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Understanding why Einstein found Maxwell's electrodynamics not relativistic 
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#1
Dec2412, 02:28 PM

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I'm trying to understand exactly why Einstein considered Maxwell's electrodynamics to be nonrelativistic. As I read Maxwell's paper, it seems to me that it is concerned only with relative motions. I'm thinking that the problem must be with the stationary ether proposed by Lorentz, for then motions must be considered relative to the coordinate system of the ether, not relative to the other poles and conductors in the system under consideration.
Here is Einstein from his 1905 paper: As I read Maxwell's equation for electromotive force (equation D in the paper), it seems to me that "electromotive force" and "electric field" are synonymous. For in the equation, electromotive force at any point is a vector quantity, and it gives rise to current; that is the definition of an electric field. Here is why I do not understand Einstein's claim that no magnetic field arises in the vicinity of the magnet: In the equation for electromotive force, the first term is the product of the strength of the magnetic field and the velocity of the conductor relative to the field. Thus, when the conductor moves and the magnet is stationary, electromotive force increases. Electromotive force is a synonym for electric field. Therefore, the movement of the conductor in the magnetic field gives rise to an electric field. Einstein also says that there is no energy which corresponds to the electromotive force, in itself. I'm not sure what he means. As to intrinsic energy in the electromagnetic field, Maxwell says that it is proportional to the magnetic intensity, independent of electromotive force; he makes no mention of whether the magnet is moving or not. Comments? Am I on the right track in thinking it is the stationary ether which causes the problem? 


#2
Dec2412, 03:00 PM

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I think the key is in that phrase in the Einstein quote: "as usually understood at the present time". The "usual" understanding he was referring to used Newtonian mechanics for mechanical phenomena, so there were going to be issues whenever you had a scenario with both mechanical motions and electromagnetic fields involved. So he wasn't just talking about Maxwell's electrodynamics by itself; he was talking about how Maxwell's electrodynamics is combined with mechanics. Some of the things he says about the combined theory "as usually understood at the present time" don't really make sense; but that's because the usual understanding at that time, trying to combine Maxwell's electrodynamics with Newtonian mechanics, didn't make sense.



#3
Dec2412, 03:36 PM

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#4
Dec2412, 04:15 PM

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Understanding why Einstein found Maxwell's electrodynamics not relativistic
There are three terms in Maxwell's equation for electromotive force: [velocity of conductor] times [magnetic intensity at that instant] rate of change of electromagnetic momentum (accounts for movement of poles, or change of intensity of stationary poles) rate of change of electric potential All three terms are vector operations. He presents the one equation as a set of three differential equations. I haven't done that kind of math in close to 30 years, so I don't pretend to understand the equations completely. I think I get the gist. I'm guessing that in the Lorentz equation, v x B covers the first two terms of Maxwell, and E covers the third. The first term of Maxwell can be eliminated if one chooses to put the origin of the coordinate system on the moving conductor. Then the electromotive force will be due to the change in magnetic intensity, from the second term. This is a trivial transformationno need for the Lorentz transformation, and no need to make a fuss over it, in my opinion. Seems to me that Einstein had a deeper objection to the asymmetry than that. 


#5
Dec2412, 05:07 PM

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Einstein showed that the Lorentz transform also satisfied the principle of relativity and that Maxwell's equations were invariant under the Lorentz transform. 


#6
Dec2412, 05:43 PM

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As an undergrad, I was given an example of what DaleSpam is talking about. I have to admit that I've never actually done the maths, but I am told that if one solves for a Bfield, then transforms it to a Galilean moving frame (x'=xvt, t'=t), it no longer satisfies ∇B=0. In other words, Maxwell+Galileo say that a common bar magnet should gain magnetic monopole characteristics just by being moved. That is not exactly consistent with observation.



#7
Dec2412, 05:50 PM

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Sounds to me like you are the right track:
but understanding historical context is even worse than trying to understand current perspectives. such as: "At the time "relativistic" meant Galilean relativity." Oh good grief!! 


#8
Dec2412, 05:50 PM

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I think the simplest way of understanding why Maxwell's equations aren't compatible with Galilean relativity is to look at what happens when you take an electromagnetic plane wave and transform into the frame in which the wave is at rest. In that frame, it clearly violates Maxwell's equations. 


