Magnetism seems absolute despite being relativistic effect of electrostatics

going from 0 current to a very high current would cause the following to occur: ...

No, I already covered the non-steady state situation in post 8. None of your suggestions are correct, neither in the transient nor in the steady-state conditions.

[....] You don't have just the fundamental particles contracting. In the extreme case, going from 0 current to a very high current would cause the following to occur:

This

into this

or

or


et cetera

It wouldn't be as simple as that. Remember the relativity of simultaneity.

Suppose that you suddenly turn the current on at time t=0 in the lab frame. So at t=0 electrons begin leaving one end of the wire at a certain rate and entering the other end of the wire at the same rate, so there is no net charge. In the moving frame the beginning of the electrons leaving one end is not the same time as the beginning of the electrons entering the other end, so there is a net charge.

I think it is perhaps worth pointing out that some people have a false impression about what Lorentz contraction is. They may think that "when something accelerates it gets shorter". Or to be a bit more precise, if Alice measures (=x) something at rest (relative to Alice) and then later measures (=y) the same thing in motion, the length contracts. There may then be some debate over whether or not the "things" this applies to are just solid objects, or gaps between objects, or "space itself".

The above description of Lorentz contraction is wrong.

In many circumstances, what I said above is true, but reason it is true is not simply Lorentz contraction alone; it is Lorentz contraction plus some other reason combined.

A more accurate description of Lorentz contraction is that when inertial observer Bob measures the length z between two things both at rest relative to Bob, and another inertial observer Alice in relative motion measures the length y between the same two things at the same time, Alice measures a shorter distance than Bob.

So, the situation I described in the first paragraph will arise if there is a reason why Alice's initial "rest distance" x between the two things beforehand is the same as the Bob's final "rest distance" z. For example if the the two things are the two ends of a rigid object that doesn't break into pieces as a result of the acceleration.

The attached illustration emphasises my point. The transformation of x to y is not Lorentz contraction. The transformation of z to y is Lorentz contraction. If there is a reason why x = z, then the transformation of x to y will be a contraction. But if there's no reason, then contraction need not occur.

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 rest-distance between them when moving to equal the rest-distance when not. In fact they will spread out to fill whatever space is available to them.

There is no "centre of contraction" because contraction-due-to-acceleration doesn't occur.

There "may be" debate about it? You know this, or is that just a way of saying that others may debate about that if they like?

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 finite-length 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?

I've witnessed a number of such debates in this forum. All based on a false notion of what "Lorentz contraction" is. It's not a comparison of before and after, it's a comparison from two different observers at the same time.

==Experimental verifications==
{{See also|Tests of special relativity}}

Since the occurrence of length contraction depends on the inertial frame chosen, it can only be measured by an observer ''not'' at rest in the same inertial frame, ''i.e.'', it exists only in a non-co-moving frame. This is because the effect vanishes after a Lorentz transformation into the rest frame of the object, where a co-moving observer can judge himself and the object as at rest in the same inertial frame in accordance with the relativity principle (as it was demonstrated by the Trouton-Rankine experiment). In addition, even in a non-co-moving frame, ''direct'' experimental confirmations of Lorentz contraction are hard to achieve, because at the current state of technology, objects of considerable extension cannot be accelerated to relativistic speeds. And the only objects traveling with the speed required are atomic particles, yet whose spatial extensions are too small to allow a direct measurement of contraction.

However, there are ''indirect'' confirmations of this effect in a non-co-moving frame. It was in fact the negative result of a famous experiment, that required the introduction of Lorentz contraction: the Michelson-Morley experiment (and later also the Kennedy–Thorndike experiment). In special relativity its explanation is as follows: In its rest frame the interferometer can be regarded as at rest in accordance with the relativity principle, so the propagation time of light is the same in all directions. However, in a frame in which the interferometer is in motion, the propagation time of the transverse beam is time dilation|time dilated, while in the longitudinal direction the interferometer is also contracted, so that speed of light is constant and the propagation time in both directions is the same in this frame as well.

Other indirect confirmations are: Heavy ions that are spherical when at rest should assume the form of "pancakes" or flat disks when traveling nearly at the speed of light. And in fact, the results obtained from particle collisions can only be explained, when the increased nucleon density due to Lorentz contraction is considered.[http://www.bnl.gov/rhic/physics.asp][http://nuclear.ucdavis.edu/~calderon...Research.html][http://www.gsi.de/forschung/kp/kp2/c.../R3B/EME.html][http://arxiv.org/abs/physics/0105022] Another confirmation is the increased ionization ability of electrically charged particles in motion. According to pre-relativistic physics the ability should decrease at high speed, however, the Lorentz contraction of the Coulomb's law|Coulomb field leads to an increase of the electrical field strength normal to the line of motion, which leads to the actually observed increase of the ionization ability.[http://en.wikipedia.org/wiki/Special...es/3528172363] Lorentz contraction is also necessary to understand the function of free-electron lasers. Relativistic electrons were injected into an undulator, so that synchrotron radiation is generated. In the proper frame of the electrons, the undulator is contracted which leads to an increased radiation frequency. Additionally, to find out the frequency as measured in the laboratory frame, one has to apply the relativistic Doppler effect. So, only with the aid of Lorentz contraction and the rel. Doppler effect, the extremely small wavelength of undulator radiation can be explained.[http://hasylab.desy.de/science/stude...ndex_eng.html][http://flash.desy.de/sites/site_vuvf...refrs_web.pdf] (PDF 7.8MB)] Another example is the observed lifetime of muons in motion and thus their range of action, which is much higher than that of muons at low velocities. In the proper frame of the atmosphere, this is explained by the time dilation of the moving muons. However, in the proper frame of the muons their lifetime is unchanged, but the atmosphere is contracted so that even their small range is sufficient to reach the surface of earth.<ref name=sexl />

