How Fast Does an Electrical Impulse Travel in a Copper Wire?

[Dale]

ummmm not really, he said ...

You have to look at the previous paragraph to see what he means by “this process”. His “this process” is not electrons moving both directions and meeting in the middle. He never says that.

Nothing meets in the middle ( half way along)

Waves propagating from both terminals certainly can meet in the middle, depending on the geometry and the setup.

 

[davenn]

You have to look at the previous paragraph to see what he means by “this process”. His “this process” is not electrons moving both directions and meeting in the middle. He never says that.

Yes he does, he's clearly refers to electrons

Consider a power supply (PS) connected to a loop of wire - basically, out of one terminal, electrons are pushed out, and in the other they are allowed in. This current is not immediately observed all around the wire. The electrons in the vicinity of the PS are moving very shortly after turning the PS on. But the electrons in the wire far from the PS are yet to begin moving. They will begin to move when the process, whatever it is, reaches them. How long it takes to reach them is dictated by "The speed of Electricity", or the alternative expression, "Signal speed".

 

[snorkack]

However we know by transmission line theory wave equations that the voltage and current in a transmission line constitute waves that travel at a speed that is a significant fraction of speed of light (66%-99% of speed of light) and these equations are known from Olivier Heaviside back at 1885, he developed them starting from Maxwell's equations, without the knowledge of this underlying microscopic model of electrons about 15 years before the electron was discovered.

Because they don´ t depend on whether the charge carriers in wire are electrons, holes or heavy ions?

But with instruments, speed of electricity is clearly not instant.

Water notoriously has ε as much as 81 (and 87 at 0 degrees).
When you try to send a telegram, or a ping, to the opposite side of Earth, like New Zealand to Spain, does your ping travel in direct line? That would be 43 ms. Through Earth core. Or does it travel around Earth? 67 ms at speed of light. Or does it follow the detours of cables under sea?
And at what speed? Since water has ε of 81, does the polarization of the sea around your ping traveling along cable (inside insulation) slow it down to 1/9 speed of light?

 

[tech99]

The idea that an E field is set up immediately all around the wire is wrong. If that was the case then there would be no such thing as signal speed.

The implication that there is an EM wave dictating everything seems weird. It's as if it is being suggested that this wave comes first and then the current results from that rather than the other way around! What if the entire current began with a capacitor for example - clearly that would be a case of electron movement first and then everything following on from that, wouldn't it?

Yes I agree with htis statement. To clarify my own thinking slightly, I imagine a wire spaced a long way from other conductors. I charge up an object such as a sphere and touch the end of the wire with it. Now we have a step impulse applied to the line, causing the first electrons to move and create magnetic fields surrounding the wire. As these first electrons move towards other electrons, we see repulsion and so on. As time goes on, the high frequency components of this discharge decay and we see progressively lower frequencies being launched until at last we approach the DC conditions. I would expect the initial high frequency electron movement to be at the surface, progressively getting deeper into the wire as the frequency falls, until near DC the entire wire carries the current. This propagation into the wire is by another slow EM wave which travels radially inwards.
If there is another wire nearby, then there is increased capacitance, so the electrons store their energy at a lower potential ie more spaced out. Now we are seeing a transverse component of electric field.
For a case where we have two wires forming a circuit, a battery and a switch, the initial impulse starts not from the battery but from the switch. I visualise that we have waves starting from each switch terminal and having opposite phase. These then travel around and around the circuit in opposite directions until Ohmic losses absorb them.
The EM radiation from a short wire terminated with resistance is broadside to the wire. This supports the view that the acceleration of the electrons is longitudinal.

 

[Delta2]

Because they don´ t depend on whether the charge carriers in wire are electrons, holes or heavy ions?

I think the speed of the waves doesn't depend on the exact nature of the charge carriers as long as the geometry of the transmission line remains the same (and ofcourse any dielectrics or magnetic permeability materials remain the same).

