet when it was below. No colors appeared at vertical black-white borders.

The experiments just described are only a small fraction of those that Goethe performed during his career. Others included novel experiments with refracted sunlight that displayed at a glance the evolution of both the Newtonian and complementary spectra as a function of distance from the prism, and careful replications and variations of many of the experiments in book 1 of Newton's Opticks.

We shall pay close attention to this description of Goethe’s work, for it is a good summary and it mentions the most important aspects of Goethe’s theory of colours. In the first paragraph cited we encounter again Goethe’s explanation of the colours observed in subjective prismatic experiments like those depicted in figure 2. Notice that Goethe’s mechanistic observation is called “general law”, although it falls well short of accounting for all subjective experiments—as it will become evident soon. The stipulations of GMore complex phenomena were seen using colored squares, which exhibited fringes with new colors not seen in the previous experiments. Goethe argued, quite plausibly, that those new colors were due to the mixing of the elementary fringe colors with the colors of the squares themselves. Goethe regarded that mixing the true explanation of Newton's observation that a red square, viewed through a prism against a black background, appears displaced slightly higher than a blue one, as seen in the upper right of Figure 3. Whereas Newton had adduced this observation to prove that different colors of light have different refrangibilities—the first proposition of his Opticks—Goethe saw it as merely a special case of the more general law of colored fringes. Goethe’s “general law” we already discussed. A more interesting observation is mentioned in the second paragraph.

More complex phenomena were seen using colored squares, which exhibited fringes with new colors not seen in the previous experiments. Goethe argued, quite plausibly, that those new colors were due to the mixing of the elementary fringe colors with the colors of the squares themselves. Goethe regarded that mixing the true explanation of Newton's observation that a red square, viewed through a prism against a black background, appears displaced slightly higher than a blue one, as seen in the upper right of Figure 3. Whereas Newton had adduced this observation to prove that different colors of light have different refrangibilities—the first proposition of his Opticks—Goethe saw it as merely a special case of the more general law of colored fringes.

This is the most important contribution Goethe made to the research into the nature of colour. It is also the only observation that truly shows deficiency in Newton’s theory—although, alas, it failed to attract the attention it genuinely deserves. In fact, as you will see, Goethe’s argument on this issue is not only quite plausible—it is undoubtedly true. We shall analyse that argument in detail, and then you can assess my claim.

Goethe's theory of colours

Johann Wolfgang von Goethe is the most famous of all those who have opposed Newton’s theory of light and colours. He fought hard not only against Newton, but also against Newton’s followers, throwing at them accusations and insults which he categorically felt were conspicuously warranted. Surely enough, his undisguised contempt was fully reciprocated, and it has remained so for two hundred years now. Goethe studied colours for more than forty years, and his particular way of analysing and reasoning has been much discussed, especially by philosophers. His massive book Zur Farbenlehre (Theory of colours) was published in 1810, and—like Newton’s Opticks—is still in publication today. If Goethe was/is loathed and ridiculed by physicists, he was/is also praised and appreciated by many others. These days his views on colours experience a new resurgence, which gives one an eerie feeling—considering Goethe’s prediction that his work will be rightfully acknowledged in the year 2000.

Then how is Goethe’s theory of colours seen today? That’s truly hard to say. Although many have talked favourably about Goethe’s understanding of colour phenomena, very few have dared to proclaim that he was right and Newton was wrong. In fact I do not believe that anyone has asserted that publicly, yet. Instead, every person who undertook the task of writing about Goethe’s foray into the nature of colour (and there have been many, many of them) has diplomatically abstained from taking a definitive stance against Newton’s theory. After all that would reveal, in the eyes of the thinkers of modern society, a certain naivety and ignorance of the soundness and rational power of scientific investigation. And no one wants to risk that, no one in academic circles, at least. See, on this subject, what the philosopher Dennis Sepper has to say in his book Goethe contra Newton:

