Magnetism seems absolute despite being relativistic effect of electrostatics

[jartsa]

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

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.

 

[kmarinas86]

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.

Right, length contraction is relative.

The problem is:
* I can have the positive charge have a greater length contraction in the frame of the negative charge.
* I can have the negative charge have a greater length contraction in the frame of the positive charge.

Following the claims of DaleSpam's comments, this would mean that the wire can appear to have net positive charge or a net negative charge, depending on the frame of reference. There is also a frame in which the length contractions of the positive and negative charges match. I suppose that is when the electric-field outside the wire disappears.

Now that I think about it terms of length contraction, the changes of the electric field with respect to the frame given is NOT linear because the equations for length contraction do not have constant derivative with respect to relative velocity with the observer. Therefore, the LT would result in different change "factors" for the electric field of the electrons and the electric field of the protons in the case when there is current.

 

[kmarinas86]

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.

I though that force dynamics weren't a part of the Lorentz transformation.

This above sounds to me more like the "deformable electron" concept of Lorentzian-Ether theory.

 

[kmarinas86]

The idea that the electric field intensity of each charge being variant with respect to the observer isn't strange to me.

What's strange is the idea that steady-state (read: DC) current should somehow be uniform through out the wire when the protons and electrons clearly cannot be subject to the same length contraction.

Let's keep this REALLY simple. Assuming that the wire is neutral (no net charge) and that the wire is 1 meter long and that I have a length contraction of electrons, why should I get from that a uniform charge distribution when the electrons are drifting through wire (current)?

In the steady state the four-current (density) is uniform and constant in the lab frame, therefore it is uniform and constant in the test-charge frame also.

I would TOTALLY expect an un-uniform distribution, assuming length contraction applies to the bulk flow of electrons.

Why? Why do you expect a gap of any kind in the steady state?

I STILL don't have an answer to my question as to what do the electrons actually length contract towards.

Length contraction occurs, as always, in the direction of motion. The word "towards" doesn't make any sense in this context. The word "towards" implies something changing over time. Length contraction does not change over time in an inertial frame.

Ok, then let me ask it this way: From the lab frame, where is the center of contraction for the bulk of electron flow in a straight wire conductor? The contraction is only "linear", so I assume that this "center" of contraction must be a geometric plane. Where is that located in relation to the observer?

SR says that objects (read: multiple particles) will length contract. So, logically speaking, you can treat the + charges and - charges as two separate "objects" at different speeds. I assume this to mean not only the particles by themselves, but the entire bulks of the particles as a whole. For an object to contract, the distance in-between also has to contract. 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

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.

If the quantity of charge in a length measured by the observer were really to vary depending of the length contraction of each set of charges (the + set vs. the - set) whose length contraction values are different, we would see not only an frame-variant electric field intensity, but also, we would see an frame-variant electric FLUX as well in that length. In reality, if we Lorentz transform a system, we do NOT create positive charge and negative charges out of nowhere. Those additional electrons somehow fitting into the wire must be present with and without the Lorentz transformation. So if the wire was uniformly charged before the length transformation and after it, then some of the - charge that was OUTSIDE the wire without the LT is instead seen as being INSIDE the wire with that LT. The same would go with the + charge.

I guess that the difference of electric flux between different LT frames means that time-retardation effects apply to electric flux as well.

 

[kmarinas86]

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).]

For a current-free wire, indeed. That isn't an issue.

I thought that the observed magnetic field was directly proportional to relative velocity v. The electric field's dependence on \gamma should contrast with the magnetic field's dependence v.

In that case, I cannot at all see how changes in the E-field can compensate precisely for changes in the B-field. 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 \varphi (with respect to LT frames, not time or acceleration, mind you), it would not be an exact match either:

Column 1: v/c
Column 2: \varphi
Column 3: \gamma
Column 4: Change in Column 2
Column 5: Change in Column 3
Column 6: Column 2 / Column 3

0.00	0.00	1.00			
0.10	0.10	1.01	0.10	0.01	19.92
0.20	0.20	1.02	0.10	0.02	6.57
0.30	0.31	1.05	0.11	0.03	3.86
0.40	0.42	1.09	0.11	0.04	2.67
0.50	0.55	1.15	0.13	0.06	1.98
0.60	0.69	1.25	0.14	0.10	1.51
0.70	0.87	1.40	0.17	0.15	1.16
0.80	1.10	1.67	0.23	0.27	0.87
0.90	1.47	2.29	0.37	0.63	0.60

Only one other possibility: The B normal to the wire is proportional to \gamma_{v\ parallel\ to\ the\ wire}. The problem is that I never heard of it.

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.