EDIT : I think after all that the charge carriers affect the parameter R of the transmission line, that is the ohmic resistance per unit length, which in turn affects the speed of waves. I had in my mind the lossless transmission line when I wrote the first paragraph if this post.

 

[Byron Forbes]

I think that your actual question is where that E-field comes from? Is it due simply to Coulomb repulsion or is it due to waves outside the wire?

Exactly!

And in fact, I am asking if there is any difference at all?

I am not even sure what the source of this EM wave is!

If the wave is a product of electron movement in the first place, then surely if an electron moves near another, then it's electric field will have a greater, if not absolute effect, on the nearby electron, since any effect of an EM wave is the product of the initial electron's movement in the first place.

I will now reply to an earlier post that has relevance here.

 

[Byron Forbes]

It sounds like the OP is visualizing the EM wavefront to be analogous to a sound wavefront. Sound propagates only via particle collisions. But when an electron moves, its field changes with infinite extent and the change propagates at speed c in a vacuum. So when the first electron moves, that pushes all the other electrons in the wire (after propagating the EM field), not just the ones immediately in front. That makes electrons unlike gaseous neutral particles.

What you have stated about electrons and their field (to infinity) holds true in both circumstances.

In either case, conductor or particle, you have electrons interspersed with nuclei (protons) which greatly neutralises everything at a distance rendering the infinite reach of fields as negligible. The only thing worth considering is the nearby particles i.e. the ones with no other particles between them.

Again, I see the idea of the initial signal "wavefront" as a longitudinal wave through the electrons.

 

[Byron Forbes]

Yes he does, he's clearly refers to electrons

Let me expand.

The only reason I even mentioned this was to avoid the situation where I'm looking at an electron yet to move, but if it was more than halfway around the wire from the terminal I was talking about then it would have already been effected by the other terminal. It was also an attempt to show that the electric field is not immediately set up all around the wire instantly when the PS is turned on.

To expand, at the PS we have an E field acting across the wiring that's within the PS. So when the PS is turned on, it pushed electrons out of one terminal, therefore at the other terminal we have an electron vacuum. Since the electron pressure in the wire at this other terminal is now greater than at the terminal, electrons flow into it.

So we now have 2 signals traveling from both terminals that will meet at the halfway point of the wire.

 

[fluidistic]

https://www.bpa.gov/news/newsroom/Pages/Hitch-a-slow-ride-on-the-Electron-Express.aspx

I am not quite convinced. If we assume that the free (or nearly free) electron model holds, then the electrons are fermions which are indistinguishable and delocalized. The ones responsible for electric conduction move at speeds comparable to about 1/100 th of c (i.e. at Fermi velocity).

 

[Byron Forbes]

 

[Dale]

Yes he does, he's clearly refers to electrons

Yes, but he also clearly says that they are pushed out of one terminal and allowed into the other terminal. That is not electrons moving both directions. So when this process meets in the middle it is not electrons moving both directions meeting in the middle.

 

[Dale]

And in fact, I am asking if there is any difference at all?

The difference is using only Gauss’ law or using all four of Maxwell’s equations. The partial derivative wrt time is non zero for both E and B, so you have to use all four.

 

[vanhees71]

Of course, you have to use all 4 Maxwell equations. The result is the "telegrapher's equation" (Heaviside) or a more elaborate wave equation in presence of the conductors (H. Hertz, who had a hard time trying to formulate it for infinitely thin wires; see Sommerfeld vol. 3 for details), and as was stated correctly several times in the very beginning of the thread, the signal velocity is the propagation velocity of the em. field and not the drift velocity of the electrons which is tiny (about 1mm/s). Also the energy transport is through the fields and not through the drift of the electrons in the wire.

 

[nsaspook]

I am not quite convinced. If we assume that the free (or nearly free) electron model holds, then the electrons are fermions which are indistinguishable and delocalized. The ones responsible for electric conduction move at speeds comparable to about 1/100 th of c (i.e. at Fermi velocity).

