kram1032


« Reply #15 on: November 28, 2013, 09:11:28 PM » 

The simplest description of the Maxwell Equation actually is possible via geometric algebra: http://en.wikipedia.org/wiki/Maxwell_equations#Alternative_formulationsOnly differential forms and geometric algebra allow you to formulate them in arbitrary space times and coordinate free form. And only in geometric algebra can you summarize the entirety of Maxwell equations into a single line with mere four symbols. (the top row) This fact actually was what got me more interested in that topic in the first place.



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jehovajah


« Reply #16 on: December 04, 2013, 12:52:24 PM » 

Thanks Kram1032.
Geometric algebra is my fundamental object of study, as is so called Electromagnetism.
The Maxwell equations are a bit controversial in my opinion. They are definitely worth study but not definitely taught correctly in most academic settings.
The topic is now being revisited by scientists who debate the two theories of Relativity,principally creations of Einstein.
The mathematical formulation tells you some of this debate exists, but not how deep a division exists in the consensus!



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jehovajah


« Reply #17 on: December 04, 2013, 03:03:37 PM » 

The concept of light has moved on, and it has further to go The source and defining object of light is the sun


« Last Edit: December 04, 2013, 06:53:37 PM by jehovajah »

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kram1032


« Reply #18 on: December 04, 2013, 04:56:46 PM » 




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jehovajah


« Reply #19 on: December 05, 2013, 10:30:27 AM » 



« Last Edit: April 06, 2015, 01:53:05 AM by jehovajah »

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hermann
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« Reply #20 on: December 05, 2013, 03:50:28 PM » 

I once read, that James Clark Maxwell original wrote his equations with quaternions? But how this will look like, I dont know. Here is my personel collection of Maxwell Equations. http://www.wackerart.de/Physik/elektrodynamik.html



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hermann
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« Reply #21 on: December 05, 2013, 07:35:37 PM » 



« Last Edit: August 23, 2014, 05:10:26 AM by jehovajah »

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jehovajah


« Reply #22 on: December 06, 2013, 12:41:08 AM » 



« Last Edit: August 23, 2014, 05:18:49 AM by jehovajah »

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hermann
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« Reply #24 on: December 07, 2013, 09:45:56 AM » 

Hallo Jehovajah, you started this diskussion with the following statement. Arago's and Fresnel set up the mathematical basis for light. It turned out that electric and magnetic phenomenon obeyed the same rules. Normaly physicist and engineers take the Maxwell equations as starting point. Which is noramly seen as one of the pillars physics is bulid on. From Maxwells equations follows a wave equation. This gives a mathematical description of elektormagnetic waves. That this waves realy exists was proven by the experiments of Heinrich Herz. http://en.wikipedia.org/wiki/Heinrich_HertzToday we see light as a electromagnetic wave. With this basic view in mind I asked my self why you started with Fresnels formula? To formulate this question I wrote down what I could remember on Fresnels formular. I ended up with a question, that may give already some anwsers. Fresnels FormularWhen you have a glas of water and have a straw in it looks as if it has been broken. This kind of phenomena can be descriped by Frenels theorie. Basicly one can have electromagnetic waves in vacum and electromagnetic waves in matter. The transition between vacum and one kind of matter can be described by frenels formula. You get information about which part of a wave is reflected and which part of the wave moves into matter. The directions of the elektrommagnetic field and the magnetic fields, their relations and the relations of the angels. Light makes things visible to our eyes. Light is reflected by the things that surrund us. This reflection change the spectra of the incomming light. That light is detected by our eyes and is then converted (I think this is not covered by Fresnel) into electromagnetic pulses that are then operaten by our neural system. But isn't this more a philosophical view than a mathematical view? Hermann


« Last Edit: December 07, 2013, 11:28:18 AM by hermann »

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hermann
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« Reply #25 on: December 07, 2013, 11:58:00 AM » 

Hallo Jehovajah, I revisited my internet page on electrodynamics after I had read your blog http://www.wackerart.de/Physik/elektrodynamik.htmland discoverd that I had not inserted an integral formulation of Maxwells equations. Which I always wanted to do but never found the time to do. This formulation I like very much for the following reason:  An integration improves the behavior of a function.
 If one looks at micro space quanten mechanics and quanten electrodynamis are the key player. Differenital equations use infiniti small items.
 Surface and a volumes can be found in reality and may make things more understandable.
Hermann


« Last Edit: December 07, 2013, 01:19:57 PM by hermann »

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jehovajah


« Reply #26 on: December 08, 2013, 10:56:59 AM » 