Resolution
Figure 7: A ladder contracting under acceleration to fit into a length contracted garage

In the context of the paradox, when the ladder enters the garage and is contained within it, it must either continue out the back or come to a complete stop. When the ladder comes to a complete stop, it accelerates into the reference frame of the garage. From the reference frame of the garage, all parts of the ladder come to a complete stop simultaneously, and thus all parts must accelerate simultaneously.

From the reference frame of the ladder, it is the garage that is moving, and so in order to be stopped with respect to the garage, the ladder must accelerate into the reference frame of the garage. All parts of the ladder cannot accelerate simultaneously because of relative simultaneity. What happens is that each part of the ladder accelerates sequentially, front to back, until finally the back end of the ladder accelerates when it is within the garage, the result of which is that, from the reference frame of the ladder, the front parts undergo length contraction sequentially until the entire ladder fits into the garage.

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.

What you say is correct except that you have the frames wrong.

The wire is neutral and carries a current in the lab frame. Charge density transforms like time and current density transforms like space. So there is "charge density dilation" and "current density contraction" in the test-charge frame. The result is that the wire is charged in the moving frame.

== The field of a moving point charge ==
|frame|'''Figure 3''': A point charge at rest, surrounded by an imaginary sphere.

|frame|'''Figure 4''': A view of the electric field of a point charge moving at constant velocity.

A very important application of the electric field transformation equations is to the field of a single point charge moving with constant velocity. In its rest frame, the electric field of a positive point charge has the same strength in all directions and points directly away from the charge. In some other reference frame the field will appear differently.

In applying the transformation equations to a nonuniform electric field, it is important to record not only of the value of the field, but also at what point in space it has this value.

In the rest frame of the particle, the point charge can be imagined to be surrounded by a spherical shell which is also at rest. In ''our'' reference frame, however, both the particle and its sphere are moving. Length contraction therefore states that the sphere is deformed into a spheroid, as shown in cross section (geometry)|cross section in Fig 4.

Consider the value of the electric field at any point on the surface of the sphere. Let x and y be the components of the displacement (vector)|displacement (in the rest frame of the charge), from the charge to a point on the sphere, measured parallel (geometry)|parallel and perpendicular to the direction of motion as shown in the figure. Because the field in the rest frame of the charge points directly away from the charge, its components are in the same ratio as the components of the displacement:

:[itex]{E_y \over E_x} = {y \over x}[/itex]

In our reference frame, where the charge is moving, the displacement x' in the direction of motion is length-contracted:

:[itex]x' = x\sqrt{1 - v^2/c^2} [/itex]

The electric field at any point on the sphere points directly away from the charge. (b) In a reference frame where the charge and the sphere are moving to the right, the sphere is length-contracted but the vertical component of the field is stronger. These two effects combine to make the field again point directly away from the current location of the charge. (While the y component of the displacement is the same in both frames).

However, according to the above results, the y component of the field is enhanced by a similar factor:

:[itex]E'_y = {E_y\over\sqrt{1 - v^2/c^2}} [/itex]

whilst the x component of the field is the same in both frames. The ratio of the field components is therefore

:[itex]{E'_y \over E'_x} = {E_y \over E_x\sqrt{1 - v^2/c^2}} [/itex]

So, the field in the primed frame points directly away from the charge, just as in the unprimed frame.
A view of the electric field of a point charge moving at constant velocity is shown in figure 4. The faster the charge is moving, the more noticeable the enhancement of the perpendicular component of the field becomes. If the speed of the charge is much less than the speed of light, this enhancement is often negligible. But under certain circumstances, it is crucially important even at low velocities.

Yes, when the current is ON then the electrons and the test charge are moving, all these effects are present, and there is a force.

In the lab frame the force is attributed to the magnetic force on the moving charge due to the current in the neutral wire. In the electron/test-charge frame the force is attributed to the electrostatic force on the stationary charge due to the net charge in the wire.

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.

The magnetic force is [itex]qv \cross B = F [/itex]. So if it is stationary then F is 0.

Charge density transforms like time and current density transforms like space. So there is "charge density dilation" and "current density contraction" in the test-charge frame. The result is that the wire is charged in the moving frame.

Hey Dale it’s obvious that universal was asking about the altered electrostatic force not about any magnetic force.

Can you put formulas to these 2 concepts?

Yes, are you familiar with four-vectors or tensors?

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.

This situation refers to your frame 1 but without the test charge moving. “If” there’s a Lorentz boost as seen from the test charge, it should feel an extra electrostatic force.

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.