For as long as I can remember I knew that my destiny is to forever roam within the fringes of the present world (despite my otherwise innate desire to find a place in the mainstream society). The reason was simple: I could never find conciliation within the boundaries of the majority's territories. My mind wouldn't let me. My reason didn't allow me to conform (or to at least compromise). My voice could not remain silent. My actions refused submission. Needless to say, all these things levied a price to be paid, a price that I have certainly been paying (some times willingly, others unwittingly) until this day. Nevertheless, on the other hand I have also been rewarded with a number of compensatory gifts in the process, and--in hindsight--those gifts have soothed all that pain into a gentle breeze of regular nostalgia.
Undoubtedly the most important gift I have been bestowed with is the freedom of thought I've enjoyed all these years. Indeed that freedom has been the main source for those moments in my life when I truly experienced the joie de vivre that makes life still worth living (in spite of its miserliness and scarcity in the lives of the most). Let me give you an example of a moment like that.
Years ago, when I was in my teens, I refused to believe the conventional wisdom of the time that the brain of a newborn was a virtual tabula rasa, and--by extension--that the individual character of a person was entirely a product shaped by environment and nurture. To my mind that idea was a colossal fallacy, demonstrably and totally false, and I could not believe that the scientists who were selling that abomination to the world (and who were supposed to be observers in a permanent look out for patterns) could be so wrong. "How could any decent rational observer fail to see the overwhelming number of patterns-data that quite clearly point towards a reality totally different to theirs? How could anyone who was born a human fail to tackle the issue by making use, first and foremost, to the best and safest guide one can resort to--personal experience? How could any rational mind fail to ponder on, if nothing else, its own inability to master those unwanted character traits that it surely must have had inherited in parallel with the human body it complements?" These and many other similar questions drove me away from the conventional view that was prevalent at the time in psychology, sociology, and other interrelated scientific disciplines. To my mind the issue was radically different and clear: All humans are born with at least a basic array of character traits, and in the process of life Nature is considerably more influential than Nurture. Years later, (many years later), I began to see a change of direction in the conventional views on this matter, and although it is still a somewhat tentative change (scientists can be even more conservative than religious or governmental systems) the conceptual paradigm is definitely undergoing a process of radical transformation. This conceptual change has already vindicated my old rebellion on this issue, and from time to time my mind rejoicingly reminds me that we knew all this a long, long time ago.
[It's been quite a while since my last page. (Three months? Maybe more?) All with good reasons, though, and although I'm absolutely certain that I want to talk to you about them, I'm not so sure if I should do it now or later. One good reason, nevertheless, is that in these past three months or so I have already written this page perhaps a dozen times. Something, however, (and until a few hours ago I did not know exactly what), stopped me from reaching that final decision of uploading them here, to be read. But even though I now know what has, until today, prevented me from deciding on the final content of this page, I couldn't tell you at this stage anything more than what I hope is to be able to share with you on this new page the latest gift of joie de vivre I've been given.]
Patterns. A dichotomous source of exaltation and depravation, of inspiration and abrogation, for me. On the one hand I've always loved being shown (and, even more so, discovering) patterns. On the other, the patterns I loved or discovered seemed to be either invisible or meaningless to the others. But, to be fair, that was also conversely a truth, and in time I have learned to live with it pretty comfortably. That reality has become over the years nowhere more evident than in my picture of the material world, and in particular in my view of energy propagation. I have already talked about that, for a while now, but I'm still a long way away from being satisfied with my output in that field to any degree I'd find acceptable. In truthfulness, though, I must tell you that I am not in any hurry, for as I told someone who queried my intentions in the past, I harbour no particular expectations or ambitions. For me this is a love affair, and I rejoice in it with the exuberance of a teenager and with the patience of a grandfather. I thought I'd tell you this, and by you I mean that handful of people who've been regular guests of this site (yet of whom I know nothing about). ( Nevertheless, let me assure you that I have thoroughly enjoyed the thought of your company. Thank you.)
On this page I touched briefly on the subject of wave propagation on water. I discussed, for example, (albeit, very briefly, as I said), the so-called gravity and capillary waves, and I also touched on the subject of the conventional wave dispersion, in which wavelength is solitarily perceived as the responsible factor. Following that I then outlined a sketchy depiction of my belief that in the observed dispersion of water waves wavelength is only an incidental factor, rather than the strictly solitary one of the conventional view, and I concluded the page with a picture I will now drop a copy of below on the left.