Thanks Hermann.
As you know, I try to look at everything with fresh eyes. I was surprised to find that Arago had created a stir by showing that a versorium was magnetically coupled to a spinning metal disc! This was one thing that Maxwell hoped to be able to explain, and he says as much in his first chapter in his Electromagnetic theory.
I was also surprised to find that this experimental data occurred at about the same time as Oersted demonstrated a versorium or magnetic compass needle was deflected toward a conductor along which a Leyden jar or a voltaic cell was being " discharged".
Thus there was a chance for a different interpretation of what was actually bing observed, but things were moving so vast that researchers were scrabbling enthusiastically to make a name for themselves in this new area of knowledge. Consequently Sir William Golberts explanations were left behind in this mad scramble, and a new subject called eventually Electromagnetism shoved magnetic philosophy into its back pocket and walked away with the prize!
There still is a society of magnetic engineers to this day, but they are in the background, only being consulted when huge magnets are needed for projects like the Large Hadron Collider. Many of them arrive at the society via the electromagnetic theory route and wrongly believe they are working in a " dead" subject area.
Maxwells equations are about the electric" field" and the magnetic" flux field", but only a few specialists ever look at the magnetic flux field, assuming it is the same as the electric field, at least as far as the mathematics is concerned. This is not the case, and much work on this was simply abandoned after 1905 when everyone rushed to make a name in the new science increasingly based on Einstein Rutherford and Bohr's model of the atom, and the photon, deliberately based on the electron.
When I looked into Arago I found he was key to Fresnel being understood and accepted as a genuine innovator. Arago was at once able to connect Fresnel, Young and Huygens into a consistent wave theory that had a chance of overturning the Newtonisn corpuscular theory of light, heat and magnetism.
While this was an undulatory aether theory, it was the first to explain all the observations of light, heat and magnetism starting with Grimakdi. Arago, a corpuscularist until he found Fresnels's mathematical and geometrical formulation undeniable, immediately switched to the undulatory theory. He needed to show that light slowed down in denser media and he set in train a group of experimenters who were able to confirm this after his death.
Now you may wonder why I included magnetism in jAragos description. Among the papers in the Royal society I found many observations of those pursuing the reigning magnetic philosophy relating to the influence of light on the magnetic versorium or compass needle. In fact, one of the first uses Gilbert's Work was put to was to establish magnetometers to record the magnetic weather. Much data was and is collected in this regard, and Weber was among those of the philosophers of magnetism who refined the instrumentation and contributed much to the theory. His work was not ignored directly, it is too valuable for naval and marine navigation, but it was subsumed academically into the electromagnetic theory and marginalised.
Maxwells equations have been written and rewritten in many forms, but these equations do not always express Maxwells and Faradays empirical or experimental thinking. In particular, the fluid dynamic elements in Maxwells original set up are often ignored or recharacterized.
Both Faraday and Maxwell belong to the Pre Electron era, as did JJ Tompson. The equations relate to the transmission of strain through the aether caused by some unknown stressor, often induction by some unknown inductor. The theoretical model was a vortex, and Helmholtz and Kelvin worked very hard to establish the mathematics of these incredible natural phenomrena. Maxwell used their lastic properties only to model strin transmission. Unlike Kelvin, he did not see much hope of using their viscous properties to describe molecular and atomic interactions.
You mentioned Hamilons Quaternions. Maxwell was n extremely able athematicins. He at once saw the benefits of using Hamilton's Quaternions, and hiked them as a breakthrough in mathematical modelling of the aether. Unfortunately his colleagues and associates were not so bright! They could not make head nor tail of this new mathematics. Minkoeski famously could not be bothered to reformulate his theories in this new mathematical format. Leis Crtol, Alice in ondrtlanf's author, penned his books as a damning criticism of the new Hmiltonisn mathematics. Kelvin condemned the Quaternions as trickery. Instead he promoted the work of a young metric sn mathematician called Gibbs. This was because Gibbs was a great promoter of Klvins Kinetic theory and statistical thermodynamic.
The iPhoto of this was Maxwells equations were not understood. They were not understood for almost 20 or more years after publication. Maxwell bitterly regretted framing his equations in Quatemion form nd wrote as much. His earlier praise was rescinded. He attempted to rewrite his equations in terms of the Gibbsin vector mathematics, but had trouble getting the sign of E the electric field correct. Gibbs vector mathematics was flawed. Eventually Heaviside devised his own vector calculus and rewrote much of Maxwells equations in this form, emphasising 5 fundamental equations of the reputed 27 , of which 4 are commonly taught in electromagnetic theory. Heaviides telegraph equation is marginalised but absolutely fundamental to any one wanting to set up a power grid!
Steinmetz fundamentally rewrote Maxwells equations in quaternion form, but using a quaternion notion called a versor. This restored the mathematical symmetry and beauty of Maxwells original conception, but mystified everyday engineers. In part this was deliberat. Steinmetz needed to make a living, and his expertise was well rewarded. But mostly it was ue to the fact that most engineers are not mathematicians and certainly most do not comprehend algebra.
While Heaviside and Steinmetz simplified basic concepts covered by the equations so engineers could do their jobs safely, there is and was much that they could not convey to hose who are not mathmically gifted.
The introduction of Ampere's law by maxwell to cover the transmission through the aether inide and sround a capacitor of the electric strain and the Magnetic strain has been lauded as the mathematical breakthrough that discovered electromagnetic waves! I hope you will view that statement with some scepticism from now on.
Maxwell from the outset was formulating a strin wave equation for the aether. His 2 constants of petmittivity and permeability derive from strain equations for the transmission of undulations in fluids like water and air. The experimental measures of these constants in these kinds of medium multiplied together to give the known speed of light. As remrkble as this was, it was actually saying tht strin prop gets in the aether at a constant but unimaginably large velocity. It says nothing snout the maximum speed an object may be accelerated to or beyond!
Maxwell added the displacemrent current term to his equations to explain how a capacitor got charged hen no current could flow through the gap in the conductor! The idea simply means that a plate of conducting material takes time to build up what was and still is called charge. At this point we are asked to switch our thinking to either a model of electons or little circles ith + in them! We then are distracted from the empirical data of ht is happening in this scenario.
To understand how badly this has affected electromagnetic theory you must read Ivor Catts work.
In doing just that I have bern brought back to the work of Arago snd Fresnel, Grimaldi, Young and Newyon and Huygens. Faraday and Maxwell built their theoretical understanding on the works of these men as well as on the empirical data of their fellow researchers.



