Newton’s theory of light and colours bears the marks of a scientific explanation: it is simple, it uses reasonable and not too many assumptions, it accounts for the results of relevant experiments, it is supported by logical reasoning and experimental evidence, it makes testable predictions. A defender of Newton’s theory could rightly describe it as such, without fear of being judged as dishonest. But, in spite of the apparent validity of such a description, the truth is—quite a bit—more complex than that. Newton’s theory of light and colours is relatively simple, it uses some pretty reasonable assumptions, it accounts for the results of some relevant experiments, it is supported by logical reasoning if the interpretation of some experimental evidence is correct, it makes testable predictions, which are nevertheless debatable. This is a more accurate assessment of Newton’s theory, and by the end of this chapter you will see why I believe this assessment to be closer to the truth.
The basic idea of Newton’s theory is simple: colours are contained in the “white” light and each colour is refracted at its specific angle when passing through a medium other than vacuum. This basic idea is indeed simple, but the unavoidable details of this idea are nowhere near as simple as that. Even leaving aside the mysterious issue of what colours are in the first place, there are many, less mysterious, issues that Newton’s theory ought to account for—and in dealing with those issues Newton’s theory is rather vague and, often, questionable. For example, how many colours are contained in the “white” light? Newton’s theory answers this question by asserting that there is an indefinite number of colours in “white” light, although only seven (nowadays we say six) are distinguishable. The distinguishable colours are red, orange, yellow, green, blue, violet—the ROYGBV acronym kids learn in order to remember the spectral colours. These colours are part of the original, or primary, colours—but they are not the only primary colours. Indeed, Newton says that “the Original or primary colours are, Red, Yellow, Green, Blew, and a Violet-purple, together with Orange, Indico, and an indefinite variety of Intermediate gradations”. Apart from the original colours Newton said that there is also an indefinite number of compounded colours, which are formed by mixing original colours.
The Newtonian description of colours was one of the reasons for my scepticism about the validity of the current understanding of light and colours. My scepticism was borne out of the conventional description (which is basically Newtonian) of what happens in the basic prismatic experiment. I’m referring here to the experiment in which Newton let the beam of light from a circular aperture pass through a prism before projecting it onto a wall. This experiment, in which the prism was fixed in a position that created a situation of minimum deviation (meaning that the angle of the incident beam of light was equal to the angle of the emergent beam) marked the beginning of Newton’s investigation into the nature of light and colours, because the spectrum generated had an unexpected oblong shape. Newton’s eventual conclusion was that the only thing that could render the original orbicular source into an oblong was an unequal refrangibility of the “coloured” rays present in the white light. A beam of white light passing through a prism, thus said Newton, results in an oblong spectrum that contains “an indefinite” number of original colours which are refracted at their specific angles. This idea is clear enough, but some believe that Newton’s description of colours poses problems. Sepper, for example, writes on this issue:
The mixing of colors, however, presented Newton with problems that he never fully resolved. Even in his first published paper, he had to allow that a mixture of two rays of different refrangibility could match the color produced by homogeneous light, light of a single refrangibility. Thus a mixture of red and yellow make orange; orange and yellowish green make yellow; and mixtures of other pairs of spectral colors will similarly match an intermediate color, provided that the components of the pair are not too separated in the spectrum.
I disagree with Sepper’s conclusion. In fact it is clearly evident from Newton’s first paper that he had considered the mixing process carefully, and indeed that he had plausibly resolved it. In Proposition 4 Newton describes how the mixing of original colours ought to be perceived.
Yet seeming transmutations of Colours may be made, where there is any mixture of divers sorts of Rays. For in such mixtures, the component colours appear not, but, by their mutual allaying each other, constitute a midling colour. And therefore, if by refraction, or any other of the aforesaid causes, the difform Rays, latent in such a mixture, be separated, there shall emerge colours different from the colour of the composition. Which colours are not New generated, but only made Apparent by being parted; for if they be again intirely mix't and blended together, they will again compose that colour, which they did before separation. And for the same reason, Transmutations made by the convening of divers colours are not real; for when the difform Rays are again severed, they will exhibit the very same colours, which they did before they entered the composition; as you see, Blew and Yellow powders, when finely mixed, appear to the naked eye Green, and yet the colours of the Component corpuscles are not thereby really transmuted, but only blended. For, when viewed with a good Microscope, they still appear Blew and Yellow interspersedly.
What I found more problematic in Newton’s description of the spectral colours is the great number of original colours which are absolutely necessary, it seems, to explain the oblong shape of the spectrum. But, then, by using Newton’s description one could account for all colours, which would make the notion of compounded colours totally redundant. That’s because, ultimately, what Newton unwittingly says is that all colours are original and all compounded colours are illusions. And this unavoidable conclusion exposes serious rational flaws in his own theory of light and colours.