In a conventional vacuum tube the free electrons from the cathode are accelerated to the anode often at a sizable fraction of C. What happens to the kinetic energy of those electrons when they hit the anode? The main problem with using a physical electron transfer for electrical energy is you don't actually get current electricity energy as the end product.

 

[jartsa]

I am not sure it directly enters into computations.
You could transmit electricity via a metallic conductor, like a copper wire wrapped in rubber insulator, where electrons are charge carriers and move. Or you could transmit electricity through nonmetallic conductor, like the same rubber hose containing not metal copper wire, but aqueous solution of copper sulphate. In which electrons cannot move, and charge carriers are copper cations of far bigger mass. When you measure travel time of switching surges and lightning surges, does the mass of charge carrier enter directly into equations?

https://en.wikipedia.org/wiki/Telegrapher's_equations#Role_of_different_components

Wikipedia says there that inductance makes it look like current has inertia, and that large inductance makes the wave move more slowly, just as waves travel more slowly down a heavy rope than a light one.I would just say that when charges have inertia, then wave moves slowly.

Anyone have some idea about when does the mass-inertia become significant compared to the inductance-inertia?

 

[Byron Forbes]

Of course, you have to use all 4 Maxwell equations. The result is the "telegrapher's equation" (Heaviside) or a more elaborate wave equation in presence of the conductors (H. Hertz, who had a hard time trying to formulate it for infinitely thin wires; see Sommerfeld vol. 3 for details), and as was stated correctly several times in the very beginning of the thread, the signal velocity is the propagation velocity of the em. field and not the drift velocity of the electrons which is tiny (about 1mm/s). Also the energy transport is through the fields and not through the drift of the electrons in the wire.

There has been some confusion about drift velocity in this thread, but not from me.

My suggestion is simple -----> the speed of electricity in a wire is a product of a longitudinal wave traveling through the electrons.

 

[f95toli]

I would just say that when charges have inertia, then wave moves slowly.

Anyone have some idea about when does the mass-inertia become significant compared to the inductance-inertia?

It depends. There are a few materials where the "kinetic inductance" can be very significant. "kinetic" here means that the inductance can indeed come the inertia of particles with a large effective mass; an example would be ballistic transport in some clean semiconductors.
However, kinetic inductance is most prominent in certain superconductors (e.g. NbN and TiN) when they are made into very thin films (~10 nm). Here the process is much more difficult to visualise (as should be evident from the fact that the kinetic inductance is strong function of film thickness). These materials are very useful because it allows us to make very small microwave filters, resonators etc since we don't need to rely on geometric inductors (such as spirals or meander) which are inevitable quite big.

 

[Byron Forbes]

It depends. There are a few materials where the "kinetic inductance" can be very significant. "kinetic" here means that the inductance can indeed come the inertia of particles with a large effective mass; an example would be ballistic transport in some clean semiconductors.
However, kinetic inductance is most prominent in certain superconductors (e.g. NbN and TiN) when they are made into very thin films (~10 nm). Here the process is much more difficult to visualise (as should be evident from the fact that the kinetic inductance is strong function of film thickness). These materials are very useful because it allows us to make very small microwave filters, resonators etc since we don't need to rely on geometric inductors (such as spirals or meander) which are inevitable quite big.

It is a simple situation of a longitudinal wave - increased density of the medium (increased mass of particles) produces a slower wave.

So if the mass of electrons was greater, then the speed of electricity would always be much less than c, even in excellent conductors.

Anyone seeing the point I'm making yet? :)

 

[Dale]

It is a simple situation of a longitudinal wave - increased density of the medium (increased mass of particles) produces a slower wave.

So if the mass of electrons was greater, then the speed of electricity would always be much less than c, even in excellent conductors.

Anyone seeing the point I'm making yet? :)

Yes. Did you see the point I made above?

As I said already multiple times, your idea just doesn’t work. Since this is dynamic you have to use all four Maxwell’s equations, not just Gauss law.

