Explanation of EM-fields using SR

[universal_101]

I do accept that. Obviously a wire with a current and a wire without a current are not related by a Lorentz transform (in the first case the electrons and protons are not moving relative to each other, in the second they are). I didn't think that was even a point of discussion.

Well thanks, this means that a wire with current on and a wire with current off does not come under the domain of applicability of SR. Since transformation only works for one particular situation and not two different unrelated ones. Am I correct ?

 

[A.T.]

Let me summarise the probem: you start with a wire with no current, with equal numbers of positive ions and negative electrons. As the electrons repel each other, they spread out over the whole wire so they are equally spaced.

Then the electrons are set in motion so a current flows. No electrons are added to or removed from the wire, so the wire remains uncharged. As the electrons repel each other, they spread out over the whole wire so they are equally spaced in the rest frame of the wire (which is therefore the same spacing as before).

So we don't really need to consider the counter movement of the holes in the wire frame, to explain why the wire stays neutral during current changes?

How is the argument based on "equal spacing" reconciled with the bottom left image below. Why is there no equal spacing of electrons throughout the entire loop?

ETA : To answer my own question. Due to different length contraction, the individual E-fields of the electrons have different sizes in the two loop parts, therefore different spacing.

 

[harrylin]

[..] How is the argument based on "equal spacing" reconciled with the bottom left image below. Why is there no equal spacing of electrons throughout the entire loop?
[picture]

The equal spacing argument is based on the symmetry in the wire's rest frame - the physical situation of the electrons is everywhere the same. That is not the case in the moving frame in which part of the electrons is approximately in rest while other electrons are speeding.
SR tells us that the electrons in the moving frame must conform with the Lorentz transformed state of that rest frame state. The Lorentz transformation tells us that according to you, the cat's ruler is contracted and so the cat will measure an increased electron distance between co-moving electrons. The electrons on the other side make up for that, as the repulsive force between moving charges is reduced, or more precisely, the Coulomb field is length contracted; this was already derived by Heaviside but can easily be understood from the PoR.

[Addendum]: This also means that in theory a current carrying wire that is fed by an appropriate energy source will be very slightly negatively charged.
And about electric fields in and around current carrying wires, I now found Jefimenko's paper in the AJP no.30 of 1961; he explains and demonstrates there how to visualize the electric fields of current carrying wires which are fed by a battery. He comments: "The structure of the fields is clearly visible not only outside the conductor, but, since the conductors are represented by transparent ink, also inside them". Of course, such a conductor likely has negative and positive charge conductors; and I see that Heald explains such electric fields in 1984 - AJP 52 - by the Poynting flux. All this means, as I now discovered, that it's a myth that current carrying wires are in general electrostatically neutral.

 

[universal_101]

universal_101

Let me summarise the probem: you start with a wire with no current, with equal numbers of positive ions and negative electrons. As the electrons repel each other, they spread out over the whole wire so they are equally spaced.

Then the electrons are set in motion so a current flows. No electrons are added to or removed from the wire, so the wire remains uncharged. As the electrons repel each other, they spread out over the whole wire so they are equally spaced in the rest frame of the wire (which is therefore the same spacing as before).

That's all there is to it, but you don't seem to accept that as an explanation.

I don't see any explanation in there, what you are doing is tacitly taking two different positions. Just because Length Contraction does not give the desired results(observed facts) you can't just drop it and say everything is fine. Instead if you don't want Length contraction to be a part of the situation then just admit it doesn't come under the domain of SR.

I think, if I interpret you correctly, you want to know why isn't the distance between the moving electrons contracted relative to the distance between the previously stationary electrons (all in the wire rest frame). Well, why should it be contracted? The argument above shows it isn't contracted. My guess here is that you have misunderstood what Lorentz contraction is. Lorentz contraction occurs when two different frames are used to analyse the same situation. It doesn't occur when one frame is used to analyse two different situations.

Why do you think particles in accelerators are compared to the particles in lab frame(Time Dilation and all). Even though they are from two different situations. In one, particles are stationary w.r.t accelerator, and in other, they are moving w.r.t accelerator, just like switching the current on and off.

 

[Dale]

Well thanks, this means that a wire with current on and a wire with current off does not come under the domain of applicability of SR.

