# Maxwell's electromagnetic theory of light.

Discussion in 'Mathematics and Physics' started by copernicus1234, Apr 15, 2014.

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1. ### copernicus1234Member

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My question is: do equations 2 and 3 represent vector field EM transverse waves? Also, you didn't state anything about Einstein's relativity, as regards to Maxwell's equations. Einstein uses Maxwell's equations, and Lorentz's daily and earthly motions. We're just having such a fantastic time (t) with Maxwell and Lorentz earth's daily and yearly motions (ronsimpson in Astronomy). Also, did you know that Einstein stated the EM field is the ether, in 1910. So, back to the beginning, where your correction is based on,

E = Ey j = (Eo cos(kx - wt) j) j

that can be written as:

E = Ey = Eo cos(kx - wt) j.............1

since the EM wave equations are being used to represent an EM wave of light.

(Note: there is a slight modification requried in the above figure since the EM transverse wave is propagating in the z direction.)

The purposed of the expansion method is the derivation a transverse wave since Ey and Ez are being used in the elimination process of the expansion of Maxwell's equations. Now, if your equation

E = Ey j = (Eo cos(kx - wt) j) j..........2

can be written as

E = Ey = Eo cos(kx - wt) j ..................3

and also to form,

B = By = Bo cos(kx - wt) k.................4

the electric field component would oscillate in the y direction and the magnetic field would oscillate in the z direction which produces a problem. But first, if we simply look at Maxwell equations,

equ 5a,b and equ 6a,b........

We can see that for the EM transverse wave equations of light, that are derived using Maxwell's curl equations, produces a serious dillema since the electric and magnetic field vectors are on different sides of Maxwell's curl equations (equ 5b and 6b); consequently, the electric and magnetic field vectors are separated by an equals sign (=) yet the electric and magnetic field vectors are pointing in different directions. The electric field vector, of the electric transverse wave equation (equ 3) is pointing in the y direction, during its oscillation, and the magnetic field vector (equ 4) is pointing in the z direction; therefore, for the derivation of the EM transverse wave equations of light results in this extremely problematic relationship that 150 years of Maxwell's EM theory of light, which is an extremely short period of time, in regards to physics theory, is now showing up.

Hey, ronsimpson, did you know that Newton stoled the derivative and the integral from Leibniz since Newton published Principia, in 1687; whereas, Leibniz published his paper on the derivative, in 1684, and the paper that included the integral symbol, in 1886 which proves Newton is a thief.

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2. ### tvtechWell-Known MemberMost Helpful Member

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Incomplete statement. You are making this stuff up as you go along.

And making everybody confused?????

3. ### copernicus1234Member

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Hi. tvtech...glad you could share your mindful post. The following pix is in regards to an EM transverse wave of light that electric field is oscillating, in the y direction, and the magnetic field vector oscillating, in the z direction, where the wave is propagating in the z direction which is pretty standard, agree?

You cannot imagine how sorry I feel about making you feel confused. It is similar to an article I was reading in a Buddtist book where the author states confusion an agression occurs when someone's ego is attacked. Physics is part of many people's super ego yet change is the only constant, yes? But I just reliezed that the figure that you induce me to post my begin great joy to steveB who's hunger for real knowledge is quite remarkable.

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5. ### tvtechWell-Known MemberMost Helpful Member

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^^^^

Ahh......thanks. I get it now.

Off to work I go at the Lab. We found this out today:http://www.timeslive.co.za/scitech/2014/05/13/square-hole-found-on-sun-s-surface

6. ### steveBWell-Known MemberMost Helpful Member

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You are incorrect here. Saying E=Ey is incorrect. And saying Ey=Eo cos(kx - wt) j is incorrect. And saying Ey=(Eo cos(kx - wt) j )j is incorrect.

The way I showed you E = Ey j = (Eo cos(kx - wt) j) is correct. This leads to Ey = (Eo cos(kx - wt) which is correct. When you use these correct equations, you do not run into a catastrophe and you get the right answers that everyone else has been getting. If you continue to use the wrong relations, which make no logical sense (as I've pointed out several times and which you have ignored several times), you obviously will keep running into the logical contradiction that i=j.

