Testing in 1 week!
Saturday, May 14, 2011
Wednesday, April 27, 2011
Saturday, April 2, 2011
Progress
In my opinion a diligent researcher should entertain a healthy level of skepticism towards preconceptions that he/she brings to the research- I do, therefore entertain the idea that this might be only a transient minor wrinkle in my own understanding of science. Nonetheless, given my skill set and the cost-benefit analysis of the potential technological breakthrough it was my choice to meld art and science, theory and experimentation, hypothesis and application, logical roots and real world implications and run with this idea as a tech-startup. The end product being offered for sale is the resulting machine.
Right now it is to me, a project management challenge involving the engineering of the technology and the development of the theoretical map (implicit in this is the validation of the idea itself - is this idea worth anyone else's time/money?) behind the technology along with all the other things that I must do to organize a business behind this idea, from legal/marketing/finance/operations purposes. The rest (sales/H.R./I.T./infrastructure management) are moot ... for now.
New prototype assembly is in progress.
Right now it is to me, a project management challenge involving the engineering of the technology and the development of the theoretical map (implicit in this is the validation of the idea itself - is this idea worth anyone else's time/money?) behind the technology along with all the other things that I must do to organize a business behind this idea, from legal/marketing/finance/operations purposes. The rest (sales/H.R./I.T./infrastructure management) are moot ... for now.
New prototype assembly is in progress.
Saturday, March 19, 2011
A Tiny Bit Of Heaviside
I spoke too soon. The last two of the parts for the prototype were in fact mailed by P. (Vielen Danke, P.! Das ist ein wunderbares geschenk und Ich war total ueberrascht mit deine freundliche hilfe!) but they hadn't arrived at my place. In the meantime, I've prepared by disassembling the old prototype to refit the new parts. They're finally here. Assembly clock starts now.
I'm currently reading a biography by Paul Nahin titled Heaviside: A Sage in Solitude. I recommend this book to all amateur physicists as a great introduction to the drama of 19th century science becoming the modern physics that we know now. Heaviside knew, corresponded, argued and propounded theories with a good number of those whose names now fill the textbooks of electromagnetism - Wheatstone, Maxwell, Poynting, Helmholtz, Faraday, Kirchhof, Boltzmann, J.J.Thomson, Searle, Tesla, Wiener etc etc.
Heaviside himself in his last days attempted to draw an analogy between gravity and electromagnetism (source: Nahin, Paul; Oliver Heaviside: A sage in solitude, pg 307, 1987 IEEE Press) "with the key link being the localization of energy in a field." Einstein had better luck than Heaviside in finding a formulation for gravity within 12 years of Heavisides own attempts, nonetheless, it is instructive to see what Heaviside made of the link between electromagnetism and gravitation.
Begin Quote "If one brings two charges together, energy is required to overcome the repulsion, and it is this energy that goes "into the field" (giving a positive field energy density in space). Two masses, on the other hand, attract each other and it takes energy to keep them apart, leading to the (strange) result of a negative field energy density for space in the case of gravitational models. This result, implying the presence of less than no energy in space, so bothered maxwell he gave gravity up as beyond 19th century physics. Heaviside too reached the same conclusion:"...it must be confessed that [negative energy density] is a very unintelligible and mysterious matter."
Heaviside based his analogy on an ether ("It is as incredible now as it was in Newton's time that gravitative influence can be extended without a medium..."), and reached the conclusion that gravity effects most likely propagate "immensely fast," probably much faster than the speed of light. This is all anti-relativistic, but of course Heaviside was writing this 12 years before Einstein published his Special Theory of Relativity. "
End Quote
One might wonder what less than no energy in a spatial region might be -perhaps, to have less than no energy in space might for example be energy that moves and carries mass away from the region of space, altering the local gravitational potential of the space itself.
Perhaps gravity's negative energy field is an acknowledgement that the energy is trapped in an 'inductive' field configuration and is therefore a reacting-entity that operates upon processes causing energy exchange in the local region of the inductive field.
We know that we can classify capacitances as positive impedances and inductors as negative impedances already. To associate positive and negative field energy correspondingly to the two kind of elements is only natural then. And we would see that a gravitational field is an energy field holding a spinning, inductively suspended earth as the central motor of the sun gyroscopically attempts to spin the earth out of the solar plane (in which our planet executes its orbits around the sun) and reaps the gyroscopic result that the input and output channels are orthogonalized - the spins the earth out the soalr plane and the earth responds by executing an orbit in the solar plane. Maybe we have difficulty comprehending gravity with our electricalized physics models because we have not used the concept of inductively suspended angular momentum as the equivalent of the electrical coil. Just a thought.
Another counterintuitive fact about electricity that Heaviside reasoned out regarding electromagnetism concerns a topic researched by Poynting first and slightly later, completely independently by Heaviside - the direction of flow of energy in a wire carrying an electric current. Like in the case of a gyroscope (my earlier prototype, whose results you have seen, most prominently in the Inductive Effect video) or in the case of an inductively suspended spinning wheel(as in my new prototype I will be testing soon), the direction of the energy's expressed movement and the direction of the wire (if it is assumed to be straight for the purpose of the analysis)are orthogonal to each other.
Heaviside and Poynting's research on this topic created a revolution in the field of eletromagnetism by changing the way physicists would model electromagnetism forever. Here is a passage regarding this important singular research with a suggestion of gyroscopic overtones of great importance to us as seekers of flying machines, from the book "Oliver Heaviside: A Sage in Solitude" by Paul J Nahin.
Pages 115-119
Begin Quote
Energy And Its Flux
By 1884 the principle of the conservation of energy was well established, but it hadn't been many years before when the idea of just energy, alone, was a new and strange one. The concept of force was the prominent one as late as the 1850s, for example, and it seemed to be intuitively the 'thing' that should be the hinge pin of dynamics, whether the system under consideration be mechanical or electromagnetic. The development of thermodynamics in the early and mid parts of the 19th century, however, began the process of elevating energy and changes in energy to the level of importance we attach to them today. Writing in 1887 Heaviside expressed this as, "There are only two things going, Matter and Energy. Nothing else is a thing at all; all the rest are Moonshine, considered as Things."
The ability to store what seemed to be astonishing amounts of energy in the newly perfected (1881) lead acid battery (by Camille Faure) led to a special flurry of interest in the matter, among even the general public. There was something about storing and transporting electrical energy (although a battery is really a box of chemicals) that was special, and particularly appealing to the Victorian mind. Coal was just a dirty rock out of the ground, while electricity was modern!
So, with all this interest in electrical energy, it is not surprising that people were also paying attention to its more abstract properties such as its conservation and even how it moves about. There is more to the conservation of energy, however than may be apparant at first glance. As Heaviside put it in 1891,
The principle of the continuity of energy is a special form of that of its conservation. In the ordinary understanding of the conservation principle it is the integral [total] amount of energy that is conserved, and nothing is said about its distribution or its motion. This involves continuity of existence in time, but not necessarily in space also. But if we can localize energy definitely in space [my emphasis- this is a most important idea, one we'll pursue with interest], then we are bound to ask how energy gets from place to place. If it possessed continuity in time only, it might go out of existence at one place and come into existence simultaneously at another. This is sufficient for its conservation. This view, however, does not recommend itself. The alternative is to assert continuity of existence in space also, and to enunciate the principle thus: When energy goes from place to place, it traverses the intermediate space.
And then a little later in the same passage, writing of the mathematical result that precisely specifies just how electromagnetic energy "traverses the intermediate space", he said,
This remarkable formula was first discovered and interpreted by Prof. Poynting, and independently by myself a little later. It was this discovery that brought the principle of continuity of energy into prominence.
