# Magnetism seems absolute despite being relativistic effect of electrostatics

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P: 17,206
 Quote by universal_101 You described the two scenarios using LT, and now you are implying that the two scenarios are different. But to have a debate, you should stand with only one of the following.
As I stated above, I mis-read your OP. The scenarios that I described using the LT correspond to your scenario (1) and to the LT of (1). They do not correspond to your scenario (2). I identified the modification that you would need to make to (2) in order to make it physically equivalent to (1).

 Quote by universal_101 Either the scenarios are different, or, they can be explained by LT.
They are different.

 Quote by universal_101 And if you still think they are different, then please explain, why does the link you provided uses LT to explain different scenarios.
It doesn't. The link I provided uses the LT to analyze the same scenario from two different reference frames. The scenario analyzed in the link is not the same as your (1) or (2).
 P: 3,187 There was a discussion here about almost the same topic a long time ago: http://www.physicsforums.com/archive.../t-327854.html I agree with what I read there on the first page; I haven't read the whole discussion. Note: Also dalespam participated. Dalespam, do you agree with your comments of then?
P: 262
 Quote by DrGreg 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 left-to-right electron flow, but also a return wire with a right-to-left 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 rest-frame 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.
DrGreg, stunning diagrams! But I disagree on the physics.

Some questions: why aren’t the electrons allowed to bunch together in the bottom left but they are allowed to bunch in the bottom right picture?

Referring to the bottom left picture, Biot-Savart tells me there’s a magnetic field present. Can you show me how length contraction is responsible for this magnetic field?
PF Gold
P: 1,847
 Quote by Per Oni Some questions: why aren’t the electrons allowed to bunch together in the bottom left but they are allowed to bunch in the bottom right picture?
The bottom left diagram is symmetrical: the upper wire is identical to the bottom wire apart from the direction of the electron flow. Therefore there's no reason for the electron distribution to be different in the two wires. The electrons just spread out to fill the space that is available to them.

The bottom right diagram is not symmetrical: in the bottom wire the electrons are at rest and in the upper wire the electrons move faster than the ions. The bottom rest diagram is obtained by considering Lorentz contraction between the two lower diagrams, as indicated by the yellow arrows. If you accept the bottom left diagram is correct, then the bottom right diagram must be correct too. Note that I could have drawn another diagram showing the frame in which the electrons in the upper wire were at rest. This diagram would look like the bottom-right diagram drawn upside down, with two static electrons in the upper wire and 14 moving rapidly to the right in the lower wire.
 Quote by Per Oni Referring to the bottom left picture, Biot-Savart tells me there’s a magnetic field present. Can you show me how length contraction is responsible for this magnetic field?
I'm not sure what you mean by length contraction "being responsible". We have moving electrons, i.e. a current, and therefore a magnetic field, as you say by Biot-Savart. I'm not sure what else there is to explain?
P: 262
 Quote by DrGreg I'm not sure what you mean by length contraction "being responsible".

From post #2 in this thread:
 Your scenarios are explicitly covered in the section "Magnetism as a Consequence of Length Contraction".
Are they not the same issues? Are you not going to explain how magnetism is a result of length contraction?
PF Gold
P: 1,847
 Quote by Per Oni Are they not the same issues? Are you not going to explain how magnetism is a result of length contraction?
OK, I see what you are asking now -- I haven't been following this thread from the beginning.

In the bottom right diagram, a static (relative to the frame) electron near to but outside the lower wire will be attracted to it due to the net positive charge on the wire. As the electron is static, magnetism is irrelevant to it.

Translating that to the bottom left picture, the electron is now moving but the wire is not charged, so there is no electrostatic force. Nevertheless, there is still an attractive force, as we proved using the bottom right picture. The explanation for this force is magnetism. If you already knew about electrostatics and relativity but knew nothing about electromagnetism, this argument would effectively define for you what electromagnetism was.
P: 3,187
 Quote by Per Oni [..] From post #2 in this thread [..] Are they not the same issues? Are you not going to explain how magnetism is a result of length contraction?
The sub title on the web page that you refer to can be a bit misleading, as I also illustrated in post #33. Magnetism is not caused by length contraction.
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P: 17,206
 Quote by harrylin There was a discussion here about almost the same topic a long time ago: http://www.physicsforums.com/archive.../t-327854.html I agree with what I read there on the first page; I haven't read the whole discussion. Note: Also dalespam participated. Dalespam, do you agree with your comments of then?
Yes, I went back and reviewed the thread, my comments are still correct AFAIK.
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P: 17,206
 Quote by Per Oni Can you show me how length contraction is responsible for this magnetic field?
Careful here. You can always use relativity to explain a magnetic FORCE as a relativistic transformation of an electrostatic force in another frame, but you cannot always use relativity to explain a magnetic FIELD as a relativistic transformation of an electric field in another frame.
P: 1,011
 Quote by DaleSpam Careful here. You can always use relativity to explain a magnetic FORCE as a relativistic transformation of an electrostatic force in another frame, but you cannot always use relativity to explain a magnetic FIELD as a relativistic transformation of an electric field in another frame.
Shouldn't the lines of force correlate with the cause of the "FORCE" in question? That you can "always use relativity to explain a magnetic FORCE as a relativistic transformation of an electrostatic force" should imply that what is caused by magnetic flux density in one frame is cause by electric flux density in another frame. How is that the former is true but the latter not?
P: 262
 Quote by harrylin Magnetism is not caused by length contraction.
OK, I agree with this statement. We’re getting closer. What then is the cause of magnetism?

