Sunday 11 September 2016
Wednesday 7 September 2016
Tuesday 6 September 2016
Tuesday 26 July 2016
Sunday 29 May 2016
Friday 15 April 2016
Monday 11 April 2016
Sunday 10 April 2016
Tuesday 5 April 2016
Logos: Driven by beauty, led by reason. Thinking Greek
There is no beauty in physicists' picture of reality. There's no coherence in their story. They're lost, and they're too proud to ask for directions. (Back where I come from it is said that a fool is not a complete fool unless he is proud too.) I decided to build my own universe because I didn't like the one I was given. I didn't like it from the first sight. I didn't like its look, and I didn't believe its stories. It was too complicated, too pretentious, too vague, it spoke too much, it said too little... and it was damn ugly too. There have been times, admittedly, when I have either been seduced or bullied into accepting that it had a certain charm, and even some believability. But those moments never lasted very long, for on the things that really mattered it always came across as ugly and as dubious as ever. If it is true that in the case of SR I could never like, or believe, the conventional understanding of what it was supposed to say about the truth, when it came to GR I entertained from time to time the thought of maybe finding common grounds with it—one good day, in the future. But in the end, I saw that that just could not ever happen. Not because the odds of being able to convince those in power that my vision is worthy of replacing theirs were so insignificant that no one would consider, but because I could never trade my model of the Truth for theirs. After all I'd seen quite early that the little they offered I already had, and that their most was irrelevant to the Truth.
A couple of quick and final thoughts about SR.
At the very best a relativist could argue that the picture painted by SR is that reality happens at the interface between one's past and one's future, and that that interface is basically formed by the inter-exchange of light signals between one and the cosmos. But even that argument is weak and undesirable. That's because the ultimate purpose of physics is not to describe reality from the limited perspective of an observer (who is irrevocably handicapped spatio-temporally). The quintessential scope of physics is to describe reality from God's perspective. You know what I mean? Of course, you do.
Objects extend in the direction of their motion, and that is true regardless of the type of motion involved. The most eloquent example of that phenomenon is presented by Newton's bucket experiment. Below on the left there is a graphic depiction of my explanation of that experiment (view from above). Then, in the middle there is an illustration of what would happen in Newton's bucket if the experiment were to be conducted in space, in absence of any gravitational field. Finally on the right there is a graphic depiction of why the effects of the so-called centrifugal force are felt on a rotating platform. These examples alone are sufficient to retire Mach's principle to the trivial pages of history. Good riddance.
The most beautiful manifestation of spatial extension in moving bodies is the gyroscope. The most familiar is the shape of the Earth. Stories for another time.
About waves (in sound, on water, in light--in space, essentially)
Let me tell you a story. As a schoolchild I used to listen with fascination at the industrial siren that marked with a long shrilling whistle the thrice-a-day change of shifts at the town's steel mill. There was nothing remarkable about that unremarkable sound, yet I remember paying full attention to it every time it played. Why? Because, to my mind (or to my ear), the whistle of the siren sounded differently from where I lived, to where I went to school, or to where my cousins lived. Although I was fascinated by my discovery, I was not in the least shocked by it. That sound changed in quality with distance--I could rather easily see its Greek beauty.
A few years later I learned about the so-called Doppler effect, and that marked the beginning of a long and lopsided confrontation with the conventional description of reality. I did not have any problems with the logic behind the Doppler effect, or with its existence as a physical phenomenon. What I had problems with was the conventional assertion that only motion creates Doppler-like effects. According to my experience, and to my understanding, sound was--firstly and foremostly--altered qualitatively by distance alone. Motion, as far as I was concerned was merely incidental to the issue.
For a long while I didn't talk to anyone about the subject. But then one day I began asking people simple questions from every day experience connected to the Doppler effect, and that has remained an exercise I still continue today, from time to time. There was a very good reason for my beginning of that exercise--no one in the world seemed to have noticed the effect I'd had!
