Magnetism seems absolute despite being relativistic effect of electrostatics

Per Oni

Because of the fact that the test charge sees a current flowing in the conductor.
Let’s look at the situation I thought I was referring to, which is a test charge stationary wrt a wire. What I ment to say is that in reality there are no different (although I said extra) electrostatic forces on the test charge whether a current flows or not. Can we agree on this?

universal_101

First, Yes, you did misunderstand my question,

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.

kmarinas86

Why would the length contraction play a role in predicting non-zero fields when the number of positive charge and negative charges are equal?

In any case, does not the relative velocity between the charges pay a role here?

It is as if both relative velocity between charges and relative velocity between the the charges and the observer both collude in determining whether or not non-zero fields are observed.

I cannot simply call that "length contraction". Like another had stated, it is "length contraction plus something else".

Also, what if we inverted things and called the protons the "current" and the electrons the "wire"? In this case, the magnetic field would be seen as being produced by the positive charges. In contrast, the negative charges would not be seen as responsible for the magnetic field. The electron frame would be the "rest" frame of the wire. Would then we say that there exists zero electric field outside the wire from the "rest" frame of the electrons? And if we would move to the proton frame, now regarded as the "rest" frame of the current, would we then say that there is a non-zero electric field outside the wire?

This begs the question, "Could the problem be interpreted such that there is ALWAYS a non-zero electric field outside the wire, depending on what one regards as being 'current'?" Obviously there is a gap in reasoning going on here. So what's up with that?

Alternatively, if you consider the fact that "ionic current" or "positive charge" current can be just as guilty in producing magnetic fields as the electron current, one would realize that for the case of a neutral wire, different Lorentz transformations do not lead to differences in the magnetic flux. The magnetic field produced by a + charge is equal and opposite of that produced by a - charge if their movements are the same. So the magnetic flux produced by the neutral wire should be frame invariant. What changes is the magnetic flux intensity (a.k.a. magnetic flux density) and corresponding area of integration (an area which is itself subject to Lorentz transformations). This is same as with the electric flux; the Lorentz transformation leaves it unaltered (with the electric field intensity (a.k.a. electric flux density) and corresponding integration being subject to exact same transformation as that of their magnetic counterparts).

Now, if we the consider the case where have only an electron beam (no positive charges), we must realize that a charge in a co-moving frame same as that of another charge, is not going to experience a magnetic force from that other charge, but only an electrostatic force. This is the same electrostatic force that one would expect if you simply had the two charges at so-called rest, separated by the same distance (correcting for the Lorentz transformation of course). However, if you have the charges moving at different speeds, there is a relative velocity between them. Only then can you say that they interact magnetically.

It appears it is the relative velocity (or lack thereof in other cases) that determines whether or not there is magnetic interaction between particles in a system.

Of course, you can predict that two electrons co-moving relative to an external observer will have a magnetic field around them, but that magnetic field is not something that the charges interact with, because in their frame, that field simply does NOT exist. So as long as nothing in the frame of the external observer interacts with those particles, the magnetic field as seen from the point of view of the external observer may as well not exist, for lack of physical significance.

DaleSpam

This is kind of a strange thing to try to analyze in a discussion about relativity. The current flowing or not flowing are two physically different situations in the same reference frame. Usually relativity is used to analyze the same physical situation from two different reference frames.

Certainly your approach could be useful for learning EM, but not for learning relativity nor for learning about the relativistic connection between electric and magnetic forces and fields. I would suggest starting a new thread in the Classical Physics forum.

In the wire frame, yes, I agree. In other frames it is not correct. The electrostatic and magnetic forces are frame-variant, so you have to specify the frame whenever you talk about them.

DaleSpam

The magnetic force was 0 in one frame and non-zero in another frame. Physics quantities don't get any more relative than that. I don't know how you came to your conclusion, but it is wrong. If a quantity depends on the reference frame then by definition it is relative, not absolute.

kmarinas86

You have positive charges. Positive charges can produce a magnetic field.

Calling electrons the current, while yet ignoring the contribution of the magnetic field by the positive charges, is completely wrong and arbitrary.

For the magnetic field of a neutral entity, a Lorentz transformation should result in equal and opposite changes in the magnetic flux contributions by the negative and positive charges. (Net field intensity should depend on length contraction, yes, but not the flux).