Tidal gravity is negligible so it is definitely within the domain of applicability of SR.

Since transformation only works for one particular situation and not two different unrelated ones. Am I correct ?

And nobody has attempted to Lorentz transform from current-on to current-off. I don't know why you think anybody has. All of the transformations have been from rest frame of wire to rest frame of particle both with current on.

 

[A.T.]

Just because Length Contraction does not give the desired results(observed facts) you can't just drop it and say everything is fine.

DrGreg doesn't drop length contraction at any point. See his image below. The flowing electrons (their E-fields) are contracted in the wire's frame. But since they are all contracted by the same amount, and their number is constant, they keep a constant spacing by distributing themselves uniformly.

Instead if you don't want length contraction to be a part of the situation then just admit it doesn't come under the domain of SR.

Length contraction is part of the situation. But Length contraction doesn't imply that the spacing in the wire's frame will decrease when the current starts flowing. If the spacing in the current's frame changes, the spacing in the wire's frame can stay constant.

 

[Dale]

Now, why is this? I read on wiki it's because of relativity of simultaneity, but I don't really understand it.

Sorry about the delay, I knew that I had worked this out in detail, but it took me a while to find it.

https://www.physicsforums.com/showpost.php?p=4019533&postcount=43

I wouldn't attribute it only to relativity of simultaneity, but it does fall out of the Lorentz transform as shown.

 

[A.T.]

I read on wiki it's because of relativity of simultaneity, but I don't really understand it.

You could also attribute it to gravitational time dilation in the accelerating frame (principle of equivalence). In the accelerating frame of the leading rocket, the acceleration program of the trailing rocket runs slower.

And when a current starts flowing, then in the accelerating frame an electron the trailing electrons move slower, and stay behind. There are also less electrons entering the straight wire segment behind, and more electrons leaving the wire in front. So during the acceleration the number of electrons reduces in the straight wire segment, when viewed from the frame of the electron (see DrGregs picture, bottom right).

 

[harrylin]

[..]
Length contraction is part of the situation. But Length contraction doesn't imply that the spacing in the wire's frame will decrease when the current starts flowing. If the spacing in the current's frame changes, the spacing in the wire's frame can stay constant.

See my reply to you in post #63. Length contraction does imply contraction of the repulsive Coulomb field between the electrons (although extremely small, in view of the extremely small drift speeds); for an induced current in a closed wire loop that is irrelevant, but it may be of relevance in a wire that is fed by a battery, at least in theory. In practice (in view of an experimental paper of 1985) it appears that other, unknown effects may play a greater role.

 

[A.T.]

But Length contraction doesn't imply that the spacing in the wire's frame will decrease when the current starts flowing.

Length contraction does imply contraction of the repulsive Coulomb field between the electrons

The contraction of the repulsive Coulomb field doesn't imply that the spacing in the wire's frame will decrease when the current starts flowing. But it might happen in reality, if the simplifying assumption about the constant number of electrons doesn't hold true any more.

 

[universal_101]

See my reply to you in post #63. Length contraction does imply contraction of the repulsive Coulomb field between the electrons (although extremely small, in view of the extremely small drift speeds); for an induced current in a closed wire loop that is irrelevant, but it may be of relevance in a wire that is fed by a battery, at least in theory. In practice (in view of an experimental paper of 1985) it appears that other, unknown effects may play a greater role.

Thanks harrylin, for addressing the issue in this, and in your post #63, but I think the problem here is unknown effects, because even if you consider any test charge moving w.r.t the wire at the drift speed of electrons in the direction of moving electrons the test charge feels a force(i.e test charge is co-moving with current producing electrons and moving w.r.t the cations). Whereas, nothing of the sort happens when the test charge is at rest w.r.t the wire and all the current electrons are moving w.r.t the test charge. Even though the situation is symmetric there are different results.

 

[A.T.]

even if you consider any test charge moving w.r.t the wire at the drift speed of electrons in the direction of moving electrons the test charge feels a force(i.e test charge is co-moving with current producing electrons and moving w.r.t the cations). Whereas, nothing of the sort happens when the test charge is at rest w.r.t the wire and all the current electrons are moving w.r.t the test charge. Even though the situation is symmetric there are different results.

