Yesterday I read for the first time in more than four years what I had written about the VBGYOR spectrum in the early pages of this site. It was an experience that brought with it a motley array of feelings and realisations, and for a while afterwards I seriously contemplated an idea which I had specifically and consciously dismissed right from the outset. That proved to be a brief disturbance in the end, however, although it nonetheless troubled me greatly for the time it lasted. Why I am telling you this I am not quite sure, especially since I have never intended to give you any details at all about what that "idea" entailed. It surely must have something to do with the fact that I've been staring at the empty screen in front of me for a few hours now, totally lost in thought and unable to string together even a couple of words that I could use to start off this page with. But since I have somehow gotten to this point this has to be as good a start as any other, come to think of it.
In physics the predominant language is that of mathematics, and one direct consequence of that fact is physicists' belief that their science, more than any other, is free of the ambiguity that is typically conveyed and spread out by the spoken language. Physics is, if not exactly an exact science, then certainly one of precision. Yeah, this is what the conventional physicists believe, and--alas--that isn't the whole story either. For instance, it is precisely because of that belief that they demand from others to "define this" and "define that", even though in many cases they do it for far less noble reasons. I heard one of them the other day, for example, claiming that unlike the general public believes physicists want to be proven wrong--for from that progress arises. Undoubtedly that's a most commendable claim, fully endorsed by wisdom and philosopher. (I, for one, do not believe it for a second though--because the physicist, like any other man, is first and foremost human.) With these thoughts fresh in mind, let me now give you a couple of the most eloquent and relevant examples that cast a totally different light on the matter.
The first prismatic experiment performed by Goethe--and indeed the one that led him to believe that Newton's theory of light and colours was wrong--is also the one that's been most talked about. I am referring to the 'white wall' observation, of course, and although I have already talked about it, here I shall return to it and discuss it once again and in more detail. Let me thus start the subject with Goethe's own recollection of his observation.
I remembered well that everything appeared many-colored, but in what manner was no longer present to my mind. 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 colored 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 color appear; finally, that the window bars appeared in the liveliest colors of all, whereas no trace of coloring was to be seen in the light gray sky outside. It did not take much deliberation for me to recognize that a boundary is necessary to produce colors, and I immediately said to myself, as if by instinct, that the Newtonian teaching is false.
The paragraph above comes from Dennis Sepper's book Goethe contra Newton, and below I shall continue with Sepper's exposition (complete with exact copies of the diagrams he used) of the conventional arguments used by Newtonians to refute Goethe's belief that his observation proved that "the Newtonian teaching is false".
Scientists have always recognized the import of this moment, for it betrays an inadequate conception of what Newton's theory requires. What Goethe saw is explicable according to Newton's doctrine that light is differentially refrangible according to color. A ray of light upon encountering a refracting surface is "decomposed" into a virtually infinite number of component color rays. In the case of direct vision through the prism we need only consider what happens along the line of sight EP (see Fig. 2.2). If, for example, EP is a ray of white light traveling toward, and refracted by, the prism, and if this ray could be isolated in camera obscura, the result would be a continuous spectrum VBGYR, with violet the most refracted, red the least. Because the paths of light rays undergoing refraction are in principle reversible, if a violet producing ray followed the indicated line from V to the prism, it would travel the line EP, as would the blue-producing ray following the line from B, and so forth across the spectrum for points VBGYR and all intermediate points. Thus EP will be a white-producing ray if we can manage to get all the components of white to follow their respective paths so as to be refracted into EP. This is precisely what happens when the wall is white; for although all the unrefracted rays coming from the wall WW produce white, the differential prismatic refraction assures that the only component of the ray from V refracted along EP is violet-producing (the other components are refracted at slightly different angles), the only component from B so refracted is blue-producing, and so forth, and for every other possible line of sight a similar conclusion holds.
