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Gaussian statics law
On 13 Mar, 08:02, Gene Fuller wrote:
Ian White GM3SEK wrote: [snip] For antenna engineering, that road is ENTIRELY built on the classical physics of the 18th-19th century. It can be a hard road to travel, but it's a reliably straight one. Any side turnings are NOT going to be short-cuts to a better understanding. Ian, For the misunderstood and unappreciated "inventor", hope springs eternal. It's all for the good, however. RRAA would simply fade away without fractals, crossed-fields, RoomCaps, unmodelable structures, traveling waves, one-second long transmission lines, Poynting vectors, etc. 73, Gene W4SZ Gene, I was just reading the archives of 2004 where you fought with everybody in ham radio,QEX as well as on this newsgroup as to how everybody was inerpretating Maxwells laws plus used a lot of accusatory words against Walt and many others. You couldn't push any of them away then so what makes you think that all are going to line up behind you to get rid of me? Now you are lining up with the amateur group and the West Coast without resolving your past disagrements with every body about your disagreements with Maxwell resolved . Are you going to start a third front about what Maxwell really meant? NASA has been in error before, remember the "O" ring saga . They then dug a hole for themselves thinking that the deeper they dug the closer they were to escaping, maybe you are of the same thinking.Think about all those clever guys that were part of MIT and you are going to take them on with respect to Maxwell's teachings or at least what you thinl he meant? I'll back MIT anyday against you and others with respect to electrical laws.He gave the mathematical analysis which all have been craving for and he gets accused of spreading mis information. What is it that this group and the West coast NASA want with respect to Gaussian arrays, remove him from all the text books and replace him by Stokes? Art |
Gaussian statics law
On 9 Mar, 18:09, John Smith I wrote:
wrote: ... No, I am far from thinking light is actually "something." (at least not a "something" we are familiar with or have "true" examples of ...) It is unthinkable that any object/particle can exist without mass ... the discovery and absolute proof of that being possible is in our future; presently we only have theories ... I don't argue that it is impossible, rather only improbable. It is more than likely, like has happened so many times, when we know why rf waves appear to be both wave and particle, that physicists and mathematicians will go scurrying to their dens and emerge with new "laws." And, finally we will have a more complete picture of the phenomenon. We only see a puzzle, although we can "work with the puzzle", although we can "seem" to get meaningful data from this puzzle, or manipulate it to do useful things for us, although we "seem" to have laws, equations and formulas to describe this puzzle--we have been there and done that before--that is, we have rewritten those laws, equations and formulas to fit our new findings and started pretending we have reached the final conclusions and "know" the phenomenon--but then, at some future date, we do it all over again ... JS --http://assemblywizard.tekcities.com |
Gaussian statics law
art wrote:
On 13 Mar, 08:02, Gene Fuller wrote: Gene, I was just reading the archives of 2004 where you fought with everybody in ham radio,QEX as well as on this newsgroup as to how everybody was inerpretating Maxwells laws plus used a lot of accusatory words against Walt and many others. You couldn't push any of them away then so what makes you think that all are going to line up behind you to get rid of me? Now you are lining up with the amateur group and the West Coast without resolving your past disagrements with every body about your disagreements with Maxwell resolved . Are you going to start a third front about what Maxwell really meant? NASA has been in error before, remember the "O" ring saga . They then dug a hole for themselves thinking that the deeper they dug the closer they were to escaping, maybe you are of the same thinking.Think about all those clever guys that were part of MIT and you are going to take them on with respect to Maxwell's teachings or at least what you thinl he meant? I'll back MIT anyday against you and others with respect to electrical laws.He gave the mathematical analysis which all have been craving for and he gets accused of spreading mis information. What is it that this group and the West coast NASA want with respect to Gaussian arrays, remove him from all the text books and replace him by Stokes? Art Art, You need to learn to read more carefully. My one and only argument with Walt Maxwell was about the fuss between him and Steve Best. My position then, and still today, was that both of these experts were correct in their technical analysis. Walt chose a novel approach involving "virtual short circuits", and Steve chose a more traditional wave model. The physical, measurable results were identical, and there would have been no way that anyone could test the difference in the two analyses by any sort of measurement. I believe there were some harsh words in addition to the technical analysis, but I was not part of that. There was also a huge amount of chatter along the lines of 2 + 2 is not equal to 7, from our favorite nit-picker. I have no idea why you have lumped me into something to do with MIT. I have been there a few times over the years, but I don't think that would have any connection to RRAA. 73, Gene W4SZ |
Gaussian statics law
On 9 Mar, 18:09, John Smith I wrote:
wrote: ... No, I am far from thinking light is actually "something." (at least not a "something" we are familiar with or have "true" examples of ...) It is unthinkable that any object/particle can exist without mass ... the discovery and absolute proof of that being possible is in our future; presently we only have theories ... I don't argue that it is impossible, rather only improbable. It is more than likely, like has happened so many times, when we know why rf waves appear to be both wave and particle, that physicists and mathematicians will go scurrying to their dens and emerge with new "laws." And, finally we will have a more complete picture of the phenomenon. We only see a puzzle, although we can "work with the puzzle", although we can "seem" to get meaningful data from this puzzle, or manipulate it to do useful things for us, although we "seem" to have laws, equations and formulas to describe this puzzle--we have been there and done that before--that is, we have rewritten those laws, equations and formulas to fit our new findings and started pretending we have reached the final conclusions and "know" the phenomenon--but then, at some future date, we do it all over again ... JS --http://assemblywizard.tekcities.com When Gauss mused over the closed volume he concentrated on flux as the basis of his law and not really on the statics side in that he was formulating an equation. True he used static particles in the concept but it was the logic that was applied by his equation that should be understood. Gauss used the projection of static images pill box styleand made is equation a matter of logic based around the arbitary border. To him he did not care as to what the static particles were resting upon since they would not be moving across the border thus he concentrated only on the movement of flux. So in todays world we can visualize a dipole or a multiple of dipoles inside the enclosed arbitary border. If the two dipoles were not in equilibrium it would not matter to Gauss when considering static particles since time is of a consideration and at that time as far as Gauss went time was not part of his consideration. If he used two dipoles which was not in equilibrium there would still be action of the cessasian of time because flux that eventually would breach the border was still on the move where gauss equation was based on equilibrium at any point in time.So a single dipole is acceptable as a carrier of static particles because at any point in time the border constitutes the state of equilibrium. So I then took on the same logic that gauss applied for his theorem when I placed a cluster of elements as carriers of static particles knowing full well that at the cessation of time flux cannot breach the walls and also remembering that radiation will not commence prior to penetrating the border. This is an important point since we will always be in a state of equilibrium only and if the contained array is in a state of equilibrium i.e.all resonant in situ. Now some have