 

[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]

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<br /> F^{\mu\nu} = \begin{bmatrix}<br /> 0 &amp; -E_x/c &amp; -E_y/c &amp; -E_z/c \\<br /> E_x/c &amp; 0 &amp; -B_z &amp; B_y \\<br /> E_y/c &amp; B_z &amp; 0 &amp; -B_x \\<br /> E_z/c &amp; -B_y &amp; B_x &amp; 0<br /> \end{bmatrix}<br />This is a rank-2 tensor whose components transform as a tensor, i.e. there's a double Lorentz transformation involved.

 

[kmarinas86]

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.

I think that using the return wire to prove a point is cheating. It does nothing for the original scenario without a return wire.

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.

 

[DrGreg]

I think that using the return wire to prove a point is cheating. It does nothing for the original scenario without a return wire.

Well it has the advantage of charge conservation in a closed system, which doesn't apply to an open-ended wire.

The ladder paradox also has some asymmetries that seem to be missing in your example:

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.

Sorry, somehow the image attachment to my post failed to upload correctly. I have now re-uploaded it and added it to that message.

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.

 

[kmarinas86]

Well it has the advantage of charge conservation in a closed system, which doesn't apply to an open-ended wire.

Sorry, somehow the image attachment to my post failed to upload correctly. I have now re-uploaded it and added it to that message.

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.

The problem is that we are talking about a single current and the fact that charge has to be conserved between frames for that single current.

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

 

[DrGreg]

The problem is that we are talking about a single current and the fact that charge has to be conserved between frames for that single current.

But both my example (restricted to the highlighted bottom wire) and the ladder example (restricted to the interior of the garage) show that this isn't true.

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.)

 

[kmarinas86]

But both my example (restricted to the highlighted bottom wire) and the ladder example (restricted to the interior of the garage) show that this isn't true.

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.

What if we suddenly broke the circuit at two places?

(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.)

Yes.

 

[DrGreg]

What if we suddenly broke the circuit at two places?

That would depend on the timing. Simultaneous breaks in one frame would not be simultaneous in another frame.

 

[kmarinas86]

That would depend on the timing. Simultaneous breaks in one frame would not be simultaneous in another frame.

Got it. Just like your answer to a similar problem on another thread.

 

[Dale]

The problem is that we are talking about a single current and the fact that charge has to be conserved between frames for that single current.

This is not true in a couple of ways.

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.

 

[kmarinas86]

This is not true in a couple of ways.

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.

I heard the first time, but I made the same mistake accidentally.

Invariant and conserved are different things!
Invariant and conserved are different things!
Invariant and conserved are different things!
...

Second, it is not true that the net charge on the wire is invariant.

I have been shown why now.

I will deal with more of your posts later, but you have really posted a lot of nonsense today.

I think it has been sufficiently been explained to me at this point. Don't worry about me. I'm done with this topic. I'm satisfied with the answer now.

P.S. I've long used the term "time-invariant" to mean conserved. I must stop doing that.

P.S.S. On another note, I wonder if (http://en.wikipedia.org/wiki/Time-invariant_system) is better termed (time-independent system). (j/k the answer is obvious)

 

[Dale]

I think it has been sufficiently been explained to me at this point. Don't worry about me. I'm done with this topic. I'm satisfied with the answer now.

Excellent! That is good to hear.

 

[Dale]

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.

This is incorrect. In the frame where the test charge is at rest, if the wire is uncharged then there is no force, regardless of the current.

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.

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.

Sure, relativity can be used to transform a magnetic force in one frame to an electrostatic force in another frame (the rest frame of the particle). It cannot be used to transform no force into some force.

 

[Dale]

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.

Oops. My apologies universal_101. I did not read your OP closely enough.

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.

 

[universal_101]

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.

 

[Dale]

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.

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.

 

[universal_101]

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.

 

[Dale]

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).

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

They are different.

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).

 

[harrylin]

There was a discussion here about almost the same topic a long time ago:
https://www.physicsforums.com/archive/index.php/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?

 

[Per Oni]

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?

 

[DrGreg]

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.

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?

 

[Per Oni]

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

For now I’m going to skip your first answer and look at your second.

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?

 

[DrGreg]

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.

 

[harrylin]

[..] 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.

 

[Dale]

There was a discussion here about almost the same topic a long time ago:
https://www.physicsforums.com/archive/index.php/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.

 

[Dale]

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.

 

[kmarinas86]

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?

 

[Per Oni]

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 traveling 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.

 

[Dale]

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.

 

[harrylin]

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.

 

[kmarinas86]

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.

This addresses it. Thanks for answering.

 

[Dale]

This addresses it. Thanks for answering.

I am glad, you are welcome!

 

[Per Oni]

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.

 

[DrGreg]

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<br /> \tilde{F}^{\tilde{\mu}\tilde{\nu}}=\Lambda^\tilde{\mu}_\alpha F^{\alpha\beta} \Lambda_\beta^\tilde{\nu}<br />where \Lambda^\tilde{\mu}_\alpha is the Lorentz boost matrix.