The situation is not symetric because the spacing of electrons in the electron's rest frame is different than the spacing of cations in the cation's rest frame.

 

[yuiop]

See my reply to you in post #63. Length contraction does imply contraction of the repulsive Coulomb field between the electrons (although extremely small, in view of the extremely small drift speeds); for an induced current in a closed wire loop that is irrelevant, but it may be of relevance in a wire that is fed by a battery, at least in theory. In practice (in view of an experimental paper of 1985) it appears that other, unknown effects may play a greater role.

In order for a current to flow in the wire, there has to be a potential difference across the length of the wire, so the Voltage at one end has to be higher than at the other so their is slight increase in the density of electrons at one end compared to the other. I think the effect is small and averages out over the length of the wire and can probably be ignored for the purposes of this thread, but it might show up in very precise practical experiments.

 

[harrylin]

The situation is not symetric [between the wire's rest frame and the electron's rest frame] because the spacing of electrons in the electron's rest frame is different than the spacing of cations in the cation's rest frame.

Indeed - for a reason that may still need a little more discussion, the electron density in the wire's rest frame is approximately equal to the metal ion density (see also below). I guess that the nearly perfect equilibrium of positive and negative charges in a stationary wire can be explained by the Coulomb force of the metal ions on the electrons. But then how about the cat's rest frame? There is an asymmetry because the metal wire's ions are strongly bound, but .. I'll have to refresh my memory about the different force and field transformations. Meanwhile, perhaps someone else can provide that "missing piece" (WannabeNewton, what does Purcell say about that?).

In order for a current to flow in the wire, there has to be a potential difference across the length of the wire, so the Voltage at one end has to be higher than at the other so their is slight increase in the density of electrons at one end compared to the other. I think the effect is small and averages out over the length of the wire and can probably be ignored for the purposes of this thread, but it might show up in very precise practical experiments.

Yes, there is a number of Coulomb effects involved with a current in a wire, but obviously they are all very small compared to the magnetic force - else the definition of the Ampere would have been messed up.

Still, this discussion gives me the feeling -and perhaps I'm not the only one - that I am "missing" something. Hopefully that feeling will disappear in the course of this thread which by now has become truly interesting for me.

 

[WannabeNewton]

Purcell doesn't address that issue verbatim unfortunately (as far as I can tell) but in the meantime, see if this piques your interest: http://www.chip-architect.com/physics/Magnetism_from_ElectroStatics_and_SR.pdf

 

[Dale]

unknown effects may play a greater role.

I think the problem here is unknown effects

As far as I know there are no known EM experimental results which are in conflict with standard EM theory. Perhaps there are some unknown influences in a given experiment where some particular condition was not sufficiently controllable to be known, but in well-controlled experiments I am not aware of anything unknown.

universal_101, certainly, your confusion on the topic at hand is not indicative of a fundamental unknown.

 

[Dale]

I think the effect is small and averages out over the length of the wire and can probably be ignored for the purposes of this thread, but it might show up in very precise practical experiments.

I agree. Typical self-capacitances are on the order of pF or even less, so you would need extremely high voltages to get any appreciable charge. And, as you said, you would need to raise both ends of the wire to a high voltage to get a net charge that isn't balanced out over the length.

 

[Noyhcat]

Lets say the loop of wire consists of 2 parallel wires (A and B), each 600m long and ignore the length of the connecting sections at each end. Let's also say there are 200 electrons in the entire circuit so they are 6m apart from each other, when equally spaced out and at rest with the wire in the wire/lab rest frame. (Yes, I know that is unrealistic but stick with me ;)

When the current is moving relative to the wire/lab, there are still 200 electrons distributed around 1200 m of wire as measured in the lab so the gap between electrons is still 6m as measured in the lab.

Now let's say the cat and the current are moving to the right at 0.8c relative to the wire/lab and the cat is at rest wrt to the electrons in wire A. (Again unrealistic, the electrons only move at something like walking pace). The gamma factor is 10/6 at 0.8c so the wire A is 360m long according to the cat. The gap between the stationary electrons in wire A is 6m*10/6 = 10m according to the cat. The number of electrons in wire A is 360/10 = 36 (according to the cat).