I'll ask you to compare now the picture on the left with the one on the right, and then to think if, and where, you might have seen patterns of water waves similar to those depicted above. Now, chances are that the picture on the right is much more familiar than the one on the left, for the simple fact that the distribution depicted in that picture is much more common than the one on the left. That is not to say that the distribution on the left is totally alien, for one may certainly see such a display--just browse through the relevant videos on YouTube, for instance. Nonetheless, I will next try to persuade you that there is more to this matter than what may seem immediately apparent.
If you have seen a distribution of water waves as that on the left I am willing to bet that you have only seen it happening either in an experimental tank or tray filled with water that is subjected to a highly regular and uniform disturbance, or--at the very best--in a somewhat less controlled environment, but nonetheless in one in which the body of water being disturbed is still a contributing factor (i.e. by being handicapped by either its volume, or its surface area, or its quantitative relation to the output of energy, or its particular boundaries of enclosure, or indeed by all of the above). "So?", you may counter. Stay with me for a little while still, I'd respond.
What about the distribution shown on the right? Can you think about where you have seen it? An answer to these questions is definitely more varied, for such a distribution is routinely part of the natural environment at large, and it must be therefore the result of a conceivably multitude of possible scenarios. Do you agree with that? I will venture and say yes in reply. This increase in possibilities is very likely to have both constructive and restrictive ramifications into the subject as a whole, you may feel justified to imagine, and that is most likely then to bear no further consequences. But the reality is in fact very different, and unambiguously definite, and in a moment you will see that yourself. Before that, however, I want to put a precursory emphasis on what I will follow this paragraph with, for it will become a great example of the frugality and the simplicity, yet at the same time of the perennial power and relevance of the investigative tools employed by the ancient Greeks of the Golden Era: (careful) Observation and (sound) Reasoning. Alas, in this era of modern investigation the old tools of the Golden Greeks have been fully replaced by those new ones, called (targeted) Experimentation and Mathematical (validation). (One may argue that the new tools are, fundamentally, imperious evolutions of the old ones. But I beg to differ. Truth, to my mind, is that both sets of tools come with inherent caveats, and that both have been used and abused. However, there is one absolute and unmitigated difference between the two eras, and there is where ultimately the truth lies: Only one era has been the benefiter of the other's work, wisdom, knowledge, and experience. Subject for another time, perhaps.)
From the myriad of the possible scenarios that would create a distribution of water waves similar to that depicted in the picture above on the right I will present you with two of the most eloquent examples I have seen many times in my quest as an observer of the physical reality. The first of the two is linked to a paragraph I once found in one of the more popular accounts of physics which was written for the general public by a rather prominent physicist some years ago, but whose name I have nevertheless forgotten in the meantime. (It is quite possible that you may have also come across the book I am talking about.) The paragraph in question sounded something like this, in my own words: "To see the Doppler effect in action simply wiggle a finger in water while slowly pulling your arm back towards you, and as you do that you will see how the distance between the successive waves created by your finger will systematically increase". (At this point I should mention, as a foregoing reassurance perhaps, that although the cited passage is specifically referring to the Doppler effect, you will see in a moment that it is just as valid an example for our own topic of discussion.) Although the cited statement is definitely true, when I heard it for the first time my mind immediately riposted: "Mate, to see how the distances between successive water waves increases it is sufficient to just wiggle your finger in the same place in water!"
A second example that will create a distribution of waves like that on the picture above on the right is one of my most favourite I've witnessed many times over the years. It involves a certain breed of wild duck, whose favourite pastime seems to be to create water waves by engaging itself into a daily ritual of regular dips underwater (without changing places, btw).
Now, to the best of my knowledge, in order to explain a distribution of water waves similar to the one we're currently discussing a physicist would invoke the conventional creed of dispersion due to the particular and different speed of each wave, as dictated by wavelength. In effect, the conventional dispersion-creed of water waves follows basically direct from the popular "pebble in the pond" scenario, which says that a pebble dropped in a pond creates a train of undulations-waves in the water, and further that the train of waves subsequently disperses due to the different velocities at which the created waves travel outwardly from their point of origin.