 

[nsaspook]

It is a simple situation of a longitudinal wave - increased density of the medium (increased mass of particles) produces a slower wave.

So if the mass of electrons was greater, then the speed of electricity would always be much less than c, even in excellent conductors.

Anyone seeing the point I'm making yet? :)

I don't because I don't really know what you mean by 'electricity'. In science current 'electricity' is normally expressed as a rate in the coulomb.

The coulomb is defined as the quantity of electricity transported in one second by a current of one ampere.

 

[Byron Forbes]

Yes. Did you see the point I made above?

As I said already multiple times, your idea just doesn’t work. Since this is dynamic you have to use all four Maxwell’s equations, not just Gauss law.

Ok, so what do you mean?

That I need to add in a little induction?

 

[Byron Forbes]

I don't because I don't really know what you mean by 'electricity'. In science current 'electricity' is normally expressed as a rate in the coulomb.

https://wtamu.edu/~cbaird/sq/2014/02/19/what-is-the-speed-of-electricity/

1. The individual electron velocity
2. The electron drift velocity
3. The signal velocity

This thread is about 3.

 

[Dale]

Ok, so what do you mean?

That I need to add in a little induction?

I mean that you are thinking of a purely "electrons pushing each other" explanation. That is governed by Gauss' law. But Gauss' law is insufficient to explain EM behavior for changing fields. When you have non-zero time derivatives then you need Faraday's law and Ampere's law also. That gives you EM waves.

Another way you could see that this is wrong is to calculate the speed of such a wave and compare it to actual transmission line speeds.

 

[Byron Forbes]

Another way you could see that this is wrong is to calculate the speed of such a wave and compare it to actual transmission line speeds.

Hmmmm, let me see now. I know the mass of the electron.

Speed of sound (c) in a medium -

where

• Ks is a coefficient of stiffness, the isentropic bulk modulus (or the modulus of bulk elasticity for gases);
• ρ is the density.

So now I simply need a way to think of conduction electrons as a medium, giving me p, and then the E field as the Ks and I'm good to go! :)

Maybe I can take a page out of QM, reverse engineer everything, playing around with the parameters and variables until everything comes out exactly the way I want it to, and then go and collect my Nobel prize! :)

 

[Dale]

Another way you could see that this is wrong is to calculate the speed of such a wave and compare it to actual transmission line speeds.

The speed of a longitudinal wave is given by $\sqrt{K/\rho}$ where $K$ is the bulk modulus and $\rho$ is the density. For the electrons in a copper conductor $K=1.4 \ 10^{11}\text{ N/m}^2$, and $\rho = 8.94 \ 10^{28}\text{ e/m}^3 \ 9.1 \ 10^{-31} \text{ kg/e}$ so $\sqrt{K/\rho} = 1.3 \ 10^{6} \text{ m/s} = 0.0045 \ c$. Actual signal velocities are much higher than that, and also actual signal velocities depend on the shape of the conductors, the relative positioning of the conductors, and the dielectric used between the conductors. None of that can be explained by the pure longitudinal model.

 

[Byron Forbes]

I mean that you are thinking of a purely "electrons pushing each other" explanation. That is governed by Gauss' law. But Gauss' law is insufficient to explain EM behavior for changing fields. When you have non-zero time derivatives then you need Faraday's law and Ampere's law also. That gives you EM waves.

As already mentioned, and proven, it is electron movement first and EM later. The EM part plays no role in the point I'm making whatsoever apart from a little inductance, which also does nothing to undermine the point.

Again, when you first turn on a power supply, the onset of electron movement at any part of the wire is dictated by a wavefront (not EM) that is simply longitudinal! i.e. a longitudinal wave traveling through the electrons, exactly the same as a sound wave.

It just is! :)

 

[Dale]

As already mentioned, and proven, it is electron movement first and EM later.

Please post your professional scientific source for this supposed "proof".

