Explanation of EM-fields using SR

[harrylin]

What do you think about this explanation of EM-fields using SR?

https://www.youtube.com/watch?v=1TKSfAkWWN0

He pretends that his explanation applies to the electromagnet in his hand. But as far as I can tell, that electromagnet creates a magnetic field in any inertial frame; it cannot be transformed away. Therefore, that explanation of magnetism looks simply misleading to me.

 

[universal_101]

He pretends that his explanation applies to the electromagnet in his hand. But as far as I can tell, that electromagnet creates a magnetic field in any inertial frame; it cannot be transformed away. Therefore, that explanation of magnetism looks simply misleading to me.

His explanation is about force(electromagnetic) and not about magnetic field, i.e. magnetic force can be zero even if the magnetic field is present.

 

[universal_101]

However I'm also curious about the situation with no holes you mentioned and nobody replied to:

Would someone care to address it?

There is NO need to address it, because hall effect clearly shows that for most of the metals the current carrying charges are electrons(mostly) and not holes. Except for beryllium(p-type semiconductors) etc. where holes dominate as charge carriers. But the point is you won't see any cross voltage in hall effect if the negative and positive charge carriers are supposed to be exactly equal.

 

[harrylin]

His explanation is about force(electromagnetic) and not about magnetic field, i.e. magnetic force can be zero even if the magnetic field is present.

No, that video pretends to give an explanation about magnets and magnetism. But in fact, it doesn't, not really.
To make it clearer, we can put a positively charged dog in rest with the wire, next to it. Now the cat, using the frame that is co-moving with the electrons as rest frame, has to explain the lack of net force on the dog despite the electric field. The cat can only explain this by the magnetic field of the moving ions and which must exactly compensate the electric field force.

 

[A.T.]

No, that video pretends to give an explanation about magnets and magnetism.

It is about the relationship between Coulomb force and Lorentz force across different frames.

 

[TrickyDicky]

There is NO need to address it

Why did you ask in the first place then?

because hall effect clearly shows that for most of the metals the current carrying charges are electrons(mostly) and not holes. Except for beryllium(p-type semiconductors) etc. where holes dominate as charge carriers. But the point is you won't see any cross voltage in hall effect if the negative and positive charge carriers are supposed to be exactly equal.

So I guess the explanation A.T and WN commented is an oversimplification that doesn't really answer Noyhcat's problem.
My own take on this is that you guys are too hung up on the spacing between charges and its putative length contraction issue, just using the customary assumption that charges are so close together that they can be considered a continuous line of charge takes away the problem, I mean this assumption can be taken also in the electrostatic-current off set up.

 

[Dale]

Your response, ignoring the issue and instead you take your starting point with the current already flowing, ignoring how did you get there(which is incompatible with the current model and SR, and this is what i thought we were discussing).

I didn't ignore the issue. I directly addressed it. The charge on the wire is under experimental control. In particular, I said:

For example, instead of having an uncharged wire you could give the wire an excess positive charge by putting it at a very high voltage. If you did that then the spacing between electrons in the wire frame would be greater than the spacing between protons.

To be more explicit, consider a wire with self-capacitance of 1 pF. If I raise it to 1 MV then it will have an excess charge of 1 μC. This is an experimentally observed fact in the lab frame, and the spacing in the lab frame must conform to that fact (further than the spacing of the protons). Once you have determined the spacing in the lab frame, then you can use the Lorentz transform to determine the spacing in any other frame.

I hope you see now what I mean by the fact that the spacing in the lab frame is a boundary condition which is used to determine the spacing in other frames. Many other people understood the explanation, so I am not sure what is not "clicking" for you. It would help if you would be more descriptive of your particular concern.

 

[TrickyDicky]

I didn't ignore the issue. I directly addressed it. The charge on the wire is under experimental control. In particular, I said:

For example, instead of having an uncharged wire you could give the wire an excess positive charge by putting it at a very high voltage. If you did that then the spacing between electrons in the wire frame would be greater than the spacing between protons.