Now we have to find room for the other 164 electrons. To the cat the length of wire B is 360m (same as the length of A to the cat). The electrons are moving at 0.8c relative to the wire and the wire is moving at 0.8c relative to the cat, so using relativistic velocity addition the electrons in wire B are moving at (0.8+0.8))/(1+0.8*0.8) = 0.97561c relative to the cat. The gamma factor at that velocity is 4.5555 recurring. The gap between the electrons in section B is 10m/4.5555 = 2.19512195m (according to the cat).

The 360m of wire B, divided by the inter electron length 2.19512195 equals 164, so our remainder of electrons fits nicely into the return length of wire (from the cats point of view).

To summarise the case when the electrons are moving relative to the wire, from the point of view of the cat co-moving with the electrons in wire A, there are 100 positive charges and 36 negative charges in wire A and 100 positive charges and 164 negative charges in wire B, so the cat is repelled from A and attracted to wire B.

Yeah, see the video does leave a lot out, doesn't it. Which makes sense, as it's meant to maybe peak the interest in science of folks in general, rather than take them through a specific example like this or provide diagrams like DrGreg's to show exactly what's going on, etc. Thanks...

 

[yuiop]

Purcell doesn't address that issue verbatim unfortunately (as far as I can tell) but in the meantime, see if this piques your interest: http://www.chip-architect.com/physics/Magnetism_from_ElectroStatics_and_SR.pdf

Thanks for the link which is very interesting. I follow how they derive $Q_L = Iv/c^2$ but I cannot fathom how they conclude that the change in charge potential is due to the relativity of simultaneity. Here is the meat of their argument quoted.

We need an understanding of what is happening as a result of non-simultaneity:
An observer in the moving test-charge frame, who moves along with the wire (say in the same direction as the electrons in the wire) will, due to non-simultaneity, 'see' into the future of the wire downstream of the electrons, and into the past at the side where the electrons enter the wire. 'Seeing' is of course the wrong word. We just redefine simultaneity different in a different reference frame. We however have to adopt our calculations as if these events in the past and future are simultaneous to our time when we are observing from the test charge's rest-frame. The future at the downstream side of the electrons means that they did stream further out of the wire there. At the other hand, the past, at the side where the electrons enter the wire, means that less electrons have streamed into the wire there. The overall result is thus that we must calculate with less electrons in the wire per unit of length as positive ions. More electrons have streamed out while less of them have streamed in.

Surely if the current is constant over time, then the amount of electrons leaving (or entering) the section of wire per second is the same in the past as it is in the future?

I can see the temptation to assume there is a connection with the RoS, because the RoS is proportional to $L v/c^2$ (where L where is the length of the section of wire as measured in the rest frame of the positive test charge) and the expression for charge density above can be rearranged to $Q/I =Lv/c^2$, ( Where $Q_L = Q/L$). but I think that is coincidental and the link is more to do with link between length contraction and RoS as in this Wikipedia section.

 

[STEMucator]

I actually give this video a thumbs up. The "cation" pun was hilarious.

 

[jartsa]

I wonder what kind of understanding could be gained by considering a charged object that is being swung around in a circle on a deck of a ship that is moving linearly?

 

[A.T.]

Surely if the current is constant over time, then the amount of electrons leaving (or entering) the section of wire per second is the same in the past as it is in the future?

In every inertial frame that is true. But when you accelerate from the inertial wire's frame to the inertial current's frame your line of simultaneity rotates. In this accelerating frame there are more electrons per second leaving the segment, than entering it. So when you arrive in the current's frame you end up with less electrons in the segment, than there were in the wire's frame.

So yes, the relativity of simultaneity can be used to explain why there a different counts of electrons in the wire segment, between the two frames: Two events (electron entering, electron leaving) that are simultaneous in the wire's frame, are not simultaneous in the current's frame (leaving comes first).

 

[universal_101]

As far as I know there are no known EM experimental results which are in conflict with standard EM theory. Perhaps there are some unknown influences in a given experiment where some particular condition was not sufficiently controllable to be known, but in well-controlled experiments I am not aware of anything unknown.

universal_101, certainly, your confusion on the topic at hand is not indicative of a fundamental unknown.

Just switching the current on and off is in conflict with the standard EM theory(i.e. SR).