But, as I've repeatedly maintained on these pages, I have never believed the conventional credo on this subject. ( Before going any further, however, let me repeat once again: To the best of my knowledge that seemed to be, at least until yesterday, the mainstream defence on the subject.) In my view, the reason for the observed dispersion has always been radically different. Thus, a pebble dropped in a pond, I contend, creates a train of undulations-waves which is a fingerprint manifestation of the disturbance created. In effect, the particular nature of the created waves is a qualitative manifestation of the quantitative attributes of the disturbance relative to the nature of the medium and the respective distance from the point of impact. Furthermore, the qualitative aspect of the train of waves changes with distance simply because the quantitative attributes of the disturbance change with distance themselves. In effect, therefore, to my mind the main reason for the dispersion of water waves is due to a systematic increase in the wavelengths of the waves, which in turn is directly and proportionally correlated with the continuous increase of the distance between the original point of the disturbance, where the waves were created, and all other subsequent points along their travelling paths. To my mind this is (briefly, without a rigorous qualification) the only rational and coherent way to explain in a satisfactory manner the distribution (or, in conventional language, the dispersion) of the water waves depicted in the picture above on the right.
There are a number of deeply interconnected reasons behind my view on this subject, and in the dozen or so previous versions of this page I discussed most of them in some detail. However, yesterday's event (of which I said nothing yet, but which I'll talk about later) has changed to a significant degree the outcome of what's about to happen. Some of the subjects I discussed on those discarded versions I will cover again in a few short moments. Before that, though, I ought to clarify one most relevant issue at this point.
It became clearly apparent to me from the very early days of my observations that the conventional belief in the dispersion of water waves due to the wavelength-speed relationship cannot account for the distribution illustrated above on the right. Nevertheless, because I had been completely unaware of what I found out yesterday, the conventionalists' apparent insistence in the wavelength-speed process troubled me greatly. Despite of my confidence in the power of the line of reasoning that, coupled with the factuality of my observations, supported the validity of my view on the matter, I could never get rid of a most irksome thought: "Could there be something so simple and so evident that everyone else sees, but me?" As I said, I had a complete, doubly-reinforced confidence in my understanding. For one, I had conducted many observations of the water wave evolution (both with the naked eye and with the help of recording devices), and the results were always the same. For the other, I was reassured by a very simple but most powerful line of reasoning of the kind I believed in most. That line of reasoning, relative to the two examples I gave you earlier (the finger-wiggling and the duck ritual), sounded like this. If the conventional view is right, and since my observations show no variability at all in the wave distribution, it must necessarily follow that all water waves in the two given examples are created sequentially and systematically shorter in wavelength. And if that must be the case, then, what are the chances of my finger--or the duck--accomplishing that feat every time and in all cases ?
Before yesterday I was convinced that only me could see spectra in all forms of energy propagation. (It's widely believed that ignorance is bliss, but in my case ignorance proved to be torment.) For those who've been regular companions of this site things will become increasingly clearer as we'll trod ahead. For instance, those of you I am referring to will begin to realise that in an evident contrast to my supposed arrogance and over the top self-assurance I have been, on certain issues, evasive and lacunar because of uncertainty (or self-doubt). Why? For a most true and simple reason: Because the things I'm saying are so diametrically opposed not only to the conventional dogma, but also to anything else that is offered out there. To you then, who are my companions, it should be quite evident now that when I said that there is only a very fine line between a prophet and a buffoon I wasn't just alluding to the contemporary physicists of conventional leanings--I was also referring to myself, for I was well aware that I could become either.
Today, however, I'm more confident than ever that, for at least a while yet, I will not become a buffoon. Hence that joie de vivre I said earlier that I want to share with you. Before yesterday I'll show you what I'd intended to put on this page.
The conventional understanding of wave propagation has remained one of the handful of my most troublesome topics in physics. In fact, and quite naturally, their interfering levels in the amount of distress that they have subjected me to over the years have unceasingly increased with the passage of time. A perfect example of that is embedded in the following two little stories about my perception of a very simple and popular conventional way of depicting visually how water and sound waves travel in a medium from one place to another.