To see one of the flaws I’m talking about consider the nature of the spectral colour orange. According to Newton (and to the current conventional understanding) orange is an original colour present in white light, with its own degree of refrangibility (its own index of refraction). Nevertheless, orange can also be obtained by mixing red and yellow, and this orange is completely indistinguishable from the other orange. In view of this fact a natural question arises: Which orange is the one observed in Newton’s spectrum? Of course, the conventional answer to that question would be that the original orange (the one with its own index of refraction), but then another natural question must be considered: Why would God bother to create an original orange, with its own index of refraction, when He could much easier achieve the same goal by simply letting the original red mix with the original yellow. After all God is the superlative master of achieving maximum efficiency with minimum effort, and our most successful theories invariably possess the same quality. Surely He couldn’t just have created the original orange in order to satisfy the requirements of Newton’s theory of light and colours. And there is not only orange that poses this dilemma, but an indefinite number of other colours as well.
This kind of reasoning, coupled with the conspicuous absence of orange and green in most subjective prismatic experiments, made me wary of Newton’s theory (in its accepted form). But I was certain that Newton had thought himself about these issues, which made even more important the question: Why did he insist that there are many more colours in the white light than the discernable ROYGBV? I could understand his insistence that orange and green have primary qualities—for those colours appeared to be refracted at their own specific angles by the second prism in his experimentum crucis—but what was the need for insisting that there is an “indefinite number” of other colours that possess the same qualities. After all, the most natural classification of colours should be determined by only one qualitative factor: the primary (or original) colours are those which cannot be created by mixing other colours; the secondary (or compounded) colours are those which can only be created by mixing other colours (i.e. by mixing two, or more, primary colours). According to Newton, however, this simple classification does not suffice, for there must also be compounded colours which possess the quality of the uncompounded colours—namely, their own index of refraction. Doesn’t it sound unnecessarily complicated?
To my mind, it does. But since I believed that Newton had thought about this issue himself I was convinced that there must have been a good reason that forced him to classify the colours as he did. And, eventually, I found that reason.
Let’s consider, in plain language, the Newtonian description of the basic prismatic experiment. A beam of white light coming from a perfectly circular source is passing through a triangular prism, positioned at minimum deviation, before being projected onto a screen. This set-up produces a coloured image in the form of an oblong. This oblong shape was described thus by Newton:
They were terminated at the sides with streight lines, but at the ends, the decay of light was so gradual, that it was difficult to determine justly, what was their figure; yet they seemed semicircular. Comparing the length of this coloured Spectrum with its breadth, I found it about five times greater...
The elongation of the spectrum into an oblong five times longer than wide is at the heart of Newton’s theory of light and colours, and the eventual success of his theory rests quintessentially on the explanation Newton offered for the reasons that could render a circular beam before the prism into an oblong one after. (Ipso facto, the main reason for the success of Newton’s theory of light and colours was the fact that its only opponent was the so-called modificationist theory—which was a ‘theory’ that could not provide any plausible explanation for the oblong shape of the spectrum. In view of this fact one could truly conclude that Newton’s theory won by default.)
Now, in the figure below I have depicted graphically the Newtonian explanation for the oblong spectral shape, as well as the reason that forced Newton to attribute a primary quality (i.e. individual index of refraction) to secondary (compounded) colours. Thus, at A is the image of a perfectly circular aperture, which is the representation of the source in the basic prismatic experiment. The coloured dots illustrate the conventional understanding of the photonic distribution of the beam of white light (which is also Newton’s corpuscular view of light). In effect, the conventional (basically Newtonian) understanding asserts that a beam of white light is formed by a great number of heterogeneous photons, with each photon possessing its own ‘colour’. (Here I am overlooking the modern concepts of wavelength, frequency, and energy. Individual ‘colour’, nevertheless, incorporates all those concepts as well.) My depiction at A is, in principle, a cross section of a beam of white light as described by Newton and his followers. At B I have depicted the spectrum formed after the refraction process in the prism, albeit with only six colours (the distinguishable ROYGBV) represented. In this graphic representation I respected Newton’s observation (the length of the spectrum is five times greater than wide). The reason for my representing only the discernable spectral colours will become evident shortly. At C I have depicted the shape of the spectrum, in white, and the circular shapes of the six discernable colours. Finally, at D is a graphic depiction of the Newtonian explanation for the oblong shape of the spectrum, with a number of inscribed circular shapes—which stand for the “indefinite” number of colours required by the theory.
Now—if an explanatory note is necessary—had Newton tried to explain the shape of the spectrum by attributing individual indices of refraction only to the distinguishable colours (as I did at B), he would have failed. That’s simply because with only six (or even seven) colours he could not account for the straight lines at the sides. Indeed, imagine how clearly any deviation from a straight line should be observed when the projected spectrum had a length of over 13 inches and a breadth of almost 3 inches! In order to account for the clearly straight lines at the sides of the spectral oblong he had to invoke an “indefinite” number of spectral colours, as I did at D. (In fact only an infinite number of colours could account for those straight lines, really.) This is the reason that forced Newton to attribute that unwarranted quality to compounded colours, in spite of being aware—I believe—that such a desperate measure would inevitably bring eventual penalties with it (as indeed it has).