Maxwell's equations don't represent EM vectors. Maxwell's equations represent the behavior and provide the relationships between the EM field components. The EM field components are strictly components of a 2nd rank tensor (often called Fμv). Maxwell's equations are often shown in vector form, which let's us think of the electric field as a vector and the magnetic field as a vector. However, even in this form, Maxwell's equations give the relationships between the field components.

Let's break down Maxwell's equations to illustrate that fact. In free space with no charges we have

Let's take the first equation and write it out.

∂Ex/∂x+∂Ey/∂y+∂Ez/∂z=0

Notice that there is no vector information here. It's a relation between the field components only, In fact this is a scalar equation from the very beginning.

Likewise we have ∂Bx/∂x+∂By/∂y+∂Bz/∂z=0 which is a scalar equation.

The remaining two equations are the real Maxwell equations and are the equations of motion for the field componentss. These are vector equations, but they each break down into 3 separate scalar equations as follows.

First, write the vector equations in rectangular coordinates.

(∂Ez/∂dy-∂Ey/∂z) i + (∂Ex/∂dz-∂Ez/∂x) j + (∂Ey/∂dx-∂Ex/∂y) k = (-∂Bx∂dt) i+ (-∂By∂dt) j+ (-∂Bz∂dt) k
(∂Bz/∂dy-∂By/∂z) i + (∂Bx/∂dz-∂Bz/∂x) j + (∂By/∂dx-∂Bx/∂y) k = (1/c ∂Ex∂dt) i+ (1/c ∂Ey∂dt) j+ (1/c ∂Ez∂dt) k

which leads to the following once the vector components of these equations are equated.

∂Ez/∂dy-∂Ey/∂z=-∂Bx∂dt
∂Ex/∂dz-∂Ez/∂x=-∂By∂dt
∂Ey/∂dx-∂Ex/∂y=-∂Bz∂dt

∂Bz/∂dy-∂By/∂z=1/c ∂Ex∂dt
∂Bx/∂dz-∂Bz/∂x=1/c ∂Ey∂dt
∂By/∂dx-∂Bx/∂y=1/c ∂Ez∂dt

In other words, we recognize that i does not equal j and k, and j does not equal i and k and k does not equal j and i.

So Maxwell's Equations represent the coupled differential equations between components of the electromagnetic field tensor Fμv. That is the answer to your question and you will ignore it as you have ignored all of my other answers.

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7. ### copernicus1234Member

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SteveB..........show me the EM transverse vector wave equations of light. In this equation, to represent the electromagnetic transverse wave equations of light, would require an equation that includes the direction of the electric and magnetic fields. This equation that you will hopefully provide, for the audience, would require that it represents the following figure,

(Note: this figure was inspired by the illustrious tvtech)

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8. ### copernicus1234Member

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http://faculty.ccriedu (page 3)............ you will find the EM transverse vector wave equations of light similar to:

Ex = Eo cos(kx - wt)j..............Bz = Bo cos(kx -wt)k...........................Equ 3a,b

with the unit vectors.

9. ### copernicus1234Member

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∂Ez/∂dy-∂Ey/∂z=-∂Bx∂dt
∂Ex/∂dz-∂Ez/∂x=-∂By∂dt
∂Ey/∂dx-∂Ex/∂y=-∂Bz∂dt
∂Bz/∂dy-∂By/∂z=1/c ∂Ex∂dt
∂Bx/∂dz-∂Bz/∂x=1/c ∂Ey∂dt
∂By/∂dx-∂Bx/∂y=1/c ∂Ez∂dt

In other words, we recognize that i does not equal j and k, and j does not equal i and k and k does not equal j and i.

-------------------------------------------------------------------------------------------------

Yes, this is true but the equations above are used in the derivation of the EM transverse vector wave equations of light; therefore, the EM wave equations are solutions to the differential equations,

dEy/dx = - (1/c)(dBz/dt] ........... - dBy/dx = (1/c)(dEz/dt)..............Equ 1a,b

but using the EM wave equations back into equations 1a,b, to test the derivation, produces a unit vector problem. The unit vector problem is formed when Maxwell's equations are used to derive a transverse wave, from eqution 1a,b, since Maxwell's equations are horizontal wave equations which contradict Maxwell's transverse waves that are used to represent polarization, by creating the unit vector catastrophe. The mathematics, of Maxwell's equations, is showing the student that a transverse EM wave vector equations cannot be derived using Maxwell's equations.