enlarged on Gausses static law without incurring equilibrium by extending the enclosed surface to make a conservative field where the time of the events is zero and thus vectors were zero in length purely as a personal aid which has now real value. And it cannot have real value over a period of time unless intercoupling and movement of particles can move despite the cessation of time thus equilibrium has been destroyed. Only when flux generated after the cessacion of time is in a static state is in equilibrium. Now with the addition of time all vectors on a conservative field can be a length of real number and direction which thus includes curl. Thus this new law supplies the logic for the formation of radiation after the border is breached but revolves only around static particles prior to after breaching the border over a particular event or time. The diference as far as antennas go is that gaussion flux as it were do not radiate or couple to other elements since it is in a state of equilibrium where as standard antennas radiate immediately on the application of power. True a hundred years later LaPlace was integrated into the main stream for the addition of electric current and magnetic fields but not via the logic that radiation does not necessarally end when power is removed because of re radiation. So Art is claiming clusters of radiators that are in total equilibrium and where the "Q" is constant as a radiating array with out parasitic actions of other parts of same array. This allow for arrays to consist of elements that are not required to be planar, parallel or even half wave length which immediately supplies the advantages of consilidation of all elements amoung other things. And there you have it, just a matter of maintaining equilibrium which is what mathematics is all about. People are so engrossed in informing other people how clever and knowelable about the matter of the universe and neglecting the simple things that are under their nose. If you still wish to ague or assalt please note that MIT supplied the mathematics that gives proof to the underlying logic and if that is not good enough Minninec will supply such arrays if you do not presteer it to form a yagi. Read, Read, Read again and digest. If you don't like it then don't use it, your choice. My sincere thanks to M.I.T for supplying another avenue of authentification Regards Arthur Unwin KB9MZ.......XG ( Born in Stepney close to the Tower of London) |
Gaussian statics law
On 13 Mar 2007 12:55:48 -0700, "art" wrote:
My sincere thanks to M.I.T for supplying another avenue of authentification Hi Art, Was this thanks for his misreading Gauss where it should have been Maxwell? 73's Richard Clark, KB7QHC |
Gaussian statics law
On Tue, 13 Mar 2007 13:57:18 -0800, Richard Clark
wrote: Was this thanks for his misreading Gauss where it should have been Maxwell? I do not understand your comment. If you go back and look at my first post on this subject (Message-ID ), you will see that I equated Gauss's law with the first Maxwell equation. Gauss's law is commonly stated as: The electric flux through a closed surface is proportional to the amount of charge enclosed by the surface. As I wrote before, this also happens to be the integral form of the first Maxwell equation: div E(x,t) = 4\pi\rho(x,t) While Gauss may have stated this law in terms of static charges, and it finds most applications in the static case, the law also holds for the dynamic case. This is why physicists equate Gauss's law with the integral form of the first Maxwell equation. And as evidence of this association, you indirectly pointed out in Message-ID that Feynman equated the two in the table 15-1 of volume II of his lectures. --John |
Gaussian statics law
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Gaussian statics law
John E. Davis wrote:
On Tue, 13 Mar 2007 13:57:18 -0800, Richard Clark wrote: Was this thanks for his misreading Gauss where it should have been Maxwell? I do not understand your comment. If you go back and look at my first post on this subject (Message-ID ), you will see that I equated Gauss's law with the first Maxwell equation. Gauss's law is commonly stated as: The electric flux through a closed surface is proportional to the amount of charge enclosed by the surface. As I wrote before, this also happens to be the integral form of the first Maxwell equation: div E(x,t) = 4\pi\rho(x,t) While Gauss may have stated this law in terms of static charges, and it finds most applications in the static case, the law also holds for the dynamic case. This is why physicists equate Gauss's law with the integral form of the first Maxwell equation. And as evidence of this association, you indirectly pointed out in Message-ID that Feynman equated the two in the table 15-1 of volume II of his lectures. --John Using the MKSA system, Gauss' law is expressed as div D = rho. Art can take the time derivative of both sides, if he wants to, in which case he gets div d(D)/dt = d(rho)/dt. This doesn't mean much except that it's what you end up with when you take the divergence of both sides of the Maxwell equation curl H = j + d(D)/dt, and then apply the equation of continuity where it fits. (You have to pretend the 'd's' in each equation are the funny little Greek letters that signify partial differentiation.) Feynman didn't like to use the magnetic field intensity vector H or the electric flux density vector D so he used their B and E equivalents in his presentation of Maxwell's equations in his _Lectures on Physics_. I guess you could start an argument over whether or not H and D have physical significance, but don't ask me to join in. John, I think you might want to re-think your equation div E(x,t)=4\pi\rho(x,t). 73, Tom Donaly, KA6RUH |
Gaussian statics law
On Wed, 14 Mar 2007 05:53:43 GMT, Tom Donaly
wrote: John, I think you might want to re-think your equation div E(x,t)=4\pi\rho(x,t). It is not my equation--- it is the first Maxwell equation (expressed using Gaussian units). I did not make it up, nor did I add the time-dependence as another poster suggested. --John |
Gaussian statics law
John E. Davis wrote:
On Wed, 14 Mar 2007 05:53:43 GMT, Tom Donaly wrote: John, I think you might want to re-think your equation div E(x,t)=4\pi\rho(x,t). It is not my equation--- it is the first Maxwell equation (expressed using Gaussian units). I did not make it up, nor did I add the time-dependence as another poster suggested. --John Different texts have Maxwell's equations in different order. What text did you get this from? Becker has it (in Gaussian CGS units) as div D = 4\pi\rho (where the backslash indicates multiplication, and D and rho have the usual meanings. You can add the 't' if you want to, but it's unnecessary. Also, since you're dealing in 3 dimensions, why not indicate them as in E(x,y,z), or E(x,y,z,t) (if the time means something to you)? 73, Tom Donaly, KA6RUH |
Gaussian statics law
On Wed, 14 Mar 2007 09:09:27 -0800, Tom Donaly
wrote: Different texts have Maxwell's equations in different order. What text did you get this from? Becker has it (in Gaussian CGS units) as div D = 4\pi\rho (where the backslash indicates multiplication, and D and rho have the usual meanings. You can add the 't' if you want to, but it's unnecessary. Also, since you're dealing in 3 dimensions, why not indicate them as in E(x,y,z), or E(x,y,z,t) (if the time means something to you)? I tend to write equations in LaTeX form as most people I exchange emails with mathematical equations use that for formatting mathematics. Here, \pi represents the greek letter pi, and \rho is the greek letter rho. I used x to represent a spatial 3-vector. I could have written it as (x,y,z) but I did not think this shorthand would cause any confusion given the context. The difference between E and D is not important here. If you use D, then \rho must be interpreted as the so-called "free" charge density. However, the fundamental field is E, and if you use it the \rho must be interpreted as the _full_ charge density. The relationship between E and D can be very complex and may well depend upon the strength of the applied field E. For simple materials a linear relationship is usually assumed, e.g., D = \epsilon E, where \epsilon is the dielectric constant of the medium. Also even here in this linear relationship, \epsilon need not be a scalar (a number). It could be a tensor (a 3x3 matrix), in which case D and E would not have the same direction. --John |
Gaussian statics law
On Mar 13, 6:33 pm, Richard Clark wrote:
On 13 Mar 2007 22:15:37 GMT, (John E. Davis) wrote: I do not understand your comment. Hi John, It was rather explicit. To have disputed Dave's assertion with additional material that substantiated him, makes for a rather strange reading of Feynman. .. You can bow out once again, of course, and become a martyr instead. Or you can indulge us with a dialog with Art. I would think this comment applied equally to Dave. Derek |
Gaussian statics law
John E. Davis wrote:
On Wed, 14 Mar 2007 09:09:27 -0800, Tom Donaly wrote: Different texts have Maxwell's equations in different order. What text did you get this from? Becker has it (in Gaussian CGS units) as div D = 4\pi\rho (where the backslash indicates multiplication, and D and rho have the usual meanings. You can add the 't' if you want to, but it's unnecessary. Also, since you're dealing in 3 dimensions, why not indicate them as in E(x,y,z), or E(x,y,z,t) (if the time means something to you)? I tend to write equations in LaTeX form as most people I exchange emails with mathematical equations use that for formatting mathematics. Here, \pi represents the greek letter pi, and \rho is the greek letter rho. I used x to represent a spatial 3-vector. I could have written it as (x,y,z) but I did not think this shorthand would cause any confusion given the context. The difference between E and D is not important here. If you use D, then \rho must be interpreted as the so-called "free" charge density. However, the fundamental field is E, and if you use it the \rho must be interpreted as the _full_ charge density. The relationship between E and D can be very complex and may well depend upon the strength of the applied field E. For simple materials a linear relationship is usually assumed, e.g., D = \epsilon E, where \epsilon is the dielectric constant of the medium. Also even here in this linear relationship, \epsilon need not be a scalar (a number). It could be a tensor (a 3x3 matrix), in which case D and E would not have the same direction. --John Thanks for explaining that, John. I am unfamiliar with the conventions of LaTex, obviously (I get my information from books that are generally older than I am, and I'm not young). I don't have any problem with Gauss' law being used in a non-static context. It applies, regardless. That's as far as I go in agreeing with Art, though, since I can't understand the rest of his theory, at all (but might if I could turn off the left side of my brain - maybe). 73, Tom Donaly, KA6RUH |
Gaussian statics law
On 14 Mar, 12:40, "Tom Donaly" wrote:
John E. Davis wrote: On Wed, 14 Mar 2007 09:09:27 -0800, Tom Donaly wrote: Different texts have Maxwell's equations in different order. What text did you get this from? Becker has it (in Gaussian CGS units) as div D = 4\pi\rho (where the backslash indicates multiplication, and D and rho have the usual meanings. You can add the 't' if you want to, but it's unnecessary. Also, since you're dealing in 3 dimensions, why not indicate them as in E(x,y,z), or E(x,y,z,t) (if the time means something to you)? I tend to write equations in LaTeX form as most people I exchange emails with mathematical equations use that for formatting mathematics. Here, \pi represents the greek letter pi, and \rho is the greek letter rho. I used x to represent a spatial 3-vector. I could have written it as (x,y,z) but I did not think this shorthand would cause any confusion given the context. The difference between E and D is not important here. If you use D, then \rho must be interpreted as the so-called "free" charge density. However, the fundamental field is E, and if you use it the \rho must be interpreted as the _full_ charge density. The relationship between E and D can be very complex and may well depend upon the strength of the applied field E. For simple materials a linear relationship is usually assumed, e.g., D = \epsilon E, where \epsilon is the dielectric constant of the medium. Also even here in this linear relationship, \epsilon need not be a scalar (a number). It could be a tensor (a 3x3 matrix), in which case D and E would not have the same direction. --John Thanks for explaining that, John. I am unfamiliar with the conventions of LaTex, obviously (I get my information from books that are generally older than I am, and I'm not young). I don't have any problem with Gauss' law being used in a non-static context. It applies, regardless. That's as far as I go in agreeing with Art, though, since I can't understand the rest of his theory, at all (but might if I could turn off the left side of my brain - maybe). 73, Tom Donaly, KA6RUH- Hide quoted text - - Show quoted text - Tom, don,t worry about it! A poster has stated it was invented years ago. I haven,t found it in any of my books so perhaps he will tell you where you can look at it. I assume my patent will now be turned down when it is pointed out where the Gaussian antennas can be seen. When he describes it it to you then it should be much easier for you to understand the logic behind it and to determine whether it is all a todo about nothing. As for me I think the subject can be said as proven, albiet over 100 years or more ago and the whole subject started by that blithering idiot, sycopath and all those other phrases can now seen as closed. I will hang around a bit to see what I could have been if only I had been born 100 or 200 years ago where somebody said I will have all the manufacturers knocking on my door. Maybe that inventor of the gaussian array left me a morsel on the cutting room floor which I can exploit and which I can reveal after the existing Gaussian presence is revealed by the poster. But that still leaves the question why haven't ham radio users not picked up the slack and tried them? Maybe it is the 'not invented in my town' thinking and where their heads still rest in the sand. I also have this other invention that I want.............no, I have learned my lesson I will take it to my grave that would be so much easier. Art The Englishman |
Gaussian statics law
"Derek" wrote in message ups.com... On Mar 13, 6:33 pm, Richard Clark wrote: On 13 Mar 2007 22:15:37 GMT, (John E. Davis) wrote: I do not understand your comment. Hi John, It was rather explicit. To have disputed Dave's assertion with additional material that substantiated him, makes for a rather strange reading of Feynman. . You can bow out once again, of course, and become a martyr instead. Or you can indulge us with a dialog with Art. I would think this comment applied equally to Dave. Derek i like the post that points out the unnecessary t in the Gauss's law equation... well done. sri i didn't state that myself, but i have had better things to do than try to argue with art. |
Gaussian statics law
On 14 Mar 2007 13:26:46 -0700, "art" wrote:
But that still leaves the question why haven't ham radio users not picked up the slack and tried them? Hi Art, That was done an hundred years ago, and people found better ways. 73's Richard Clark, KB7QHC |
Gaussian statics law
On Mar 14, 2:39 pm, "Dave" wrote:
i like the post that points out the unnecessary t in the Gauss's law equation... well done. sri i didn't state that myself, but i have had better things to do than try to argue with art. As I remember it you were arguing with John. Derek |
Gaussian statics law
"Derek" wrote in message ups.com... On Mar 14, 2:39 pm, "Dave" wrote: i like the post that points out the unnecessary t in the Gauss's law equation... well done. sri i didn't state that myself, but i have had better things to do than try to argue with art. As I remember it you were arguing with John. Derek i was probably arguing with a couple of them... all the blabbering looks the same after a while. |
Gaussian statics law
On Mar 9, 2:11 pm, John Smith I wrote:
Cecil Moore wrote: wrote: EM waves depart when energy is applied, not particles. Quantum Electrodynamics tells us that EM waves consist of photons which are particles. -- 73, Cecil, w5dxp.com So, which is the real question: 1) Why do waves act like particles? --OR-- 2) Why do particles act like waves? JS --http://assemblywizard.tekcities.com When a field is traveling at/near the speed of light it has mass(acts as a particle) slower and it is a wave. EM lives on the hairy edge of both worlds. vAt least thats what my Phd girlfriend told me once. Who knows though, she was pretty weird. JIMMIE |
Gaussian statics law
JIMMIE wrote:
... When a field is traveling at/near the speed of light it has mass(acts as a particle) slower and it is a wave. EM lives on the hairy edge of both worlds. vAt least thats what my Phd girlfriend told me once. Who knows though, she was pretty weird. JIMMIE Yes. Just thinking about this one aspect can keep me up for hours from a restful sleep ... :( Regards, JS -- http://assemblywizard.tekcities.com |
Gaussian statics law
...
