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Maxwell's electromagnetic theory of light.

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

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  1. steveB

    steveB Well-Known Member Most Helpful Member

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    I used Jenkins & White for an undergraduate optics class in 1984. We used the 4'th edition published in 1976, but I imagine it is essentially the same as that 3rd edition you referred to.

    Feel free to identify the chapter and section number that talks about a "unit vector catastrophe", but I can't find it in that book, nor have I ever heard of that phrase.

    The only "catastrophe" I've every heard of that in any way relates to what you are talking about is the "ultraviolet catastrophe". If this is what you are referring to, then (as I mentioned above) I basically agree with you. The ultraviolet catastrophe relates to a prediction of classical electromagnetic theory that does not agree with experiments, and is in fact wrong. As I mentioned, what is missing from classical theory is quantum physics, and the ultraviolet catastrophe can only be resolved by using quantum theory.

    Anyway, it's no fun trying to guess what you are talking about, so if you have a genuine question or comment, please be clearer about what you are trying to ask or say.
     
  2. nsaspook

    nsaspook Well-Known Member

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    Some background on the 'ultraviolet catastrophe' and it's solution.

    http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html
    http://physics.about.com/od/quantumphysics/a/blackbody_2.htm
    http://spiff.rit.edu/classes/phys314/lectures/planck/planck.html

    I would say that classic EM theory is incomplete not wrong. Ptolemy’s theory using epi-circles was wrong and Copernicus was right. Classic Em theory can explain the movement of energy in nano-scale antennas that collect energy from light waves for solar power panels and plants (the molecules that collect energy for photosynthesis) or for rf in your FM radio. In the areas (atomic scale interactions of EM energy with matter) where quantum effects dominate it fails but we now know the reason why.

    http://en.wikipedia.org/wiki/Quantum_electrodynamics
    http://en.wikipedia.org/wiki/Nantenna
     
    Last edited: Apr 27, 2014
  3. steveB

    steveB Well-Known Member Most Helpful Member

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    I agree.

    I would say that all theories we use, and even just know about, are incomplete. It is the predictions of a theory that can be right or wrong, not the theory itself, unless that theory is completely unfounded. "Right and wrong" is a "black and white" distinction, while the success of a theory is a matter of degree or "shades of grey".

    Classical EM theory is a particularly successful theory because it makes so many correct predictions. It even obeys Lorentz invariance, as all modern theories are expected to do. That's pretty good work for all those guys working in the 19th century.

    I think the mistake that many people make (and this perhaps applies to our friend Copernicus asking these questions) is that they think that physics is about explaining "why", when it is really about predicting or describing "how and when". If we were to judge theories on their ability to explain "why" they would all be failures and would all be wrong. But, if we judge them on their ability to make predictions within the constraints of understood limits, they can be right, even though incomplete.

    Theories work double time for us by making right predictions and by making wrong predictions. We learn something new either way and make progress with new discoveries and newer and more complete theories.
     
    Last edited: Apr 28, 2014
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  4. dave

    Dave New Member

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  5. copernicus1234

    copernicus1234 Member

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    ...............The gradient (horizontal) method, http://en.wikipedia.org/wiki/Electromagnetic_wave_equation , results in EM wave equations of light that represents a horizontal wave.


    In the expansion (transverse) method (Jenkins, Francis and White, Harvy. Fundamentals of Optics. 3rd ed. McGraw-Hill. 1957. p. 410) just after Maxwell's equations are expanded first order differential equations are produced,


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


    that are used to derive


    (d"E/d"x) = c(d"E/d"t).......................................................................Equ 2


    Equation 2 is used in the derivation of the x-direction EM transverse wave equations of light.


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


    Using the electromagnetic transverse wave equations, in equations 1a forms,


    d/dx (Eo cos(kx - wt)j) = - (1/c) d/dt(Bo cos(kx - wt)k).......................Equ 4


    Using Bo = Eo, in equation 4 forms,


    j = k (unit vectors). ........................................................................Equ 5


    Equation 1b also produces equation 5 which I calls the unit vector of catastrophe. In addition, Condon also uses the expansion method to derive the EM transverse wave equations of light, using equation 2, but neglects the representation of equations 1a,b (Condon, Handbook of Physics. McGraw-Hill. 1958. 4-108). Furthermore, Hecht also uses the expansion method to derive the EM transverse wave equations of light, using equation 2, and neglects the represenation of equations 1a,b (Hecht, Eugene. Optics. Addison-Wesley. 4th ed. p. 44). In general, physicists uses Condon-Hecht expansion method or the divergence method but physicists are intensionally concealing an extremely important and critcal fact, unit vector catastrophe, formed by equation 1a,b.
     