"Maxwell's electrodynamics proceeds in the same unusual way already analysed in studying his electrostatics. Under the influence of hypotheses which remain vague and undefined in his mind, Maxwell sketches a theory which he never completes, he does not even bother to remove contradictions from it; then he starts changing this theory, he imposes on it essential modifications which he does not notify to his reader; the latter tries in vain to fix the fugitive and intangible thought of the author; just when he thinks he has got it, even the parts of the doctrine dealing with the best studied phenomena are seen to vanish. And yet this strange and disconcerting method led Maxwell to the electromagnetic theory of light!" (Duhem, 1902).

Duhem, Pierre. Les theories electriques de J. C. Maxwell. Paris. 1902.

La Marseillaise "Casablanca (1942)"

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10. ### steveBWell-Known MemberMost Helpful Member

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Your link is not working. Please correct it so we can find the source of your error. The equation is incorrect, whereever you obtained it. Let's look closer.

Two interesting things I note. You are trying to reference CCRI which is right down the road from where I work. I also note that this is their 50th anniversary, meaning they started the year I was born. This used to be known as Rhode Island Junior College (RIJC) and people referred to it in a derogatory tone calling it "REJECT", however despite this negative view and despite your negative statements about junior colleges, this is an outstanding school and people who do 2 year engineering degrees there are well prepared to obtain a 4 year BS engineering degree. I had the pleasure of teaching some of these students in a senior level University Course, and the two top students in the electronics class I taught were CCRI graduates. Once we find the source of you error, I'm sure the professor you are referencing just made a typographical error and would never conclude, as you did, that Maxwell's Equations lead to the contradiction that i=j.

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11. ### steveBWell-Known MemberMost Helpful Member

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There can be no unit vector problem because Ey, By, Bz and Ez are not vectors and are not represented with unit vectors in them. This is the source of your mistakes. Field components are not vectors. Vectors are represented with components and unit vectors. Vector components are represented as scalar functions of space and time. It's as simple as that.

12. ### copernicus1234Member

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Ey = Eo cos(kx - wt) ...............................Equ 1

Bz = Bo cos(kx -wt) ................................Equ 2

My question is: do equations 1 and 2 represent EM field vector transverse waves of light?

(Note: this figure was inspired by the illustrious tvtech). The following site (faculty.ccri.edu/.../2150-Powerpoint/Chapt32-SP2013-Maxwells-Apps.pdf), page 3, describes EM field vector transverse wave equations of light similar to:

Ey = Eo cos(kx - wt) j ...............................Equ 3

Bz = Bo cos(kx -wt) k ................................Equ 4

with the unit vectors.

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13. ### steveBWell-Known MemberMost Helpful Member

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Once again your link is broken, but this time I was able to find it. So that others can see your continuous lying, here it is again with the click working.

http://faculty.ccri.edu/jbernardini...0-Powerpoint/Chapt32-SP2013-Maxwells-Apps.pdf

Who do you think you are fooling with this nonsense? Anyone can look at page 3 and see that the relations shown are

E = Eo cos(kx - wt) j

B = Bo cos(kx -wt) k

not

Ey = Eo cos(kx - wt) j ...............................Equ 3

Bz = Bo cos(kx -wt) k ................................Equ 4

So, you are trying to blame a CCRI professor for your stupid mistakes, it seems. Well those tricks don't work here.

Despite my repeated attempts asking for a reference for your eqns. 3 and 4, you can't provide one. Basically, you made them up yourself.

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14. ### copernicus1234Member

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Who do you think you are fooling with this nonsense? Anyone can look at page 3 and see that the relations shown are

E = Eo cos(kx - wt) j ................1

B = Bo cos(kx -wt) k.................2

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Equations 1 and 2 represents the EM transverse vector equations of light (note the unit vector of equations 1 and 2) that form the unit vector catastrophe using the EM wave equations in,

dEy/dx = - (1/c)(dBz/dt] ........... - dBy/dx = (1/c)(dEz/dt)..............Equ 3a,b

Your statements that Ey, Bz and By are not vectors is incorrect since E and B represent electromagnetic fields which are represented with vectors. Plus, Maxwell equations are vector equations.
.

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15. ### steveBWell-Known MemberMost Helpful Member

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OK Copernicus. Good luck to you. I tried my best to show you the light, but you are free to believe your own ideas. I will not be responding to your posts anymore.

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Excellent....