Newton’s partial success, compounded by subsequent deformations of his theories in the course of the 18th century optics, created a situation that justified Goethe’s criticisms and his attempts to lay a new foundation grounded upon a more scrupulous regard for articulating the proper approaches to the phenomena of color. Yet to argue that Goethe’s Farbenlehre and his polemics have been largely misunderstood is not to argue that they are unproblematic or simply right. I have come to believe that Goethe has an ampler conception of science than Newton, that he has a sounder notion of what an empirical methodology requires and a firmer grasp on the epistemological and philosophical issues involved; however, in the competition for scientific achievement Newton must take the palm of victory. (I do not, by the way, expect that everyone who reads this book will agree with my assessment of Goethe, but I do think most will understand that these claims are not groundless.) Although Goethe is not as amathematical as people think, he nevertheless did not resolve the question of how mathematical conception and calculation are to be reconciled with seeing and experiencing the appearances, and thus despite his intention to present an all-encompassing science of color—and not a merely qualitative science (whatever that might be), as some enthusiasts have claimed—we must conclude that, even on his own terms, he failed to realize this project. 

Nevertheless, it appears that one prominent mathematical physicist has come closest, thus far, to declaring an unabated allegiance to Goethe, but even that example is quite inconclusive (for he merely declared that “Goethe had been right about colour”). 

From a personal perspective Goethe’s theory of colours is fundamentally wrong. What I found surprisingly correct in his work, however, is his explanation of the real causes for the apparent displacement of blue-coloured objects in subjective prismatic experiments. On the other hand, I found surprisingly odd his modificationist views of the spectral colours, considering how close he came (through his experiments) to the correct explanation. Another disconcerting aspect of the Goethe-Newton saga was the extremely poor arguments used by physicists in ‘explaining away’ the anomalies in prismatic experiments presented by Goethe. Furthermore, I also found greatly disturbing the completely unwarranted complications of the main issues in the debate between Goethe’s commentators and Newton’s followers. The principal culprits in the unnecessary chaos that was created have been, unsurprisingly, the philosophers who have found that there is an inevitable necessity of their epistemological-syllogistic expertise to resolve a dispute between two theories both wanting. I will talk in detail about all these issues later.

Goethe began his own investigation into the nature of colours after observing that a white wall remained white when he looked at it through a prism. He wrote about this event the following:

Like everyone in the world I was convinced that all the colours were contained in light; I had never been told otherwise, and I had never had the slightest reason for doubting it, since I had taken no further interest in the matter… As I was now thinking about approaching colours from the perspective of physics, I read in some compendium or other the customary account, and, since I could not derive anything for my purposes from the theory as it stood there, I undertook at least to see the phenomena for myself…  At that very moment I was in a room that had been painted completely white; I expected, mindful of the Newtonian theory as I placed the prism before my eyes, to see the light that comes from there to my eye split up into so many coloured lights. How astonished I was, then, when the white wall, observed through the prism, remained white just as before; that only there, where darkness adjoined on it, did a more or less determinate colour appear…It did not take much deliberation for me to recognize that a boundary is necessary to produce colours, and I immediately said to myself, as if by instinct, that the Newtonian teaching is false.

This episode, especially Goethe’s conclusion based solely on this observation, has been heavily criticised and derided by Newtonians. Even those who have defended Goethe’s work on the origin of colours have (wisely, it seems) refrained from attempting to back up Goethe on his ‘white wall’ conclusion. Sepper, for instance, writes about this episode in Goethe contra Newton:

He [Goethe] appears to have committed an incredible blunder at the outset of his physical studies of color by rejecting Isaac Newton’s theory of white light and colors as demonstrably false. A few casual observations with a prism appear to have settled his opinion: Observing that a white wall viewed through a prism remains white, and that colors appear only where there are contrasts of dark and light, he concluded that the notion that white light is separated into the various colors that compose it was wrong. Yet the phenomena he observed were not unknown to Newton, and so it seems that his insight amounted to nothing more than a misunderstanding of the theory. Although not a few scientists, both friends and strangers, tried to put him right, in person and in print, Goethe nevertheless held fast to his belief and continued his studies outside the traditional framework of optics and color science.

It is interesting the rather non-committing use of words like “he appears” and “it seems”, Sepper uses. Why those terms, Dennis? Are you doubting the validity of the explanation with which scientists have refuted Goethe’s conclusion?

I have tried for a long time to engage in a debate with physicists about the validity of the conventional understanding of light and colours (of which the ‘white wall’ episode would have been a definite topic), without any success. As a consequence I’ve had to rely only on the superficial ‘explanations’ I managed to find—for, on this topic, there is an incredible drought of detailed scientific explanations out there. Indeed, what I have invariably found are short comments followed by absolute assertions that Newton was right and Goethe was wrong. The explanations I managed to get ranged from “the violet and red parts of the spectrum come from different parts...” to the two most elaborate I will cite below.