To be more explicit, consider a wire with self-capacitance of 1 pF. If I raise it to 1 MV then it will have an excess charge of 1 μC. This is an experimentally observed fact in the lab frame, and the spacing in the lab frame must conform to that fact (further than the spacing of the protons). Once you have determined the spacing in the lab frame, then you can use the Lorentz transform to determine the spacing in any other frame.

I hope you see now what I mean by the fact that the spacing in the lab frame is a boundary condition which is used to determine the spacing in other frames. Many other people understood the explanation, so I am not sure what is not "clicking" for you. It would help if you would be more descriptive of your particular concern.

This seems a kind of awkward way to say that we impose the condition that the charge density, in this case charge per length unit must be the same both with the apparatus on and off, IOW charge must be conserved as we all know.
Universal seems to think this is incompatible with SR's length contraction (he is of course wrong) and how exactly this is made compatible(what mechanism makes sure that the spacing between charges is both compatible with length contraction and charge conservation) is what he says you are ignoring.
Something similar motivated Maxwell's introduction of the displacement current.

 

[WannabeNewton]

He pretends that his explanation applies to the electromagnet in his hand. But as far as I can tell, that electromagnet creates a magnetic field in any inertial frame; it cannot be transformed away. Therefore, that explanation of magnetism looks simply misleading to me.

I really suggest you purchase this book: https://www.amazon.com/dp/1107014026/?tag=pfamazon01-20

 

[Dale]

Does this mean that since electrons aren't rigid bodies, the distance between them doesn't change when they move?

Yes. Consider Bell's spaceship scenario. The spaceships are not rigidly connected, so it is possible to set up an acceleration profile such that the distance between them doesn't change in the launch frame. Once you have established (as an imposed boundary condition) the distance in one frame, then you can transform to any other frame (e.g. the momentarily co-moving inertial frame) to find the distance in that other frame.

Imagine we have a bunch of space probes (or whatever object you like) moving through space in a very long line, all at the same velocity. Observer A is moving parallel to the line of probes and at the same velocity while observer B is our stationary rest frame. Is the distance between the probes different for observers A and B?

Yes. They are related by the Lorentz transform. Once you specify the distance for either observer A or for observer B then the distance for the other one is uniquely determined.

 

[Dale]

This seems a kind of awkward way to say that we impose the condition that the charge density, in this case charge per length unit must be the same both with the apparatus on and off

Yes. Hopefully between my awkward way and your simple way it gets through to him.

 

[Drakkith]

Yes. Consider Bell's spaceship scenario. The spaceships are not rigidly connected, so it is possible to set up an acceleration profile such that the distance between them doesn't change in the launch frame. Once you have established (as an imposed boundary condition) the distance in one frame, then you can transform to any other frame (e.g. the momentarily co-moving inertial frame) to find the distance in that other frame.

I don't know what an imposed boundary condition is. Could you elaborate on that?

Yes. They are related by the Lorentz transform. Once you specify the distance for either observer A or for observer B then the distance for the other one is uniquely determined.

Okay. Now, if I take two probes, one right in front of the other, and accelerate them at exactly the same rate until they reach some arbitrary velocity, will the distance between them, according to themselves, be different after the acceleration, or will it remain the same as before? (Trying to understand Bell's spaceship scenario a bit better)

 

[Dale]

I don't know what an imposed boundary condition is. Could you elaborate on that?

The laws of physics are differential equations. Differential equations don't have a unique solution. To get a unique solution you have to impose additional constraints which are known as boundary conditions. These additional constraints contain the description of the particular physical scenario to which you want to apply the physical laws and are generally considered to be "given" in the problem scenario.

For example, in projectile problems you use the law of physics $-mg=m d^2x/dt^2$ which does not give a unique solution until you supply the initial position and velocity of the projectile. The initial position and velocity are the boundary conditions which describe the particular problem and allow you to obtain a unique solution.

Similarly, the Lorentz transform doesn't give us a unique solution until we completely specify the problem. We cannot know the distance in one frame until it is specified in sufficient detail in another frame. I call that specification a "boundary condition" (taking a bit of license), in keeping with the term's use elsewhere for describing the specific problem, even though the Lorentz transform is not usually specified as a differential equation.