My own investigation into the nature of light in prismatic experiments led me to believe that there must be another reason for the observed oblong shape of the spectrum—a reason neither detected by Newton nor considered by his followers. I believed that because there are too many little things that just refuse to “hang out naturally” (as someone, whose name I’ve forgotten, had said about another theory) in Newton’s understanding of light and colours. For instance, one of the most compelling of those little things that hangs unnaturally in Newton’s theory is the fact that in subjective prismatic experiments the spectral colours “appear contrariwise to the naked eye”. Lucas had observed this fact, but his explanation for it does not hold any water. After all today we can see that even if one disregards other considerations and accepts the idea that the brain has learnt to put things in the right perspective (in spite of what the eye registers), to a brainless camera the spectral colours still appear contrariwise. We have seen that Newton was aware of this fact, but he never offered any explanation about its possible causes. Disconcertingly, no one since Lucas has even spoken about this observational fact, let alone offer an explanation. There is no doubt that there is an explanation for this observation, however, but there is also no doubt that that explanation does not spring naturally from Newton’s theory. Otherwise, three hundred years of theoretical scrutiny and scientific progress would have certainly uncovered it by now.
Until Newton’s time no one had doubted that the Aristotelian explanation for the rainbow-like display of light passing through a prism was correct. According to that modificationist view, the homogeneous white light passing through a prism is ‘corrupted’ by the glass (it looses its purity). The degree of ‘corruption’ the white light suffers is dictated by the thickness of the glass it travels through. Thus, said the modificationists, towards the vertex of the prism—where the light passes through less glass—the loss of purity is relatively low and it becomes violet. Towards the base of the prism, however, the glass is considerably thicker and at that point the white light suffers a greater loss of purity, becoming red in the process. And, of course, in between those two extreme points the degrees of corruption vary commensurately, which results in the observed display of the other colours. Now, what evidence did modificationists have to substantiate their claim? The answer is disarmingly simple: visual observation. Indeed, look at any source of light through a prism and you will clearly see the same spectral distribution as in the figure below.
This spectral distribution is the inverted image of the spectral distribution in Newton’s theory: VBGYOR, instead of ROYGBV. Now, there was no doubt about the observation, but that did not at all mean that that particular observational fact was a consequence of light losing purity (or getting ‘corrupted’) upon passing through the prism. It was that explanation that Newton questioned, not the observation itself, and it was his scepticism about the validity of that explanation that eventually drove him to his experimentum crucis. Nevertheless, in a most curious turn of events, although Newton’s crucial experiment has become the prima facie evidence that the modificationist theory was wrong, the experimentum crucis does not at all account for the observational fact that had led to the modificationist explanation of the basic prismatic experiment. Let me reiterate that in other words: The explanation that provided some answer for the observational fact of the basic subjective prismatic experiment was proven wrong by an experiment that provided no answer at all for that observational fact! This is Voltairean irony, don’t you think?
The little things I have discussed so far (and others I will not discuss here) have driven me into a personal investigation of the behaviour of light in prismatic experiments. It was clear to me that there must be a coherent explanation for the two different spectra observed: the ROYGBV in the so-called objective prismatic experiments (in which the spectrum is projected onto a screen), and the VBGYOR in the so-called subjective experiments (where the spectrum is observed directly with the naked eye, a camera, or any other similar device). And, to my surprise, it was rather easy to find that explanation. Following a line of reasoning I’ll discuss shortly, I conducted a simple experiment which revealed a way of explaining, coherently, how the subjective spectrum (VBGYOR) could be linked to the objective one (ROYGBV). But the most satisfying thing of my work was the manner in which that explanation “hanged out” with the other aspects relevant to prismatic experiments and to the nature of light and colour. Naturally. Seamlessly. Unforced.
Short Intermezzo
Over a year ago (in 2007, that is) I posted on You Tube a couple of videos with three simple experimental observations and I invited physicists around the world to explain them by using Newton’s theory. To maximize the chances of getting physicists to watch those videos I sent e-mails to more than 200 of them, luring them (through a harmless trick) to answer my challenge. I know that many of them watched the videos, but in fifteen months of waiting I received the grand total of one reply. (I’d gotten, in fact, another reply early into my campaign, from a Nobel prize laureate, be he did not venture into a genuine answer to my question. I wrote about this episode here.) The reply I got was from a Professor at a distinguished American University, and it is worth showing you what he had to say in relation to the inverted spectrum observed in subjective experiments.