    Last edited: Apr 28, 2014
  6. steveB

    steveB Well-Known Member Most Helpful Member

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    OK, so you decided to call it the "unit vector catastrophe". Honestly, I am not able to follow your logic at all. Your above description is not at all understandable and it is not clear how you arrive at the result j=k.

    I conclude that you are confused or trolling. Either way, I wish you good luck and enjoyment in your endeavors.
     
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  7. copernicus1234

    copernicus1234 Member

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    steveB........................I added some more parts, to the previous post. Please indicate which lines you have problems with.
     
    Last edited: Apr 28, 2014
  8. steveB

    steveB Well-Known Member Most Helpful Member

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    Equations 4 and 3a,b are complete misstatements of what is presented in Jenkins and White. You started with differential equations that relate the components of vectors in 1a,b. These equations are scalar type equations and not vector equations. The components of vectors are not vectors themselves and those equations (for example 1a,b are relating component values Ey Ez By and Bz.

    All of a sudden, out of the blue, you decided to insert j and k unit vectors into the equations 3a,b. This is incorrect.

    To make it clearer. If the vector E is E = Ex i + Ey j + Ez k, then you do not say that Ey=Eo cos(kx-wt) j. Instead you say Ey=Eo cos(kx-wt) and leave the j out because it is already part of the representation of the vector E.

    Equations 3a,b do not even show up in that section of Jenkin's and White. Wherever you picked up those relations, it was a typographical error, or maybe you misunderstood the presentation.
     
    Last edited: Apr 29, 2014
  9. steveB

    steveB Well-Known Member Most Helpful Member

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    Let me paraphrase what you are saying here.

    So, you are saying that Maxwell saw this problem but presented a bogus theory anyway. Somehow he thought no one will notice or that all future physicists would go along with his deception. Then, over the last 150 years, all physicists saw this problem and decided to keep the scam going. Also, millions of students have studied this subject and not one of them has noticed the catastrophe you pointed out. You are the only one smart enough to see the problem, and all those millions of students are complete idiots. The few that are smart enough to see the problem immediately join the ranks of the physicist and every single one of them decides to join the conspiracy. That is, until you showed up.

    You are smart enough to see the problem and ethical enough to report the problem. Apparently you are the only physicist that is both smart and ethical.

    Now, let's apply Occam's Razor to this situation. What is more likely? Are there millions of physicists that are either not smart or not ethical, without exception? Or, did you just make a bonehead mistake?

    If you think I'm being harsh, remember that you first implied that we here in this forum are deceptive and unethical because we are "intentionally concealing an extremely important and critical fact", either that, or we are all too stupid to notice the "unit vector catastrophe", even after you point it out.
     
    Last edited: Apr 29, 2014
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  10. copernicus1234

    copernicus1234 Member

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    SteveB said:

    "These equations are scalar type equations and not vector equations. The components of vectors are not vectors themselves and those equations (for example 1a,b are relating component values Ey Ez By and Bz."

    Answer by Copernicus1234:

    I humbly disagree since Maxwell's equations are vector equations.

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

    SteveB said:

    "Equations 3a,b do not even show up in that section of Jenkin's and White. Wherever you picked up those relations, it was a typographical error, or maybe you misunderstood the presentation."

    Answer by Copernicus1234:

    I'm using Jenkins and White as a reference. Example, I can derive the x, y or z direction electromagnetic wave equations using the expansion method described by Jenkins and White; therefore, the derivation of the x direction EM wave equations is different from the derivation of the z and y direction EM wave equations but similar.

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

    SteveB said:

    Now, let's apply Occam's Razor to this situation. What is more likely? Are there millions of physicists that are either not smart or not ethical, without exception? Or, did you just make a bonehead mistake?

    Answer by Copernicus:

    Mistake? You're looking directly at the derivation and suggesting I'm making a mistake?

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

    Thank you for your completely thoughtful and compelling posts. Your friend Copernicus1234.
     
    Last edited: Apr 29, 2014
  11. steveB

    steveB Well-Known Member Most Helpful Member

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    Yes Maxwell's Equations are vector equations as typically written in vector notation (that vector formulation actually comes from Heaveside http://en.wikipedia.org/wiki/Oliver_Heaviside ). However, eqns 1a,b are not vector equations, but they are scalar equations that relate the components of the field vectors, much in the same way that Maxwell originally wrote his field equations.