Take the photos below in the centre, which show the two expositions characteristic to the wave propagation on water. The picture on the centre-left is part of a photo taken by a British fighter pilot in 1943 of the effects of a bomb dropped by an Italian airplane in an attempt to hit a British submarine which was located at A. The bomb missed the submarine and landed instead at E, creating an explosion whose effects on the water were shortly thereafter photographed. From this outline of the events behind the origin of the photo above you can picture in your mind the magnitude of what this photo has captured, as well as the importance and the rarity of being able to obtain such evidence. (See here for the complete article, which you can download in PDF format.) The author of the article (Dr. Katherine Socha), says the following about it and about its counterpart on the centre-right:
This photograph is fascinating for scientific as well as historical reasons. Its most striking features are the patterns of circular wavefronts visible at the edges of the frame and around point E. The motion of such surface water waves has been the subject of scientific and mathematical study for hundreds of years. For comparison, examine the photograph of raindrops on a slow-moving portion of the Red Cedar River, on the campus of Michigan State University, shown in Figure 2. Observe the qualitative difference between these waves and those in Figure 1. The battle photograph shows larger wavelengths toward the outside of the rings, indicating that these waves have traveled further (hence, faster) than the inner waves of shorter wavelengths. The raindrops photograph clearly shows larger wavelengths toward the inside of the rings, indicating that these waves have traveled more slowly than the outer waves of shorter wavelengths.
It is fascinating that the same physical impetus (an object striking the water surface) can generate qualitatively opposite behavior. This particular wave motion is an example of dispersion, where wave speed depends on wavelength. The waves resulting from an impact on a surface are dispersive, spreading away from each other over time.
In spite of having read over the years many accounts of the conventional understanding concerned with the wave propagation on water I am still experiencing the same feeling of bewilderment when I think about it today as I felt back at the time when I first heard about it. The reason for that is simple. I have never been able to find a clear and definitive sense to it, which is an absolute requirement for acceptance and accommodation by my mind. Taking a close look at the array of the so-called capillary and gravitational water waves above, for example, to my mind the conventional assertion of the speed-related reason for their dispersion (which is used as explanation for their distribution) is not the essential factor responsible for what it is observed--it is merely incidental to it. As far as I'm concerned the distribution of the water waves seen in the picture is fundamentally equivalent to the spectra displayed (and observed, I need to tell you--if for no other reason then only as an unplanned but timely confirmation for my confessed belief in the dichotomous nature of the Universe) in the waves of light propagation. OK, it may be a fact that water waves of longer lengths travel faster than shorter ones, but this (to my mind, yeah?) is by no means the crucial factor in energy propagation on water. Of course, I am fully aware that the physicists of conventional leanings will vehemently scoff at my saying that, but in my view the reality is that their stubbornness and unwieldy dependency and reliance on the speed-related reason for the dispersion of waves (in any form of energy propagation, by the way) as being at the crux of the matter is clearly showing lameness and inadequacy when it 'flexes its muscles and influence' between the larger boundaries of its apparent relevance and usefulness. (Stay with me, it'll become much clearer a little later.)
To my mind it is impossible to understand the rationale that is supposed to support and validate the following statements of Dr. Katherine Socha, which I've extracted from the paragraphs above:The battle photograph shows larger wavelengths toward the outside of the rings, indicating that these waves have traveled further (hence, faster) than the inner waves of shorter wavelengths. The raindrops photograph clearly shows larger wavelengths toward the inside of the rings, indicating that these waves have traveled more slowly than the outer waves of shorter wavelengths. There are a number of reasons for why I have problems with the rationality that is inferred to exist, and on the basis of which it's supposed to consequentially find validity the assertions expressed in these statements. However, for my present purpose it suffices at this point to mention only one of them, which is concerned with the reasoning in the second statement of the excerpt I extracted from the cited paragraphs above. That sole reason, which I'll mention here, is (surprisingly and disconcertingly, to my mind) concerned with a readily available observational fact. Thus, it is demonstrably a fact that in the case of the wave distribution created by raindrops (or by any other water disturbances similar in scale), there are relatively considerable differences (spatial, as well as temporal) between the waves created and involved in the process. For instance, the short, capillary waves seen in the photograph above as the outer rings are created both later in time and further in space than the inner, longer, gravitational waves in the same picture. Anyone can verify this simply by visiting YouTube. In view of this fact alone, then, I find it impossible to see any rationality in the conventional assertions, as they are expounded by Dr. Socha above. You know what I mean? Think about it.