So let’s say we have a very narrow slit allowing sunlight to pass through a spectrum and project on a screen to give a fairly pure spectrum. Violet light bends more, red less, so we have a spectrum with red on top and violet below. If you put your eye in the beam of colors you’ll see just one color (actually a narrow range of colors). Let’s say you put your eye in the green part of the spectrum. You’ll see only green. The red light is hitting above your eye and the violet below. To see red light, we’d need a second slit positioned so its red light hits your eye. Since the red light from the first slit is hitting too high on your face, we need the second slit positioned below the first slit. And to see violet light, we need a third slit above the first one. So to get all three colors, we need three slits, and you’ll see violet on top, green in the middle, and red below, just the opposite of what you see when the spectrum is projected on the screen.
This answer left me flabbergasted, and I know that anyone who has ever used his eye (or the eye of a camera) instead of a screen in a prismatic experiment would have felt the same way. That’s because there are so many things this professor (whose name I won’t mention, unless he wants me to) is clearly not aware of, that I was convinced he had never conducted such an experiment. Instead he ventured (veeeery unwisely) into a kind of ‘explanation on the run’ which is, frankly, just gibberish. I will not spend time now on explaining all those unwise things in the paragraph above because they will become evident later.
From the conventional explanation of the basic prismatic experiment to my own crucial experiment
A narrow beam of white light is emitted from a source, it travels in a straight line through air, it enters a triangular glass prism, it is dispersed in the prism into its constituent colours, every colour is refracted (bent) at a different angle (less than the incident) in the prism, every colour is refracted again upon exiting the prism, the resulting spectrum is projected onto a screen. That’s, in a nutshell, how the conventional physicist describes the basic prismatic experiment, and the picture below is a graphic depiction of this description (taken from Encyclopaedia Britannica).
Now, according to the currently accepted theory, the reason for refraction is that light travels at different speeds in different media. In the basic prism experiment, for instance, light travels faster in air than in glass. The degree of refraction is governed by Snell’s law—a law created some 40 years before Newton’s experiments. Snell’s law stipulates that the degree of bending suffered by the light depends on the angle the incident light makes with the surface, and on the ratio between the refractive indices of the media. (Each medium has a different index of refraction—which is just a factor by which the known velocity of light in vacuum is slowed down in that medium.) Furthermore, the index of refraction of each medium varies with the colour of the light, creating the dispersion of the spectral colours as in the figure above. In effect, the reason for the characteristic display of spectral colours (with red at the top, violet at the bottom, and the other colours in between) is that red is slowed down the least (has the lowest index of refraction), violet is slowed down the most (has the largest index of refraction), and the other colours are slowed down, individually, in between the two extremes (each colour with its own specific index of refraction). That’s all there is to the basic prism experiment, says the conventional physicist.
But this Newtonian description, which provides an explanation for what is seen in the basic setup (where the spectrum emerging from the screen is intercepted by a screen), fails to account for what is seen when the screen is substituted by a “naked eye” (or the eye of a camera, camcorder, etc.). In such a case the spectrum seen by the eye displays the colour composition VBGYOR—instead of the ROYGBV displayed on a screen. If the Newtonian description of the basic prismatic experiment is correct, the only spectral display an observer should see (either directly or projected onto a screen) is the ROYGBV one. The picture above illustrates this perfectly. Now, consider for a moment the ‘explanation’ I received from that American professor. He seems to believe that what an observer sees is the ROYGBV display, and then he concocts some incomprehensible story about the need of a slit for each spectral colour, placed in a certain order, etc., etc. The simple truth of the matter is that you only need one slit to see the full spectrum, and that that spectrum will always have the VBGYOR composition. I think I’ve already said this, but I’ll repeat it again: In all prismatic experiments the Newtonian spectrum ROYGBV is only observed when the spectrum is intercepted by a screen of some kind. In all other cases, where the spectrum is intercepted by the eye (camera, etc.), the observed spectrum is VBGYOR. Below are two photos showing the spectra produced by different slits and apertures.
The most important aspect one should be aware of when analysing a subjective observation (i.e. when using one’s eye instead of a screen) in a prismatic experiment is that what the eye sees is not really the spectrum emerging from the prism. One may be tempted to think that what the eye (or the camera) sees are strictly the spectral rays that have been dispersed in the prism and which are subsequently collected by the retina. But that’s incorrect. Light—‘white’ or ‘coloured’—is virtually invisible! In the basic subjective prismatic experiment, for instance, what the eye sees (in fact, what the brain registers) is the image of the prism, which itself contains the contentious spectrum we’re discussing. Obviously, if you place your eye in the beam of light (as suggested in the intermezzo) the colours you are seeing are lined up with the colours projected onto a screen, but only someone who has conducted such an experiment can realise that so it should be, in this case. But to see the VBGYOR spectrum you don’t need to place your eye directly in the beam! And that is the spectrum I’m talking about. Alas, one who has never conducted such an experiment but who has been taught to visualise prismatic experiments strictly within the framework of Newton’s theory of light and colours, can be quite easily fooled (especially by a graphic depiction as in the figure I showed you from Encyclopaedia Britannica) into believing that the spectrum the eye should see is the Newtonian ROYGBV. But that is not the case at all. As you can establish yourself (simply by looking through a prism), and as it’s evident from the photos above, the only spectrum seen by the eye is the one I like to call (for obvious reasons) the Aristotelian spectrum—which has the VBGYOR distribution. Where is this spectrum coming from? This is the question, and—ultimately—this question demands a definite answer. Nevertheless, Newton’s theory (at least in its conventional form) cannot provide it.