 

[universal_101]

DrGreg doesn't drop length contraction at any point. See his image below. The flowing electrons (their E-fields) are contracted in the wire's frame. But since they are all contracted by the same amount, and their number is constant, they keep a constant spacing by distributing themselves uniformly.

He specifically mentions there is NO Length Contraction when switching the current on. To me it's a drop.

Length contraction is part of the situation. But Length contraction doesn't imply that the spacing in the wire's frame will decrease when the current starts flowing. If the spacing in the current's frame changes, the spacing in the wire's frame can stay constant.

What does the Length Contraction implies then ?, because standard theory says there should be length contraction and as a result closer spacing and higher density of electrons and as a result some negative charge.

 

[universal_101]

The situation is not symmetric because the spacing of electrons in the electron's rest frame is different than the spacing of cations in the cation's rest frame.

This should result in excess charge, since different spacing of electrons and cations means different density, which in turn means some net unbalanced charge.

 

[universal_101]

In order for a current to flow in the wire, there has to be a potential difference across the length of the wire, so the Voltage at one end has to be higher than at the other so their is slight increase in the density of electrons at one end compared to the other. I think the effect is small and averages out over the length of the wire and can probably be ignored for the purposes of this thread, but it might show up in very precise practical experiments.

Not always, Superconducting wire can easily contain the current for long time without needing any potential difference. But for ordinary wires the implications are correct, but again as you said they can be ignored safely.

 

[harrylin]

As far as I know there are no known EM experimental results which are in conflict with standard EM theory. Perhaps there are some unknown influences in a given experiment where some particular condition was not sufficiently controllable to be known, but in well-controlled experiments I am not aware of anything unknown.

Yes, I dug a little deeper and found that the results could not be reproduced.
- http://rsi.aip.org/resource/1/rsinak/v61/i10/p2637_s1

 

[A.T.]

The situation is not symetric because the spacing of electrons in the electron's rest frame is different than the spacing of cations in the cation's rest frame.

This should result in excess charge,...

It does, in all except one frame, where the differential length contraction makes the charge densities equal. That is the wire's frame.

...since different spacing of electrons and cations...

You seem to be comparing spacing of electrons and cations in different frame each. That doesn't make any sense except to check if the situation is symmetrical (as I did above). Read exactly what I wrote in the top quote and pay attention to reference frames. Try to be more precise in your language by always stating the reference frame (as I did above). This is the most common source of confusion.

 

[harrylin]

[..] I cannot fathom how they conclude that the change in charge potential is due to the relativity of simultaneity. [..] Surely if the current is constant over time, then the amount of electrons leaving (or entering) the section of wire per second is the same in the past as it is in the future? [..] I think that is coincidental and the link is more to do with link between length contraction and RoS [..].

Yes, exactly. The challenge that we face (if we don't satisfy ourselves with superficial arguments) is to explain the near-steady state force balance in the cat's rest frame. I have seen similar wrong explanations for other problems, and I think that you correctly nail down the cause of that misunderstanding. However already the next section, which I did not yet have time to study, looks very interesting - thanks WannabeNewton!

 

[universal_101]

It does, in all except one frame, where the differential length contraction makes the charge densities equal. That is the wire's frame.

i think you are considering the situation rather casually, I'm not questioning a regular Lorentz transform. Let me say it again then, the situation you should be considering is switching the current on and off all in the wire's frame. There is no need to transform the constant flowing current for different inertial frames, which you are describing and many others before you.

You seem to be comparing spacing of electrons and cations in different frame each. That doesn't make any sense except to check if the situation is symmetrical (as I did above). Read exactly what I wrote in the top quote and pay attention to reference frames. Try to be more precise in your language by always stating the reference frame (as I did above). This is the most common source of confusion.

Alright, let's consider a particle accelerator, and suppose there are highly energetic(fast moving) Muons in the tunnel, and there is a sample of them in a stationary lab w.r.t the accelerator. Now, my question is since the particles in the tunnel are length contracted, time dilated etc. compared to the samples in the stationary lab because of the relative motion(this is all in the lab's frame). Why does the same not follow for the case of switching the current on from off because of the relative motion between electrons and protons(this is all in the wire's frame).