Okay. Now, if I take two probes, one right in front of the other, and accelerate them at exactly the same rate until they reach some arbitrary velocity, will the distance between them, according to themselves, be different after the acceleration, or will it remain the same as before? (Trying to understand Bell's spaceship scenario a bit better)

If the distance is the same in the launch frame then the distance will be different in the momentarily co-moving inertial frame (greater).

 

[universal_101]

I didn't ignore the issue. I directly addressed it. The charge on the wire is under experimental control. In particular, I said:

For example, instead of having an uncharged wire you could give the wire an excess positive charge by putting it at a very high voltage. If you did that then the spacing between electrons in the wire frame would be greater than the spacing between protons.

I think what you are suggesting is unbalance of the charge, but ofcourse if a part of conductor is positively charged then spacing between electron and proton is different, because there are more protons and less electrons and they all have to share the same volume, so their respective spacing changes accordingly.

Once you have determined the spacing in the lab frame, then you can use the Lorentz transform to determine the spacing in any other frame.

Why would I Lorentz transform anything, Lorentz transform is for analyzing a particular situation from different reference frames. As I mentioned earlier you can't have any Lorentz transform for the situation when switching the current on and off.

I hope you see now what I mean by the fact that the spacing in the lab frame is a boundary condition which is used to determine the spacing in other frames. Many other people understood the explanation, so I am not sure what is not "clicking" for you. It would help if you would be more descriptive of your particular concern.

you want me to understand something without even talking about it. Why don't you just accept that switching the current on and off makes two different situations, which can be Lorentz transformed separately but cannot be transformed into each other.

 

[harrylin]

It is about the relationship between Coulomb force and Lorentz force across different frames.

If the movie said that, then I would have no objection - it does neatly, although too simplistic, illustrate how EM fields appear differently in different frames. I also like the way of presentation, it's cool. If he had added my charged dog to his charged cat, that would have been really cool. This topic has a lot of similarity to elements of Bell's spaceship example (and a little also with Ehrenfest's rotating disc, in view of the coil).

 

[harrylin]

I really suggest you purchase this book: https://www.amazon.com/dp/1107014026/?tag=pfamazon01-20

I have other books at my hand, such as Alonso&Finn's and Feynman's. Does Purcell disagree with them?

 

[Drakkith]

I call that specification a "boundary condition" (taking a bit of license), in keeping with the term's use elsewhere for describing the specific problem, even though the Lorentz transform is not usually specified as a differential equation.

Awesome. Thanks.

If the distance is the same in the launch frame then the distance will be different in the momentarily co-moving inertial frame (greater).

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

 

[Dale]

I think what you are suggesting is unbalance of the charge, but ofcourse if a part of conductor is positively charged then spacing between electron and proton is different, because there are more protons and less electrons and they all have to share the same volume, so their respective spacing changes accordingly.

Yes. I am suggesting that the charge balance is under expermiental control. It can be balanced or unbalanced depending on the voltage applied to the wire.

Why would I Lorentz transform anything, Lorentz transform is for analyzing a particular situation from different reference frames.

The point of the Lorentz transform is to transform to understand the magnetic force in one frame from the reference frame of a moving charge.

you want me to understand something without even talking about it. Why don't you just accept that switching the current on and off makes two different situations, which can be Lorentz transformed separately but cannot be transformed into each other.

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.

 

[DrGreg]

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 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.

The misunderstanding occurs because we often consider the distance between two things rigidly connected. In that special case it's possible to show that a rigid object accelerated from rest gets shorter. This only applies to rigid objects. However, in our case we have freely moving electrons not rigidly separated, so that special case doesn't apply.

 

[Drakkith]

The misunderstanding occurs because we often consider the distance between two things rigidly connected. In that special case it's possible to show that a rigid object accelerated from rest gets shorter. This only applies to rigid objects. However, in our case we have freely moving electrons not rigidly separated, so that special case doesn't apply.