 

[Per Oni]

You refer perhaps to explanations (often accompanied by nice looking calculations) according to which magnetism is claimed to be a kind of illusion due to length contraction.

The most basic and simple case (although very high tech) that I can imagine, as it completely avoids issues with electron source and drain, is that of a closed loop superconductor in which a current is induced.

We thus start with, I think, an insulated wire containing a number of electrons N and an equal number of protons N.

I think that the following situation sketch is correct:

In the wire's rest frame:
- length contraction can play no role at all
- a magnetic field is observed

In any inertial moving frame:
- length contraction plays a role in predicting non-zero electric fields
- a magnetic field is observed that can't be transformed away

Is that correct?
Such a magnetic field looks reasonably "absolute" to me.

Harald

Thanks harrylin and DrGreg you’re a great help.

Such a magnetic field looks reasonably "absolute" to me.

Is this field absolute because we also have none moving +ve charges in the wire’s rest frame? Would it still be absolute if those charges were not present?

 

[harrylin]

Thanks harrylin and DrGreg you’re a great help.

Is this field absolute because we also have none moving +ve charges in the wire’s rest frame? Would it still be absolute if those charges were not present?

I don't think that the positive charges are important for the discussion. The magnetic field is here "absolute" in the sense that the magnetic field of a current loop can't be transformed away in SR. This is simply because it's impossible to transform all the velocities away in SR. Similarly, length contraction and time dilation can't be transformed away completely in such situations (see Ehrenfest paradox and twin paradox).

 

[Dale]

Is this field absolute because we also have none moving +ve charges in the wire’s rest frame? Would it still be absolute if those charges were not present?

I don't think that the positive charges are important for the discussion. The magnetic field is here "absolute" in the sense that the magnetic field of a current loop can't be transformed away in SR.

The word "absolute" doesn't merely mean that it can't be transformed away. By that definition time and length would also be absolute.

The magnetic field is relative to a given reference frame, not absolute. Just like time and length and energy and momentum and velocity and all of the other relative quantities we are familiar with.

 

[harrylin]

The word "absolute" doesn't merely mean that it can't be transformed away. By that definition time and length would also be absolute. [..]

You misunderstood: the magnetic field is an effect that is not compared with length or time, but with length contraction and time dilation. Such effects can be transformed away in special cases.

 

[Dale]

I was primarily objecting to the use of the term "absolute". Whether you are comparing it to length or to length contraction, the magnetic field is not absolute. It makes no sense to use that word to describe it.

 

[universal_101]

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.

This is very nice analysis, how can time (from twin paradox) be relative when effects are totally absolute !

 

[universal_101]

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).

They are different.

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).

But if you apply charge-symmetry, then I think we should be able to transform the two scenarios.

That is, scenario(1) is exactly in conjugation with the scenario(2) according to C-symmetry.

Do you still believe the two scenarios are different and we cannot transform one to other.

 

[Dale]

But if you apply charge-symmetry, then I think we should be able to transform the two scenarios.

That is, scenario(1) is exactly in conjugation with the scenario(2) according to C-symmetry.

Do you still believe the two scenarios are different and we cannot transform one to other.

Sure, but that is not a Lorentz transform. The Lorentz transform preserves charge.

Also, you would have to have completely symmetric charge carriers, i.e. no high-mass fixed "lattice" and no low-mass "free current" charge carriers. For real wires and currents you cannot transform (1) into (2) even including both charge conjugation and a boost.

EDIT: Actually, even with symmetric charge carriers you cannot change (1) into (2) because in one the test charge is at rest wrt the same polarity charge carriers and in the other the test charge is at rest wrt the opposite polarity charge carriers. Changing charge conjugation doesn't change that discrepancy.

While (1) and (2) are both perfectly valid scenarios, you cannot simply Lorentz transform from one to the other. So relativity is not going to explain them.

 

[Per Oni]

This is simply because it's impossible to transform all the velocities away in SR.

I go along with that.
But that would still be true even when your traveling particles are not charged. Therefore the properties you attached to the magnetic field really should be attached to a different property of physics.

Therefore, and for other reasons as well, I go along with Dale’s point of view in that magnetism is not absolute but is totally and completely dependent on the frame of reference we wish to chose. (Hoping he is happy with the way put it).

 

[Dale]

Therefore, and for other reasons as well, I go along with Dale’s point of view in that magnetism is not absolute but is totally and completely dependent on the frame of reference we wish to chose. (Hoping he is happy with the way put it).

I am happy with that. I think "magnetism" refers both to the "magnetic force" and the "magnetic field", and your comment applies to both.

 

[chingel]

I haven't understood and followed the entire thread and I'm sorry if this has already been answered, but if two parallel wires have current going in the same direction and then from the electrons frame the wires are positively charged and they feel a electrostatic force from the other wire, why don't the electrons feel the electrostatic force from their own wire, equalizing the electron and proton ratio?