Ultimately, this contentious issue can be summarised in one paragraph. If one accepts Newton’s theory as the correct explanation for what is observed in prismatic experiments, then even if one overlooks the flawed belief that what one’s eye sees are the spectral colours coming from the prism, the theory cannot provide an explanation for the inverted distribution of colours (VBGYOR, instead of ROYGBV) seen by one’s eye. (This is illustrated below in the left figure.) On the other hand, if one accepts that Newton’s theory correctly explains prismatic experiments, and if one is also aware that what one’s eye sees is the image of the prism instead, then even if one overlooks the fact that the depicted dispersion inside the prism is merely an assumption (I’ll talk about this shortly) and accepts it as correct and observable, the theory still cannot provide an explanation for the fact that the spectrum observed has the VBGYOR distribution. (This is illustrated in the figure on the right.) Think about it.
The basic prismatic experiment is truly a quantum experiment, and in many respects it confronts an observer with very similar issues to those encountered in the so-called two-slit experiment, or in Schrodinger’s cat experiment. In those experiments we know what we start with and what we end up with—but we have no idea what happens in between. In the basic prismatic experiment we also know what we start with (a narrow beam of white light) and what we end up with (Newton’s ROYGBV spectrum). But just like in those two famous quantum experiments, we have no idea what takes places in-between—inside the prism. Newton’s theory offers an explanation for that, but his explanation is by no means a fact. That is why I said that the Newtonian explanation for the dispersion inside the prism is nothing more than an assumption. Newton’s theory of light and colours is to the basic prismatic experiment what the quantum theory is to the two experiments I mentioned. Interestingly, both theories present huge interpretational problems—and this is not a trivial fact. In the world of mainstream physics, however, there is a general tendency to sweep under the carpet inconvenient facts, especially when the theories involved have no commensurate contenders—as indeed has been the case with Newton’s theory of light and colours. Of course, sooner or later the theory that presents “inconvenient truths” will invariably be superseded by a theory that will explain them—although many a time this will only happen long after the creation of the theory itself. The inverted spectrum seen in subjective prismatic experiments is such an inconvenient truth, and I have a theory to explain it. The theory I have developed contains, like Newton’s, a crucial experiment.
Newton’s theory of light and colours does certainly have a number of strengths. But it also shows undeniable weaknesses, when closely scrutinised. One of its strengths is the simplicity and apparent plausibility of the explanation he offered for the chromatic dispersion inside the prism. Although that explanation is really an assumption, as I’ve mentioned, one must admit that it appears to be a natural and safe one. That’s because it does not only seem able to explain the spectrum projected on a screen, with its ROYGBV composition and its oblong elongation, but because it also appears to explain the results of his experimentum crucis. Indeed there are some strong arguments in its favour, and that’s why Newton was so confident about its veracity.
Newton’s theory is based on two assumptions, however. One of them is the one I’ve just mentioned—which states that each spectral colour has its own individual index of refraction (in all media other than vacuum). The other assumption Newton proposed was that the spectral colours were existent in the so-called white light—indeed, that they formed it. Personally, I have never had any problems with that assumption. As far as I was concerned that assumption was not only plausible; it was also necessary and inevitable. To my mind, though, Newton’s other assumption was unacceptable—in spite of its apparent confirmation by his crucial experiment. To Newton’s mind, on the other hand, his two main proposals were not assumptions at all: They were facts, clearly demonstrable and proved. Interestingly, Newton’s opponents of modificationist leanings have usually been willing to accept the different refractions of colours, although they have vigorously opposed the idea of the coloured lights being contained in the white light. Interesting.
The most disconcerting fact about Newton’s theory, in my view, is that more than three hundred years later a great number of anomalies (both theoretical and experimental) have remained unexplained in the conventional physics. I found this unacceptable from the beginning of my investigation. Most of those anomalies have been either discretely swept under the carpet, or swiftly thrown in the courts of other scientific disciplines. Even more distressing is the absence of empirical evidence for the most important ideas of Newton’s theory. For instance, I could never find out if there is any experimental confirmation for the supposed difference in the velocities at which the “coloured” lights travel in glass. It was clear to me that such evidence is absolutely vital, if one wants to convince the world that the foundation of Newton’s theory—the idea of different refractions for different colours—is rock-solid and fully warranted. Indeed, without such evidence even the results of the experimentum crucis are circumstantial, at best. Years later, I still do not know if such evidence exists—although I’m willing to place a decent bet that it doesn’t. That’s why that central idea of Newton’s theory remains merely an assumption, in spite of a huge number of experiments, similar to the experimentum crucis, which have been conducted and whose results appear to confirm the hypothesis. As I said (and as many others agree) that evidence is purely circumstantial. And when it comes to Newton’s other assumption—that the spectral colours are contained in the white light—there isn’t any evidence to confirm it either. In spite of all these shortcomings, however, Newton’s theory of light and colours is still regarded as a good theory. But I believe that that is mainly because it hasn’t had any serious contender.
