"Electromagnetic waves" do NOT EXIST!!!

You claim to be competant at electromagnetism. I don't believe you.

It took you more time to write your last post than it did for me to solve those questions.

Yes, you and I have met before. And once you made it obvious you don't know any mainstream physics or maths and you have no intention of learning any, despite making wild claims about such things, I stop sugar coating my responses. It's generally easy to tell the difference between crank newcomers and sane new comers. Within seeing about 3 of CptBork's posts, I could tell he was sane and knowledgable. Hence why I didn't jump down his throat when he said "I've studied string theory". I see from his posts he's knowledgable in the right things for that to be entirely possible and since he doesn't seem to stretch the truth, I believe him.

You've made claims about the standard model, electromagnetism and a variety of simpler mathematical and physical concepts and none of those times have you shown you're competant at them. Just now on PhysOrg you claimed that solutions to the wave equation are spanned by a 2 dimensional basis because it's second order.

And yet \(y(x,t) = \sum_{n=1}^{\infty} \sin\left( \frac{n \pi x}{L} \right) \left( A_{n}\sin\left( \frac{n \pi c t}{L} \right) + B_{n}\cos\left( \frac{n \pi c t}{L} \right)\) is a solution to the wave equation over the infinite dimensional orthogonal basis \(\sin(k n x)\) and \(\cos(k n x)\). As I said to you in either this thread or the one on PhysOrg, degree n equations need n independent boundary conditions to uniquely specify a solution. A general solution over functions will be spanned by infinitely many basis vectors.

If you don't want people to instantly think you're fulll of BS, show some level of competancy at the topics you discuss. Then I'll be cordial, just like I'm polite to people like Ben and QuarkHead. Until you earn my respect, I don't give it. Infact, you're earnt my scorn by your nonsense claims.

 

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Ok, then I'm wrong in that statement but stilll my main claim remains: "There is no possible source of electric and magnetic fields for the "electromagnetics waves" solutions derived from the Maxwell's equations."

I know, even with my poor knowlledge in electromagnetism that this is valid for the more known "electromagnetic plane waves" solutions of Maxwell's equations.
I just believe now that it will be valid for all the other possible solutions and this is the challenge now, to demonstrate if this is right or wrong, true or false...

 

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Ok, here's what you do, and I'm not going to write out the full details because these equations are fairly long. You start with Maxwell's equations with sources, i.e. \(\vec{\nabla}\cdot\vec{E}=\rho/\eps_0\), etc. There are a few ways to approach solving this problem, but the most popular one is to use the method of potentials, typically in the Lorenz Gauge (see link). You set \(\vec{B}=\vec{\nabla}\times\vec{A}\) and \(\vec{E}=-\vec{\nabla}V-\frac{\partial\vec{A}}{\partial t}\), plug in the Lorenz gauge condition and then you get a classical wave equation with sources for the potentials \(V\) and \(A\).

You then solve these equations with time-dependent retarded time Green's functions plus (if I recall correctly) an undetermined homogeneous solution which is fixed by the boundary conditions, which I believe we can neglect due to the \(\vec{E}\) and \(\vec{B}\) fields vanishing at infinity. Usually it's easiest to simplify the potentials for your specific situation, then to calculate \(\vec{E}\) and \(\vec{B}\) afterwards. However, you can go straight to the finish and get a general solution called Jefimenko's equations (see link).

You can see directly from those equations (make sure you read the bit about retarded times), that any changes in your sources and currents produce ripples in the electric and magnetic fields which travel at the speed of light. Then if you apply the equations to systems like a loop of oscillating current, some of the energy in the fields carries off to infinity and is interpreted as radiation. Mathematically, you can take such solutions and write them in terms of the sums of plane waves, spherical waves, cylindrical waves etc., and then you can physically do all sorts of filtering and shaping on those waves to get various other kinds of shapes in real lab conditions. I'm not really interested in going into details with this, but the point is it's clear from Jefimenko's general solution to Maxwell's equations with sources, that it's physically viable and indeed inevitable that EM waves are produced by any non-static charges and currents.

 

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Maxwell's equations imply that the fields obey the wave equation. This is clear by just plugging them into one another.

In any field system where communication is not instantaneous, it's a physical inevitability that waves occur because they represent the forefront of changes in the field propogating. Hence why Newtonian gravity doesn't have gravity waves but relativity does.

Hence movements in the sources of electric fields, ie charges, will cause a propogation of electric field variations. Changing electric fields generate changing magnetic fields and vice versa. This propogation of mutually generating perturbations of the electric and magnetic fields is called 'light'.

Martillo, all of this, and a great deal more, can be justified via such methods as CptBork outlines. Undoubtedly you are not familiar with the methods Cpt talks about, you don't even basic principles of differential equations, never mind the specifics of electromagnetism.