@DrGreg. It is perhaps a useful exercise to look at what happens in different frames with test charges and so on but as you stated there’s a magnetic field present in the left bottom picture. Now we have to find out why this magnetic field is there. I do not need any test charges travelling or not. Fact is we have a magnetic field. So we have to find out why the power supply had to inject an extra amount of energy. We have to find out why the energy contribution of the 2 parts of wires is increased as we increase the distance between those parts.
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P: 17,206
 Quote by kmarinas86 That you can "always use relativity to explain a magnetic FORCE as a relativistic transformation of an electrostatic force" should imply that what is caused by magnetic flux density in one frame is cause by electric flux density in another frame. How is that the former is true but the latter not?
Remember that the magnetic field by itself does not describe the force on a charge, but you also need the velocity of the charge. The magnetic field is not proportional to the force on a charge, and knowing information about one does not uniquely determine the other without some additional information.

Furthermore, the magnetic field does not have a rest frame, whereas the magnetic force always acts on a particle which does have a rest frame. So, in general, you can always transform to a frame where the particle is at rest and be guaranteed that the magnetic force is 0, but in that frame the magnetic field may be non-zero. In general, there is not necessarily any frame where the magnetic field is 0.
P: 3,187
 Quote by Per Oni OK, I agree with this statement. We’re getting closer. What then is the cause of magnetism?
According to Ampere-Maxwell, magnetism is caused by the motion of the charges - perhaps we might say, by moving electric fields.

It's a bit similar to time dilation and length contraction which according to SR are caused by speed, and while for special cases all relevant speeds can be transformed away, in general this is not possible.
This it should perhaps not surprise that the same type of "absolute" vs. "relative" discussions can arise about magnetic fields as with for example the twin paradox.
P: 1,011
 Quote by DaleSpam Remember that the magnetic field by itself does not describe the force on a charge, but you also need the velocity of the charge. The magnetic field is not proportional to the force on a charge, and knowing information about one does not uniquely determine the other without some additional information. Furthermore, the magnetic field does not have a rest frame, whereas the magnetic force always acts on a particle which does have a rest frame. So, in general, you can always transform to a frame where the particle is at rest and be guaranteed that the magnetic force is 0, but in that frame the magnetic field may be non-zero. In general, there is not necessarily any frame where the magnetic field is 0.
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I am glad, you are welcome!
P: 262
 Quote by harrylin According to Ampere-Maxwell, magnetism is caused by the motion of the charges - perhaps we might say, by moving electric fields.
That’s the way I see it.

To expand on this:
What happens when we Lorentz boost an electric field (E0)? Well we get E’=γE0. Same question regarding a magnetic field (B0). Similar, B’=γB0. How then do we get from one to the other? Clearly not by Lorentz boosting!

For the purpose of transferring between electric and magnetic fields we have 2 equations which deal with moving fields.
The following 2 formulas are copied from “Introduction to electrodynamics 3rd edition D.J.Griffiths” Formula 12.108.
Ey’=γ(Ey – vBz) and By’=γ(By + v/C^2 Ez) where v is in the x direction.
(Some time ago I lost LaTex for Microsoft Word due to a virus, does anyone know where to buy a copy?)

When we say “moving fields” I think the correct expression is “time varying fields”. But I also visualise them as moving. I’m fairly confident that these 2 formulas can also be derived from Dale’s four-vectors equation (# 30) but not sure.
See post #57 and apply$$\tilde{F}^{\tilde{\mu}\tilde{\nu}}=\Lambda^\tilde{\mu}_\alpha F^{\alpha\beta} \Lambda_\beta^\tilde{\nu}$$where $\Lambda^\tilde{\mu}_\alpha$ is the Lorentz boost matrix.