    In effect, eqs 1a,b are the result of matching up and equating the i, j and k field components to establish the separate relations. They result from the fact that i, j and k are not equal vectors, but are orthogonal vectors. You are not free to then reinsert contradicting unit-vectors in the wrong places. The catastrophe you are so worried about is a catastrophe of your own making. It is a catastrophe that results from a little bit of knowledge being a dangerous thing.

    Yes. It's a very obvious and amateurish mistake.


    You are welcome.
     
    Last edited: Apr 29, 2014
  12. nsaspook

    nsaspook Well-Known Member

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    Wow, the world-wide conspiracy of Maxwell.
    This is the view of quacks and crackpots.

    http://math.ucr.edu/home/baez/crackpot.html
     
  13. tvtech

    tvtech Well-Known Member Most Helpful Member

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    LOL :)

    Rather leave it and bail out.

    Like me :)

    The ever thick,
    tvtech
     
  14. copernicus1234

    copernicus1234 Member

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    steveB........"However, eqns 1a,b are not vector equations, but they are scalar equations that relate the components of the field vectors, much in the same way that Maxwell originally wrote his field equations."

    Equation 1a,b are used in the derivation of the EM wave equations of light (equ 3a,b). The term Ey (Equ 1a) of

    dEy/dx = - (1/c)(dBz/dt).............................equ 1

    is represented with
    Ex = Eo cos(kx - wt)j...............................Equ 2

    that is an electric transverse field vector equation, in the y direction, and the term Bz represented with,

    Bz = Bo cos(kx -wt)k................................Equ 3

    describves a magnetic transverse field vector equation, in the z direction. When the EM wave equations of light (equ 2 and 3) are used in equ 1, the unit vector catastrophe is produced,

    j = k (unit vectors). ..................................Equ 4

    "You are not free to then reinsert contradicting unit-vectors in the wrong places." (steveB). I inserted Ex = Eo cos(kx - wt)j, (equ 2) and Bz = Bo cos(kx -wt)k, (equ 3) in equation 1 that is part of Jenkins and White derivation (Jenkins, Francis and White, Harvy. Fundamentals of Optics. 3rd ed. McGraw-Hill. 1957. p. 410). Please explain to me your statement of "contradicting unit vectors in the wrong places" since the unit vectors of equations 2 and 3 are not contradicting. The contradiction occurs when Ex = Eo cos(kx - wt)j and Bz = Bo cos(kx -wt)k, are used in

    dEy/dx = - (1/c)(dBz/dt).............................equ 5

    In addition, Condon also uses the expansion method to derive the EM transverse wave equations of light but neglects the representation of equations 1 (Condon, Handbook of Physics. McGraw-Hill. 1958. 4-108). Furthermore, Hecht also uses the expansion method to derive the EM transverse wave equations of light and also neglects the represenation of equations 1 (Hecht, Eugene. Optics. Addison-Wesley. 4th ed. p. 44). In general, physicists use Condon-Hecht expansion method or the divergence method but physicists are intensionally concealing an extremely important and critcal fact: equation 1----->> to avoid the Arcata unit vector catastrophe.

    stevenB............."Also, millions of students have studied this subject and not one of them has noticed the catastrophe you pointed out. You are the only one smart enough to see the problem, and all those millions of students are complete idiots."

    Answer: by Copernicus1234............stevenb you seem to be also having problems with the derivation. Blaming students is not very manly, and next time how about an Oath or a declaration to GOD, regarding your next statement. Thank you for your completely thoughtful, highly interesting and compelling posts. Your best friend Copernicus1234.
     
  15. nsaspook

    nsaspook Well-Known Member

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    Last edited: May 1, 2014
  16. steveB

    steveB Well-Known Member Most Helpful Member

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    I'm not going to go into all your confusing comments and misinterpretations of what I said. I'm not having trouble with these derivations at all. I mastered them years ago. You are the one that is having trouble with the derivation, which is why you arrived at your nonsensical conclusion that there is a unit vector catastrophe, and this is why you have posted this question on 3 or more technical forums and cant get one person in the world to agree with you.

    I already explained, but I can try again. Let's put it in a nutshell. Here is your mistake in bold underlined font ...

    Equations 2 and 3 above are incorrect. (imagine the sound of trumpets as you read that)

    If you think they are correct, please provide a reference for them.