What Goethe saw is perfectly explicable on Newtonian principles. Had the light passing through his prism come from a point-source, as in a camera obscura, and so been effectively a single ray, he would have seen the phenomenon he expected, a ray of white light dispersed into a sheet of coloured bands. When many rays pass through the prism together, as when it is held up to a window, the spectra produced by the dispersal of the individual rays overlap and reconstitute the original white effect. Only when the source is limited or interrupted... will the rays along its edge be able to produce a spectrum that is not overlaid by any others and so remains separately visible to the observer. Goethe tells us that he soon came to hear this explanation from ‘a nearby physicist’—possibly J. H. Voigt, Wiedenburg’s successor as professor of mathematics in Jena—whom he felt he ought to consult in view of his own lack of experience in these matters, but ‘whatever objections I made... whatever display I made of my experiments and convictions, I heard nothing but his initial credo and had to tolerate being told that experiments in the camera obscura were much more suitable for acquiring a true view of the phenomena’.  (Goethe—Nicholas Boyle)

It’s hard to imagine that no one ever explained to Goethe why the white wall still appeared white when viewed through the prism, and why it was perfectly consistent with Newton’s conception of differential refrangibility. The explanation can basically be read directly off of Newton’s 1665 drawing, or by simply reversing the directions in the basic projection schematic, as shown below. According to Newton, every ray of light emanating from the white wall consists of a mixture of all the spectral colors, but only the red component of the upper ray is refracted into the ray entering Goethe’s eye, and only the violet component of the lower ray is refracted into that ray. (The other components of the upper and lower rays are refracted at different angles, and hence do not emerge from the prism along that particular ray leading to the eye.) In effect, the final ray of white light entering Goethe’s eye is composed of all the spectral colors gathered from different points on the wall. It might seem miraculous that it should work out this way – until we realize that it’s just the reversal of the original experiment, the one that projected the spectrum of colors onto the wall.

The two explanations are expressed rather differently, but the process is the same: The image the observer will get, according to Newton’s disciples, will simply be a single ray of white light—hence no colours. It seems that this explanation is compelling enough to clarify the ‘white wall’ observation and to conclude that Goethe was wrong and Newton was right. But the situation is nowhere near as simple, and certainly not compelling enough. I am amazed that Goethe, or one of his defenders, did not reply to that explanation with the following: If that explanation is correct, and if what the observer sees is a single ray of white light, then another prism (placed in the path of the ray of white light, like in the figure below) should disperse that ray of light into a full spectrum! This is indeed what the observer should expect, in the context of the accepted theoretical understanding and of the given explanation.

Nevertheless, if you perform this simple experiment nothing will change! The observer will still not see any colours. Then what could Newton’s defenders say about this observational fact?

As I said, the ‘white wall’ situation is nowhere near as simple and it is not compelling enough to so easily declare Newton a winner. In fact I can think up a way of defending (from a Newtonian perspective) even the two prisms set-up I have given above, to which I have also developed yet another way of defending Goethe’s conclusion—which reinforces what I said about the difficulty of comprehensively solving the ‘white wall’ mystery. This is just one of the reasons for my trying to engage physicists into a proper debate. The most important reason for my trying, however, is the fact that there is a way of understanding all prismatic experiments—although, naturally, there is also a necessary price to pay in the process. It will all become evident later, but for now let us return to the main discussion.

A most interesting offshoot of the accepted ‘explanation’ for the ‘white wall’ observation is perfectly illustrated by an elaboration of the situation described by the author of the paragraph (and drawing) I cited earlier.

Of course, this also explains (in Newtonian terms) why Goethe saw colors near boundaries. If, for example, we darken the part of the wall where the violet and blue components originate, then the ray entering the eye will no longer be white. Indeed, we could make the wall appear red by darkening or blocking all except the rays coming from the wall at the angle that refracts red light through the prism. (This is reminiscent of diffraction gratings.) So, not only does Newtonian theory account for Goethe’s observations, it immediately suggests new phenomena, and ways of manipulating the elements of the experiment to produce specified results. This interesting explanation, although perhaps not intuitively obvious (as it obviously wasn’t to Goethe), follows mathematically from Newton’s conception of light and differential refrangibility.