Heaviside was referring, of course, to John Henry Poynting (1852-1914). Professor of physics at the University of Birmingham, Poynting combined his considerable ability in physics with that f a skilled mathematician and this double edge to his powers led to the writing of many papers which Oliver Lodge called "sledge-hammer communications". This certainly was the right way to describe the impact of Poynting's powerful paper "On the transfer of energy in the electromagnetic field," published by the Royal Society in its Philosophical Transactions in 1884. Starting with the Maxwellian idea of localized field energy Poynting was able to derive the elegantly simple vector expression E x H, now called the Poynting vector, for the flow of electromagnetic energy through space.
Poynting's paper, as well as some of the odd implications of the result, attracted a good deal of attention. Oliver Lodge, in particular, was tremendously impressed by it and wrote a curious paper (with a very long title!) in response. Lodge was particularly fascinated by the idea of being able to track a individual "bit of energy", writing ".. the route of the [bit of] energy maybe discussed with the same certainty that its existence [is] continuous as would be felt in discussing the route of some lost luggage which turned up at a distant station in however battered and transformed a condition." This semi-metaphysical paper seems not to have had much impact, but its opening words, describing Poynting's paper were prophetic, calling it "a paper which cannot but exert a distinct influence on all future writings treating of electric currents."
One of its most profound influences was the complete overthrowing of how people think of energy flowing in a wire carrying an electric current. In fact according to ExH the electromagnetic energy doesn't flow through the wire but into it, sideways from the fields surrounding the wire! This seemingly "crazy" conclusion was not greeted with Lodge's excitement by many of the "old-time" electricians. In 1891, for example, Silvanus Thompson and John Sprague became embroiled in a dispute over the nature of energy flow in electric circuits. Sprague held tot he old view of energy transfer through a wire, while Thompson argued for the revolutionary new viewpoint. The debate appeared over an extended period of time in the Correspondence sectin of The Electrician, and finally the journal felt it necessary to terminate the issue with an editorial: ..although we undoubtedly side with Prof. Thomson's views, there is no doubt much which appears, at first sight, highly artificial in the elaborate structure of lines of electric and magnetic force and induction, complicated still further, as it is, by the more recently discovered lines of energy-flow .. the idea that energy is located at all, and that, when it changes it position, it must move along a definite path, is quite a new one. The law of the conservation of energy implies that energy cannot disappear from one place without appearing in equal quantity somewhere else; but although this fact has long been accepted, it is only within the last few years that the idea of transference of energy has been developed, or that anyone has attempted to trace out an actual path along which energy flows when it moves from place to place. The idea of an energy current is of more recent date than the electro-magnetic theory, and is not to be found explicitly stated anywhere in Maxwell's work. I believe that the first time it was applied to electrical theory was in the pages of The Electrician, by Mr. Oliver Heaviside, to whom so much of the extension of Maxwell's theory is due. The idea as also independently developed and brought to the notice of the Royal Society in a Paper by Prof. Poynting.
In fact, The Electrician was perfectly correct in this proud claim for the priority of Heaviside. Poynting's paper certainly did not appear in print until sometime after June 19, 1884 and yet, in the June 21, 1884 issue of The Electrician Heaviside wrote (in a passage entitled "Transmission of Energy into a Conducting Core"):
The direction of maximum transference [of energy] is therefore perpendicular to the plane containing the magnetic force and the current directions, and its amount per second proportional to the product of their strengths and to the sine of the angle between their directions.
These words are not remembered today, and it wasn't until Jan 10, 1885 that Heaviside published the same result as is found in Poynting's paper (which is why historians today always write of Heaviside's discovery as dating from "the year after" Poynting's). Heaviside took a somewhat different view of history, however, and while he never disputed Poynting's credit, he also took care to remind his readers of the June 21 date, as when he wrote (in March 1885):
The transfer of energy in a conductor (isotropic) takes place not with the wire, but perpendicular thereto, as I showed in The Electrician for June 21, 1884, thus being delivered into a wire from the dielectric outside.
It is not clear when Heaviside first learned of Poynting's paper, but there is an interesting note on one of his copies of Nature (dated March 26, 1885) which was prompted by a report on a mechanical model (made of wheels and rubber bands) invented by FitzGerald, "illustrating some properties of ether." In particular, this model showed how "the energy of the medium was conveyed into" was a wire and "not along its length according with that Prof. Poynting has recently shown to be the case in all electric curents." Heaviside's note shows he was by them most familiar with Poynting's work, and thought his own more comprehensive:
But it is only true for conduction current, not for all currents. Not true in the dielectric [where the displacement current cannot be ignored]. The general formula for energy current ...[was] proved by me for conductors in the summer of 1884, and in January 1885 extended to all media non-homogenous as regards capacity, conductivity and permeability.
While Poynting may have beatenHeaviside into recognized print, and while Poynting's mathematics was impeccable, it is curious to note that his physics has a flaw which seems to have fone unnoticed, or at least uncommented upon, for the last one hundred years, except for Heaviside's own comments about it. Even with impeccable mathematics, however, many found Poynting's (and Heaviside's) ideas on energy transfer hard to believe, and not all of the skeptics were "old timers" like John Sprague. As Professor J.J. Thomson wrote two years after Poynting's paper,
This interpretation [the Poynting vector] of the expression for the variation in the energy seems open to question. In the first place it would seem impossible a priori to determine the way in which energy flows from one part of the field to another by merely differentiating a general expression for the energy in any region with respect to time, without having any knowledge of the mechanism which produces the phenomena which occur in the electromagnetic field...
These words show Professor Thomson, the bright young academic star of English physics at the time, was still committed to the Maxwellian goal of mechanical model building. But eventually even Thomson came around and in 1893 he called Poynting's result "a very important theorem" and "of great value." There was no mention of Heaviside's contributions to the energy flux theorem by Thomson, and I find this particularly ironic because this slighting by Thomson was to be his fate too, with another equally important result. And to make it doubly ironic, Heaviside was also involved in this (Heaviside's role is again forgotten,, along with Thomson's).
End Quote
Asa parting thought, let me remind you that as J. J. Thomson pointed out in 1893, the Poynting Vector product equation does indeed require a priori knowledge of the mechanism which produces the phenomena rather than being a general energy expression and such is also the fate of gyroscopic and inductively suspended angular momenta
This tells us that the true understanding of the phenomena rests on a higher level model that incorporates this a priori knowledge.
I'm currently reading a biography by Paul Nahin titled Heaviside: A Sage in Solitude. I recommend this book to all amateur physicists as a great introduction to the drama of 19th century science becoming the modern physics that we know now. Heaviside knew, corresponded, argued and propounded theories with a good number of those whose names now fill the textbooks of electromagnetism - Wheatstone, Maxwell, Poynting, Helmholtz, Faraday, Kirchhof, Boltzmann, J.J.Thomson, Searle, Tesla, Wiener etc etc.
Heaviside himself in his last days attempted to draw an analogy between gravity and electromagnetism (source: Nahin, Paul; Oliver Heaviside: A sage in solitude, pg 307, 1987 IEEE Press) "with the key link being the localization of energy in a field." Einstein had better luck than Heaviside in finding a formulation for gravity within 12 years of Heavisides own attempts, nonetheless, it is instructive to see what Heaviside made of the link between electromagnetism and gravitation.
Begin Quote "If one brings two charges together, energy is required to overcome the repulsion, and it is this energy that goes "into the field" (giving a positive field energy density in space). Two masses, on the other hand, attract each other and it takes energy to keep them apart, leading to the (strange) result of a negative field energy density for space in the case of gravitational models. This result, implying the presence of less than no energy in space, so bothered maxwell he gave gravity up as beyond 19th century physics. Heaviside too reached the same conclusion:"...it must be confessed that [negative energy density] is a very unintelligible and mysterious matter."