In addition to violating Maxwell's equations, your idea does not appear to explain the following:
1) the speed of the EM waves
2) the dependence on the conductor geometry
3) the dependence on the dielectric outside the conductor

 

[Byron Forbes]

Please post your professional scientific source for this supposed "proof".

My capacitor example.

But if you want to tell us about this mysterious EM wave that is apparently in existence before any electron even moves, then I'm all ears.

Just to be clear - are you suggesting that signal velocity is in no way related to the forces of repulsion between electrons?

 

[Dale]

Just to be clear - are you suggesting that signal velocity is in no way related to the forces of repulsion between electrons?

No, I am not suggesting that at all. Gauss' law is part of Maxwell's equations. It is just not all of Maxwell's equations. You need all of Maxwell's equations.

Your personal capacitor example is insufficient. You need an actual scientific reference

 

[nsaspook]

https://wtamu.edu/~cbaird/sq/2014/02/19/what-is-the-speed-of-electricity/

1. The individual electron velocity
2. The electron drift velocity
3. The signal velocity

This thread is about 3.

Then this thread is not about the speed of 'electricity' as a thing, it's about electrical science, the speed of EM waves and mass-less particles.

 

[Byron Forbes]

Your personal capacitor example is insufficient. You need an actual scientific reference

How about something like a paper on the Michelson-Morely Experiment that leads to the debunking of The Luminiferous Aether? Is that the type of thing you mean?

 

[Dale]

How about something like a paper on the Michelson-Morely Experiment that leads to the debunking of The Luminiferous Aether? Is that the type of thing you mean?

No. I mean a paper that claims, as you do, that the velocity of the signal in the wire is due entirely to longitudinal current waves as you have described. Such waves would be based on Gauss' law (or equivalently Coulomb's law) and Ohm's law and the Lorentz force only.

 

[Byron Forbes]

Then this thread is not about the speed of 'electricity' as a thing, it's about electrical science, the speed of EM waves and mass-less particles.

So tell us what's meant by "signal velocity". You realize it means that distance from a PS just after it's turned on, that electrons in the wire have not begun to move yet, right?

 

[Dale]

So tell us what's meant by "signal velocity". You realize it means that distance from a PS just after it's turned on, that electrons in the wire have not begun to move yet, right?

The question is not whether or not they are moving. It is a question of why they are moving. Is it due to Gauss' law (longitudinal current wave) or all of Maxwell's equations (EM wave)?

 

[Byron Forbes]

The question is not whether or not they are moving. It is a question of why they are moving. Is it due to Gauss' law (longitudinal current wave) or all of Maxwell's equations (EM wave)?

So you are suggesting that it is possible that signal speed is entirely unrelated to the forces of repulsion between electrons?

 

[Dale]

So you are suggesting that it is possible that signal speed is entirely unrelated to the forces of repulsion between electrons?

I already told you that I am not suggesting that (see post 79). You are apparently missing some of my posts above. In particular, did you miss the calculation of the speed of the longitudinal waves above (see post 75)? That is pretty conclusive that your approach does not work.

 

[nsaspook]

So tell us what's meant by "signal velocity". You realize it means that distance from a PS just after it's turned on, that electrons in the wire have not begun to move yet, right?

By analogy what is the velocity of water (electrons) when a rock (signal energy) skips above it? Just like in electric circuits, signals are all about energy and the speed of that energy, not charge (electricity) in a system of wires that guides (and modifies the speed of energy vs pure vacuum) electrical energy in space. We normally design signal circuits to reduce the amount of energy in charge (electrons) to the lowest point possible unless we need to generate heat or utilize the particle KE in things like semiconductor doping.

The fact that the signal velocity of the EM field is much higher than the electron drift speed means we can have charge separation across the length of a wire (a good conductor with lots of free electrons) in things like a simple antenna of a single wire. The electrons can't move at the speed needed to keep the conductor neutral in response to the changing fields surrounding it so we have a phase shift of the applied potential across the single wire. This is a needed condition for EM radiation where the wire charges just giggle back and forth very small distances while energy flows continuously forward from the RF energy source to free space.