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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!



hermann
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« Reply #27 on: December 08, 2013, 02:42:04 PM » 

Hallo Jehovajah, thank you very for your long answer. But I miss one point in your overview, that is the work of Heinrich Hertz who proved the existens of elektomagnetic waves by experiment. Only this breackthrough opened the way to the success of Maxwells theorie? http://www.seefunknetz.de/hhertz1.htmHertz Heinrich: Gesammelte Werke, Band 1, 11 und 111, Leipzig, 1894. Hertz, Heinrich: 鈁er die Beziehungen zwischen Licht und Elektrizit酹, Bonn, 1900.


« Last Edit: December 08, 2013, 03:16:18 PM by hermann »

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jehovajah


« Reply #28 on: December 08, 2013, 08:50:43 PM » 

You are right ,Hermann. Hertz provided conclusive experimental evidence by mapping the standing undulations. However if he had not done his work, Lord was about to publish on the same topic. However it is a moot point, one that may be doubtful, if Hertz understood Maxwells theory. Certainly Lord only had a cursory grasp of it.
Hertz was among the one or two people in the whole of western Europe who had even heard of Maxwells theory, let alone read it.Hetz evidence was the more remarkable because he happened on the righ gap to see the transmitted spark.
In Maxwells theory were detailed Equipotential maps and a discussion of how to construct them. The work that Hertz did verified a theoretical equipotential diagram Maxwell had already drawn. In that light Hertz validated a detail of a theory and so in turn sparked an interest in a theory that was hardly known and barely understood.
Thanks for the article link. I had missed the detail that Faraday first proposed electromagnetic waves that propagated by electric / magnetic induction. This is actually the part of the theory that is in question! Faradays varying magnetic field supposedly produces an electric current in a wire? We now know it cannot produce " electric" current inside a wire. The varying energy ( magnetic ) produces a varying energy about the wire! It is now highly probable that this is a magnetic current that runs vorticularly around the wire.
While the electric terminology remains it is increasingly demonstrated that active surfaces are involved in energy transmission through the dielectric . The magnetic nature of the conductor has a bearing on how that energy propagates around the "wave guides" and with what efficiency.


« Last Edit: December 08, 2013, 10:15:32 PM by jehovajah »

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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!



jehovajah


« Reply #29 on: December 08, 2013, 09:53:44 PM » 

There is an emerging pattern which envelops the Electromgnetic spectrum. Light is propagated ith heat and magnetism . The higher the energy the greater the proportion of light o heat to magnetism.
Thus we ought to think of light as combined ith heat nd magnetism in such a way that the theories of light, heat or thermo dynamics and Electromagnetim are combined in a proportion.
At the moment, the electromagnetic spectrum is divorced from thermodynamics by a notion of " radiation" . This notion is unspecific, and in fact, experts when pushed are not able to explain the difference between heat and infra red radiation.
In fact it is relatively simple and most children see the connection immediately. It is the experts who stumble because thy have theoretical positions to mintsin.
Light is not divorced from matter. There is very litte visible light in the whole spectrum, so it is perhaps natural to think light travels divorced from matter. What is increasingly the case is that we find there is more matter than we can " see" because it does not carry visible light. But as soon as those Frequencies impact on that invisible matter, they reveal themselves by absorption or reflection or re radiation of those frequencies and through polarisation of light at those frequencies.
The wavelength of light is a concept of dubious merit, it was principally introduced to explain sinusoidal wave interference. However it is very unlikely that dinø ideal wave propagation is the norm. A trochoidal description of propagation exists and is more general. In fact the model for all,waves, water waves are generally best described by trochoids.
The significance of this is we do,not need a sinusoidal wave propagation model where in particular electric fields are said to generate magnetic fields. We only need rotating expanding idled of varying Frequency.


« Last Edit: December 08, 2013, 10:21:09 PM by jehovajah »

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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!



