Magnetism seems absolute despite being relativistic effect of electrostatics

[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?