Heaviside based his analogy on an ether ("It is as incredible now as it was in Newton's time that gravitative influence can be extended without a medium..."), and reached the conclusion that gravity effects most likely propagate "immensely fast," probably much faster than the speed of light. This is all anti-relativistic, but of course Heaviside was writing this 12 years before Einstein published his Special Theory of Relativity. "
End Quote
One might wonder what less than no energy in a spatial region might be -perhaps, to have less than no energy in space might for example be energy that moves and carries mass away from the region of space, altering the local gravitational potential of the space itself.
Perhaps gravity's negative energy field is an acknowledgement that the energy is trapped in an 'inductive' field configuration and is therefore a reacting-entity that operates upon processes causing energy exchange in the local region of the inductive field.
We know that we can classify capacitances as positive impedances and inductors as negative impedances already. To associate positive and negative field energy correspondingly to the two kind of elements is only natural then. And we would see that a gravitational field is an energy field holding a spinning, inductively suspended earth as the central motor of the sun gyroscopically attempts to spin the earth out of the solar plane (in which our planet executes its orbits around the sun) and reaps the gyroscopic result that the input and output channels are orthogonalized - the spins the earth out the soalr plane and the earth responds by executing an orbit in the solar plane. Maybe we have difficulty comprehending gravity with our electricalized physics models because we have not used the concept of inductively suspended angular momentum as the equivalent of the electrical coil. Just a thought.
Another counterintuitive fact about electricity that Heaviside reasoned out regarding electromagnetism concerns a topic researched by Poynting first and slightly later, completely independently by Heaviside - the direction of flow of energy in a wire carrying an electric current. Like in the case of a gyroscope (my earlier prototype, whose results you have seen, most prominently in the Inductive Effect video) or in the case of an inductively suspended spinning wheel(as in my new prototype I will be testing soon), the direction of the energy's expressed movement and the direction of the wire (if it is assumed to be straight for the purpose of the analysis)are orthogonal to each other.
Heaviside and Poynting's research on this topic created a revolution in the field of eletromagnetism by changing the way physicists would model electromagnetism forever. Here is a passage regarding this important singular research with a suggestion of gyroscopic overtones of great importance to us as seekers of flying machines, from the book "Oliver Heaviside: A Sage in Solitude" by Paul J Nahin.
Pages 115-119
Begin Quote
Energy And Its Flux
By 1884 the principle of the conservation of energy was well established, but it hadn't been many years before when the idea of just energy, alone, was a new and strange one. The concept of force was the prominent one as late as the 1850s, for example, and it seemed to be intuitively the 'thing' that should be the hinge pin of dynamics, whether the system under consideration be mechanical or electromagnetic. The development of thermodynamics in the early and mid parts of the 19th century, however, began the process of elevating energy and changes in energy to the level of importance we attach to them today. Writing in 1887 Heaviside expressed this as, "There are only two things going, Matter and Energy. Nothing else is a thing at all; all the rest are Moonshine, considered as Things."
The ability to store what seemed to be astonishing amounts of energy in the newly perfected (1881) lead acid battery (by Camille Faure) led to a special flurry of interest in the matter, among even the general public. There was something about storing and transporting electrical energy (although a battery is really a box of chemicals) that was special, and particularly appealing to the Victorian mind. Coal was just a dirty rock out of the ground, while electricity was modern!
So, with all this interest in electrical energy, it is not surprising that people were also paying attention to its more abstract properties such as its conservation and even how it moves about. There is more to the conservation of energy, however than may be apparant at first glance. As Heaviside put it in 1891,
The principle of the continuity of energy is a special form of that of its conservation. In the ordinary understanding of the conservation principle it is the integral [total] amount of energy that is conserved, and nothing is said about its distribution or its motion. This involves continuity of existence in time, but not necessarily in space also. But if we can localize energy definitely in space [my emphasis- this is a most important idea, one we'll pursue with interest], then we are bound to ask how energy gets from place to place. If it possessed continuity in time only, it might go out of existence at one place and come into existence simultaneously at another. This is sufficient for its conservation. This view, however, does not recommend itself. The alternative is to assert continuity of existence in space also, and to enunciate the principle thus: When energy goes from place to place, it traverses the intermediate space.
And then a little later in the same passage, writing of the mathematical result that precisely specifies just how electromagnetic energy "traverses the intermediate space", he said,
This remarkable formula was first discovered and interpreted by Prof. Poynting, and independently by myself a little later. It was this discovery that brought the principle of continuity of energy into prominence.
Heaviside was referring, of course, to John Henry Poynting (1852-1914). Professor of physics at the University of Birmingham, Poynting combined his considerable ability in physics with that f a skilled mathematician and this double edge to his powers led to the writing of many papers which Oliver Lodge called "sledge-hammer communications". This certainly was the right way to describe the impact of Poynting's powerful paper "On the transfer of energy in the electromagnetic field," published by the Royal Society in its Philosophical Transactions in 1884. Starting with the Maxwellian idea of localized field energy Poynting was able to derive the elegantly simple vector expression E x H, now called the Poynting vector, for the flow of electromagnetic energy through space.
Poynting's paper, as well as some of the odd implications of the result, attracted a good deal of attention. Oliver Lodge, in particular, was tremendously impressed by it and wrote a curious paper (with a very long title!) in response. Lodge was particularly fascinated by the idea of being able to track a individual "bit of energy", writing ".. the route of the [bit of] energy maybe discussed with the same certainty that its existence [is] continuous as would be felt in discussing the route of some lost luggage which turned up at a distant station in however battered and transformed a condition." This semi-metaphysical paper seems not to have had much impact, but its opening words, describing Poynting's paper were prophetic, calling it "a paper which cannot but exert a distinct influence on all future writings treating of electric currents."
One of its most profound influences was the complete overthrowing of how people think of energy flowing in a wire carrying an electric current. In fact according to ExH the electromagnetic energy doesn't flow through the wire but into it, sideways from the fields surrounding the wire! This seemingly "crazy" conclusion was not greeted with Lodge's excitement by many of the "old-time" electricians. In 1891, for example, Silvanus Thompson and John Sprague became embroiled in a dispute over the nature of energy flow in electric circuits. Sprague held tot he old view of energy transfer through a wire, while Thompson argued for the revolutionary new viewpoint. The debate appeared over an extended period of time in the Correspondence sectin of The Electrician, and finally the journal felt it necessary to terminate the issue with an editorial: ..although we undoubtedly side with Prof. Thomson's views, there is no doubt much which appears, at first sight, highly artificial in the elaborate structure of lines of electric and magnetic force and induction, complicated still further, as it is, by the more recently discovered lines of energy-flow .. the idea that energy is located at all, and that, when it changes it position, it must move along a definite path, is quite a new one. The law of the conservation of energy implies that energy cannot disappear from one place without appearing in equal quantity somewhere else; but although this fact has long been accepted, it is only within the last few years that the idea of transference of energy has been developed, or that anyone has attempted to trace out an actual path along which energy flows when it moves from place to place. The idea of an energy current is of more recent date than the electro-magnetic theory, and is not to be found explicitly stated anywhere in Maxwell's work. I believe that the first time it was applied to electrical theory was in the pages of The Electrician, by Mr. Oliver Heaviside, to whom so much of the extension of Maxwell's theory is due. The idea as also independently developed and brought to the notice of the Royal Society in a Paper by Prof. Poynting.
In fact, The Electrician was perfectly correct in this proud claim for the priority of Heaviside. Poynting's paper certainly did not appear in print until sometime after June 19, 1884 and yet, in the June 21, 1884 issue of The Electrician Heaviside wrote (in a passage entitled "Transmission of Energy into a Conducting Core"):
The direction of maximum transference [of energy] is therefore perpendicular to the plane containing the magnetic force and the current directions, and its amount per second proportional to the product of their strengths and to the sine of the angle between their directions.