What do you think about what is asserted above? Keeping in mind what we have discussed so far, consider what colour the observer will see if he darkens the wall right below where the violet component is supposed to come from. With the prism oriented as in the drawing he would see red. What about if he darkened the wall right above where the red component comes from? In that case he’d see violet. Ah, but the author of the above meant completely the opposite, didn’t he? He certainly meant that the wall should be darkened above the violet, and below the red. He’d just forgotten to specify. OK, then what about if the observer, clumsily, darkens the wall below the red just where the violet originates? And vice-versa, above violet where red originates? What about if the observer, even more clumsily, darkens the wall above and below, covering both points where the red and violet components originate? What about above and below where the rest of the colours originate? And so on, and so forth.

Goethe’s ‘white wall’ observation, as well as most of the other contentious observations in the saga of light-colour debate, is not compellingly explainable in Newtonian terms because Newton’s theory of light and colours (in its current form) is deficient. Something, some vital thing, is missing, and for as long as that thing will remain missing there will continue to be a Lucas or a Goethe crying foul. Goethe, however, did not merely believe that Newton’s theory was deficient—he was convinced that the theory was fundamentally wrong. He also believed that he had the proofs, to that end. He developed and conducted a large number of experiments (most of them subjective prismatic experiments), which were designed to demonstrate the inability of Newton’s theory to explain their observational facts. Goethe’s experiments have created a kind of cult following among those interested in the nature of light and colours, and have even managed to sway the attention of physicists away from the principal factors that affect the results of prismatic experiments. To see what I mean I will cite below from a number of authors who have undertaken the task of explaining Goethe’s understanding of colour. Some of these authors are philosophers, while others are physicists, and I have no doubt that—in view of what we’ve discussed thus far—you’ll find the conclusions of these authors very interesting.

A short note of clarification

This post, as well as the previous two and the next dozen or so that will follow it, have been written almost a decade ago, and they used to be part of a website and a blog (called jaccuse.info and newjaccuse.info, respectively) which I discontinued just before the end of last year. Now I am putting them back online, and before doing it I had decided to leave them by and large as they were originally conceived. That inevitably means that they will contain some lost or obsolete references and perhaps many broken links within. But that is not even of a mild concern to my mind, and it shouldn't be to anyone else's either. Moreover, I had also decided to not publish the entire content of my former sites, which is likely to result in some missing coherence as a whole, at times. Nonetheless, having thought about these issues I had also decided that in certain situations I ought to bend the rules I made, and one of those situations has arisen now. 

I am referring to the so-called issue of Goethe's 'white wall' observation. This is an issue that really drives me absolutely mad, when Newtonians are quick to explain 'away' Goethe's apparently gross misunderstanding. Take as a perfect example just the last paragraph above, in red. Now let me tell you that the guy who wrote it (and whose name I never cared to mention) has to be some thing of a physics and mathematics Grand Master of sorts--judging only by his massive website of that kind, which he's been most likely running ever since probably the very first Atari must have been dropped into this modern world. And for that I, the infidel, can only say "Kudos, dude!" Nevertheless, as from the point of order that we are discussing here the guy is very much a most ordinary, mediocre specimen of dudes. Not that he realises that at any given time, of course. (But, after all, how could he, come to think of it, when what he does is merely repeating what legions of others have been saying for more than 200 years to all those who may, or who indeed have, had the incredible audacity and nerve to question anything that none other than Sir Isaac Newton had chosen to bestow upon humanity as a perennial legacy and gift.)And then I certainly cannot feel any calmer either when I see yet another simpleton declaring that

What Goethe saw is perfectly explicable on Newtonian principles. Had the light passing through his prism come from a point-source, as in a camera obscura, and so been effectively a single ray, he would have seen the phenomenon he expected, a ray of white light dispersed into a sheet of coloured bands. 

Say what, dude, are you kidding me?! What camera obscura have you ever seen in which a 'single ray of light' was ever shone? How do you dare to even contemplate the thought, let alone throw it straight in the face of a man who had dedicated (for no other reason than perhaps his personal love for truth and his unquenchable thirst for knowledge) 40 years of his life to that noblest of the most noble human causes. 

But this is all I will say here, now. Nevertheless, let me assure you that the 'white wall' subject will play one of the leading roles in the development of my unfolding saga. For now though I'll bid you goodbye.