Now, since you are reading this, how about doing the exercise in question with you? All you have to do is answer, in the privacy of your own mind, a few very simple questions. For example:
1) Imagine that you are 5m away from a stage on which your favourite band plays your favourite song. Imagine next that you are 500m away from the same stage, on which the same band plays the same song. Finally picture the same scenario with you listening from a distance of 1km away. And now the question: Would the song sound exactly the same to your ear-brain in all three cases? (Pitch wise, of course.)
2) Imagine that you are a couple of metres away from a lumberjack, listening with great attention at the sounds made by his big axe as he's cutting a tree. Move your imaginary point of observation next to a distance of a couple of hundred metres away from our lumberjack and listen with the same attention to those sounds. Finally, do exactly the same from a distance of 500m and then answer the now familiar question: Was that wood-cutting sound identical to your ear-brain in every case?
3) Last question. Consider the same scenarios as above by imagining that you are a spectator now at a tennis game, or at a golf tournament, or at a hollering competition, and then answer what should by now be the obvious question.
Now I do not know what your answers to the three questions have been, but I would be extraordinarily surprised if your answers were to be different than those I have invariably heard from people over the years. Anyway, here are those answers. To question number 1 the answer I have always been given was an emphatic "Yes, a song sounds exactly the same, regardless of the distance from which it is listened to". To the questions 2 and 3, however, the answers I've been given (invariably and emphatically, noteworthily) were completely opposite to the first one: "No, the sounds produced in the cases mentioned do not 'sound' the same at different distances--they definitely appear to change their pitch". Not only that, in answering the questions 2 and 3 all those I asked described with confidence how the pitch changed with distance, i.e. from a higher pitch when closer to the source, to a lower one when further away from it.
To my ear-brain there is no doubt that distance alone affects the quality of sound. I remember how on a May night of 1983 as we were coming down a long, lazy hill, leaving behind white crosses spread-out strangely sparingly onto its crest, I was listening captivated to the sounds of a village that lay 2-3 km in a gully ahead of us. There was a wedding taking place, with loud music and a hum of happy voices. The music was well known to me, and I remember listening intently to the ever so slight, but definite, difference between the sound of the music that was vibrating in my ear-brain then and the one I knew so well from the times I had myself been to weddings, christenings, and other celebrations.
Needless to say, to a physicist the answers above would only manage to ignite his ridicule, or his contempt (or, probably most likely, both), even though I have a strong gut-feeling that in his ear-brain the sound of a tennis racket striking a ball does also 'sound' differently with distance. (That is unless he is severely impaired ear-brainy, or if he's never seen a game of tennis. Or one of golf. Or one of hollering.)
I am a Greek, fundamentally. I am driven by beauty and I am led by reason. My only goal is the Truth, and my only desire is to be able to discern It. I'm well aware of the very few things I could say that I know, and I'm even more aware of those so many I know I do not know. I believe that the Truth is, in principle, discernable and comprehensible to any mind, if a number of simple caveats are respected. I believe that any prophet either was, is, or will become a buffoon, at some point. This is the non-negotiable price one must be prepared to pay for his beliefs.
I never liked the conventional wave-belief. I didn't like its sound waves, I didn't like its water waves, and I didn't like its light waves. I didn't like them, primarily, for one and the same reason. According to my reason and experience I believed that any kind of energy propagation was affected both quantitatively and qualitatively by distance. Certainly, from a Greek perspective of what constitutes beauty, such relationship is highly desirable. But, more importantly, my observations revealed quite convincingly that such seemed to be the case indeed. And that, before anything else, forced me to ponder painfully long and hard why physicists couldn't see it.
In a nondispersive wave medium, waves can propagate without deformation. Electromagnetic waves in unbounded free space are nondispersive as well as non-dissipative and thus can propagate over astronomical distances. Sound waves in air are also nearly nondispersive even in the ultrasonic frequency range. If not, that is, if high frequency notes (e.g., piccolo) and low frequency notes (e.g., base) propagate at different velocities, they would reach our ears at different times, and music played by an orchestra would not be harmonious. Most waves in material media are dispersive, however, and wave forms originally set up are bound to change in a manner that the wave energy is more spatially spread out or dispersed.