Even in a AC circuit (50/60Hz) without EM radiation we have the same effect of wire charges just giggle small distances while the signal energy flows in one direction continuously from source to load.
http://amasci.com/elect/poynt/poynt.html
http://amasci.com/miscon/speed.html

 

[snorkack]

Consider a telegraph circuit. A battery. Two insulated wires. A telegraph key on another continent. And a measuring device.
In silent condition, there is no current, and no magnetic field. There IS electrostatic field between two wires, and each wire to infinity - for the potential of each wire is different from other wire as well as infinity.
When the key is pressed, what changes?
Electrostatic field between wires existed before pressing the key. There was electrostatic field between the open sides of switch, it just caused no current. When switch is closed, the change is in electron movement. Therefore electron movement must be the cause of electromagnetic field, not vice versa.

 

[Dale]

When switch is closed, the change is in electron movement. Therefore electron movement must be the cause of electromagnetic field, not vice versa.

The other change that you neglected to mention is in the magnetic field. (Edit: actually, the E field changes too, both inside and outside the wire)

The question is what causes the signal to propagate to the next part of the cable after the first bit of current. Is it purely due to Gauss’ law (the electrical equivalent of an acoustic wave) or is it necessary to include the rest of Maxwell’s equations?

I think it is pretty clearly the latter.

 

[anorlunda]

Forgive me from being almost off-topic, but this thread reminds me of the following true anecdote.

From: Edison, His Life and Inventions by Dyer, Frank Lewis; Martin, Thomas Commerford.

Edison was now asked if he thought he could get a greater speed through submarine [telegraph] cables with this system than with the regular methods, and replied that he would like a chance to try it. For this purpose, twenty-two hundred miles of Brazilian cable then stored under water in tanks at the Greenwich works of the Telegraph Construction & Maintenance Company, near London, was placed at his disposal from 8 P.M. until 6 A.M. "This just suited me, as I preferred night-work. I got my apparatus down and set up, and then to get a preliminary idea of what the distortion of the signal would be, I sent a single dot, which should have been recorded upon my automatic paper by a mark about one-thirty-second of an inch long. Instead of that it was twenty-seven feet long! If I ever had any conceit, it vanished from my boots up. I worked on this cable more than two weeks, and the best I could do was two words per minute, which was only one-seventh of what the guaranteed speed of the cable should be when laid. What I did not know at the time was that a coiled cable, owing to induction, was infinitely worse than when laid out straight, and that my speed was as good as, if not better than, with the regular system; but no one told me this."

 

[Dale]

Forgive me from being almost off-topic, but this thread reminds me of the following true anecdote.

Good example. That result cannot be explained only by current pushing inside the wire.

 

[Delta2]

Therefore electron movement must be the cause of electromagnetic field, not vice versa.

I think that's half the truth only. The other half is that the field affects or causes the current. It's a dynamic relation between the current and the field that works in both ways: current->field but also field->current so it is actually current<->field.

 

[gmax137]

Forgive me from being almost completely off-topic, but this thread reminds me of a story I heard. Google:

only there is no cat einstein

The attribution to Einstein is certainly false, maybe it should have been Maxwell .

 

[Byron Forbes]

I already told you that I am not suggesting that (see post 79). You are apparently missing some of my posts above. In particular, did you miss the calculation of the speed of the longitudinal waves above (see post 75)? That is pretty conclusive that your approach does not work.

Yes, I did miss that somehow. Is there delays in posts appearing on here at times? Anyway, I'll respond to that now.

 

[tech99]

In the following link, there is an explanation of plasmon oscillations, where an electron in a metal can mechanically vibrate at optical frequencies. This does not agree with the constraints imposed by the mechanical model mentioned in Post 75. If an electron can vibrate at such frequencies, it seems likely that it can form a transmission medium.