It was within this framework that I began my own investigation of the behaviour of light in prismatic experiments. I was convinced that both experimental setups—objective and subjective—had a common explanation, and I firmly believed that the results of both kinds had a physical basis, rather than the purported view that the objective prismatic experiments had a physical explanation while, the subjective experiments required a physiological one. That meant that I had to find a clear explanation for the inverted spectrum (VBGYOR) observed in subjective experiments. Furthermore, I had to also link that spectrum to the Newtonian spectrum (ROYGBV), which is observed in objective experiments. Finally, I had to find a way of linking the two spectra through a physical process which could take place inside the prism—for, after all, no one can claim to know what truly happens inside the prism.
Now, in order to achieve all that I began by analysing the results of prismatic experiments in terms of images. That’s because the spectra observed, either directly or on a screen, are images. They are snapshots of light. They are frozen moments of light, at a particular time and in a particular place. There is no doubt that the two images are intimately connected, for they both contain the same subjects. Nothing more, nothing less. The most telling fact about the two images is that one is the mirror image of the other, which must really reveal something. Something important. Something that had a simple yet fundamental explanation. These thoughts convinced me that the explanation I was searching was discoverable. Had we observed these two images scrambled, rather than inverted, would have made the task much more difficult—if not impossible. Remember, God is subtle, but never malicious. This Einsteinian creed, when properly understood, can often lead one to that momentous thought we call (rather crudely) gut feeling. For instance, I thought, what could be the simplest way of getting from VBGYOR to ROYGBV? The answer to this question was quite easy. But that didn’t answer the most important question: Where does VBGYOR come from in the first place?
An answer to that question may seem difficult, but a simple process of elimination can actually indicate from where the VBGYOR image comes into the view of the observer. Consider the basic setup of a subjective prismatic experiment, which I’ve already discussed. The observer’s eye does not see the spectrum ROYGBV coming from the prism. What the eye sees, instead, is the image of the prism—which also contains the VBGYOR spectrum. This means that VBGYOR comes into the observer’s view either from somewhere in the prism or from somewhere before the prism. But since light is virtually invisible (meaning that it becomes visible only when it interacts with matter), ultimately there is only one possibility from where the VBGYOR image of the spectrum can come into the eye of the observer: from the prism itself.
This realisation, however, does not solve the riddle. There are quite a few other things that need to be considered. For instance, from which part of the prism does VBGYOR come into view? From the inside, or from one of the two sides of the prism that are involved in the basic setup of the experiment? And, most importantly, how (by what process) does VBGYOR come into being? Could it exist in that form in the white light? All these questions needed unambiguous answers. Moreover, I wanted all those answers to be backed up by direct and solid empirical evidence. I did not want to find an answer to those questions by using some hypothesis, however plausible or seemingly able to explain indirect observations it might have been. Newton had done that when he developed his theory of light and colours, and three centuries of that legacy have brought only controversy and no real progress in mankind’s understanding of either. Sure, the conventional physicist would dispute that, but the plain truth is that there is neither direct evidence for the existence of the spectral colours in white light, nor similar support for the idea of different chromatic refractions. With all these thoughts in mind I conceived and conducted my first subjective experiment.
My own experimentum crucis
On a black, flat surface, perfectly horizontal, I placed a piece of paper with a short message written on it. Then, looking at the same level on the plane of the surface, I slid a prism between my eye and the piece of paper. And, lo and behold, I could read the message!
See the difference? Now consider what you’ve just seen in conjunction with the following observation. When one looks through a prism at a source of light, one sees a spectrum. When one looks through a (rectangular) block of glass at a source of light, one doesn’t see a spectrum. Of course, there is an explanation for this failure in the current understanding, but it is rather... evasive. In fact it is no explanation at all, for it only says that when light enters perpendicularly into a rectangular block of glass there is no refraction—and therefore no spectrum. Why is there no refraction in this case? There is no answer to this question in the current conventional understanding, as far as I know. If there is an answer, however, I would love to hear it from someone.