My question is, when current is flowing, how are the electrons not length contracted from the moving observers frame if the wire as a whole is?

 

[Bill_K]

My question is, when current is flowing, how are the electrons not length contracted from the moving observers frame if the wire as a whole is?

I believe it's necessary [as depicted in #27, thanks Dr Greg!] to take into account that the current flows in a closed loop. Either a circular loop, or easier to analyze, a rectangular loop. In a frame moving along with the flow, the electrons on one side of the rectangle appear at rest and are not length contracted. However the ones returning on the other side have a different rest frame and do appear to be length contracted.

 

[DrGreg]

My question is, when current is flowing, how are the electrons not length contracted from the moving observers frame if the wire as a whole is?

In the moving observer's frame the electrons are at rest, so their separation in that frame is greater than their separation in any other frame (i.e. in other frames their separation would be length-contracted compared with the frame in which they are at rest).

See my diagram in post #27 (which also illustrates Bill_K's point in post #56).

 

[Noyhcat]

That tends to be the point that confuses most of the people that actually understand the argument being presented, so kudos on understanding the argument.

The spacing of the electrons in the wire frame is determined by the observed fact that the wire is uncharged in the wire frame. This is a "boundary condition" that can be experimentally controlled.

For example, instead of having an uncharged wire you could give the wire an excess positive charge by putting it at a very high voltage. If you did that then the spacing between electrons in the wire frame would be greater than the spacing between protons.

Once the spacing is determined in the wire frame, then it is determined in all frames.

After reading everything and watching the video a few more times, I think I see the problem with this otherwise good video.

At 1:15 he applies a boundry condition of equal positively and equal negatively charged particles, sitting there at rest relative to the man. Then suddenly, and perhaps a bit too casually, at 1:27, he replaces this boundry condition with an entirely NEW one where the negatively charged particles are now moving relative to the man. Then he makes a huge point at 1:38 about how something that wasn't moving in reference to him now is, and accelerates the cat.

He didn't do anything like that at 1:27. Instead he sort of jumped into another lab down the hall, presumaly in the interest of reaching a broader audience.

If I get it right and am not just confusing matters, if the wire at 1:24 was the same wire at 1:17 then at 1:17, it should have had a positive charge because the negatively charged particles would have been spaced out and therefore fewer in number. Once they started moving in reference to the man, they would experience contraction, and the charge would subside, at 1:27. Then the cat moves relative to the man at 1:38 and relative to the cat, there's an equal charge acting on it, pushing it away.

 

[yuiop]

...
If I get it right and am not just confusing matters, if the wire at 1:24 was the same wire at 1:17 then at 1:17, it should have had a positive charge because the negatively charged particles would have been spaced out and therefore fewer in number. Once they started moving in reference to the man, they would experience contraction, and the charge would subside, at 1:27. Then the cat moves relative to the man at 1:38 and relative to the cat, there's an equal charge acting on it, pushing it away.

The point is that the gap between the electrons does not contract, not from the point of view of the man in the lab at rest with the wire and not from the point of view of the cat co-moving with the electrons when the current is flowing.

The gap between electrons in the lab frame is the same whether or not the current is flowing. Imagine the electrons are initially at rest wrt to the lab and the wire and then accelerated slowly and progressively along with the cat so that the cat is always alongside a given electron. If the cat has a ruler that initially extended from its electron to a neighbouring electron, it would see the gap between the two electrons progressively getting larger relative to its ruler which retains its proper length. In the lab/man/wire rest frame the gap between the electrons remains constant and the ruler being carried by the cat is length contracting. This is a bit like the Bell's rocket paradox, whereby when the gap between two accelerating rockets remains constant relative to an inertial reference frame, the gap is increasing according to an accelerating observer on board one of the rockets.

Technically length contraction still applies. The gap between two electrons, as measured by the man in the rest frame of the wire, is always less than the gap measured by the co-accelerating cat when the current and cat are moving relative to the wire.

 

[yuiop]

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.

 

[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.