These words are not remembered today, and it wasn't until Jan 10, 1885 that Heaviside published the same result as is found in Poynting's paper (which is why historians today always write of Heaviside's discovery as dating from "the year after" Poynting's). Heaviside took a somewhat different view of history, however, and while he never disputed Poynting's credit, he also took care to remind his readers of the June 21 date, as when he wrote (in March 1885):
The transfer of energy in a conductor (isotropic) takes place not with the wire, but perpendicular thereto, as I showed in The Electrician for June 21, 1884, thus being delivered into a wire from the dielectric outside.
It is not clear when Heaviside first learned of Poynting's paper, but there is an interesting note on one of his copies of Nature (dated March 26, 1885) which was prompted by a report on a mechanical model (made of wheels and rubber bands) invented by FitzGerald, "illustrating some properties of ether." In particular, this model showed how "the energy of the medium was conveyed into" was a wire and "not along its length according with that Prof. Poynting has recently shown to be the case in all electric curents." Heaviside's note shows he was by them most familiar with Poynting's work, and thought his own more comprehensive:
But it is only true for conduction current, not for all currents. Not true in the dielectric [where the displacement current cannot be ignored]. The general formula for energy current ...[was] proved by me for conductors in the summer of 1884, and in January 1885 extended to all media non-homogenous as regards capacity, conductivity and permeability.
While Poynting may have beatenHeaviside into recognized print, and while Poynting's mathematics was impeccable, it is curious to note that his physics has a flaw which seems to have fone unnoticed, or at least uncommented upon, for the last one hundred years, except for Heaviside's own comments about it. Even with impeccable mathematics, however, many found Poynting's (and Heaviside's) ideas on energy transfer hard to believe, and not all of the skeptics were "old timers" like John Sprague. As Professor J.J. Thomson wrote two years after Poynting's paper,
This interpretation [the Poynting vector] of the expression for the variation in the energy seems open to question. In the first place it would seem impossible a priori to determine the way in which energy flows from one part of the field to another by merely differentiating a general expression for the energy in any region with respect to time, without having any knowledge of the mechanism which produces the phenomena which occur in the electromagnetic field...
These words show Professor Thomson, the bright young academic star of English physics at the time, was still committed to the Maxwellian goal of mechanical model building. But eventually even Thomson came around and in 1893 he called Poynting's result "a very important theorem" and "of great value." There was no mention of Heaviside's contributions to the energy flux theorem by Thomson, and I find this particularly ironic because this slighting by Thomson was to be his fate too, with another equally important result. And to make it doubly ironic, Heaviside was also involved in this (Heaviside's role is again forgotten,, along with Thomson's).
End Quote
Asa parting thought, let me remind you that as J. J. Thomson pointed out in 1893, the Poynting Vector product equation does indeed require a priori knowledge of the mechanism which produces the phenomena rather than being a general energy expression and such is also the fate of gyroscopic and inductively suspended angular momenta
This tells us that the true understanding of the phenomena rests on a higher level model that incorporates this a priori knowledge.
Saturday, February 19, 2011
Would Kron Recognize The Idea Behind The Relativistic Machine?
When one realizes the enormity of his work, one might wonder why Gabriel Kron's name isn't more commonplace than it is. An Electrical Engineer by education and apprenticeship, he formulated an equation that applies to all types of machinery ever designed and ever will be designed in the future. He then used this tensor equation to analyze and systematically design induction motors. He is also responsible for a method called 'Diakoptics' which he used to design the automatic electrical load flow distribution system of the state of New York, the first such system anywhere in the world. However, one might wonder endlessly about a great many things that have come to pass, like for example, the strange fact that Kennelly's & Steinmetz's introduction of the concept of impedance didn't give rise to a wider scientific discussion of the nature of induction in electrical coils and a search for its mechanical analogue beyond the simple spring-and-block arrangements of the early mechanical physicists.
Throughout the later half of the 19th and the early half of the 20th century, so many important scientific discoveries were happening in so many different fields that one may be forgiven for pleading ignorance in certain esoteric areas. If the field is too vast however, one must seize aspects of the science that help us to focus on understanding the general plan of the field before plunging into the details as this leads to the common syndrome of being unable to see the forest for the trees. In this endeavor, Kron's Tensor Equation will be your everlasting friend, willing to venture with you in your searches into the most exotic designs for machines of your choice, no matter what your field or your time - always helping you design better machines by teaching you how to classify the components that form the machine. By neatly classifying the underlying components of the machine in question into purely inductive, resistive and capacitive components and using his trademark analytical method, Kron is able to set up equations and analyze everything from say, a steam turbine governing system (divided into the governor, the linkage, the pilot valve, and the turbine) to the electric speed drive/control (divided into the synchronous motor, the induction motor, and the stationary network).
Although his field of work was circumscribed by his assignments at GE (General Electric, where he worked), Kron sensed that he was playing with something much bigger than 'just' Electro-Magnetism. In reading Kron's work, I am convinced that he would approve of the relativistic machine's theory and design and see that it meshes with his own thinking. The following is an attempt to cite evidence for this supposition.
Inductive Angular Momentum And Kron's Tensor Equation
Gabriel Kron is the author of a method of analysis of rotating electrical machinery, in which one and the same tensor equation applies to ever conceivable type of machinery. - P. le corbellier in the preface to his book on the analysis of rotating electrical machinery.
IEEE Transactions On Circuit Theory, September 1968 noting the passing away of Gabriel Kron summarize that "Dr. Kron was the author of the classic paper entitled, “Non-Riemannian Dynamics of Rotating Electrical Machinery,” that became the basis of his theories covering all types of rotating machines and power systems. The pioneering work of Gabriel Kron demonstrated convincingly the superior organizational powers of the matrix-tensor notation in network theory."
All types of electrical machinery can be analyzed using the one tensor equation that Kron discovered in his intense theoretical and experimental forays. When one first come's across this promise in his work, one might wonder what kind of an equation can accomplish this mammoth task. There is however, more than just an equation involved in the analysis of a given machine. The equation is only relevant if you first break the machine down into components according to the rules that Kron gives, and in addition you set up the tensors for the various components. Kron found that he could reduce any conceivable machine (even a completely mechanical one)into a network of components which could be solved for the behavior of the specific machine using a single tensor equation. Kron himself went on to make clear that to him, "It is surprising how few ultimate types of elements there are that form the building blocks of the great variety of engineering structures. Most stationary networks consist of a collection of one-dimensional "coils" only; all rotating machines consist only of a collection of two dimensional "windings." The great variety of structures differ only by the manner of interconnections of these ultimate coils and windings, and the variety of theories differ only by the type of hypothetical reference frame assumed. It is only the study of the ultimate building blocks that requires analytical work. The interconnection of these units into a given system is a routine procedure."
The main tensor equation itself is analogous to the statement for Kirchhoff's Voltage Law in a circuit with tensors replacing vectors. As Banesh Hoffman notes in his paper (Kron's Non-Riemannian Dynamics, Hoffman, Banesh, Reviews of Modern Physics, July 1949) "The work of Gabriel Kron constitutes a significant enlargement of the domain of application of tensor analysis." Hoffman also wrote in the introduction to the book Tensors for circuits (authored by Kron) that he (Kron) uses tensors to unify great classes of physical systems. "With him, a tensor transformation changes, the equations of one electrical machine to those of another eletrical machine of a different type. He constructs (the equations of) a prototype machine -the primitive machines - from whose equations he obtains those of all other electrical machines by applying appropriate tensor transformations."
It turns out that Kirchhof's 2 circuit laws - the voltage law and the current law - can help us accomplish an unbelievable amount of modeling of the physical world. Nor is their usefulness restricted to electrical circuits. Kirchhoff's circuit laws laid the foundations also for the field of Topology. (Topology is highly relevant to General Relativity).