And there's another disconcerting thing in Dr. Socha's paper, as far as I'm concerned. I am referring to this sentence: It is fascinating that the same physical impetus (an object striking the water surface) can generate qualitatively opposite behavior. That's because in spite of the apparent "fascinating [fact] that the same physical impetus..." nor Dr. Socha, nor anyone else, seems to have delved deeper into its possible origins, or extensional potentialities.
Nevertheless, I myself had pondered on those issues, for to my Greek mind there most certainly must be a sound and beautiful reason behind any physical phenomenon. Moreover, to my mind it is incumbent that all forms of energy propagation share a common underlying principle--at the very least. For instance, let me show you how I think that water waves and sound waves should be connected and related to each other.
According to the mainstream dogma water and sound waves have very little in common, beside the fact that both are forms of energy propagation. As one and only difference between the two, for example, sound waves are strictly longitudinal in nature, while water waves combine both longitudinal and transversal qualities. In fact, according to the mainstream dogma there's not much commonality at all between any forms of energy propagation. This, to my mind, is a grave--very grave--error. More on this later, though. For now let me show you, as I said a moment ago, what I perceived to be the common ground between water waves and sound waves. It is commonly illustrated in the conventional quarters that the propagative nature of the sound waves is very much like that of a coiled spring. As a concrete example...
A coiled spring that is compressed at one end and then released experiences a wave of compression that travels its length, followed by a stretching; a point on any coil of the spring will move with the wave and return along the same path, passing through the neutral position and then reversing its motion again. Sound moving through air also compresses and rarefies the gas in the direction of travel of the sound wave as they vibrate back and forth.
Another picture of waves involves the movement of a slinky or similar set of coils. If a slinky is stretched out from end to end, a wave can be introduced into the slinky by either vibrating the first coil up and down vertically or back and forth horizontally.
And to make absolutely clear what the fundamental difference between sound and water waves is, pictures like the one below, coupled with the explanation following it and accompanied by its own graphical depiction, are common tools of communication between physicists and the rest of us.
One of the most powerful moments for student thinking was the use of a Rubens’ Tube apparatus to show the connection between waves of energy pulsing through a gas and transverse wave representations. A Rubens’ Tube is a metal tube sitting horizontally with tiny holes drilled in a line along the top. One end of the Rubens’ Tube is connected to a small tank of propane like those used when camping, and the other end of the Tube is connected to a speaker. When a sound is played through the speaker, the wave of energy compresses the propane gas inside of the tube and propane escapes out of the tiny holes on top. If the gas coming out of the holes is ignited, the flames will be taller where the gas is compressed and shorter where the gas particles are less dense. The resulting image helps students “see” both the compressions/rarefactions of a gas carrying a sound wave and the relationship between compressions and a transverse wave.
Now, to complement this basic presentation the conventional establishment can add at any time a vast amount of apparently supporting evidence, both theoretical (i.e. mathematical) and experimental. To argue thus against it seems to be pretty much sheer lunacy. But, in accordance to my kind of Greek understanding, there are a number of rather compelling reasons to nonetheless do it. In fact, as you know, I have already done it to some extent in the past, and I'll definitely continue to do it in the future. So far though my opposition to the conventional perspective on this matter has been limited to a brief exposition of my belief that sound waves change their pitch (effectively their frequency) with distance.
The propagating evolution of sound waves, according to my mind, bears all the hallmarks inherently associated with all other forms of energy propagation. For instance, the mechanics of the media that allows and governs the propagation of sound from one place to another is fully consistent with that of wave propagation on water. (I will explain in detail this point in detail a little later.) Not only that, I'll argue in due time, it is also consistent and basically similar in nature to that governing the propagation of the electromagnetic waves. That's why sound waves display an evolving spectrum in their travels, just like all other carriers of energy in the Universe (or at least in my own universe). See the three pictures above for a visual illustration of what I'm talking about, which I believe are self-explanatory and require therefore no additional comments from me. And after that I'll ask you to compare those pictures (which are mine) to the one above them, which I have borrowed from this page, for although it is a product and a carrier of the mainstream view, it is also a perfect visual depiction of everything I said in this last paragraph. Think about it, and I'll see you soon.
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