If there is some boundary in the field of vision (e.g., an area of black), the result is somewhat different. As one gets close to the boundary, the superposition of rays will no longer be complete. In Fig. 2.3, for certain lines of sight such as EP, all the components of white can be gathered from the segment VR. But lines of sight such as E'P will lack some of the components; the violet constituent must come from point V', but no light is coming from this point, so that the color of the light along E'P will be the "sum" of red, yellow, green, and blue, but not violet (the result is presumably a shade of yellow). For lines of sight below E'P, even more components will be lost. Eventually, the process reaches a point at which only red will contribute a component to the line of sight and, finally, a point from which no light travels along the line of sight.
(Before proceeding to an analytical assessment of Sepper's exposition, which is basically synonymous with the conventional understanding of the subject in question, I should make clear that although I am far from happy with Sepper's irksome diagrams--for obvious reasons, like the stupid way in which the "differential refraction" is depicted--I have reluctantly decided to reproduce them exactly as they appear in his book. As I'll advance in my analysis, however, I will make use of better graphics.)
There are three things in Sepper's exposition of the conventional arguments which have been used to refute Goethe's conclusion that are of interest for my current objective, and I'll discuss each of them individually, in order of their relative importance. The first one is somewhat less important (for my current scope, at least) than the other two, and thus I will direct your attention to it now. This thing is candidly expressed in a single sentence:
A ray of light upon encountering a refracting surface is "decomposed" into a virtually infinite number of component color rays.
To those who have read Sepper's book such nonchalant expression and acceptance of this Newtonian argument should appear rather bizarre, considering how much time and effort he puts later on in dissecting and scrutinizing what the conventional definition and understanding of a "ray" is (or, rather more accurately, might be. The truth is that this is one little subject of great concern, and many others apart from Sepper have tried over the years--in vain, it must be said--to get from the conventional physicists a precise description of what a Newtonian "ray of light" is. My own demand from the defender of the conventional theory would be much simpler. "Don't tell me anything, just draw me a picture. A simple picture of your ray of white light that shows not the distribution, or arrangement, of its 'virtually infinite number of component colour rays', but only of those 5-6-7 distinguishable spectral colours." Now, although I said a moment ago that this thing is of less interest to me than the next one that I will discuss, that is only a relative qualification particular to my present scope (as you perhaps have already realised). The fact is that the Newtonian/conventional idea of a ray of light of infinitesimal dimensions that is composed of an infinity of coloured rays is nothing but most imprecise and equally ambiguous, whether it is expressed in mathematical or in plain spoken language. To my mind this idea is on a par with that of the point particles of zero size, or with that of the one-dimensional strings that are supposed to make all matter.
The second aspect of the conventional refutation of Goethe's 'white wall' observation is much more clear-cut and obvious than the first one. Indeed it is so conspicuously cut and obvious that I find it extraordinarily difficult to believe that for more than two hundred years no one seems to have seen or done anything about it. In any event, I want to assure you right from the outset that by the end of this little chapter you will see it as clearly as the sun looks in a cloudless sky. But first let me replace Sepper's irksome diagrams with a couple of much better ones, shown below.
The diagrams above are my renditions of the originals that are displayed on this website belonging to the Institut für Theoretische Physik from Hannover, Germany. The only difference between the original diagrams and my renditions is the number of the illustrated spectral colours (three in the original, five in my renditions). The picture above on the left is the equivalent of Sepper's Fig. 2.2, and the one on the right is my replacement for his Fig. 2.3. As you most certainly must have already noticed, in these diagrams the "differential refraction" is properly depicted, and the orientation of the prisms is in the more familiar position with the refractive angle--or vertex--pointing "up". Finally, you surely must have also noticed that my picture above on the right is different from the one it is replacing, but I trust that it's all for the better and that you won't have any problems understanding the message that it was meant to carry and convey. In effect--if there's any need of me to explain--the bluish ray that enters the observer's eye is due to the absence of the red and yellow components (drawn in dashed lines of the respective colours) of the otherwise white ray that would enter the observer's eye if there was no dark boundary present.