When a field is traveling at/near the speed of light it has mass(acts as a particle) slower and it is a wave. EM lives on the hairy edge of both worlds. vAt least thats what my Phd girlfriend told me once. Who knows though, she was pretty weird. JIMMIE Yes. Just thinking about this one aspect can keep me up for hours from a restful sleep ... :( Regards, JS --http://assemblywizard.tekcities.com So, if I pass the wave through a slit it speeds up or slows down? If I pass the particle through a slit it speeds up or slows down? denny - enquiring mind and all that... |
Gaussian statics law
Denny wrote:
... So, if I pass the wave through a slit it speeds up or slows down? If I pass the particle through a slit it speeds up or slows down? denny - enquiring mind and all that... Are you asking me to check my speedometer next time I pass under a bridge? See: http://en.wikipedia.org/wiki/Double-slit_experiment JS -- http://assemblywizard.tekcities.com |
Gaussian statics law
John Smith I wrote:
Denny wrote: ... So, if I pass the wave through a slit it speeds up or slows down? If I pass the particle through a slit it speeds up or slows down? denny - enquiring mind and all that... Are you asking me to check my speedometer next time I pass under a bridge? See: http://en.wikipedia.org/wiki/Double-slit_experiment JS Perhaps this URL: http://www.thekeyboard.org.uk/Quantum%20mechanics.htm will put everyone on "the same page" and point out that quite a few of the debates/arguments/discussions here are probably "centered", roughly, on the same points of dispute/contention ... or, the unknown/unseen/unmeasured are a mystery that traditional physics attempts to ignore and gloss over and use "place holders" to compensate for--yet hamper our complete understanding of forces/affects/effects we attempt to take for granted and claim a "good understanding" of. Hey, I probably shouldn't complain--a world without mystery could get a bit stale--I suppose ... Regards, JS -- http://assemblywizard.tekcities.com |
Gaussian statics law
On 14 Mar, 12:40, "Tom Donaly" wrote:
John E. Davis wrote: On Wed, 14 Mar 2007 09:09:27 -0800, Tom Donaly wrote: Different texts have Maxwell's equations in different order. What text did you get this from? Becker has it (in Gaussian CGS units) as div D = 4\pi\rho (where the backslash indicates multiplication, and D and rho have the usual meanings. You can add the 't' if you want to, but it's unnecessary. Also, since you're dealing in 3 dimensions, why not indicate them as in E(x,y,z), or E(x,y,z,t) (if the time means something to you)? I tend to write equations in LaTeX form as most people I exchange emails with mathematical equations use that for formatting mathematics. Here, \pi represents the greek letter pi, and \rho is the greek letter rho. I used x to represent a spatial 3-vector. I could have written it as (x,y,z) but I did not think this shorthand would cause any confusion given the context. The difference between E and D is not important here. If you use D, then \rho must be interpreted as the so-called "free" charge density. However, the fundamental field is E, and if you use it the \rho must be interpreted as the _full_ charge density. The relationship between E and D can be very complex and may well depend upon the strength of the applied field E. For simple materials a linear relationship is usually assumed, e.g., D = \epsilon E, where \epsilon is the dielectric constant of the medium. Also even here in this linear relationship, \epsilon need not be a scalar (a number). It could be a tensor (a 3x3 matrix), in which case D and E would not have the same direction. --John Thanks for explaining that, John. I am unfamiliar with the conventions of LaTex, obviously (I get my information from books that are generally older than I am, and I'm not young). I don't have any problem with Gauss' law being used in a non-static context. It applies, regardless. That's as far as I go in agreeing with Art, though, since I can't understand the rest of his theory, at all (but might if I could turn off the left side of my brain - maybe). 73, Tom Donaly, KA6RUH- Hide quoted text - - Show quoted text - Tom I was rereading this thread as to why people have a hard time in understanding Gauss's law with respect to conservative fields and a transition to a non conservative field where with the addition of time one can consider what is outside the enclosed surface. Since you pursued the mathematical side of the subject to a minor conclusion ( you stated you didn't understand what I was proposing) with John E Davis of M.I.T. I wish to share with you some notes on the Internet by David J Raymond called "a radically modern aproach" which to me is the best I have seen on Radiation in it's entirety. Obviously there is a lot written that as hams it is not essential reading for hams but what it does do is explain in a very clear way the mechanics of radiation with specific applications with respect to the transition from conservative fields ala Gaussian law of statics to non conservative fields where at the cessation of time one can reconcile what is outside the enclosed surface with that which is inside the surface where what is inside the enclosure is in equilibrium and the enclosing surface is frictionless. As can obviously seen a Yagi inside the enclosed border cannot be considered since at the cessation of time interaction between elements is still taking place after the cessation of time. The notes are so well written that one not conversant with upper math can still follow the implications of the discussion at hand and thus can be considered as recommended reading for all hams interested in antennas as a subject. It also gives a very clear mathematical progression from Gaussian law to the subject of non conservative fields can be formed with the activation of curl during a moment in time. It is this progression that leads designers to design around cluster arrays that are in equilibrium regardless of orientation ie without continuing coupling effects after the cessation of time and is very well chronicalled in the above stated notes. Best regards Art |
Gaussian statics law
On 18 Apr 2007 13:07:43 -0700, art wrote:
I was rereading this thread as to why people have a hard time in understanding Gauss's law with respect to conservative fields and a transition to a non conservative field where with the addition of time one can consider what is outside the enclosed surface. Hi Art, That single, obscure, and ponderously long sentence is a clue as to why... since at the cessation of time interaction between elements is still taking place after the cessation of time. One has to wonder what new meaning you have for the word "cessation." How can there be any time (for anything to take place) when there is no more time (for anything to take place). 73's Richard Clark, KB7QHC |
Gaussian statics law
On 18 Apr, 13:36, Richard Clark wrote:
On 18 Apr 2007 13:07:43 -0700, art wrote: I was rereading this thread as to why people have a hard time in understanding Gauss's law with respect to conservative fields and a transition to a non conservative field where with the addition of time one can consider what is outside the enclosed surface. Hi Art, That single, obscure, and ponderously long sentence is a clue as to why... since at the cessation of time interaction between elements is still taking place after the cessation of time. One has to wonder what new meaning you have for the word "cessation." How can there be any time (for anything to take place) when there is no more time (for anything to take place). 73's Richard Clark, KB7QHC When power supply is stopped to an array inside an enclosed surface kinetic energy is in evidence by radiation between elements PRIOR to emerging from the enclosed surface. You cannot have an equation with reference to time if equality is not obtained at the cessation of the time under consideration. You should read up on conservative and non conservative fields before you succumb to temptation by replying while you still have your foot in your mouth. I have responded to you this one time only to show others how stupid you can be when you allow animosity to over ride cfommon sense. |