 

[Byron Forbes]

I think that's half the truth only. The other half is that the field affects or causes the current. It's a dynamic relation between the current and the field that works in both ways: current->field but also field->current so it is actually current<->field.

I disagree with this completely.

Clearly, everything is initiated by electron movement. At that time you get a little inductance, depending on the magnitude of the acceleration of an electron. This would slow down the propagation because it is akin to increasing the mass of an electron. i.e. it is akin to increasing the density of a medium sound might travel through, thus yielding a slower speed.

Any other effect you might want to introduce, and I don't know what it would be, is surely not going to happen before or instead of the forces of repulsion between the electrons.

Lets take a length of wire and touch it against an object with static electricity. At the moment of touching, an electron flows from the object into the wire. At the onset, there is no EM wave. All there is is that electron accelerating toward another and an increase in the force of repulsion between them. How could any other force be in play? Clearly, if any EM effects are the result of the electron acceleration, they are neither happening before or even during the onset of acceleration. At a time shortly after the onset of acceleration there would be inductance from lateral electrons. But this inductance simply means a lesser resultant E field of repulsion.

The electrons push the ones ahead of them through the wire - the EM is a product of this and plays zero roll in it other than inductance.

 

[jartsa]

The speed of a longitudinal wave is given by $\sqrt{K/\rho}$ where $K$ is the bulk modulus and $\rho$ is the density. For the electrons in a copper conductor $K=1.4 \ 10^{11}\text{ N/m}^2$, and $\rho = 8.94 \ 10^{28}\text{ e/m}^3 \ 9.1 \ 10^{-31} \text{ kg/e}$ so $\sqrt{K/\rho} = 1.3 \ 10^{6} \text{ m/s} = 0.0045 \ c$. Actual signal velocities are much higher than that, and also actual signal velocities depend on the shape of the conductors, the relative positioning of the conductors, and the dielectric used between the conductors. None of that can be explained by the pure longitudinal model.

@Byron Forbes didn't mention this important thing:

Bulk modulus of copper is a measure of how much energy is needed to force some more copper atoms into some volume filled with copper.

Energy needed to force some more electrons into some volume filled with copper is much larger. This latter "bulk modulus" is relevant here.

(Let's assume that the lattice of positive charges just stays still when an electron density wave is passing through a wire)

 

[Byron Forbes]

The speed of a longitudinal wave is given by $\sqrt{K/\rho}$ where $K$ is the bulk modulus and $\rho$ is the density. For the electrons in a copper conductor $K=1.4 \ 10^{11}\text{ N/m}^2$, and $\rho = 8.94 \ 10^{28}\text{ e/m}^3 \ 9.1 \ 10^{-31} \text{ kg/e}$ so $\sqrt{K/\rho} = 1.3 \ 10^{6} \text{ m/s} = 0.0045 \ c$. Actual signal velocities are much higher than that, and also actual signal velocities depend on the shape of the conductors, the relative positioning of the conductors, and the dielectric used between the conductors. None of that can be explained by the pure longitudinal model.

There are values for the electron density in a conductor that make it the same as the density of a medium that might carry air? And also values for it's bulk modulus in the same manner?

I doubt this very much but I'd be happy for you to point these out to me so that I can see who worked this out and how.

Do you have a scientific paper? :)

 

[Dale]

Energy needed to force some more electrons into some volume filled with copper is much larger. This latter "bulk modulus" is relevant here.

They are essentially the same. It is not much larger. This should not be too surprising since most of the properties of a material are related to its electrons and how they interact with each other and with the nuclei.

 

[Byron Forbes]

Good example. That result cannot be explained only by current pushing inside the wire.

Assuming I'm interpreting that story properly, you can.

There is a ton more inductance, akin to making the electrons heavier, and so the longitudinal wave travels slower. Or the modulus less - either way, electron acceleration is less and so a slower longitudinal wave.

It is always a case of electron repulsion minus inductance, which simply adds up to a reduced force of repulsion.