If you are a physicist, or a layman with an interest in this subject, or if you have followed with some degree of care the evolution of this website, then you must be aware that there is one radical difference between the order of the spectral colours projected on a screen (as Newton had done for the most part of his investigation) and that seen by the naked eye through a prism (as, in turn, Goethe did). That one radical difference is, in the words of Newton himself, that "Prismaticall colours appeare in the eye in a contrary order to that in which they fall on the paper". Now, as I believe that there's no further need to elaborate on that matter, let me direct your attention to the picture above on the right. Superficially, at a first glance one might be tempted to draw from that picture a seemingly safe conclusion that the conventional understanding is correct, for it appears to be able to explain the distribution of the spectral colours as they are seen by the eye directly through a prism. In effect, one may tempted to explain, as the picture above on the right directly shows the eye sees the blue end of the spectrum displayed at the top of the image--toward the vertex of the prism--just like the case is in a real observation. Moreover, one may be tempted to continue the argument further, from the same picture it is quite clear that the other end of the spectrum (which typically is formed by the red-yellow combination) can also be accounted for--just push the object under observation forward, or alternatively move the prism and the eye of the observer backwards.
Alas, if one is led into that temptation one should better ask God, and the world, for forgiveness--for one then has been wrong all along. Now, if you don't know exactly why one has been wrong all along, then chances are that you are not a physicist. And, on the other hand now, if you are a physicist and yet still do not know exactly why one has been wrong all along, then chances are that you're either incompetent, or perverse, or both. (I, personally, have knowledge of only one conventional physicist who should--by all accounts--know exactly why one has been wrong all along, but sadly I haven't been given the chance to find out what his stance is in this particular matter.) Let's see next why one has been wrong all along, and in order to do that I will drop below a visual aid, in the form of yet another picture. This time, however, the picture on its own is not sufficient--you also need a prism to see, and understand, why I have been so emphatic in tone and in assertions.
Now, position yourself comfortably in front of your monitor's screen at a distance of about 0.5 metre and then place your prism in front of your favourite eye of observation with the angle of refraction--the vertex--pointing towards your left. At this point I ought to perhaps explain--if there's a need really to do it--that due to the shape of the picture I have been forced to change the prism's orientation from its more familiar "vertex up" position to the current "vertex on the left" situation. This shouldn't be in any way detrimental to our final objective. On the contrary, in many ways this orientation is handier than the one with the vertex pointing up. There is of course only one thing that shouldn't be forgotten--that what you see now on the left is what in the previous pictures (and usually in our discussion) was displayed towards the top of the image under observation, while at the same time what is now displayed on the right was at the relative bottom.
A careful observation of the diagram above yields a significant amount of information about the nature of light and the spectra it displays. For our subject of contention here, though, we shall restrict ourselves to discussing only one specific part of it, which is of direct relevance to our present goal. Later, however, I shall cover other aspects of the prismatic-spectral information too.
From a distance of approximately 0.5 metre an observer will see through a prism a spectral display of the diagram above similar to the picture I shall drop below in a moment. What I will ask you at this point is to direct your attention to the spectral colours that appear to be laying on the outside along the boundaries of the white rectangles, which are demarcated by the green lines atop and at the bottom of each of them. The colours I'm referring to are the red, the dark blue, and the violet, respectively. I can assure you that these colours are definitely laying along, but nonetheless beyond, the vertical borders of each rectangular source of light--as indeed the demarcating green lines are indicating. (In the case where the white rectangles are very narrow the dark blue-violet combinations are in fact well separated from their respective boundaries--as in the two cases on the left.) Nevertheless, if you have any doubts about my assurance you should certainly double check if indeed it is so. You can easily and convincingly do that with the help of your mouse pointer. Place the tip of the arrow on any green line and then look at it through your prism. (Do not be disturbed or confused by the spectral images of the arrow--you should realise pretty quickly how you can establish exactly where the pointer is at all times by learning that you can alternate your perspective from looking through the prism to looking directly at the screen without changing position or moving the prism.)