The Voltage Law turns out to also be at the heart of analyzing rotating electrical machinery (infact, all machinery ever made or to be made) and it requires a tensorial statement and methods of analysis. This is not a coincidence. Kron himself comments that in his research,he had found that it is interesting that Kirchhof laid the foundations of topology even while working simply with circuits. "It is not a coincidence but a consequence of some hitherto hidden relation between the properties of space and those of electricity that the science of electrical engineering and that of topology meet again on a common ground when both are viewed from an invariant point of view."
It was Kirchhof's laws that laid the foundations for Topology. Topology had hitherto used tensors and now Kron was using a tensorial version of Kirchhof's law to analyze rotating electrical machinery. Tensors used in topology were now also in the very heart of the analysis of rotating electrical networks;
It is worth our while to ponder what we are to make of the fact that nature has designed the phenomenon of electricity such that one equation can serve to model all manner of electrical machinery? Is it something innate to the phenomenon of electricity? Or is the breathtakingly sophisticated mathematical edifice describing all electromagnetic phenomena with the aid of just a few parameters such as impedance (inductive and capacitive), voltage and current and rate of change of current something that derives its seeming perfection from other, even more fundamental?
Kron himself is clear on this subject. He commented that "Although the method of reasoning will be employed [by him in his book Tensors for Circuits] only for stationary and rotating electrical networks, exactly the same reasoning applies also to mechanical and other physical systems. That is, all reasonings and all symbolic formulas to be studied are independent of electrical engineering. The electrical applications are only illustrations."
Kron emphasized that mechanical systems behave in ways that are identical to electrical systems and that they can therefore be studied analogously to electrical systems, using infact the same methods and tensor equation he discovered for (all )electrical machinery.
Impedance is one of that small set of basic building blocks making up the wide variety of electrical structures. It represents the opposition from the medium and is mathematically represented as a combination of three different kinds kinds of opposition possible - purely resistive, pure capacitive and purely inductive.
The one dimensional coils and two dimensional windings mentioned by Kron are in fact inductances. Now, while the purely resistive and purely capacitive opposition of the medium are known and extensively used in both electrical and mechanical machinery, the third kind of opposition possible, the inductance makes a prominent appearance hitherto only in electrical machinery - there it is everywhere. But there has not been the recognition that the inductive suspension of angular momentum is the mechanical equivalent of the one-dimensional coils in electrical machinery. The incorporation of this new type of opposition into mechanical machinery will bring the possibility of designing a new class of mechatronic machines that will revolutionize manufacturing systems in the way induction coils transformed electrical engineering into the modern electronics engineering. Putting aside the more arcane aspects of Gabriel Kron's work, looking directly at the main equation governing electrical machinery are presented by Kron in his book, we cannot but wonder what the shape such mechanical systems might take.
A passage from Kron's book Tensors for Circuits is reproduced below to illustrate not only Kron's mastery of the subject of the analysis of machines but also an inkling of how electromagnetic devices and mechanical devices are different manifestations of the same fundamental geometric and physical phenomenon. (Click on the images to open a larger version)
[Experimental Update: All parts are ready. Assembly starts now. Prototype unveiling in 3 wks. Testing in 4.]
Throughout the later half of the 19th and the early half of the 20th century, so many important scientific discoveries were happening in so many different fields that one may be forgiven for pleading ignorance in certain esoteric areas. If the field is too vast however, one must seize aspects of the science that help us to focus on understanding the general plan of the field before plunging into the details as this leads to the common syndrome of being unable to see the forest for the trees. In this endeavor, Kron's Tensor Equation will be your everlasting friend, willing to venture with you in your searches into the most exotic designs for machines of your choice, no matter what your field or your time - always helping you design better machines by teaching you how to classify the components that form the machine. By neatly classifying the underlying components of the machine in question into purely inductive, resistive and capacitive components and using his trademark analytical method, Kron is able to set up equations and analyze everything from say, a steam turbine governing system (divided into the governor, the linkage, the pilot valve, and the turbine) to the electric speed drive/control (divided into the synchronous motor, the induction motor, and the stationary network).
Although his field of work was circumscribed by his assignments at GE (General Electric, where he worked), Kron sensed that he was playing with something much bigger than 'just' Electro-Magnetism. In reading Kron's work, I am convinced that he would approve of the relativistic machine's theory and design and see that it meshes with his own thinking. The following is an attempt to cite evidence for this supposition.
Inductive Angular Momentum And Kron's Tensor Equation
Gabriel Kron is the author of a method of analysis of rotating electrical machinery, in which one and the same tensor equation applies to ever conceivable type of machinery. - P. le corbellier in the preface to his book on the analysis of rotating electrical machinery.
IEEE Transactions On Circuit Theory, September 1968 noting the passing away of Gabriel Kron summarize that "Dr. Kron was the author of the classic paper entitled, “Non-Riemannian Dynamics of Rotating Electrical Machinery,” that became the basis of his theories covering all types of rotating machines and power systems. The pioneering work of Gabriel Kron demonstrated convincingly the superior organizational powers of the matrix-tensor notation in network theory."
All types of electrical machinery can be analyzed using the one tensor equation that Kron discovered in his intense theoretical and experimental forays. When one first come's across this promise in his work, one might wonder what kind of an equation can accomplish this mammoth task. There is however, more than just an equation involved in the analysis of a given machine. The equation is only relevant if you first break the machine down into components according to the rules that Kron gives, and in addition you set up the tensors for the various components. Kron found that he could reduce any conceivable machine (even a completely mechanical one)into a network of components which could be solved for the behavior of the specific machine using a single tensor equation. Kron himself went on to make clear that to him, "It is surprising how few ultimate types of elements there are that form the building blocks of the great variety of engineering structures. Most stationary networks consist of a collection of one-dimensional "coils" only; all rotating machines consist only of a collection of two dimensional "windings." The great variety of structures differ only by the manner of interconnections of these ultimate coils and windings, and the variety of theories differ only by the type of hypothetical reference frame assumed. It is only the study of the ultimate building blocks that requires analytical work. The interconnection of these units into a given system is a routine procedure."
The main tensor equation itself is analogous to the statement for Kirchhoff's Voltage Law in a circuit with tensors replacing vectors. As Banesh Hoffman notes in his paper (Kron's Non-Riemannian Dynamics, Hoffman, Banesh, Reviews of Modern Physics, July 1949) "The work of Gabriel Kron constitutes a significant enlargement of the domain of application of tensor analysis." Hoffman also wrote in the introduction to the book Tensors for circuits (authored by Kron) that he (Kron) uses tensors to unify great classes of physical systems. "With him, a tensor transformation changes, the equations of one electrical machine to those of another eletrical machine of a different type. He constructs (the equations of) a prototype machine -the primitive machines - from whose equations he obtains those of all other electrical machines by applying appropriate tensor transformations."
It turns out that Kirchhof's 2 circuit laws - the voltage law and the current law - can help us accomplish an unbelievable amount of modeling of the physical world. Nor is their usefulness restricted to electrical circuits. Kirchhoff's circuit laws laid the foundations also for the field of Topology. (Topology is highly relevant to General Relativity).
The Voltage Law turns out to also be at the heart of analyzing rotating electrical machinery (infact, all machinery ever made or to be made) and it requires a tensorial statement and methods of analysis. This is not a coincidence. Kron himself comments that in his research,he had found that it is interesting that Kirchhof laid the foundations of topology even while working simply with circuits. "It is not a coincidence but a consequence of some hitherto hidden relation between the properties of space and those of electricity that the science of electrical engineering and that of topology meet again on a common ground when both are viewed from an invariant point of view."
It was Kirchhof's laws that laid the foundations for Topology. Topology had hitherto used tensors and now Kron was using a tensorial version of Kirchhof's law to analyze rotating electrical machinery. Tensors used in topology were now also in the very heart of the analysis of rotating electrical networks;
It is worth our while to ponder what we are to make of the fact that nature has designed the phenomenon of electricity such that one equation can serve to model all manner of electrical machinery? Is it something innate to the phenomenon of electricity? Or is the breathtakingly sophisticated mathematical edifice describing all electromagnetic phenomena with the aid of just a few parameters such as impedance (inductive and capacitive), voltage and current and rate of change of current something that derives its seeming perfection from other, even more fundamental?
