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Simple relativity question 
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#1
Aug3106, 02:37 AM

P: 30

I'm reading how the Lorentz equations allow for relativistic transformation that can include Maxwell's equations but I'm a bit confused on how it solves the problem of Maxwell's equations being variant under a Galilean transformation. The example I'm looking at says that if you are moving away from an infinitely long wire and point charge, and use yourself as the frame of reference, then you would see the wire and point charge system moving away from you and you'd have to consider the magnetic field that would arise, which you wouldn't consider if you were looking at the system from its own frame of refrence. Can someone explain how the Lorentz equations solves this problem, because I can't figure it out. Thanks.



#2
Aug3106, 03:08 AM

P: 893

Found this on the web:
http://physics.weber.edu/schroeder/m...nsformation%22 I not quite sure, or don't remember, why the usual discussion uses the model of negative and positive charges moving in opposite directions instead of something closer to what's actually going on in a wire. 


#3
Aug3106, 11:05 AM

P: 15,319

"simple relativity question"
Hee! Put that in the bin along with "jumbo shrimp" "military intelligence" "deafening silence" "original copy" 


#4
Aug3106, 11:15 AM

P: 482

Simple relativity question
1. starts by pointing out that the Maxwell equations do not conserve form when passing from one inertial frame to another one UNDER the Galilei transforms 2. continues by proposing another set of transforms (the ones that were given his name much later by Poincare) that solve the problem. The paper can be found in a book that also contains the Einstein 1905 paper. I'll give you the exact name of the book in a few hours. "Original copy" , ha,ha,ha. The book is "The Principle of Relativity" The article is : Electromagnetic Phenomena in a System Moving with any Velocity Less than that of Light" by Lorentz. 


#5
Aug3106, 12:30 PM

P: 30

I thought I understood the answer to this question in terms of the speed of light being constant regardless of the sources motion and therein the failure of the classical transformation, but now considering the example regarding the magnetic field I can't understand how the Lorentz equations compensate mathematically. Is this is a matter of logic in some way, i.e. when a reference frame moves relative to the wire and an observer in this frame then sees the wire moving, he simply ignores its apparent motion? 


#6
Aug3106, 12:54 PM

Emeritus
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P: 7,598

I'm not positive I understand your question. You do realize that the total force on a point charge, the four force, transforms covariantly according to the Lorentz transform, don't you? I believe this was mentioned recently in another thread.
The description of the force, i.e. describing what parts of the force are due to "electric" fields and what parts are due to "magnetic" fields, changes, but the total force itself is Lorentz covariant. The manifestly covariant description of forces in special relativity is the "four force". 


#7
Aug3106, 01:03 PM

P: 30




#8
Aug3106, 01:14 PM

Sci Advisor
P: 1,135

derivation of magnetism as a relativistic sideeffect of electrostatics. The figure at the right shows how the positivechargepart of the wire becomes longer as the negativechargepart of the wire... This does not happen. The wire doesn't split. Imagine for example a semiconductor where the electrons don't hop from one free position to another but end up hopping to arbitrary positions in the middle... It's the Coulomb fields of the electrons and ions moving relative to the testcharge which become Lorentz contracted and therefore cause an imbalance in the forces felt from the positive and negative charges resulting in a nonzero force acting on the moving test charge. Regards, Hans. 


#9
Aug3106, 01:26 PM

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P: 7,598

http://en.wikipedia.org/wiki/Electromagnetic_field writes this down, there is a more detailed explanation as well at u of fla You start here: http://www.phys.ufl.edu/~rfield/PHY2...ativity_11.pdf then visit _12, _13, _14, etc... This was recently discussed in another thread here on PF, too... 


#10
Aug3106, 02:00 PM

P: 482

Electromagnetic Phenomena in a System Moving with any Velocity Less than that of Light 


#11
Aug3106, 02:42 PM

P: 30




#12
Aug3106, 03:40 PM

Emeritus
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P: 7,598

He discusses this issue in some depth (i.e. how general electromagnetic fields transform under the Loretnz boost). You'll probably be able to get most of it from the web if you look hard enough, but if you can get a hold of Griffiths from the library, it might be helpful. 


#13
Aug3106, 04:32 PM

P: 893

Do you know of a source for a more realistic derivation? 


#14
Sep106, 09:17 AM

P: 1,545

If you’re only considering the distant wire stretched perpendicular to your travel and a stationary point charge near it or on it as a system with no other charges or magnetic fields, any complete Lorentz transformation would still show wire and point charge to hold fixed relative positions. If however you are using any magnet and/or point charge moving with you; then you would detect an EM effect from that system moving away from you – but that system would also see the same thing due to your magnet and/or point charge moving away from them. So why does your problem think you would see something any differently than the system you observing would see from there view? I don’t see a problem or conflict for Lorentz equations to solve. 


#15
Sep406, 10:51 AM

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#16
Sep506, 09:02 AM

P: 1,545




#17
Sep506, 01:18 PM

P: 30




#18
Sep506, 01:50 PM

P: 1,545

Where is there a difference or error? As far as I can tell Maxwell’s EM does not depend on or need Classical, Lorentz, or Relativity. 


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