The problem of my contention on this subject should be quite obvious now for all interested parties--from laymen to physicists alike. I'm saying this because fundamentally this problem is simple and straightforward. In essence the whole issue at stake is contained in the following question: Can the conventional theory (which is quite clearly and comprehensively illustrated in the two pictures shown at the beginning of this chapter) account for the red, dark blue, and violet colours (which are located--relative to their particular sources--as in the diagram above)? The answer to this question is a precise, unambiguous "No"--regardless of how vehemently I hear the current establishmentarians protesting. Let me give you one concrete example of why I'm convinced about that.
On this page I cited, right at the beginning, from an article written by reputable conventional physicists (with superlative credentials) exactly on the topic we are discussing now. I urge you to read the article (you can find it here on page 18), especially the explanation given in relation to the figure below.
Now, as I was saying on this page (albeit, rather too briefly and somewhat tentatively), the explanation given by the authors for the spectral colours illustrated in the picture above is terribly obfuscated. (That was in fact the reason for my being too brief and tentative in the first place, if you're going to accept this justification.) I do not intend to over elaborate on why I said that the explanation in question was terribly obfuscated, except for one thing which is most relevant to our topic. As you must have already noticed the figure 7a above is supposed to be, in principle, identical to the figure on the right from the diagram above it. But if that was without doubt the authors' intention, the fact is that they have made a real mess of it. Why? Well, first of all because obviously they have 'misplaced' the red part of the spectrum. Second of all, because they have depicted (both verbally and graphically) the process and distribution of the spectral colours as is particular to the Newtonian case--where the spectrum is projected onto a screen--in what it's supposed to be the Gothean case--where the spectrum is observed directly through the prism. (Assuming that you have done what I'd urged you a few moments ago I don't need to explain this point, do I? Just remember that "Prismaticall colours appeare in the eye in a contrary order to that in which they fall on the paper" and then think a little.) Now at this point some may be inclined to suggest that, since what I am saying is undeniably correct, the authors of this article must have made an honest mistake, and that--therefore--this is not a "concrete example" that the conventional theory is in any way deficient (as I claimed earlier). I hope you're not one of those, but if you are consider this. Regardless of how one tries to manoeuvre the type of explanation used by the authors of the article we're discussing (and in a moment I will clarify "the type"), which they fancily described as "the overlap of monochrome slit images", the fact is that it's absolutely impossible to account for the distribution and location of the spectral colours seen in the Gothean prismatic experiments by making use of that particular type. And now let me clarify what I mean by that.
It has come to my attention, and maybe to yours too, that when it comes to defending the Newtonian theory of light and colours the conventional physicists use two types of explanations. The first type is based on the arguments used by the authors of the article we've been discussing, while the second type is based on the arguments used by Sepper in his description of the 'white wall' and it's graphically illustrated in my two earlier renditions of those pictures I mentioned from the Institut für Theoretische Physik. And to make even clearer my point let me add to what I've said that "the overlap of monochrome slit images" is just a fancy description of the original Newtonian argument that the typical display of the spectral colours seen in prismatic experiments is the result of the total number of individually coloured images of the source of light as they've been refracted by the prism, each by a specifically characteristic amount.
So, then, it should be clear now that no conventional explanation of "the first type" can account for what is seen directly through the prism, simply because the refraction/bending of every colour is supposed to happen in the same direction--even if by a different and specific amount! The only way that the conventional argument of the first type could possibly account for the distribution and location of the spectral colours observed directly through the prism would be if some spectral colours could refract/bend in a direction opposite to the others. For instance, if the red part of the spectrum could refract/bend in a direction opposite to the one obeyed by the dark blue-violet part, then one conceivably may be able to account for the locations of both ends of the visible spectrum in the so-called subjective prismatic experiments. As it stands, though, the conventional theory can only account for one end. You know what I mean? Think about it.
