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Magnetism seems absolute despite being relativistic effect of electrostatics 
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#55
Feb1612, 03:56 PM

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In that case, I cannot at all see how changes in the Efield can compensate precisely for changes in the Bfield. They simply do not match. So it can undershoot or overshoot the requirement for compensating for the difference of the B between different LT frames. Alternatively, if B varied with the rapidity [itex]\varphi[/itex] (with respect to LT frames, not time or acceleration, mind you), it would not be an exact match either: Column 1: [itex]v/c[/itex] Column 2: [itex]\varphi[/itex] Column 3: [itex]\gamma[/itex] Column 4: Change in Column 2 Column 5: Change in Column 3 Column 6: Column 2 / Column 3
Meanwhile, in SR, the "relativistic energy" of a particle is relative to LT frames. So the idea that the magnetic field is simply the relativistic component of the electric field appears doomed. SR would have no problem having the change in the E field be more than and/or less than what would be needed to compensate for the magnetic field, for it appears to be required to have the "relativistic energy" of a particle to vary. By the way, if some E fields and some B fields cannot transform away, then the claim that electric fields and magnetic fields are part of the same "electromagnetic field" seems dubious at best. Maybe we should move away from the field concepts and stick with the vector potential instead. 


#56
Feb1612, 04:25 PM

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PF Gold
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Attached to the bottom of this post is a diagram to help explain things. As was mentioned earlier in this thread, one way to approach the problem is to consider it a variant of the ladder paradox, and consider the different definitions of simultaneity.
But my approach here considers length contraction only. And I am going to consider a complete circuit: not just a single wire with a lefttoright electron flow, but also a return wire with a righttoleft flow. Apart from the ends of the wires, we keep the two wires far apart so they have negligible influence on each other. The diagram is a highly idealised simplification, considering just 16 electrons in the circuit. The ends of the wires should be in contact with each other but I've drawn them as separated to keep the diagram simple. The top left part of the diagram shows the wires with no current flowing, in the restframe of the wires. 16 electrons equally spread out along the wire. The top right part of the diagram again shows the wires with no current flowing, but now in a frame moving at the velocity that electrons would flow in the bottom wire if the current were on. We see length contraction as indicated by the yellow arrows. I'm assuming a Lorentz factor γ=2. So far so good. The two bottom diagrams now show what happens when the current is flowing. In the bottom left diagram, as we are told the wires remain electrically neutral, there must still be 16 electrons in the wires. There's no reason for the electrons to bunch together anywhere, they will remain spread out around the whole circuit as shown. Finally, let's look at the bottom right diagram, which I think some people are having difficulty to imagine. We already know what happens to the red positive ions, their separation contracts just as before. The electrons in the lower wire are now stationary, so their separation must be larger than the bottom left diagram as shown. On the other hand, the electrons in the upper wire are moving faster than in bottom left diagram, so their separation must be less than in bottom left diagram. No electrons have escaped so the total number of electrons in circuit must still be 16. But now there are fewer electrons in the lower wire and more in the upper wire. So the lower wire has a positive charge and the upper wire has a negative charge. 


#57
Feb1612, 04:39 PM

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It doesn't seem to have been mentioned in this thread yet. The E and B fields are used to construct a 4×4 matrix[tex]
F^{\mu\nu} = \begin{bmatrix} 0 & E_x/c & E_y/c & E_z/c \\ E_x/c & 0 & B_z & B_y \\ E_y/c & B_z & 0 & B_x \\ E_z/c & B_y & B_x & 0 \end{bmatrix} [/tex]This is a rank2 tensor whose components transform as a tensor, i.e. there's a double Lorentz transformation involved. 


#58
Feb1612, 04:39 PM

P: 1,011

The ladder paradox also has some asymmetries that seem to be missing in your example: Figure 4: Scenario in the garage frame: a length contracted ladder entering and exiting the garage Figure 5: Scenario in the ladder frame: a length contracted garage passing over the ladder The two frames do not see the same number of rungs inside the garage in each case. If we assumed that the protons were represented as tiles on the garage floor, the garage as the wire, and the ladder as the electron current in and out of the wire, then clearly the charge inside the boundary of the garage is not invariant. However, considering that the electric field intensity increases by the same amount that the boundary of the garage in the LT frame is length contracted, this would keep the electric flux around that boundary of the garage a constant. 


#59
Feb1612, 05:25 PM

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If you ignore my return wire and concentrated on my lower wire only, it seems to me that my diagram agrees with your ladder diagram, so I haven't grasped what your problem is. 


#60
Feb1612, 05:37 PM

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There can be charge outside the wire ends (say at the ends of a capacitor or what not). 


#61
Feb1612, 06:13 PM

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In my example the number of electrons decreases from 8 to 2. In the ladder example, the number of rungs within the garage decreases from more than 11 to about 7. (Note: on a technicality "conserved between frames" should really be described as "invariant". "Conservation" refers to lack of change over time within a single frame.) 


#62
Feb1612, 06:34 PM

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#63
Feb1612, 06:53 PM

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#64
Feb1612, 07:42 PM

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#65
Feb1612, 07:48 PM

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First, there is no such thing as "conserved between frames". Conservation means that something is the same across time. When a quantity is the same in different frames it is called "invariant", not "conserved". The two concepts are completely different. Second, it is not true that the net charge on the wire is invariant. I will deal with more of your posts later, but you have really posted a lot of nonsense today. 


#66
Feb1612, 07:53 PM

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Invariant and conserved are different things! Invariant and conserved are different things! Invariant and conserved are different things! .... P.S. I've long used the term "timeinvariant" to mean conserved. I must stop doing that. P.S.S. On another note, I wonder if (http://en.wikipedia.org/wiki/Timeinvariant_system) is better termed (timeindependent system). (j/k the answer is obvious) 


#67
Feb1612, 10:41 PM

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#68
Feb1612, 10:47 PM

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Also, your reasoning doesn't make sense: a current is moving charges, forces transform, therefore there is a force on a stationary test charge. If you could step through your reasoning in a little more detail then I could probably point out where it falls apart, but as it is all I can say is that the premises don't imply the conclusion. 


#69
Feb1612, 11:02 PM

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Scenario (1) and scenario (2) are NOT identical w.r.t the principle of relativity. They are physically different scenarios. In (1) the test charge is at rest relative to the protons and in (2) the test charge is at rest relative to the electrons. There is no way to Lorentz transform (1) into (2). If you want the identical scenario then you need to change (2) so that the test charge is moving with the same velocity as the protons. That way the test charge will be at rest wrt the protons in both scenarios. 


#70
Feb1612, 11:48 PM

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I'm sure you know this already, but then I can't seem to figure out why are you implying anything like this. 


#71
Feb1712, 07:07 AM

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The LT can be applied to any scenario to generate an infinite number of other scenarios which are, in fact, physically identical to the original scenario. However, two arbitrary scenarios are not necessarily related to each other via a LT. In your case, (1) and (2) are not related by a LT. 


#72
Feb1712, 11:24 AM

P: 303

Either the scenarios are different, or, they can be explained by LT. And if you still think they are different, then please explain, why does the link you provided uses LT to explain different scenarios. 


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