Each time you've made a basic claim about electromagnetism or differential equations you turn out to be wrong. And yet you never stop to think "Maybe I should stop making claims about topics I don't know about?". Yet again, you ignored my challenge. Do you not have 3 minutes to spare to prove you know the simplest thing about vector calculus?

I imagine you have plenty of time, you just don't spend it learning.

 

I wasn't wrong!
A linear differential equation of nth order can have n linearly independent solutions and the general solution can be expressed as a linear combination of them.
See at wikipedia: http://en.wikipedia.org/wiki/Linear_differential_equation
or for example: http://www.efunda.com/math/ode/linearode_terms.cfm

So what now???

 

Alphanumeric didn't solve the claim, just posted some srguments about fields' propagation so you did nothing.
CptBork at least presented a way to find possible sources for the fields. At a first look my theory disagree with the concept of retarded potentials since it is based in the classical approach and the fields are instantaneous independent of the distance but I will analize if his solutions don't have some fail (if I could find it...). One first problem I see is that now we are not talking about Maxwell's equations anymore but about Jefimenko's equations...

 

The unique problem is that the mentioned equations involves only the variable "Y" what implies in our case one coordinate.
In a three-dimensional space we must consider three coordinates to solve our general problem. I'm thinking now that this could be accomplished easily if the general solution could be "decoupled" in the coordinates getting one linear differential equation for each coordinate alone, separatedly.
This will imply we would have in total a sixth degree of freedom in the solutions...
I'm not sure but I think that here I'm getting something interesting...

 

For those who don't read PhysOrg, I pointed him at Fourier series and how group and wave velocities can be different and this leads to infinitely many solutions to the wave equation of independent pure modes.

Despite Martillo claiming to be very familiar with Fourier series, he has now just suddenly realised there's more to his analysis (yes Martillo, it's spelt with a 'y') than just single velocity systems.

Because Cpt had already said plenty and I've mentioned sources to you before when I mentioned dF = d*J in terms of differential forms. Though I doubt you understood.

Never mind the fact that electromagnetism has been used for more than a century to accurately describe effective field theory in electromagnetic fields and is put into literally thousands of different bits of technology you have dotted around your home and (I hope) work.

Given your lack of knowledge of vector calculus, I doubt you'll manage that, since what you're talking about involves precisely the methods you'd need to use to solve the question I linked you to a few posts ago. If you couldn't immediately see it's an easy question, you don't have the knowledge of vector calculus to do what you talk about doing.

Feel free to prove me wrong and answer the question I asked you.

What about electrodynamics, the including of special relativity to the classical field theory model? There's plenty of complication in that.

Laughed at?

 

It's not a problem at all. Jefimenko's equations can be derived from Maxwell's equations by following the steps I outlined. Indeed, Maxwell's equations can be derived from Jefimenko's equations, as long as you include the assumption of charge conservation, \(\frac{\partial \rho}{\partial t}+\vec{\nabla}\cdot \vec{J}=0\). Just a note for you though, Jefimenko's equations are very rarely the actual method used to solve these problems- usually you derive the retarded potentials and simplify them first before calculating the fields, based on the specific physical system. Jefimenko's equations are what you get if you carry the calculation through all the way without simplifying.

I was working out a simplified example for you of how a charging/discharging capacitor can be used to produce a nice approximate wavefront for you, and trying to assume enough simplifying factors to make it a 1-dimensional calculation, but I came upon a rather difficult Fourier transform which I believe can only be evaluated by truncation approximations, which defeats the whole purpose. The point is that if you whip out a text like Jackson's "Electrodynamics" or something even more advanced, you can read about the detailed (and very messy) calculations which give rise to various kinds of wavefronts. The problem is you need to know a lot of math to understand this stuff, concepts like generating functions etc. Seeing your misunderstanding above comparing ordinary differential equations to partial differential equations, I think you're not yet at this level, though you can learn it if you dedicate yourself to doing so.

 

You can take an nth order differential equation in 1 variable and break it down into n coupled 1st order equations, or vice versa, but you can't do that with a partial differential equation. The methods used are very different, you should seriously learn this stuff in detail because it's really good to know. Then you don't have to take people's words for granted on many of these issues.

 

CptBork:

Don't forget that inthe plane electromagnetic waves the electric field is parallel to the plane and this cannot be achieved by a capacitor.

You know, I never heard about "Jefimenko" before even looking a lot about "electromagnetic waves". I always heard that they were predicted by Maxwell's equations and not Jefimenko's ones. I agree that to agree with Relativity Theory which seem to state that the electric and magnetic fields travel at velocity C Jefimenko should be considered but it isn't...
Now as you say they seem quite equivalent and may be if the "electromagnetic waves exist for one of them they will also exist for the other. So I will stay with Maxwell's equations and prediction and refute the "electromagnetic waves" existence. I will do it in a next post.