(A corollary example of what we're talking about here occurs, quite naturally, in the so-called objective prismatic experiments too. So how do the conventional physicists deal with that? Very simply, I can tell you. Listen, for example, (or remember, as the case might be), to how one of them dealt with it in an email he sent me a few years ago: "This, incidentally, explains your "paradox" of the white rectangle with colored fringes. When you split the rectangle in two with the pen, you get two large white sources, and on the screen each has a red and a violet fringe. The fringes fall on the black background where they're uncontaminated by competing light. In the middle the images of all the other colors overlap to create white". At the time I thought about replying with the following message: "Whatever you say, Mr. Dutch, but what ever is that that you're saying?")
Could there be at all possible that some spectral colours refract/bend in a direction opposite to that stipulated by the conventional theory? Is it conceivably possible that a prism may refract/bend the spectral colours that make up white light in a manner akin to that illustrated below?
All things considered, that seems to be categorically impossible--if for no other reason then for the fact that the specific direction of refraction/bending that is stipulated by the conventional theory is well backed up both theoretically and experimentally. We know, after all, that light travels slower in glass than in air, and that's why all refractions/bendings of the coloured lights happen at an angle less than that at which the incident beam of light enters the prism. If, therefore, one or more of the spectral colours could refract/bend in an opposite direction that would necessarily imply that some lights travel faster in glass than in air, which contradicts all experiments hitherto. This by itself is a very strong argument against the suggested possibility. And yet I can show you an experiment which by all accounts seems to agree with my suggestion.
One of the first prismatic experiments conducted by Newton was the following one (as described by the great man himself in "Of colours" and with his own accompanying illustration):
On a black peice of paper I drew a line opq, whereof one halfe op was a good blew the other pq a good deepe red (chosen by Prob. of Colours). And looking on it through the Prisme adf, it appeared broken in two twixt the colours, as at rst, the blew parte rs being nearer the vertex ab of the Prisme than the red parte st. Soe that blew rays suffer a greater refraction than red ones
This experiment is comprehensively analogous to the first experiment that appears in Newton's much later written Opticks. Now, before going any further it is worth mentioning that Newton concludes from this experiment alone that blue light is refracted more than red light, and--furthermore--that his followers (the past ones as well as the contemporaneous ones) have not hesitated to use this experiment as confirmatory of his theory of light and colours even though the direction of the supposed refraction of the blue light is completely opposite to the one normally stipulated for all spectral colours. Indeed so many have done that over the years that virtually all of them have done it. (Sepper too, in his Goethe contra Newton, by the way.) Ultimately, then, by siding with Newton in his conclusion and this experiment the conventional physicist--whether unwittingly or unconcernedly--is indirectly saying that blue light travels faster in glass than in air, and consequently that the suggestion I made is quite possible. I nonetheless shall take it all as a gaffe--a very silly, infantile gaffe. At this point, though, I want to show you something that Newton and his followers have all missed. Something reeeally interesting.
Let us next replicate Newton's experiment as he described it in Of Colours, but with a little addition I'll say nothing about just yet. I'll ask you to take your prism now, to point its vertex to your left, and then to look through it at the picture below on the left from a distance of approx. 0.5 m. Look carefully and think about what we've been talking about thus far, for what you'll see is definitely worthy of that.
Now, the picture you have seen through your prism was very similar to the one above on the right (with the exception of some things of peripheral importance at this point, which I have deliberately omitted). What matters most at this stage is the fact that the blue and the red lines appear to have been definitely refracted in opposite directions! That such seems to be the case can be easily established, and there's no need of me to repeat how that can be satisfactorily done. Neither Newton nor any of his many followers, however, appear to have become aware of this fact--at least not to my knowledge--and this is truly one of those genuine "food for thought" realities. Indeed this subject begs a lot of questions, but for now I will only say that it is quite disappointing that Newton has failed to consider this possibility--especially after seeing the result in his own version of the experiment. However, to my mind it is even more disappointing that not one of his myriad of proselytes have done that either. Had they considered that possibility they would have been led toward other experiments which are logically related to the one illustrated above, like the one below--and that would have in turn led them to other realisations. Like, for example, the fact that in the so-called subjective experiments two particular colours appear to remain un-refracted by the prism. At this point you should instantly realise at least one of the two colours I'm referring to. In any event, take your prism, follow the same set of instructions we've been using all along, and then look through it at the picture below to see which colours are the two I am talking about.