Kron himself is clear on this subject. He commented that "Although the method of reasoning will be employed [by him in his book Tensors for Circuits] only for stationary and rotating electrical networks, exactly the same reasoning applies also to mechanical and other physical systems. That is, all reasonings and all symbolic formulas to be studied are independent of electrical engineering. The electrical applications are only illustrations."
Kron emphasized that mechanical systems behave in ways that are identical to electrical systems and that they can therefore be studied analogously to electrical systems, using infact the same methods and tensor equation he discovered for (all )electrical machinery.
Impedance is one of that small set of basic building blocks making up the wide variety of electrical structures. It represents the opposition from the medium and is mathematically represented as a combination of three different kinds kinds of opposition possible - purely resistive, pure capacitive and purely inductive.
The one dimensional coils and two dimensional windings mentioned by Kron are in fact inductances. Now, while the purely resistive and purely capacitive opposition of the medium are known and extensively used in both electrical and mechanical machinery, the third kind of opposition possible, the inductance makes a prominent appearance hitherto only in electrical machinery - there it is everywhere. But there has not been the recognition that the inductive suspension of angular momentum is the mechanical equivalent of the one-dimensional coils in electrical machinery. The incorporation of this new type of opposition into mechanical machinery will bring the possibility of designing a new class of mechatronic machines that will revolutionize manufacturing systems in the way induction coils transformed electrical engineering into the modern electronics engineering. Putting aside the more arcane aspects of Gabriel Kron's work, looking directly at the main equation governing electrical machinery are presented by Kron in his book, we cannot but wonder what the shape such mechanical systems might take.
A passage from Kron's book Tensors for Circuits is reproduced below to illustrate not only Kron's mastery of the subject of the analysis of machines but also an inkling of how electromagnetic devices and mechanical devices are different manifestations of the same fundamental geometric and physical phenomenon. (Click on the images to open a larger version)
[Experimental Update: All parts are ready. Assembly starts now. Prototype unveiling in 3 wks. Testing in 4.]
Tuesday, January 25, 2011
Thursday, December 9, 2010
Unclamp it for Milgrom (Clamp it for Euler)
Cambride University's website has the following experiment: Gyroscope hanging over the top of a table.
Please note carefully that there are two versions of the same experiment on the page. The first experiment shows the unclamped gyro staying stable until the 12th line from the right. The third video with the clamped gyro shows the gyro system as being able to maintain balance only until the 9th line.
According to the good engineer's own description of the results "When the gyroscope is clamped so hanging out from the table the couple due to its weight causes the stand to topple....With the pivot point unclamped precession still occurs even when the stand is "upside down"
i.e.: An unclamped gyro behaves differently from a clamped gyro. Why? What's different about the clamped condition as opposed to the unclamped condition?
The extra advantage an unclamped gyro has over a clamped gyro is that it can sustain an infinitesimal net positive acceleration about an X-axis passing through the pivot point (with Y being the vertical axis and Z being the gyro's spin axis) - and its this situation that activates MOND - Modified Newtonian Dynamics. This is something which a clamped gyro is denied because the clamping causes the automatic transmission of even infinitesimal accelerations to the rest of the framework holding the gyro in an infinitesimal time.
Under such conditions, we must use the compound object concepts I have proposed to analyze the behavior of the unit. We can no longer consider the system under study as one object -rather we view it as two objects undergoing sequentially a collision and a decay process with a certain specific frequency we will call the Characteristic Frequency of the system.
Milgrom's boundary condition for MOND (Modified Newtonian Dynamics): Milgrom noted that Newton's law for gravitational force has been verified only where gravitational acceleration is large, and suggested that for extremely low accelerations the theory may not hold. MOND theory posits that acceleration is not linearly proportional to force at low values.
It maybe possible that MOND theory is applicable to infinitesimal systems with relatively large angular momenta suspended in an inductive state. (What is an inductively suspended angular momentum? That question is addressed in the rest of this Upaya- thought post and a direct definition of inductive suspension of spinning wheels is given in this link to my earlier Upaya from last year.)
The condition of an unclamped gyroscope in precession is analogous to Milgrom's boundary condition for MOND. The unclamped gyro in precession is able to possess an infinitesimal acceleration - something which a clamped gyro is denied. Under such conditions, we must use the compound object concepts I have proposed to analyze the behavior of the unit. This reveals that there is a way to resonate the energy transfer processes to navigate the gravitational field.
In order to properly analyze systems with angular momentum as the dominant player, we must first discover its suspension type to understand the behavior of the system. If the system has only capacitive suspension (the axis of the spinning object is secured firmly to an inertial frame containing the spinning object), then spin effects are minimal - if however the spinning object has some about of inductive suspension then the effects will be different and can be analyzed using the equivalent electrical loaded lines as an analogue.
For the rest of this Upaya-post and the next Upaya-post, I will focus on explaining how to construct an an equivalent electrical lines by first reviewing the development of lattice theory and analogies between electrical loaded lines and mechanical systems.
Background And Issues In Lattice Theory
Newton and Euler were among the original architects of a Lattice Theory of Space. In 1658 in the midst of a very unusually strong storm, Newton measured the velocity of the wind using his very own method involving performing long jumps with the wind on his back - comparing it to how much he could jump on his own power gave him the total force which when divided by the surface area of his body's cross section in the plane perpendicular to the wind velocity gives the pressure of the wind accurately.
Yet Newton also imagined that in the midst of all that turblulence, that air was in fact best modeled by imagining it as a continuous chains of point masses connected to their next nearest neighbors on either side (1-Dimensional model) by elastic springs. Newton adopted that model when he attempted to calculate the speed of sound. Newton assumed that sound was propagated in air in the same manner in which an elastic wave would be propagated along a lattice of point masses. He asssumed the simplest possible such lattice (as luck would have it, it was the only sort for which, he knew how to apply the newly invented calculus)- one where each point mass is connected to its neighbors on either side, along the line of propagation.
Taking the elastic force constanst to be e, the particles to be of mass m and the distance between the masses to be d, Newton calculated the
velocity of propagation, V to be d*sqrt(e/m) - sqrt(e*d/rho) where rho = density of air.
Newton then attempted to take the (e*d) term and substitute the isothermal bulk modulus of air in its place, possibly arguing that since the maximum displacement possible for the springs is d, the behavior of the arrangement resembles that of elastic material in Hookes Law of Elasticity (Hooke has just proposed his Law of Elasticity just 5 years earlier). History records that it was Laplace in 1822 who substituted the correct value i.e. the adiabatic elastic constant and first correctly computed the speed of sound.
Euler is credited with being one of the first to apply calculus to physics. He carried Newton's work forward with his theories. He constructed his own theory of light and its propagation by analogy with sound. Now, among several theoretical leaps to occur as a result of such an analogy, there was also an issue: The theoretical models implied longitudinal vibrations - obviously contrary to later findings that light and all Electro-Magnetic waves are transverse in nature, but it is nonetheless informative. This important problem tells us that the scientists who originally grappled with the problem of energy propagation intuited energy as transmitted through the perturbation of the lattice's elastic space. The matter points might be viewed as the nodes of a string instrument and the elastically bound fields then vibrate back and forth and the stretched string sets off waves along a line of points of matter connected to their two nearest neighbors by elastic springs.
Might I also remind the science historians, Eulerian theory of colour accounted for clolours by means of a specific resonance excitation;
Euler explains colours in the following way: the ray incident upon a surface or the matter of light hitting the surface, puts the smallest particles of this surface into vibration. The more elastic the particles, the quicker the vibrations proceed are so that the same ray produces a different number of vibrations per second. The number of vibrations per second determines the colour like that of a string determines the tone."
