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Magnetism seems absolute despite being relativistic effect of electrostatics 
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#19
Feb1412, 06:32 PM

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The rest frame of the straight conductor is chosen. If the negative charge of the free electron steady current is seen uniformly spread throughout the wire, then I have no choice but to assume that the free electron charge density is inversely proportional to the factor [itex]\sqrt{1\left(\frac{v}{c}\right)^2}[/itex], where v is the electron drift velocity of the current. Logically then, the amount free electrons in the same conductor must increase to the same degree as the free electron charge density does. The density and count of other charges is not affected. This would violate the neutral wire assumption. If that is not the case, prepare or find a picture of what you think actually happens.



#20
Feb1412, 06:38 PM

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I think the following comment I made 2 years ago applies here:
The application to this thread is that the electrons are not rigidly linked to each other so there's no reason for the restdistance between them when moving to equal the restdistance when not. In fact they will spread out to fill whatever space is available to them. There is no "centre of contraction" because contractionduetoacceleration doesn't occur. 


#21
Feb1412, 07:12 PM

P: 1,011

In this example, the center of contraction exists (NOT "occurs") halfway through the baseball. No assumption about acceleration or deceleration of the baseball is required. If I had two baseballs moving inline at the same velocity, I might imagine the center of contraction exists (NOT "occurs") between the two baseballs. I can compare Lorentz contractions of electron velocities at different moments. Let's compare the free electron density before and after switching on the current. The "contraction" we speak of is a NOUN not a verb. We are not concerned with the contracting, but the contracTION. We can say that before and after turning the current ON, the electrons move at different speeds. It's therefore logical that BOB sees them as length contracted. Again, we are not talking about Alice. The electrons in motion can be described as a region between two points. The distance between the two points falls. A baseball contains electrons, protons, and neutrons. Its "length contracTION" is relative to the observer. I believe you agree with that. Or am I mistaken? 


#22
Feb1412, 08:27 PM

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kmarinas86, I haven't time to make a detailed response now, and I'll be offline for the next 20 hours or so.
In this scenario there is no "front" or "back" of a "train" of electrons. They are continually being pushed into one end of the wire and pulled out of the other. It is a continuous stream, not a finitelength train. So all you can say is that the length of the stream is the same as the length of the wire, in whatever common frame you make both measurements. The electrons spread out to fill whatever "vessel" they are in. Baseballs don't do that. The electrons behave more like a gas than a solid. For the purpose of the thought experiment you might as well consider the wire bent to form a continuous circular loop. Now which part of the circumference of a circle is its centre? 


#23
Feb1412, 08:35 PM

P: 1,011

BTW: The electrons do not always "spread out" to fill whatever "vessel" they are in. Sometimes they must "be compressed inwards" to match the new "specific volume" encountered. The problem is that what you say is likely false, considering why the concept of length contraction was conceived in the first place: http://en.wikipedia.org/wiki/Length_contraction 


#24
Feb1412, 09:40 PM

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It seems to me that the Ladder paradox is relevant here:
http://en.wikipedia.org/wiki/Ladder_paradox 


#25
Feb1412, 09:46 PM

Mentor
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#26
Feb1412, 10:07 PM

P: 1,011

http://en.wikipedia.org/wiki/Relativ...g_point_charge But is there another affect on the Efield, due to time dilation? The following graphic suggests to me there is also an effect due to relativistic aberration: Is there any good summary of these effects? 


#27
Feb1512, 12:05 AM

P: 303

But I think what you are describing here is the magnetic force WHEN THE TEST CHARGE IS ALSO MOVING with the charges in wire. Whereas, my question is, why don't we see this magnetic force to come in play(or act) when the test charge is STATIONARY w.r.t the wire. Since, even without motion of the test charge there should be the length contraction of the moving charges in the wire, when there is current, and therefore there should be a force even on the stationary test charge. 


#28
Feb1512, 06:01 AM

Mentor
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#29
Feb1512, 07:32 AM

P: 262

Also earlier on you said: Personally I've also got big troubles believing that magnetism is no more then a Lorentz boosted electrostatic field. 


#30
Feb1512, 07:53 AM

Mentor
P: 17,344

In units where c=1 define the fourcurrentdensity: [itex]J^{\mu} = (\rho,j_x,j_y,j_z)[/itex] where [itex]\rho[/itex] is the charge density and the j's are the current density in each direction in an inertial reference frame. Then: [itex]J^{\mu'}=\Lambda^{\mu'}_{\mu}J^{\mu}[/itex] where [itex]\Lambda[/itex] is the Lorentz transform. 


#31
Feb1512, 08:19 AM

Mentor
P: 17,344

In case I was misunderstanding universal's previous question, let me clarify the situation:
Frame 1 (lab frame): Wire is neutral and carries a current. Test charge is moving. Electrostatic force on test charge is 0 because wire is neutral. Magnetic force on test charge is nonzero since charge is moving. Frame 2 (testcharge frame): Wire is charged and carries a current. Test charge is at rest. Electrostatic force on test charge is nonzero because the wire is charged. Magnetic force on test charge is 0 since charge is not moving. 


#32
Feb1512, 09:24 AM

P: 262

I think I have the same (perhaps faulty) thought process as universal, when he says: My take on it is (and the reality is) that no such extra electrostatic force is present therefore this whole idea of a magnetic field being a Lorentz boosted electrostatic field is for a lot of us hard to believe. 


#33
Feb1512, 10:00 AM

P: 3,187

You refer perhaps to explanations (often accompanied by nice looking calculations) according to which magnetism is claimed to be a kind of illusion due to length contraction.
The most basic and simple case (although very high tech) that I can imagine, as it completely avoids issues with electron source and drain, is that of a closed loop superconductor in which a current is induced. We thus start with, I think, an insulated wire containing a number of electrons N and an equal number of protons N. I think that the following situation sketch is correct: In the wire's rest frame:  length contraction can play no role at all  a magnetic field is observed In any inertial moving frame:  length contraction plays a role in predicting nonzero electric fields  a magnetic field is observed that can't be transformed away Is that correct? Such a magnetic field looks reasonably "absolute" to me. Harald 


#34
Feb1512, 10:05 AM

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P: 17,344

In this physically different situation there is no force since the wire is uncharged (no electrostatic force) and the test charge is not moving (no magnetic force). In other frames there will be both an electrostatic and a magnetic force, but they will cancel each other for 0 total EM force. However, I would also disagree with the idea of a magnetic FIELD being a boosted electrostatic FIELD, the math doesn't support that. The correct statement would be that a magnetic FORCE is a "boosted" electrostatic FORCE, which the math supports. If you just have the field then you don't have a rest frame. You need a test charge on which there is a force so that you can boost to the test charge's rest frame where there is no magnetic force. 


#35
Feb1512, 11:19 AM

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#36
Feb1512, 12:22 PM

P: 303

Second, I believe that whole point of this debate/discussion is that we want to understand magnetic force as a relativistic effect of electrostatics. But, you are explicitly using the two types of forces to explain the experimental observations. Which puts the magnetic force in the categories of absolute forces. Because, if we are unable to explain the motion of charged particles without introducing the magnetic force then it compels us to think of it as an absolute property. 


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