Gaussian statics law
art wrote:
When power supply is stopped to an array inside an enclosed surface kinetic energy is in evidence by radiation between elements PRIOR to emerging from the enclosed surface. You cannot have an equation with reference to time if equality is not obtained at the cessation of the time under consideration. You should read up on conservative and non conservative fields before you succumb to temptation by replying while you still have your foot in your mouth. I have responded to you this one time only to show others how stupid you can be when you allow animosity to over ride cfommon sense. Yes, and well-done |
Gaussian statics law
On 18 Apr 2007 13:54:19 -0700, art wrote:
When power supply is stopped to an array inside an enclosed surface kinetic energy is in evidence by radiation between elements PRIOR to emerging from the enclosed surface. You cannot have an equation with reference to time if equality is not obtained at the cessation of the time under consideration. Hi Art, Unless the enclosed surface is immense, all times (even for HF) considered are on the scale of nanoseconds. At common excitations considered for Amateur application would reveal power issues in the microwatts. The ratio of scales (energy/time-volume) would be 9 orders of magnitude and well outside the accuracy of any modeler, and vastly beyond the cares of useful theory. 73's Richard Clark, KB7QHC |
Gaussian statics law
On 18 Apr, 13:07, art wrote:
On 14 Mar, 12:40, "Tom Donaly" wrote: John E. Davis wrote: On Wed, 14 Mar 2007 09:09:27 -0800, Tom Donaly wrote: Different texts have Maxwell's equations in different order. What text did you get this from? Becker has it (in Gaussian CGS units) as div D = 4\pi\rho (where the backslash indicates multiplication, and D and rho have the usual meanings. You can add the 't' if you want to, but it's unnecessary. Also, since you're dealing in 3 dimensions, why not indicate them as in E(x,y,z), or E(x,y,z,t) (if the time means something to you)? I tend to write equations in LaTeX form as most people I exchange emails with mathematical equations use that for formatting mathematics. Here, \pi represents the greek letter pi, and \rho is the greek letter rho. I used x to represent a spatial 3-vector. I could have written it as (x,y,z) but I did not think this shorthand would cause any confusion given the context. The difference between E and D is not important here. If you use D, then \rho must be interpreted as the so-called "free" charge density. However, the fundamental field is E, and if you use it the \rho must be interpreted as the _full_ charge density. The relationship between E and D can be very complex and may well depend upon the strength of the applied field E. For simple materials a linear relationship is usually assumed, e.g., D = \epsilon E, where \epsilon is the dielectric constant of the medium. Also even here in this linear relationship, \epsilon need not be a scalar (a number). It could be a tensor (a 3x3 matrix), in which case D and E would not have the same direction. --John Thanks for explaining that, John. I am unfamiliar with the conventions of LaTex, obviously (I get my information from books that are generally older than I am, and I'm not young). I don't have any problem with Gauss' law being used in a non-static context. It applies, regardless. That's as far as I go in agreeing with Art, though, since I can't understand the rest of his theory, at all (but might if I could turn off the left side of my brain - maybe). 73, Tom Donaly, KA6RUH- Hide quoted text - - Show quoted text - Tom I was rereading this thread as to why people have a hard time in understanding Gauss's law with respect to conservative fields and a transition to a non conservative field where with the addition of time one can consider what is outside the enclosed surface. Since you pursued the mathematical side of the subject to a minor conclusion ( you stated you didn't understand what I was proposing) with John E Davis of M.I.T. I wish to share with you some notes on the Internet by David J Raymond called "a radically modern aproach" which to me is the best I have seen on Radiation in it's entirety. Obviously there is a lot written that as hams it is not essential reading for hams but what it does do is explain in a very clear way the mechanics of radiation with specific applications with respect to the transition from conservative fields ala Gaussian law of statics to non conservative fields where at the cessation of time one can reconcile what is outside the enclosed surface with that which is inside the surface where what is inside the enclosure is in equilibrium and the enclosing surface is frictionless. As can obviously seen a Yagi inside the enclosed border cannot be considered since at the cessation of time interaction between elements is still taking place after the cessation of time. The notes are so well written that one not conversant with upper math can still follow the implications of the discussion at hand and thus can be considered as recommended reading for all hams interested in antennas as a subject. It also gives a very clear mathematical progression from Gaussian law to the subject of non conservative fields can be formed with the activation of curl during a moment in time. It is this progression that leads designers to design around cluster arrays that are in equilibrium regardless of orientation ie without continuing coupling effects after the cessation of time and is very well chronicalled in the above stated notes. Best regards Art- Hide quoted text - - Show quoted text - Tom, I thought I would add the following as a former mechanical engineer. I do believe that electrical students are taught that displacement current is some sort of electrical current when it is no such thing. If students were taught what they read as displacement current is really the displacement of flux under time varying conditions there would not be a barrier inferred between statics and electromagnetics. If you review what is termed as displacement current in text books and view again it in terms of flux movement during a space of time all that I am espousing will become so much clearer and understandable. Ofcourse ,those who passed exams by memory alone instead of knoweledge of first principles will never be able to understand the underlying logic to which I am referring Regards Art |
Gaussian statics law
On 9 Mar, 07:49, Gene Fuller wrote:
art wrote: But Jimmie my friend, now you have an understanding of Gaussian law what is preventing you adding the metric of time or a length of time to the statics law? Art, Adding the "metric of time" is exactly what J.C. Maxwell did, in 1865. The detailed hard work surrounding Maxwell's Equations, as we know them today, was probably more attributable to Oliver Heaviside. However, Maxwell gets the credit for adding the time contribution. 73, Gene W4SZ Yes, but he never made it in terms of reference to antennas. By using the conservative field transition to a non conservative field as a follow up example the equation now has more meaning than just mathematics in that it provides a datum for maximum efficiency. I don't believe anybody evoked Gaussian law to express a situation for maximum efficiency of radiation by specifying an array of resonant radiators which also was never included in Maxwells laws. Science is improved by what is seen to many as minor steps that apparently everybody was aware of but did not know how to take advantage of that knoweledge to provide a fresh data base for the state of the art. The World was aware of adding the time contribution but no one, no college, no scientist, no author, just nobody provided a kernel of knoweledge regarding equilibrium in connection to efficient electromagnetic radiation. Knoweledge of a relationship is one thing , puting that knoweledge to use is required for the advancement otherwise it plays dead for centuries. In life everybody claims that an invention is nothing but only one gets off the couch. When the application is published you and others have the right to petition the PTO showing prior publication or prior knoweledge with respect to the state of the art. This ofcourse requires more than just words such as spouted off from this newsgroup .You really have to walk the walk and if you don't understand the underpinnings of what I term a Gaussian antenna or challege it as a sample of nonsense then it is you that must provide the facts that make it so and this thread shows your inadequacy to do so. Only one person came forward to acknoweledged the presence of conclusive mathematical support supplied by John Davis and where the rest of this long thread are in denial, occupied by empty words of denial without proof. Seems like most threads are reaching the hundred mark on this group because of collective confusion of what is really tought at teaching institutions and the effects of time that make these teachings all different. Art |
Gaussian statics law
On 19 Apr 2007 09:56:45 -0700, art wrote:
Only one person came forward to acknoweledged the presence of conclusive mathematical support supplied by John Davis Hi Art, He confirmed it was Maxwell's (Heavisides actually) equations. I provided the actual quotes. If you wish, you can consult the same reference we BOTH used: "The Feynman Lectures on Physics," or I can rummage up that material again. 73's Richard Clark, KB7QHC |
Gaussian statics law
art wrote:
On 9 Mar, 07:49, Gene Fuller wrote: art wrote: But Jimmie my friend, now you have an understanding of Gaussian law what is preventing you adding the metric of time or a length of time to the statics law? Art, Adding the "metric of time" is exactly what J.C. Maxwell did, in 1865. The detailed hard work surrounding Maxwell's Equations, as we know them today, was probably more attributable to Oliver Heaviside. However, Maxwell gets the credit for adding the time contribution. 73, Gene W4SZ Yes, but he never made it in terms of reference to antennas. By using the conservative field transition to a non conservative field as a follow up example the equation now has more meaning than just mathematics in that it provides a datum for maximum efficiency. I don't believe anybody evoked Gaussian law to express a situation for maximum efficiency of radiation by specifying an array of resonant radiators which also was never included in Maxwells laws. Science is improved by what is seen to many as minor steps that apparently everybody was aware of but did not know how to take advantage of that knoweledge to provide a fresh data base for the state of the art. The World was aware of adding the time contribution but no one, no college, no scientist, no author, just nobody provided a kernel of knoweledge regarding equilibrium in connection to efficient electromagnetic radiation. Knoweledge of a relationship is one thing , puting that knoweledge to use is required for the advancement otherwise it plays dead for centuries. In life everybody claims that an invention is nothing but only one gets off the couch. When the application is published you and others have the right to petition the PTO showing prior publication or prior knoweledge with respect to the state of the art. This ofcourse requires more than just words such as spouted off from this newsgroup .You really have to walk the walk and if you don't understand the underpinnings of what I term a Gaussian antenna or challege it as a sample of nonsense then it is you that must provide the facts that make it so and this thread shows your inadequacy to do so. Only one person came forward to acknoweledged the presence of conclusive mathematical support supplied by John Davis and where the rest of this long thread are in denial, occupied by empty words of denial without proof. Seems like most threads are reaching the hundred mark on this group because of collective confusion of what is really tought at teaching institutions and the effects of time that make these teachings all different. Art Art, All I can say is that Dr. Davis is a lot smarter than the rest of us. He quickly recognized pure BS and bailed out from this discussion in a hurry. 73, Gene W4SZ |
Gaussian statics law
On 19 Apr, 11:22, Gene Fuller wrote:
art wrote: On 9 Mar, 07:49, Gene Fuller wrote: art wrote: But Jimmie my friend, now you have an understanding of Gaussian law what is preventing you adding the metric of time or a length of time to the statics law? Art, Adding the "metric of time" is exactly what J.C. Maxwell did, in 1865. The detailed hard work surrounding Maxwell's Equations, as we know them today, was probably more attributable to Oliver Heaviside. However, Maxwell gets the credit for adding the time contribution. 73, Gene W4SZ Yes, but he never made it in terms of reference to antennas. By using the conservative field transition to a non conservative field as a follow up example the equation now has more meaning than just mathematics in that it provides a datum for maximum efficiency. I don't believe anybody evoked Gaussian law to express a situation for maximum efficiency of radiation by specifying an array of resonant radiators which also was never included in Maxwells laws. Science is improved by what is seen to many as minor steps that apparently everybody was aware of but did not know how to take advantage of that knoweledge to provide a fresh data base for the state of the art. The World was aware of adding the time contribution but no one, no college, no scientist, no author, just nobody provided a kernel of knoweledge regarding equilibrium in connection to efficient electromagnetic radiation. Knoweledge of a relationship is one thing , puting that knoweledge to use is required for the advancement otherwise it plays dead for centuries. In life everybody claims that an invention is nothing but only one gets off the couch. When the application is published you and others have the right to petition the PTO showing prior publication or prior knoweledge with respect to the state of the art. This ofcourse requires more than just words such as spouted off from this newsgroup .You really have to walk the walk and if you don't understand the underpinnings of what I term a Gaussian antenna or challege it as a sample of nonsense then it is you that must provide the facts that make it so and this thread shows your inadequacy to do so. Only one person came forward to acknoweledged the presence of conclusive mathematical support supplied by John Davis and where the rest of this long thread are in denial, occupied by empty words of denial without proof. Seems like most threads are reaching the hundred mark on this group because of collective confusion of what is really tought at teaching institutions and the effects of time that make these teachings all different. Art Art, All I can say is that Dr. Davis is a lot smarter than the rest of us. He quickly recognized pure BS and bailed out from this discussion in a hurry. 