    The correct equations are as follows.

    Ey = Eo cos(kx - wt) ...............................Equ 2
    Bz = Bo cos(kx -wt) ................................Equ 3

    Notice that I left the j and k unit vectors out of the equations because including them is mathematical nonsense, in the context of this derivation.

    Now, use these correct equations and you will not bump into your unit vector catastrophe.

    Why is it nonsense? Well a vector that is represented as E is writen as E = Ex i + Ey j + Ez k and if we substitute your equations with your suggestion of Ey = Eo cos(kx - wt) j, Ex=0 and Ez=0, then E is ...

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

    The presence of two j unit vector reveals the nonsense of your viewpoint. The presence of two unit vectors would normally indicated a dyad (http://en.wikipedia.org/wiki/Dyad_product) and would imply a tensor of higher rank than a vector. This is utter nonsense in the context of this derivation.

    So, I ask you to provide your reference for equations 2 and 3, and then we can track down your mistake. Did another author mislead you or did you misinterpret another author? It might be useful to identify which is the case, and we can do so, if you provide your reference. I pointed out that your eq. 2 and 3 do not appear in Jenkins & White, while the correct versions I showed do show up there.
     
    Last edited: May 1, 2014
  17. steveB

    steveB Well-Known Member Most Helpful Member

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    Copernicus1234,

    I attached scans of three different pages of Jenkins and White in the section that is being used. It can be seen that the field components are never shown with i, j and k vectors inserted.

    Please post scans of the pages of the reference you used that shows why you chose to incorrectly insert those k and j unit vectors. If you are unable to scan and post, then post the reference. Most likely I have the book.

    Oh, and let's not forget that I posted a link to a Leonard Susskind's lecture in which he steps through the whole method and derivation. You won't find unit vectors incorrectly inserted in those eqs. 2 and 3 in his presentation. His views on astronomy also contradict your comments in the other thread. I know you don't respect noted scientists that have proved their worth, but surely a guy that had an intellectual battle with Stephen Hawking () is more qualified than you are to talk about these subjects.
     

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  18. copernicus1234

    copernicus1234 Member

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    Does Jenkins and White's derivation form the EM transverse wave equations of light? Also, can a x-direction transverse wave's EM field be represened with j and k unit vectors? Furthermore, can a extremely humble person, add addition parts, to a derivation, to clarify the derivation?


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

    stevenB............."I'm not going to go into all your confusing comments and misinterpretations of what I said. I'm not having trouble with these derivations at all. I mastered them years ago."

    Copernicus1234...........But I was having this distinct feeling that you just found the Jenkins and White derivation, that is at issue. So, perhaps that could be the source of your confusion regarding the comments and interpretations that you may or may not be having. I would not want to putin words into your mouth since that would be so impolite. Your friend Copernicus, love and peace, brother, stevenB.
     
    Last edited: May 3, 2014
  19. steveB

    steveB Well-Known Member Most Helpful Member

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    Humble? You took one of the most brilliant derivations and pieces of scientific work in the history of science and instead of clarifying it, you changed it with a stupid mistake. In doing so, you arrived at a nonsensical contradiction, and instead of blaming it on your own ignorance, as you should, you blamed the entire scientific community, for the past 150 years. You then accused them of conspiring to hide a contradiction and inconsistency that you (erroneously) thought was there.

    That is not humbleness. That is arrogance in its worst form.

    But, to answer your question, yes, a humble (or even arrogant) person can indeed add additional parts to a derivation to clarify it. But, the burden is on him to do it correctly. This is where you failed. You did not do it correctly. Even worse, you did not discover your mistake after you failed to do it correctly.
     
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  20. copernicus1234

    copernicus1234 Member

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    steveB..............I already explained, but I can try again. Let's put it in a nutshell. Here is your mistake in bold underlined font ...

    Equations 2 and 3 above are incorrect. (imagine the sound of trumpets as you read that)

    If you think they are correct, please provide a reference for them.

    The correct equations are as follows.

    Ey = Eo cos(kx - wt) ...............................Equ 2
    Bz = Bo cos(kx -wt) ................................Equ 3

    Notice that I left the j and k unit vectors out of the equations because including them is mathematical nonsense, in the context of this derivation.

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

    Are equations 2 and 3 transverse waves.
     
    Last edited: May 5, 2014
  21. steveB

    steveB Well-Known Member Most Helpful Member

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    What do you think? Tell me your opinion and then I will tell you mine.
     
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