I found the paragraph above somewhere online, and I liked it so much that I collected it for future use. I want to tell you exactly what I liked about it. Firstly, I liked the third statement in the paragraph, especially for its use of the word "nearly". As soon as I saw that word my mind immediately took me a number of years back to a much similar answer given by a conventional physicist to someone who had asked why the blades of fans, the spokes of wheels, or the propellers of airplanes, appear at times to rotate in the opposite direction to the real one. Listen to the answer: "Usually that seemingly change of rotation is seen in movies..." (And so on and so forth--unimportant, within the context, really.) That "usually" is on a par with our "nearly". Why? Because they both have been used as strategic terms, designed to conceal (or at least obscure), the truth about some undisclosed realities. To my mind the word "usually" was therefore chosen for a two-fold reason. Firstly, in order to provide some sort of justification to the answer given, and secondly, to camouflage the conventional ignorance about the real factors behind the phenomenon in question. The obvious matter of fact (as far as I'm concerned, yeah) is that the benevolent physicist did neither mention that the observation is just as visible on the real landscape to the naked eye, nor did he make any attempt to either answer it, or, otherwise, truthfully confess not knowing it. As for the word "nearly", it is sufficient to read the third and the fourth statements in the paragraph together, to see the contradiction that lies (indecently, insolently) in-between the two.
The last statement in the paragraph is also quite interesting, for a number of reasons. Water waves, for example, are considered dispersive in the conventional physics, but even in that case the establishmentarian explanation is too rigid and too linear, for my liking, and--as a direct consequence, I contend--it has been for more than 100 years utterly mute, totally idle, and comprehensively sterile. Take that most popular lay-description of water wave dispersion created by the dropping of a rock in a pond. The impact of the rock with the water creates a number of concentric waves that travel outwardly from the point of impact, says that description. As those concentric waves travel further and further away from the point of impact the distance between them systematically increases (the waves become "more spatially spread out, or dispersed", as the last sentence ends the paragraph I cited above). The reason for that dispersive effect, we're told, is that water waves of different wavelengths travel at different speeds. Specifically, the impact of the rock with the water creates a train of undulations (waves) which are progressively longer in wavelength from centre outwards, and whose individual speeds are also progressively faster in the same manner. The longer waves travel faster on water than their shorter counterparts, say those with conventional beliefs, hence the dispersion in question.
Now, the conventional idea of wavelength-speed relationship may be neat--indeed may it even be true, as it is stated--but comprehensive in scope, and simple in implementation, it certainly ain't. And this (to my Greek mind, let me specify), is yet again a matter of concern, and (equitably, wisely) one of suspicion also. In an all too typical display this shows, once again (yeah, to my mind), the propensity of conventionality to cumber even the simplest into the most complicated (or to get tangled, or start tripping, on nothing more than a proverbial pair of shoelaces).
It turns out that the simple idea that water waves with longer lengths travel faster than their shorter counterparts is no longer able, on its own, to account for the propagation of energy in water. There is a need, it seems, in water propagation for two kinds of waves. One kind is formed by those so-called gravity waves; the other kind contains the so-called capillary waves. In the two pictures above both gravity and capillary waves are shown, but I'm not at all disposed to discuss them to any significant degree at this stage. I will only mention in passing that in gravity waves the longer wavelengths travel faster than shorter ones, while in the case of the capillary waves the situation is exactly the opposite! Furthermore, there is another radical difference between the gravity and the capillary waves: in one of them the group velocity is higher (and, conversely, the phase velocity is lower), while in the other the situation is exactly the opposite. And then there is one third contrasting difference between the two kinds of water waves, which is rather more subtle in nature, but which--to my mind--it could be quite safely said that they appear to disperse, again, in opposite directions. These three differences between the so-called gravity and capillary waves I will discuss in detail in due (and in good) time. (A note of special importance. Of all the three peculiar characteristics-differences between the gravity and the capillary waves the third is the most far-reaching in scope and consequence. All in good time, though, as I said.)
