Magnetism seems absolute despite being relativistic effect of electrostatics

Let's consider a simple model of a conducting wire,

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Now, let's suppose there is some current in the wire and the electrons are moving at speed 'v' w.r.t the the wire,
secondly, a stationary test charge w.r.t the wire lying around.

Naming the above scenario as (1)

Now, the test charge starts moving in the direction of electrons with the same speed 'v'.
This time in the reference frame of the test charge, electrons are stationary and nucleus(positive charge) is moving at speed 'v'.

Naming this scenario as (2)

And so the question arise, the two scenario are identical w.r.t principle of relativity. That is, in the first case only negative charges are moving, but there is no force on the charge. But in the second case when positive charges are moving there is a force on the test charge(magnetic force towards wire). Whereas, the two cases are essentially identical w.r.t principle of relativity.

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.

If this is how you see it, then how are you able to explain different scenario with Lorentz transformation. Or, can LT be applied on different scenarios/situations too ?

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

Here is probably the best resource for this question:
http://physics.weber.edu/schroeder/mrr/MRRtalk.html

Your scenarios are explicitly covered in the section "Magnetism as a Consequence of Length Contraction".

Sorry, I don't know if there is a language barrier, but I cannot really parse your post. I will answer what I guess is your question, but if I guess wrong please try to clarify your question carefully.

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.

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.

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.

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.

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?

I'm not sure what you mean by length contraction "being responsible".

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?

[..] 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?

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?

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.

Magnetism is not caused by length contraction.

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?

OK, I agree with this statement. We’re getting closer. What then is the cause of magnetism?