I Coulomb's law taken to the extreme

[Orodruin]

The electromagnetic field is a [pair of] field(s) in this sense.

... a rank 2 antisymmetric tensor field to be precise.

 

[tech99]

I notice that when I discharge the dome of the Van de Graaff machine it discharges immediately and I do not have to await energy to travel back in from the outer reaches of space.

 

[SredniVashtar]

A "field" in the sense that we use the term is a function defined over a space.

...
Similar to the way that it makes sense to speak of the speed of surface waves on a lake without needing to talk about the speed of the lake. The water is already there. Its surface has a height everywhere, even before we throw a rock in.

That seems just semantics. But ok, the perturbation in the field between creation and annihilation is say 100 ns long and, from a distance, I have 100 feet in space where the electric field is non zero, while it is zero before and after. In the middle I only have the static electric field of the (pair of) charge(s) pointing where the source was r/c seconds before.
Is that a wave? If the charges were held fixed after the initial transient separation, all we have in the middle is an electrostatic field. No accompanying magnetic field that can justify a wave propagation.
It's as if we raised the level of the lake. Yes, there is a perturbation at the start when the tsunami hits you and you go from no field to yes field, but then - imagine you do not annihilate the charges - it no longer is a perturbation. It's like the electric field of every other existing charge.

 

[Orodruin]

The argument of the field being 'already everywhere' should not apply here because the charges responsible for it were not always there.

Sorry, but that’s just nonsense. The field is always there whether nonzero or not. Zero is a perfectly valid field value.

Charges are not responsible for the existence of the field itself, they are the cause of divergences in the field, as described by Maxwell’s equations.

 

[SredniVashtar]

Sorry, but that’s just nonsense. The field is always there whether nonzero or not. Zero is a perfectly valid field value.

Charges are not responsible for the existence of the field itself, they are the cause of divergences in the field, as described by Maxwell’s equations.

I am seeing this from the point of view of classical ED. Fields are an expression of the presence of a charge.

 

[Orodruin]

I am seeing this from the point of view of classical ED. Fields are an expression of the presence of a charge.

That is a common misconception due to Maxwell’s equations being linear. It is however not really accurate, in classical electromagnetism, the field is always present. It may be zero, but it is present.

Divergences in the field are the expressions of the presence of charges.

 

[jbriggs444]

Is that a wave?

Yes.

I am seeing this from the point of view of classical ED. Fields are an expression of the presence of a charge.

Right. You created a dipole, allowed it to exist for a short duration and then extinguished it. From a classical viewpoint, the result is a wave. A wave that persists after the dipole is gone.

 

[SredniVashtar]

That is a common misconception due to Maxwell’s equations being linear. It is however not really accurate, in classical electromagnetism, the field is always present. It may be zero, but it is present.

Divergences in the field are the expressions of the presence of charges.

Are we still talking of classical electrodynamics? Because, to my knowledge, charges are the sources of the electric field, and currents are the sources of the magnetic field. They still are the sources (in the sense of the reason for the field presence - or if you prefer it "the nonzero value of the ever-present field") even when the field lines curl around each other. The 'curling' is the result of the relativistic transformation of the electric field of charges in a moving frame reference and of the finite speed of propagation of light.

 

[SredniVashtar]

Yes.

Right. You created a dipole, allowed it to exist for a short duration and then extinguished it. From a classical viewpoint, the result is a wave. A wave that persists after the dipole is gone.

Ok, let's change the timescale: instead of 20 ns, let's make it 4 billion years. We sit in the middle of this event. Would you call that perturbation that has been static for 2 billion years minus the few microseconds or milliseconds during the initial transient a "wave"? I wouldn't . I call that a static field. If I create a dipole in the lab, by bringing two spheres with opposite charge close to each other in the arc of say ten seconds, in the time I turn around to the instrument to measure the field, there is an electrostatic field, not a wave. We should rewrite ALL books of physics if that were not the case.

Granted, the distinction between statics, quasi-statics, and dynamics can be seen as artificial, since it is essentially centered on human timescales, but it is useful nonetheless. As John Percy Hammond put it:

[missing quote from one of Hammond's books or papers where he explain why it is useful to differentiate between static, quasi-statics, and dynamics - I have been looking for that for days but I can't find it]

If we want to put all these phenomena under the same category, instead of "wave" (which is indeed the solution to the full set of Maxwell equations, and not selectively maimed subsets) I'd use the term "solution of Maxwell's equations". Because after the first million years, I am pretty sure we can consider the transient that changed the value of the electric field from zero to a nonzero value spent and no longer relevant to all practical purposes.

And this is what I mean when I say that the electric field travels at the speed of light from the source: the information about the updated value travels with that speed. It is the convective part of the Lienard-Wichert formula. It is preceded by a wave-like transient corresponding to the radiation part of the Lienard-Wiechert formula. The existence of a mathematical structure that represent a 'global' electric field extending to all space does not seem that important in classical ED.

Anyway, even if we use this concept of all-present electric field with the special value of zero where some would say there is no electric field, like a the surface of a lake at zero height, the point I was trying to make is that the level of the lake cannot rise all 'together'. There needs to be faucets and sinks from where the water either enters or exits the lake, and the rest of the lake will change its level after a time r/c from these sources/sinks.

 

[renormalize]

Because after the first million years, I am pretty sure we can consider the transient that changed the value of the electric field from zero to a nonzero value spent and no longer relevant to all practical purposes.

This is nonsense. In an otherwise empty universe that initially contains an electron and positron at rest, they will attract and annihilate, thereby emitting electromagnetic radiation. Afterwards that universe is charge-free, but the outward-propagating radiation persists for all time, as it must since energy is conserved.

 

[jbriggs444]

Ok, let's change the timescale: instead of 20 ns, let's make it 4 billion years. We sit in the middle of this event. Would you call that perturbation that has been static for 2 billion years minus the few microseconds or milliseconds during the initial transient a "wave"?

2 billion light years from the position of the temporary dipole there will be a wave, yes. What is your point?

 

[SredniVashtar]

This is nonsense. In an otherwise empty universe that initially contains an electron and positron at rest, they will attract and annihilate, thereby emitting electromagnetic radiation. Afterwards that universe is charge-free, but the outward-propagating radiation persists for all time, as it must since energy is conserved.

Who ever said they are in an empty universe and they are free to recombine?

 

[SredniVashtar]

2 billion light years from the position of the temporary dipole there will be a wave, yes. What is your point?

My point is that the wave is the transient, and the static field we perceive after the transient has died out is... a static field. Not a wave.

 

[jbriggs444]

Who ever said they are in an empty universe and they are free to recombine?

If the universe is non-empty then an argument that the local region has a static field becomes invalid. If they are not free to recombine then how do we explain the hypothetical situation in which they did recombine.

If your only point in posting here was to point out that we can have a large local region over which the electromagnetic field is static and at least approximately zero-valued then I think we are in agreement.

 

[renormalize]

Who ever said they are in an empty universe and they are free to recombine?

I did. It's a simplified model that is both consistent with physics and represents a counterexample that clearly invalidates your reasoning and assertions.