It is hard to believe that for more than three hundred years no one seems to have discovered that two of the spectral colours, green and yellow, are not subjected to any refraction by a prism. But this is an undeniable fact--at least in subjective prismatic experiments--and I have good resons to believe that you have only learned about it a moment ago.
What about in the so-called objective experiments? Do yellow and green refract in those too? To be honest, I have no idea. That's because the truth is that I have never conducted Newton's experimentum crucis, which should really answer that question. I had simply accepted its results as a matter of faith. (Faith in the integrity and competence of those who had done so, and who testified on its behalf.) Now, the physicists of the conventional establishment are adamant that Newton's experimentum crucis demonstrates with absolute certainty that all spectral colours are refracted in a prism, as you know. Nonetheless, I for one have lately begun to experience strong pangs of doubt about it, and because of that I will most certainly perform Newton's crucial experiment in some near future. In the meantime, though, maybe one of you will do (or redo) it, and might perhaps succeed in determining what the truth is by taking into serious consideration the non-refraction of yellow and green observed in the subjective prismatic experiments. To my mind, which looks at things from a personal perspective of the Greek kind, the two colours ought to behave in the same manner in both cases--if for no other reason then simply because I strongly believe that God can only be subtle. To my mind it is conceivably possible that physicists may have been seduced into seeing and interpreting the observations of the experimentum crucis strictly from Newton's perspective, while a completely different process may have been at work all along. You see, from my perspective it is not a mere coincidence that yellow and green form one third of the visible spectrum, that they also are the centre of the spectrum, and that they do not refract in prisms. More on this later.
The third problem that is plaguing the conventional theory regarding the spectral display observed in the so-called subjective prismatic experiments is illustrated in the three pictures below.
Consider the following. Starting from the setup illustrated in the first picture above on the left, which is from Institut für Theoretische Physik and is shown again simply for convenience, imagine that you enlarge the white part of the wall (as is indicated by the two arrows in the picture above on the right) without changing anything else in the set-up. (Needless to say, there have been some idealizations in the original pictures designed to make life easier for all, and I followed in manner--so don't get tangled in semantics.) In this case, then, the observer will no longer see a white wall, as in the previous case, but a white wall with "coloured fringes"--to use the expression favoured by physicists. In effect the observer will see a picture identical in principle with those depicted in the illustrations. The orientation of the spectral colours will also conform, as it is illustrated, to the orientation of the prism. In the third picture, just above, I have also depicted the colours seen by the observer as they would appear in reality, along the top and the bottom of the 'white wall'.
Now, in view of everything that's been discussed and come into consideration, one crucial question ought to be answered: How can one account for the observations by using the conventional theory? Well. according to those establishmentarians from the Institut für Theoretische Physik, quite easily. Please listen to them:
Looking at a broader white strip on dark background, the central portion remains white, while the borders become coloured fringes: yellow – red the one, ice-blue (cyan) – purple-blue the other one. The central white is easily understood: light reaching one point at the eye's retina does not originate from one point of the surface looked at, but instead from different points along a line. This is sketched to the right for three selected rays, which have been coloured according to their wavelength for simplicity. (This last sentence is a reference to the original illustration I rendered and used as a substitute for Sepper's Fig. 2.2--and which is basically present in all three pictures above.)
The explanation of the coloured fringes is simple too. (In the above sketch one may keep the light paths unchanged, but think the white area moved to the left or to the right – if no ray emerges from the dark, which colour is seen if the viewing direction is not changed?
That's it. I mean that's all that's being said by those from the Institut für Theoretische Physik who have created this website about the "coloured fringes" seen in the so-called subjective prismatic experiments--that the explanation for their provenance is simple!
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