73, Gene W4SZ- Hide quoted text - - Show quoted text - Well Gene you have admitted in the past to having an extensive background in physics, three educational degrees no less, are you still in denial with respect to the authenticity of the mathematics provided by Dr Davis? You never have enunciated a change from your prior comments regarding that subject. Also you have pointed out that all is known by you yet you keep stating that the Gaussian connection with respect to static fields have no connection academically with radiation but never with any proof. You and many of the other naysayers can point to an example of radiation that stems from Gaussian law. Many have even stated that there is no connection between Gaussian law of statics and radiation even in the face of irrifutable mathematics evidence provided. On the other side of the coin people state it WAS already known in total opposition to other posts that they have made. Ofcourse every body knew it they all read it somewhere where the subject was discussed but memories appear to be to hazy to recall exactly where it was discussed, used or totally trashed. Now we have moved to Feynman and his series of teachings, did he have a volume on the subject that was stolen at the outset? Gene you have been given mathematical backing to what I have stated did you get all those degrees without studying math? With all those degrees you have you should be able to understand not only the math supplied but also give a scientific analysis as to why conservative fields and non conservative fields can prove or disprove a continuum between statics and electromagnetism in a legible form that enphasises your background knoweledge that you claim. Only once in a while does a person get a real chance to show the value of his wisdom and knoweledge to his peers and it should not be seen as digging a hole for himself to hide in but sharing the benefits obtained by obtaining many degrees in physics.You don't need to refer to any books that discuss the subject you can teach it in your own right, I for one is all ears for evidence gained from your many years used to attain your honors that you talk about Art |
Gaussian statics law
On 19 Apr, 10:59, Richard Clark wrote:
On 19 Apr 2007 09:56:45 -0700, art wrote: Only one person came forward to acknoweledged the presence of conclusive mathematical support supplied by John Davis Hi Art, He confirmed it was Maxwell's (Heavisides actually) equations. I provided the actual quotes. If you wish, you can consult the same reference we BOTH used: "The Feynman Lectures on Physics," or I can rummage up that material again. 73's Richard Clark, KB7QHC It was only AFTER the intervention did you aknoweledged the undeniable truth of what Dr Davis presented. Before then the debate was about the legitamacy of adding time to both sides to the Gaussian law on statics. You posted often in that debate as did all the other experts all in total denial of the veracity of what I stated. True many of your posts are clounded with flowery language to emphasis your position but never did a specific point make it thru to any sort of objective. At any time you or anybody could have turned around in your thinking and point your spear in the ground alongside me but none did. Even after the intervention of Dr Davis only one person followed thru until personal satisfaction was obtained regarding the mathematics. I seem to remember an obscure posting that you made towards Dr Davis that seemed to have undertones of disagreement but ithe prose was difficult to understand so there is no personal credit you can steal for your self, you had posted so many times prior to that time in dissent. In years to come this thread will be read time and time again as evidence of the multi pseudo experts who lived on this newsgroup that argued without any grounds whatso ever about science and Gaussian antennas and I will cherish that time as the so called experts are finally exposed for what they are to the amateur radio fraternity. Ofcourse you could re write all of your posts such that true scientific data could penetrate the maze place in the way to prove your position one way or another or even point to the chapter that you were first to disclose to the world the veracity of what I had to say but then you can't because it doesn't exist, many have spoken of this proof but none have been able to deliver and neither can you. Richard you are a fraud. |
Gaussian statics law
art wrote:
On 19 Apr, 10:59, Richard Clark wrote: On 19 Apr 2007 09:56:45 -0700, art wrote: Only one person came forward to acknoweledged the presence of conclusive mathematical support supplied by John Davis Hi Art, He confirmed it was Maxwell's (Heavisides actually) equations. I provided the actual quotes. If you wish, you can consult the same reference we BOTH used: "The Feynman Lectures on Physics," or I can rummage up that material again. 73's Richard Clark, KB7QHC It was only AFTER the intervention did you aknoweledged the undeniable truth of what Dr Davis presented. Before then the debate was about the legitamacy of adding time to both sides to the Gaussian law on statics. You posted often in that debate as did all the other experts all in total denial of the veracity of what I stated. True many of your posts are clounded with flowery language to emphasis your position but never did a specific point make it thru to any sort of objective. At any time you or anybody could have turned around in your thinking and point your spear in the ground alongside me but none did. Even after the intervention of Dr Davis only one person followed thru until personal satisfaction was obtained regarding the mathematics. I seem to remember an obscure posting that you made towards Dr Davis that seemed to have undertones of disagreement but ithe prose was difficult to understand so there is no personal credit you can steal for your self, you had posted so many times prior to that time in dissent. In years to come this thread will be read time and time again as evidence of the multi pseudo experts who lived on this newsgroup that argued without any grounds whatso ever about science and Gaussian antennas and I will cherish that time as the so called experts are finally exposed for what they are to the amateur radio fraternity. Ofcourse you could re write all of your posts such that true scientific data could penetrate the maze place in the way to prove your position one way or another or even point to the chapter that you were first to disclose to the world the veracity of what I had to say but then you can't because it doesn't exist, many have spoken of this proof but none have been able to deliver and neither can you. Richard you are a fraud. This is just SO absurd. I no longer know who needs to just get a life and who needs a significant change in medication. I've seen this behavior in other groups and, for a while, it is mildly entertaining. Now it is annoying. Antennas, remember? |
Gaussian statics law
On 19 Apr 2007 12:48:58 -0700, art wrote:
It was only AFTER the intervention did you aknoweledged the undeniable truth of what Dr Davis presented. Hi Art, Well, in fact it was Dr. Davis (who came into the discussion rather late) who had to agree in the end with those who presented the simple connection between Maxwell (actually Heaviside) with his time variant magnetic fields and Gauss with his time invariant magnetic fields. Every antenna modeler on the market employs the time variant magnetic fields' math described by Maxwell (actually Heaviside). Maxwell is about dynamics, which means time variant; and Gauss is about statics, which means time invariant (or constant, never changing). If you inject a "cessation of time" you are already in the dynamics side of magnetics = Maxwell. Are you declining the invitation to review Feynman? He is pretty accessible, not much math - except for what really counts. 73's Richard Clark, KB7QHC |
Gaussian statics law
On 19 Apr, 15:21, Richard Clark wrote:
On 19 Apr 2007 12:48:58 -0700, art wrote: It was only AFTER the intervention did you aknoweledged the undeniable truth of what Dr Davis presented. Hi Art, Well, in fact it was Dr. Davis (who came into the discussion rather late) who had to agree in the end with those who presented the simple connection between Maxwell (actually Heaviside) with his time variant magnetic fields and Gauss with his time invariant magnetic fields. Every antenna modeler on the market employs the time variant magnetic fields' math described by Maxwell (actually Heaviside). Maxwell is about dynamics, which means time variant; and Gauss is about statics, which means time invariant (or constant, never changing). If you inject a "cessation of time" you are already in the dynamics side of magnetics = Maxwell. Are you declining the invitation to review Feynman? He is pretty accessible, not much math - except for what really counts. 73's Richard Clark, KB7QHC You are lying again. You never convinced the Doctor in any sort of corrective way, only one person stated agreement with his summation of mathematics No body in this group has brought forward prior knowledge or agreement between conservative and not conservative fields by use of the Gaussian method. Oh how quickly people forget their anger of the idea of connecting static with non static situations. My goodness how soon you forget the slander projected because of this supposedly silly idea. As far as going with you to review Feynman forget it. If you can find proof of anything relevent fine it would give a good starting point as to why antenna engineers declined to pursue the discovery. Frankly I am getting close to the position that most do not understand antennas, what I am proposing and just want to prove their masculinity by way of slander, this ofcourse does not apply to you. I believe this thread will make a wonderfull story in the future as to how rank amateurs tried to stop science from advancing. The material is here both funny and sad which will come into focus when the patent is awarded and interest picks up. True I have provoked people to verbalise their thoughts but for good reason I want to show all what you really are in the near future.Sooner or later this all will be discussed in all educational institutions and the next generation can move forward without hindrence from the agrivation of a bunch of old men. |
Gaussian statics law
On 19 Apr 2007 16:26:33 -0700, art wrote:
As far as going with you to review Feynman forget it. If you can find proof of anything relevent fine it would give a good starting point as to why antenna engineers declined to pursue the discovery. Hi Art, Feynman merely confirmed the math of 70 years of antenna design before him. Nothing has altered since 1963, dynamic magnetic fields are still defined by Maxwell's (Heaviside's) equations, and static magnetic fields are still defined by Gauss' equations. Any discussion of the "cessation of time" immediately casts all work into Maxwell's (Heaviside's) math. Nothing had to be invented because Maxwell (Heaviside) had done the basic math long before antennas were ever discovered. In fact, about 190 years ago Augustin-Jean Fresnel beat them all to the punch without a flicker of electricity or magnetism ever entering the picture. Antenna engineers have been using Fresnel math too. Amateur radio operators respond to it every time they complain of picket-fencing on 2M. That math is contained in EVERY antenna modeler that offers radiation characteristics. 73's Richard Clark, KB7QHC |
Gaussian statics law
On 19 Apr, 19:41, Richard Clark wrote:
On 19 Apr 2007 16:26:33 -0700, art wrote: As far as going with you to review Feynman forget it. If you can find proof of anything relevent fine it would give a good starting point as to why antenna engineers declined to pursue the discovery. Hi Art, Feynman merely confirmed the math of 70 years of antenna design before him. Nothing has altered since 1963, dynamic magnetic fields are still defined by Maxwell's (Heaviside's) equations, and static magnetic fields are still defined by Gauss' equations. Any discussion of the "cessation of time" immediately casts all work into Maxwell's (Heaviside's) math. Nothing had to be invented because Maxwell (Heaviside) had done the basic math long before antennas were ever discovered. In fact, about 190 years ago Augustin-Jean Fresnel beat them all to the punch without a flicker of electricity or magnetism ever entering the picture. Antenna engineers have been using Fresnel math too. Amateur radio operators respond to it every time they complain of picket-fencing on 2M. That math is contained in EVERY antenna modeler that offers radiation characteristics. 73's Richard Clark, KB7QHC |
Gaussian statics law
On 19 Apr, 19:41, Richard Clark wrote:
On 19 Apr 2007 16:26:33 -0700, art wrote: As far as going with you to review Feynman forget it. If you can find proof of anything relevent fine it would give a good starting point as to why antenna engineers declined to pursue the discovery. Hi Art, Feynman merely confirmed the math of 70 years of antenna design before him. Nothing has altered since 1963, dynamic magnetic fields are still defined by Maxwell's (Heaviside's) equations, and static magnetic fields are still defined by Gauss' equations. Any discussion of the "cessation of time" immediately casts all work into Maxwell's (Heaviside's) math. Nothing had to be invented because Maxwell (Heaviside) had done the basic math long before antennas were ever discovered. In fact, about 190 years ago Augustin-Jean Fresnel beat them all to the punch without a flicker of electricity or magnetism ever entering the picture. Antenna engineers have been using Fresnel math too. Amateur radio operators respond to it every time they complain of picket-fencing on 2M. That math is contained in EVERY antenna modeler that offers radiation characteristics. 73's Richard Clark, KB7QHC It was Gauss who started a progression from statics to electromagnetics by defining a clustered array as being in equilibrium within a closed surface in his law of statics Nobody used this law in the design of a electromagnetic array. There were mathematical equations in existance that linked statics and electromagnetic functions in mathematical terms but there was never a clue as to how to demonstrate it. Only Gauss gave an "at rest" example of such an array with his law of statics but even he did not continue with his line of thought with respect to static particles as being at rest on a radiating array where the condition of equilibrium could be stated. If Gauss had continued with his line of thought by being aware of radiation in terms of radio I am quite sure he would have continued the exercise with the addition of time. However it is my understanding that at that time he was residing in Italy and was more interested in other things. I do not recall Gauss, Maxwell and other masters making a point of using such a cluster as one of maximum efficiency with respect to radiation. Nor do I recall any mention where scientists have used such an example in print and either lauding or decrying its properties in the light that the ratio of elements vs boom length does not apply and where a Gaussian array was an example of a non scalar array. I am sure that it is possible after the event that many clever people played with such arrays and like you decided it wasn't worth writing about and so forgot about it. There are also people who never linked the subject of statics with the subject of antennas as mentioned on this newsgroup and I don't remember seeing such an array in Krauss and Jasik or even the ARRL antenna books which to me is a real puzzle since you apparently have known about the hints that Gauss supplied for maximum efficiency radiating arrays for many years. So I think the time has come since I have described the antenna in detail that somebody should come forward and share with all exactly where this application to antennas was reviewed in print or the IEEE or equivalent so that we can all benefit from this peer review. |
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