DaleSpam

I agree. I don't know if others are ignoring some of the charge carriers, but I am not.

I doubt that this is correct, but I almost never work with the integral form of Maxwell's equations so I am not certain. I would want to see a proper derivation before making a strong statement either way, or at least work a couple of examples.

universal_101

This is very well put, but I'm not questioning the relative nature of magnetic force in different frames, actually, nobody is. The problem is why do we have to invoke the magnetic force if the magnetic force itself is supposedly can be explained as the relativistic effect of the electrostatics.

jartsa

When line of objects starts moving, length contraction may be observed, or length contraction may not be observed. Rigid bodies contract, other things may either contract or not.

When observer observing line of objects, starts moving, he will observe length contraction.

So I'm saying scenario1 and scenario2 differ this way. (motion without length contraction vs. motion with length contraction)

DaleSpam

You don't have to invoke the magnetic force in the rest frame of the test particle. Once you have the total force in the rest frame, you can then transform and find the total force in any other frame, without ever invoking the magnetic force.

The magnitude of the total force in the other frame is a relativistic effect of electrostatics. It differs from the electrostatic force in the other frame by a certain amount, that amount is called the magnetic force. Thus, the magnetic force is a relativistic effect of electrostatics.

kmarinas86

How do the formulas of SR recognize rigidity? Is it quantifiable? What happens if I have an egg container, and in each egg placeholder I have either a "rigid" body or a non-rigid body. How does that work? I thought that SR does not permit "fully" rigid bodies.

jtbell

We don't have to. In principle, we can start in the particle's rest frame and Lorentz-transform the force (which is purely electrostatic in that frame) into the frame that we actually use for observing the particle.

However, for practical problem-solving, it's usually more convenient to use only one reference frame, namely the one in which we observe the particle. So we invoke both electric and magnetic forces in that frame, and the net force gives the same result as the first approach.

Doing the Lorentz transformation is fairly simple if the motion is uniform. If the motion isn't uniform, it becomes messy.

jartsa

Move one part of rigid body, other parts of rigid body will follow.

Well maybe I meant elastic body.

Let's consider a line of cars driving 50 mph, making a 90 degrees turn at street corner. We newer see any car moving at any other speed than 50 mph, so the line does not contract. Cars do contract. When a car contracts its rear end moves faster than its front.

Electron flow in rectangular circuit behaves the same way.

universal_101

Well, transformation of one force into another is easy to understand and follow, but as long as the transformation is consistent all the way.

Please, try to analyse the situation,

when there is a current, the charges in the wire start moving in a particular direction, but when there is NO current there is NO motion. Therefore, according to the transformation of one force into other, there should be a force on a stationary charge standing near by, towards the current carrying wire, when there is current.

Remembering, that my original post/question is exactly same situation, to which the answer was the transformation of one force into another, to explain the magnetic force.

harrylin

In a frame in which the charges are moving at different velocities, the charge distribution may be inhomogeneous. However I suppose that that is not the point of this discussion: I merely noticed that for such a case length contraction may play a role in what is not under discussion here. My point is that according to my analysis, magnetic fields can in general not be transformed away.
Sorry I can't follow that; a magnetic field appears as the result of whatever moving charges - no matter if those are the protons or electrons or both.
A non-zero (at least, non negligible) electric field can be measured.
For a current-free wire, indeed. That isn't an issue.
The Lorentz transformation does the same as the introduction of a magnetic force; that realisation is the basis for this kind of discussions. However, as I illustrated, more insight can be obtained if one doesn't limit one's thinking to linear cases and instead considers a more basic magnet such a made with a single wire loop.
Your argument doesn't apply to more general cases as I illustrated. Magnetic and electric fields are relative in the way that length contraction and simultaneity are relative; it doesn't mean that one of the concepts should be discarded.

kmarinas86

What is the quantity and its symbol? How is it used in the equations of SR? Can it be plugged into Lorentz transforms?

jartsa

Are you trying to bully me or what? Collection of free particles may retain its shape when accelerated, without any stresses. When free particles are glued together, we have a rigid body, which must length contract, when accelerated, or else stresses are generated in the body.