At this point it is important to ponder for a little while on the organ that helps us to perceive and make sense of the world around. The eye is an amazing organ indeed, but it has limitations. Perhaps the most severe limitation of the eye is that it gathers the information of the three-dimensional world around onto a two-dimensional screen. We believe that in its long history of evolution, however, the brain has learnt to process the two-dimensional information it receives from the eye and to put it into a three-dimensional awareness (which makes that severe limitation quite manageable). Nevertheless, in spite of this remarkable achievement we still see only two of the three dimensions, at any point. The dimension we don’t (really) see is the depth. Of course, we are instinctively aware of this fact, and that’s why I did not expect to be able to read the short message on the piece of paper I laid in front of my eye. But, then again, I did not expect to see that the prism gave me a perspective of that dimension normally denied to the eye, either. The undeniable truth, however, is that this is exactly what the prism does. In fact, as I came to realise in time, all transparent objects with a prism-like shape do the same thing—albeit, with varying degrees of success. Generally, the greater the difference between the narrowest and the widest parts of the object, the fuller perspective of the depth of the field of vision the observer gets. In effect, what the prism does is that it literally lifts that normally prohibited dimension into (almost) full view. And lenses, which are prism-like objects, do that too. The fact is, then, that we don’t see in only two dimensions; in fact we see in two dimensions and a bit (of the third). Think about why I said that.
The simple experiment I performed had a profound revelation on me. In an instant I could see a beautiful way of explaining the VBGYOR spectrum observed in subjective prismatic experiments. And that was not all. I also realised that many (perhaps all) of the anomalies that Newton’s theory cannot explain, would suddenly become quite trivial expectations. And, ultimately, I saw that Newton’s central idea—colours are connate properties of the white light—can be empirically proven. How can that be done? Just have a look at the two pictures below.
The prism allows the observer to see the structure of the field of light on a plane parallel to the direction of travel. There was no doubt in my mind that this is a fact, but I was fully aware that there were many more issues related to it that needed to be clarified and explained. One of those issues, which I found thoroughly satisfying, was the fact that the perspective observed through the prism was not restricted to a beam of light oriented perpendicularly to the prism (as was the case in the experiments presented thus far). To see exactly what I mean I have depicted graphically how the prism lifts the image of the beam of light, bringing it into the view of the observer. Below on the left there is an illustration of how this process takes place in the case where the beam of light enters the prism at a right angle to the prism. In the figure on the right I have illustrated how the same process takes place even when the incident beam of light enters the prism at an angle less than 90 degrees. In fact you can still get a perspective of the third dimension even when the angle is much more acute than in the illustration below. This confirmation was very important, for reasons so obvious that I’ll not even mention. I urge you to perform this simple experiment (use a printed strip of paper, for example, like I did in the photos above, but hold it at angles less than perpendicular, like in the illustration below), and I guarantee you’ll be amazed from what angles you’ll be able to see what is printed on it.
Prismatic experiments and the chromatic structure of light
In the previous chapter we talked extensively about subjective prismatic experiments. I believe I made my point clear that subjective prismatic experiments have been largely misunderstood, and that the observations they yielded can be, coherently, explained. Indeed I showed that the spectral colours observed in subjective prismatic experiments can be accounted for by my law of colour-display. This is in direct contradiction to the conventional view, which asserts that a comprehensive law of the colours observed in subjective experiments cannot be derived, due to factors that range from complexity to insufficient understanding of the physiology of sight. The law I presented, however, explains and predicts the spectral colours generated in all conceivable subjective experiments. But to fully understand the phenomena that is not enough. This fact becomes evident simply by considering the case of Goethe, who himself derived a law (albeit, limited) of what colours should be observed in subjective prismatic experiments, without bringing any real benefit to the overall understanding of light. (For those with modificationist leanings, Goethe’s speculations about the origins of colours have no scientific back-up at all.) Although my law goes further than Goethe’s, it is still a basically phenomenological law—it shows what, but it does not say how and it doesn’t explain why. In what follows I will attempt to answer those two vital questions.
Let’s assume that in subjective experiments the prism indeed presents the observer with a perspective of the composition of light along its axis of travel. If this view of light is correct, we should rightfully expect to see it bringing additional benefits into the current understanding. Moreover, it should be able to explain—coherently—how relevant experiments produce their observational facts. Furthermore, it should also accommodate itself—unforced—within the (better) understood framework of physics. This will be my uncompromising expectation, and—with it in mind—will see how it fares. Before doing that, however, I have to make clear one issue of utmost importance. This issue should be relatively easily understood, first by looking through a prism (vertex up) at the figure below from a distance of about 20 cm.
If the black part of the figure is not in the view of your prism, you will not see any colours. Why? Because from that distance the third dimension is entirely occupied by the white part of the image coming into your eye. This white part is formed by the mixing of the spectral colours, which—unmixed—are out of your view at this time, however. If you want to see the unmixed spectral colours you must have at least one edge of the white rectangle into view. For example, if you increase the distance between the prism and the figure you will see the unmixed colours running along the top and bottom edges of the white rectangle. In a way, this is like stepping back from a wall right in front of you in order to see what lies beyond it. (Remember also that beautiful saying about the trees and the forest.) This is not some desperate analogy, and you’ll understand even better what is happening by looking through your prism, from a distance of about half a metre, at the figure below left.