Physicists are convinced that they have 'sorted-out' the wave propagation in water. After all, they have been boasting for a while now that they can derive mathematically the exact wavelengths of the capillary waves from the data related to the so-called surface tension of the water-medium. But that achievement falls well short of my minimum personal threshold for impressiveness, and here is why.
According to the conventional wisdom, apart from the dispersive water waves discussed thus far, there is another type of water waves, still. That type is formed by gravity waves of identical wavelength, which are, say the conventional physicists, completely non-dispersive. I dispute that. On two grounds. First, because the idea runs in a direction totally against the reason-logic-beauty-truth I have seen underlying the physical reality. Second, because I have good evidence which proves that that idea is completely flawed.
Now let me say beforehand that physicists have never written textbooks after my liking, or in my language. That's why the "gravity waves of identical wavelength are non-dispersive" statement is as vague as it is authoritarian, as far as I'm concerned. Why are gravity waves of the same wavelength non-dispersive? What real physics--beside the conventional wavelength-velocity invocation--is allowing that type of water waves to preserve their physical attributes, and for how long can that state of affairs be maintained? How many such waves are--if they are--necessary to insure non-dispersiveness? This is just a sample of the questions I have never found clear and direct answers to from those following the reigning establishmentarianism. In spite of that, nevertheless, there always has been one main thing I knew with certainty--that the mainstream establishment of physicists was absolutely adamant that the gravity water waves of the same wavelength are decidedly non-dispersive, and in the end that was enough to help me in deriving a conclusive picture of why I'm not a follower of the reigning establishmentarianism.
If the conventional belief is that water waves of the same wavelength are non-dispersive a graphic illustration of that must necessarily look just like the picture I will draw below.
But to my Greek mind the above is not an image typical for a phenomenon of the living Universe--it is rather an image of a netherworld. It is most depressing to see that the physicists of our era, who are the inheritors and beneficiaries of all human knowledge and wisdom from the beginning to this point in time, and who therefore should be thinkers of hitherto unparalleled potential, are not able to see--for one reason, or for another--why no transmission or propagation of energy could take place in the manner of the above illustration.
There are two physical mechanisms that control and maintain wave motion. For most waves, gravity is the restoring force that causes any displacements of the surface to be accelerated back toward the mean surface level. The kinetic energy gained by the fluid returning to its rest position causes it to overshoot, resulting in the oscillating wave motion. In the case of very short wavelength disturbances of the surface, i.e., ripples, the restoring force is surface tension, wherein the surface acts like a stretched membrane. If the wavelength is less than a few millimetres, surface tension dominates the motion, which is described as a capillary wave. Surface gravity waves in which gravity is the dominant force have wavelengths greater than approximately 10 cm (4 in.).
The paragraph above is from the Encyclopaedia Britannica, and it describes the conventional understanding of the "two physical mechanisms that control and maintain wave motion". There are two things of interest here. The first one is concerned with the description of how a disturbance in the body of water is understood to create the two types of waves routinely observed. I find it most interesting that although the two types of waves (gravity and capillary) are considered, and treated, by physicists as different and independent entities, in fact there is one and the same mechanism responsible for both types. Now, in order to dispel any possibility for confusion about what I've just said read with attention the second, the third, and the fourth sentences in the paragraph, and then think: the process described in the second and the third sentences (concerning the creation of the so-called gravity waves) is very much the same as the one covered in the fourth sentence (describing the generation of the so-called capillary waves). Indeed, the only difference between the two seems to be one of magnitude. But in fact, even that cannot withstand close observational scrutiny.
Monday 4 April 2016
Friday 25 March 2016
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.
Tuesday 22 March 2016
Tuesday 15 March 2016
Monday 14 March 2016
Sunday 13 March 2016
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.
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