Euler is invoking here, the second law of vibrating strings which states that
Second Law :
When the length ( l ) and the linear density ( m ) are constant , the frequency of vibration ( n ) of a stretched string vibrating in one segment is proportional to the square root of the tension ( T ) in the wire .
i.e n ∝√(T)
or n/√(T) = constant
Euler was thus viewing the distance between each successive particle within the matter of the surface reflecting the light as having the same role as the length of a stretched string on a musical instrument and each set of two nearest neighbors have the same role as the two nodes of the string producing one single wave between them. In this fashion, Euler subscribed implicitly to a lattice theory for all energy generally.
Baden-Powell's treatment of Newton's model and its application to a cubic lattice represents the first successful mathematical analysis of a 1-D elastic wave. He computed the velocity of a wave propagating along one axis of the cubic lattice structure as a function of a which is defined as (1/applied wave length).
The figure below shows the distribution of the wave velocity against a, the inverse of the wavelength of elastic wave. As the figure shows one major factor is d, the distance of the point masses from one another in the lattice. Baden-Powell's equation for the propagation velocity V of the elastic wave is V = Vinfiniti * |sin pi()*d/lambda|/(pi()*d/lambda).
Take Baden-Powell's velocity formula above. Substituting v infiniti/nu = lambda, we get a constant velocity wave i.e. a wave that travels at a constant speed for example a light wave or a sound wave with a medium. All the other waves have a velocity dependent upon the wavelength implying that except for a completely monochromatic source, the wave would become diluted in space quickly due to the different distances covered by non-monochromatic waves, where as a completely monochromatic source is able to proceed as a soliton. It was Kelvin who gave a complete treatment of 1-D elastic waves. Kelvin assumed the same lattice as Newton and Baden-Powell and numbered it as shown in the following diagram.
By the time we go from Baden-Powell in 1841 to Kelvin in 1881, the lattice model has transformed from suffering longitudinal movements to transverse movement. This change was necessitated by experimental evidence of the transverse nature of most waves and which made it possible to include frequency but also in my opinion, brings about the Size Problem. The particles' transverse movement made it possible to sustain an analysis that held the lattice spatially stationary and of constant volume and shape during the wave propagation - a condition which fit the vast majority of wave interactions - while the longitudinal models fit only piezoelectric crystals.
The Size Problem: In Kelvin's models, significant numbers of point masses can rise upward and fall downward about their mean position. The question is how can the entire chain of masses be really continue to stay within their allocated maximum travel distance, d if you assume that a transverse movement takes away longitudinal length. Since each point mass's loss of longitudinal length will add to the rest, the entire chain must exhibit significant, measurable size changes between its vibrating and non-vibrating states. By the laws of probability, in a vibrating crystal or material of any kind with a large number of point masses, far more point masses are in non-equilibrium positions, as opposed to the equilibrium position of which there is only one, If a vast number of pointmasses are in nonequilibrium positions this implies that the crystal should visibly change size (the large the crystal, the greater the net change in the size of the crystal). Piezoelectric crystals for instance show measurable dimensional change. However a vast majority of interaction do not show such dimensional change.
The way we currently view Kelvin's lattice model (and all other newer models in modern lattice theory) is that we assume that the transverse movement of the point masses happens a seperate dimension whose gain will not be the longitudinal dimension's loss, and yet is somehow determined by d, the longitudinal wavelength.
Take this specific problem of how the model used by Kelvin so successfully later on to model all manner of waves, nonetheless throws up this issue: The original longitudinal model has been replaced by a transverse model because it works. However, there doesn't seem to be a reconciliation done of how it is possible that there is no size change in such a model along the longitudinal direction? What happened to it? Its not there, so its ignored. Its the dog that didn't bark.
One can reconcile the Size Problem of the transverse wave model by accepting that a large amount of inductively suspended spin angular momentum would serve as the fundamental unit of a SpaceTime lattice. Like a gyroscopic problem, the mechanism inside will then seem to have somehow orthogonalized the energy input and output channels, thereby allowing for transverse waves. The lattice model survives, but we no longer see the point masses as moving logitudinally because the gyroscopic effect of the Spin units causes the input and output channels to be orthogonal and therefore the absence of longitudinal reaction to the advance of a longitudinal wave is not a show stopper. Conventional physics doesn't really address these issues currently. It may be that the all interactions involving transverse waves are ultimately all mediated through gyroscopic exchanges of energy between nearest neighbhors possessing large quantities of inductively suspended spin angular momentum.
Much of what is in this post is derived from the work of Leon Brillouin's Wave Propagation in Periodic Structures. I am indebted to him for fantastically original works that make the inner workings of nature crystal clear to the student. Another minor source is the book "Discoverer's of Space" by Erich Lessing. *Also cited is a statement of the first law of vibrating strings from http://www.tutorvista.com/physics/laws-of-vibrating-strings and Euler's opinions from Leonhard Euler: Beitraege zu Leben und Werk by Johann Jakob Burkhardt. Also cited is the wikipedia entry on Modified_Newtonian_dynamics .
Please note carefully that there are two versions of the same experiment on the page. The first experiment shows the unclamped gyro staying stable until the 12th line from the right. The third video with the clamped gyro shows the gyro system as being able to maintain balance only until the 9th line.
According to the good engineer's own description of the results "When the gyroscope is clamped so hanging out from the table the couple due to its weight causes the stand to topple....With the pivot point unclamped precession still occurs even when the stand is "upside down"
i.e.: An unclamped gyro behaves differently from a clamped gyro. Why? What's different about the clamped condition as opposed to the unclamped condition?
The extra advantage an unclamped gyro has over a clamped gyro is that it can sustain an infinitesimal net positive acceleration about an X-axis passing through the pivot point (with Y being the vertical axis and Z being the gyro's spin axis) - and its this situation that activates MOND - Modified Newtonian Dynamics. This is something which a clamped gyro is denied because the clamping causes the automatic transmission of even infinitesimal accelerations to the rest of the framework holding the gyro in an infinitesimal time.
Under such conditions, we must use the compound object concepts I have proposed to analyze the behavior of the unit. We can no longer consider the system under study as one object -rather we view it as two objects undergoing sequentially a collision and a decay process with a certain specific frequency we will call the Characteristic Frequency of the system.
Milgrom's boundary condition for MOND (Modified Newtonian Dynamics): Milgrom noted that Newton's law for gravitational force has been verified only where gravitational acceleration is large, and suggested that for extremely low accelerations the theory may not hold. MOND theory posits that acceleration is not linearly proportional to force at low values.
It maybe possible that MOND theory is applicable to infinitesimal systems with relatively large angular momenta suspended in an inductive state. (What is an inductively suspended angular momentum? That question is addressed in the rest of this Upaya- thought post and a direct definition of inductive suspension of spinning wheels is given in this link to my earlier Upaya from last year.)
The condition of an unclamped gyroscope in precession is analogous to Milgrom's boundary condition for MOND. The unclamped gyro in precession is able to possess an infinitesimal acceleration - something which a clamped gyro is denied. Under such conditions, we must use the compound object concepts I have proposed to analyze the behavior of the unit. This reveals that there is a way to resonate the energy transfer processes to navigate the gravitational field.
In order to properly analyze systems with angular momentum as the dominant player, we must first discover its suspension type to understand the behavior of the system. If the system has only capacitive suspension (the axis of the spinning object is secured firmly to an inertial frame containing the spinning object), then spin effects are minimal - if however the spinning object has some about of inductive suspension then the effects will be different and can be analyzed using the equivalent electrical loaded lines as an analogue.
For the rest of this Upaya-post and the next Upaya-post, I will focus on explaining how to construct an an equivalent electrical lines by first reviewing the development of lattice theory and analogies between electrical loaded lines and mechanical systems.