#9
Dec2512, 08:22 AM

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As I read your statement, the energy is determined by either E or B; not the combination of the two. I'm not saying you are wrong; I trying to understand how what Maxwell says corresponds to what Einstein says. Whether it is "E and B" or "E or B", in the case under discussion there is energy in the field due to the magnet. That energy produces the electromotive force. Here I would go back to my original post and argue that Maxwell's equation says that the movement of the conductor in the magnetic field produces an electric field. For the electromotive force that the equation predicts has exactlyno more, no lessthe characteristics of an electric field: a force vector at any point in space. In fact, the same equation, the one for electromotive force, is the one that predicts the rise of an electric field due to the movement of a magnet relative to a stationary conductor. The electric field due to the movement of the conductor in a magnetic field is in the first term of the equation; the electric field due to the movement of a magnet is in the second term of the equation. (The second term is the rate of change of electromagnetic momentum, which is magnetic energy stored in the field. Maxwell says that a moving magnetic pole, or moving current, or a change in intensity of pole or current, changes the electromagnetic momentum at a point in space.) As far as the case under discussion is concerned, it seems to me that Maxwell's equation for electromotive force is invariant with respect to a Galilean transformation. It must be: as noted above, this equation is used to calculate the electromotive force in both cases, when the magnet is stationary and when the conductor is stationary. The answer is the same in both cases. 


#10
Dec2512, 09:28 AM

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Greg: I am also having trouble how to interpret frames here.....Crowell's comment.
there is some interesting easy to follow background here: http://en.wikipedia.org/wiki/Relativ...ectromagnetism and I think Crowell's statement is consistent with this: and a more formal mathematical discussion in a link from the above article: http://en.wikipedia.org/wiki/Formula...ial_relativity and here: http://en.wikipedia.org/wiki/Formula...energy_tensor the electromagnetic stress energy tensor seems to be dependent on BOTH E[SUP]2 B^{2}..... a lot of this math is above my pay grade, but I am guessing the frame of T sets E and B?? I knew I had seem something like Crowell's explanation: from Dalespam: "See here for a rigorous proof based on established mainstream science demonstrating that the power density delivered by an EM field is given by E.j in all cases" : http://farside.ph.utexas.edu/teachin...es/node89.html this thread: http://www.physicsforums.com/showthr...c+field+energy [I gave up following it after the first few pages.] 


#11
Dec2512, 09:46 AM

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#12
Dec2512, 10:04 AM

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#13
Dec2512, 11:47 AM

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#14
Dec2512, 12:24 PM

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What I had in mind is this: So long as one or the other of the two bodies under consideration (magnet or conductor) is at rest relative to the ether, Maxwell's equation for electromotive force predicts one and the same outcome regardless of which one moves, and the energy which drives the outcome is the same in either case. I did not think about it in terms of "at least one body at rest in the ether" because Maxwell never stipulates the rest frame of the ether. But, it is implicit in the equations that the ether is at rest in the frame of the coordinate system. Part of my difficulty in understanding Einstein's claim of asymmetry is that Maxwell never uses the term "electric field" in any of his published papers. (That claim is true if a search of the pdf file is to be trusted.) I have not seen "electric field" in the 1864 paper on electrodynamics. He talks mostly about the electromagnetic field; sometimes he says magnetic field; once (in On Faraday's Lines of Force) he says magnetoelectric field. Maxwell does talk about electromagnetic force. As noted earlier, Maxwell's electromotive force is a vector quantity at any point in space that forces movement of electric charge. My understanding of an electric field is precisely that: a vector quantity at any point in space that forces movement of electric charge. If my definition of electric field is correct, then I believe I am on solid ground when I say that the equation for electromotive force is the equation for the electric field. In that equation, there are three contributors to the electric field at any point: motion of a conductor, change of intensity of magnetization (includes motion of a magnetic pole), and change of electric potential. So for Maxwell, movement of a conductor in a magnetic field produces an electric field, as does movement of a magnet. Here is the equation (in three parts) for electromotive force, from the paper: Maxwells' explanation: The energy which produces the electric field is in the magnetic field, regardless of whether it is the conductor moving, or the magnet, or both. Maxwell says that the electromagnetic energy is stored in the field; he also says that the field is magnetized. He means this literally, because he believes that the ether is a material substance: 


#15
Dec2512, 02:14 PM

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However, honestly my interest in historical matters is pretty minimal so I wouldn't be surprised that there was one that I am just not aware of. So I will let it rest with that. I think that the only necessary historical point is that it was clear to scientists at the time that Maxwell's equations were not (Galilean) relativistic, but the specific details of the attempted patches are not so critical to understand. 


#16
Dec2512, 03:08 PM

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#17
Dec2512, 09:03 PM

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Turns out both DaleSpam and I were wrong in our guesses about the history and physics of how E and B would transform and were thought to have transformed under a Galilean transformation. This is apparently quite subtle, and was not worked out until recently.
Marc De Montigny, Germain Rousseaux, "On the electrodynamics of moving bodies at low velocities," http://arxiv.org/abs/physics/0512200 See pp. 25, 22, 23 (pdf page numbers). 


#18
Dec2612, 04:20 AM

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