 

My plan was to calculate a wave propagating transverse to the distance between the capacitors, i.e. being radiated out the sides, not between the plates. I could see from the nature of the integrals I got that indeed I get a very interesting wave shape propagating at c, but the integral is too messy and there are lots of simplifications and assumptions involved in treating it as a 1-dimensional wave which aren't worthwhile considering the result is still a mess. There's limits to what you can do by solving Maxwell's equations in vacuum. If you only use the vacuum equations, you have to restrict them to applying only in regions with no charges and currents, meaning any charges and currents can only have an effect on the boundary values which you use to specify your solutions.

What I'm saying is that Maxwell's and Jefimenko's equations are two forms of the exact same thing. You can derive Jefimenko's equations as the general solutions to Maxwell's equations, and you can derive Maxwell's equations from the Jefimenko equations. Jefimenko is a better place to start from when possible, because that's how you can directly calculate the fields from your charges and currents. Maxwell's equations themselves only describe the equations governing these fields, not the actual solutions. Jefimenko's equations are the actual solutions themselves.

 

Well, here is the final demonstration of my claim:

First I will consider that, as I wrote, there is no possible source of electric and magnetic fields for the plane "electromagnetics waves" solutions derived from the Maxwell's equations. It is obvious for the plane waves.
Second I will consider that in the three dimensional Space the plane waves can travel in any direction and that the general solution for the waves equation can be expressed as a linear combination (superposition) of a finite or infinite number of plane waves.
Third I will state that if for any plane wave there is no possible source for both the electric and magnetic field to generate it then any wave obtained by a linear combination of plane always also don't have a possible source of electric and magnetic fileds that could generate it.
Then it can be concluded my claim: "There is no possible source of electric and magnetic fields for the "electromagnetics waves" solutions derived from the Maxwell's equations."
Finally it can be then stated that the "electromagnetic waves" derived from Maxwell's equations cannot exist.

Done.

 

Oh and a word of caution: the fields in Jefimenko's equations are not instantaneous. If you look carefully, the whole point of using the retarded time \(t_r\) is to show that any changes in charges and currents in one place leads to changes propagating at c in the fields located elsewhere. As for where \(t_r\) comes from, it's derived directly from solving Maxwell's equations, no physical assumptions required. There is an accompanying advanced time solution as well, but it's ruled out because changes in the future don't cause changes in the past.

 

You don't need to be able to generate every plane wave in order to generate a superposition of such plane waves. Think of water waves like you originally mentioned- you can generate a finite bump spreading out as ripple waves, that's easy to do. Yet the result can be decomposed into an infinite superposition of unphysical 1-dimensional infinite plane waves, none of which are possible for us to generate on their own.

 

Funny, you call my wordy post arm waving and don't accept what it says but when you make a claim a wordy demonstration of your claim is enough to satisfy yourself. Nice hypocrisy.

You keep saying things like "...which doesn't exist". Can you prove that mathematically? There's plenty of mathematics to do with the proof of the (non)existence of particular things, like solutions to given integrals or PDEs in terms of elementary functions. That's how we know there's no nice way of expressing the Erf function. Or there's no general expression for the roots of 10th order polynomials.

You claim to demolish a HUGE area of physics but you cannot demonstrate your claim in a precise way. You just waffle and assume your assumptions about the nature of differential equations are right. Already that's been shown to be wrong. You don't know much about ODEs and you assume the same results for ODEs carry over to PDEs. They don't in general. Hence your mistake about solutions to differential equations. The wave equation and Maxwell's equations are PDEs. They don't trivially factorise into a series of non-coupled ODEs. If they did, the life of a physicist would be much easier.

 

Interesting that someone can construct a theory that denies the existence of things they are using at the time to construct their theory.

I guess there must be nothing like it...

 

Vkothii:

I'm not denying, the new theory states that actually signal transmission is carried by photons: http://www.geocities.com/anewlightinphysics/sections/Section7-3_Communicating_with_photons.htm

 

And where does mainstream physics actually deny that? Nowhere. Mainstream physics says that light is a huge collection of photons. Maxwell's equations are an effective field theory to QED. It 'smooths over the quanta'. Just as we know gravity is a quantised force and GR is an approximation, when you deal with distances long enough to 'smooth over the quanta'.

Take fluid mechanics. The Navier-Stokes equation assumes water or air or any fluid is a continuous medium, which we know is false. So why do people designing cars, boats and planes use it? Because it's a valid approximation over large distances. Once you consider scales which are only a few orders of magnitude over inter-molecular scales so things like Van der Valls forces are important, you cannot use the effective theory.

Someone building a TV antenna doesn't need to know about photons because the antenna needs only large distance considerations. Someone building a quantum computer needs to know about photons because the light pulses involved as over such small distances.

You don't even understand this concept in physics, never mind the specifics of it in terms of approximations QED with electromagnetism. But what would I know, it's not like I use super gravity effective field theory to give approximate description of string vacua in M theory.

Oh wait. I DO.

 

So, you are believing in such things.
My Blatt's book in Physics not even mention those kind of things...

Anyway, that has nothing to do with the subject of this thread.