Background And Issues In Lattice Theory
Newton and Euler were among the original architects of a Lattice Theory of Space. In 1658 in the midst of a very unusually strong storm, Newton measured the velocity of the wind using his very own method involving performing long jumps with the wind on his back - comparing it to how much he could jump on his own power gave him the total force which when divided by the surface area of his body's cross section in the plane perpendicular to the wind velocity gives the pressure of the wind accurately.
Yet Newton also imagined that in the midst of all that turblulence, that air was in fact best modeled by imagining it as a continuous chains of point masses connected to their next nearest neighbors on either side (1-Dimensional model) by elastic springs. Newton adopted that model when he attempted to calculate the speed of sound. Newton assumed that sound was propagated in air in the same manner in which an elastic wave would be propagated along a lattice of point masses. He asssumed the simplest possible such lattice (as luck would have it, it was the only sort for which, he knew how to apply the newly invented calculus)- one where each point mass is connected to its neighbors on either side, along the line of propagation.
Taking the elastic force constanst to be e, the particles to be of mass m and the distance between the masses to be d, Newton calculated the
velocity of propagation, V to be d*sqrt(e/m) - sqrt(e*d/rho) where rho = density of air.
Newton then attempted to take the (e*d) term and substitute the isothermal bulk modulus of air in its place, possibly arguing that since the maximum displacement possible for the springs is d, the behavior of the arrangement resembles that of elastic material in Hookes Law of Elasticity (Hooke has just proposed his Law of Elasticity just 5 years earlier). History records that it was Laplace in 1822 who substituted the correct value i.e. the adiabatic elastic constant and first correctly computed the speed of sound.
Euler is credited with being one of the first to apply calculus to physics. He carried Newton's work forward with his theories. He constructed his own theory of light and its propagation by analogy with sound. Now, among several theoretical leaps to occur as a result of such an analogy, there was also an issue: The theoretical models implied longitudinal vibrations - obviously contrary to later findings that light and all Electro-Magnetic waves are transverse in nature, but it is nonetheless informative. This important problem tells us that the scientists who originally grappled with the problem of energy propagation intuited energy as transmitted through the perturbation of the lattice's elastic space. The matter points might be viewed as the nodes of a string instrument and the elastically bound fields then vibrate back and forth and the stretched string sets off waves along a line of points of matter connected to their two nearest neighbors by elastic springs.
Might I also remind the science historians, Eulerian theory of colour accounted for clolours by means of a specific resonance excitation;
Euler explains colours in the following way: the ray incident upon a surface or the matter of light hitting the surface, puts the smallest particles of this surface into vibration. The more elastic the particles, the quicker the vibrations proceed are so that the same ray produces a different number of vibrations per second. The number of vibrations per second determines the colour like that of a string determines the tone."
Euler is invoking here, the second law of vibrating strings which states that
Second Law :
When the length ( l ) and the linear density ( m ) are constant , the frequency of vibration ( n ) of a stretched string vibrating in one segment is proportional to the square root of the tension ( T ) in the wire .
i.e n ∝√(T)
or n/√(T) = constant
Euler was thus viewing the distance between each successive particle within the matter of the surface reflecting the light as having the same role as the length of a stretched string on a musical instrument and each set of two nearest neighbors have the same role as the two nodes of the string producing one single wave between them. In this fashion, Euler subscribed implicitly to a lattice theory for all energy generally.
Baden-Powell's treatment of Newton's model and its application to a cubic lattice represents the first successful mathematical analysis of a 1-D elastic wave. He computed the velocity of a wave propagating along one axis of the cubic lattice structure as a function of a which is defined as (1/applied wave length).
The figure below shows the distribution of the wave velocity against a, the inverse of the wavelength of elastic wave. As the figure shows one major factor is d, the distance of the point masses from one another in the lattice. Baden-Powell's equation for the propagation velocity V of the elastic wave is V = Vinfiniti * |sin pi()*d/lambda|/(pi()*d/lambda).
Take Baden-Powell's velocity formula above. Substituting v infiniti/nu = lambda, we get a constant velocity wave i.e. a wave that travels at a constant speed for example a light wave or a sound wave with a medium. All the other waves have a velocity dependent upon the wavelength implying that except for a completely monochromatic source, the wave would become diluted in space quickly due to the different distances covered by non-monochromatic waves, where as a completely monochromatic source is able to proceed as a soliton. It was Kelvin who gave a complete treatment of 1-D elastic waves. Kelvin assumed the same lattice as Newton and Baden-Powell and numbered it as shown in the following diagram.
By the time we go from Baden-Powell in 1841 to Kelvin in 1881, the lattice model has transformed from suffering longitudinal movements to transverse movement. This change was necessitated by experimental evidence of the transverse nature of most waves and which made it possible to include frequency but also in my opinion, brings about the Size Problem. The particles' transverse movement made it possible to sustain an analysis that held the lattice spatially stationary and of constant volume and shape during the wave propagation - a condition which fit the vast majority of wave interactions - while the longitudinal models fit only piezoelectric crystals.
The Size Problem: In Kelvin's models, significant numbers of point masses can rise upward and fall downward about their mean position. The question is how can the entire chain of masses be really continue to stay within their allocated maximum travel distance, d if you assume that a transverse movement takes away longitudinal length. Since each point mass's loss of longitudinal length will add to the rest, the entire chain must exhibit significant, measurable size changes between its vibrating and non-vibrating states. By the laws of probability, in a vibrating crystal or material of any kind with a large number of point masses, far more point masses are in non-equilibrium positions, as opposed to the equilibrium position of which there is only one, If a vast number of pointmasses are in nonequilibrium positions this implies that the crystal should visibly change size (the large the crystal, the greater the net change in the size of the crystal). Piezoelectric crystals for instance show measurable dimensional change. However a vast majority of interaction do not show such dimensional change.
The way we currently view Kelvin's lattice model (and all other newer models in modern lattice theory) is that we assume that the transverse movement of the point masses happens a seperate dimension whose gain will not be the longitudinal dimension's loss, and yet is somehow determined by d, the longitudinal wavelength.
Take this specific problem of how the model used by Kelvin so successfully later on to model all manner of waves, nonetheless throws up this issue: The original longitudinal model has been replaced by a transverse model because it works. However, there doesn't seem to be a reconciliation done of how it is possible that there is no size change in such a model along the longitudinal direction? What happened to it? Its not there, so its ignored. Its the dog that didn't bark.
One can reconcile the Size Problem of the transverse wave model by accepting that a large amount of inductively suspended spin angular momentum would serve as the fundamental unit of a SpaceTime lattice. Like a gyroscopic problem, the mechanism inside will then seem to have somehow orthogonalized the energy input and output channels, thereby allowing for transverse waves. The lattice model survives, but we no longer see the point masses as moving logitudinally because the gyroscopic effect of the Spin units causes the input and output channels to be orthogonal and therefore the absence of longitudinal reaction to the advance of a longitudinal wave is not a show stopper. Conventional physics doesn't really address these issues currently. It may be that the all interactions involving transverse waves are ultimately all mediated through gyroscopic exchanges of energy between nearest neighbhors possessing large quantities of inductively suspended spin angular momentum.
Much of what is in this post is derived from the work of Leon Brillouin's Wave Propagation in Periodic Structures. I am indebted to him for fantastically original works that make the inner workings of nature crystal clear to the student. Another minor source is the book "Discoverer's of Space" by Erich Lessing. *Also cited is a statement of the first law of vibrating strings from http://www.tutorvista.com/physics/laws-of-vibrating-strings and Euler's opinions from Leonhard Euler: Beitraege zu Leben und Werk by Johann Jakob Burkhardt. Also cited is the wikipedia entry on Modified_Newtonian_dynamics .
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