If you look through your prism (oriented diagonally at a 45 degree angle, vertex up) at the white rectangle on the left you will see a picture similar to the one above on the right. Now I have good reasons to believe that no further explanations are necessary. Think about it, if you have to, and you’ll understand everything I tried to say (admittedly, not as eloquently as I’d have wished). The essential point is that in order to see through a prism all spectral colours of an image you must have the whole image in your view. And just as essential is understanding that when you see the full array of the spectral colours that accompany an image you are, in fact, seeing the chromatic structure of the light that carries that image along its axis of travel (which is the third dimension, the dimension virtually prohibited to the naked eye). Of course, you can also get a partial perspective of the third dimension, which will result in a partial display of the spectrum. There’s no need to elaborate on when this situation occurs, or why—I believe. That’s because a picture does not only tell a thousand words; it also conveys a message far more expressively than any verbal description.
The first, not insignificant, benefit my view of light brings to the table is the simplicity with which it explains the so-called “white wall” dilemma that puzzled Goethe. You cannot see colours when you look at an object that completely blocks your view. Compare this explanation with the conventional one, which I discussed in the previous chapter, and judge for yourself. I won’t say anything more on this subject now, but I want to talk about another simple observation related to the “white wall” dilemma, which I have never seen discussed anywhere. Look at the white rectangle in the figure above not through a prism, but with the naked eye. Consider next the conventional description of what is happening. The rectangle is a source of light, and the reason you see it white is due to the fact that the image of that rectangle is actually formed by a great number of photons of six (or maybe seven) colours which are landing on your retina with a great frequency. So far, so good. But now consider this. According to the conventional understanding, the photons coming from the source into your eye are truly independent entities and randomly distributed at every point on every plane. This means that at every conceivable point in time and space, your retina receives an image of the rectangle similar (in principle) to the one below.
The image registered by the brain, then, is a succession of many (thousands per second) images similar to the one above, with each image slightly different than the others. This extraordinarily fast succession of different slides create the image you’re seeing: a white rectangle. It is a plausible scenario, I admit. But I say that if one were to conduct a comprehensive statistical analysis of this scenario, I guarantee that there will arise situations where there will be a succession of, say, only blue photons at points in the figure. Not only that, due to factors I won’t discuss (for that will be a long and tedious story) I guarantee that such situations would arise rather too often not to be noticed! Furthermore, there will also arise many more other similar (in principle) situations that should be noticed by the observer (like a succession of, say, blue-yellow-blue-yellow-blue-yellow), which I’ll also not dwell on. Even further, the observer could substitute his eye with a very-fast-shutter camera—which would notice such situations much better than the eye. To cut a long story short, however, what I am getting at is that regardless for how long an eye or a fast camera looks at the rectangle above, it will always register an entirely white rectangle. This is a real problem for the conventional description, but not at all for my understanding of light. That’s because at every point of the rectangle there will be a perfect succession of VBGYOR, VBGYOR, VBGYOR...
But the most significant benefit my view of light brings with it is the coherence with which it can explain how things work at quantum level. If light has a chromatic structure, as subjective prismatic experiments suggest, then the conventional interpretation(s) of quantum phenomena is inadequate. This is a most distressing realisation if you believe that the conventional understanding of the quantum world is correct, and I was fully aware of it right from the beginning. But the cold fact is that our understanding of the quantum world has always been marred by a logical and rational incoherence which not even the staunchest conventional physicist could deny. This reality I found nowhere better expounded than in the following musings of J. A. Wheeler:
Today the quantum is recognised as the central principle of every branch of physics. However, in its many features of indeterminism, complementarity, and interference of probability amplitudes, it has sometimes seemed something strange, incomprehensively imposed from outside on an unwilling world of physics. If it were fully understood, would its inevitability in the construction of the universe not stand out clearly for all the world to see? And could it not then be derived, along with all its mathematical superstructure, from some utterly simple first principle? Until we shall have arrived at this basic idea we can even say that we have not understood the first thing about the quantum principle. That rationale is what is missing from the quantum story.
Indeed, that “basic idea”, that “rationale” that should make our description of the quantum world coherent, is conspicuously “missing from the quantum story”. Neils Bohr, perhaps the main designer of the conventional description of quantum phenomena, may have succeeded in convincing the world that the quantum theory was an objective description of how things work at quantum level, but it has always been manifestly clear (to those who’ve been willing enough to remain objective) that it is merely the description of a game whose rules it is totally ignorant of. Bluntly, the quantum theory is nothing more than a naively-pretentious description of a reality it doesn’t understand. That’s why the creators of the quantum story have pushed hard to convince the world that in order to understand what’s going on at quantum level one must abandon common sense. Subjective prismatic experiments, however, were showing me how things do truly happen in the quantum world. The chromatic structure of light I was seeing pointed unequivocally towards a description of the quantum phenomena not only fully accommodated by common sense, but to a rather prosaic description. Nevertheless, I must make clear that to my mind that description was not dull, or banal—it was simply ordinary and familiar. And, to my mind, it was therefore thoroughly beautiful.
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