I was thinking of using a high-frequency trading example, but here's a case that's a bit more normal: stadium concert audio for a live band. Stadiums are big enough that you need to deal with latency issues for audio, because the back of the venue will get its audio a bit later than the front of the venue (assuming the sound is wired so the board is in the front of the floor and no adjustments are made). That is obviously disconcerting to the audience. Adjustments usually are made to handle this problem.

Then were somehow able to turn the light bulb on and apply a charge to the that rod at the same time. While also having a detector that can sense a photon and a change in electric field some equal distance away from the bulb and rod.

Then the photon (from the bulb) would reach our detector before the detection of the change in electric field (from the rod)?

Let's suppose the medium is just plain air, and not particularly humid.

Copper is clearly a different medium than fiber optic.

That is why I stipulated a single medium for the experiment.

It's close enough to c that you should just use c but it can be observed that it's less.

"In a vacuum, electromagnetic waves travel at the speed of light, commonly denoted c."

I would expect that in air, that the photon from the light source and the perturbance of the electric field from the charge to reach the detector at the same time.

The perturbation of the electrical field causes EM radiation (radio), which moves at the speed of light.

The complicating factor here is that when you have electricity flowing in a wire, the fields are generally mostly outside the conductor, not in it. That is, the signal propagation delay depends more in what you are using as an insulator around wire than the material of the wire. This has had practical consequences in the past; if you replace the insulating jacket of one wire in a twisted pair with a slightly different material, on long runs it will ruin your signal.

Is the only part that's not wrong in your post.

Photons only have one speed in empty space. They slow down when traveling through any medium other than vacuum.

> However, electrical conduction is the movement of electrons, not photons.

Electrons move because they influence each other through their fields, which are transmitted by photons. Electrical conduction happens at the speed of the fields, not at the speed of the electrons. When you push one more electron into one side of a conductor, an electron flows out the other side when the fields reach the other side, not when the electron does.

(As an analogy, consider a rubber hose full of steel balls. When you slowly push an additional ball in from one side, another ball starts to fall out of the other side as you push the first ball in, perceptually instantenously⁰, regardless of the speed you are pushing the new ball in.

(0): After a delay of (length of tube)/(speed of sound in steel)

It's only after the fields interact with electrical charges (atoms and their electrons for example) that a secondary field is induced as these charges begin to oscillate. This field will add over the original field, "shielding" an external observer from the original oscillation and apparently slowing down the propagation of electromagnetic waves.

There's a very good video by 3Blue1BRown that explains this kind of weird concept way better than I could: https://www.youtube.com/watch?v=KTzGBJPuJwM

Overall the picture is like this:

- massless particles like photons travel at speed c in empty space, in a straight line

- massive particles like electrons travel at a speed slightly less than c even in empty space, in a straight line

- inside a medium, any particle traveling in a straight line will quickly bounce off/be absorbed and re-emitted in a new direction because of some field given off by another particle; so, the average speed at which particles actually traverse through the material is lower than c. How low depends on properties of the medium, mainly how dense it is; for copper and most metals commonly used in electronics, this varies between 60-80% of c.

- When applying a potential difference to a metal wire, the electrons which normally are moving at speeds very close to c in the empty space between atoms in random directions (amounting to an overall speed of 0 along the wire) will start collectively moving in the direction of the potential difference (towards the positive node), at a very low average speed called "drift speed"; this is caused by their normally completely random bounces now being biased in the direction of the electric field;

- However, the current in the wire (the EM radiation) moves extremely fast along the wire, at the same speed that light moves (on average) through the wire. You can think of this as being caused by photons (since EM waves are photons) moving much more easily than electrons through the wire, simply because they don't have a charge of their own and so don't get caught so easily by other atoms as electrons do.

So you have 5 speeds relevant to this: the speed of light/photons/EM waves in vacuum (c), the speed of an electron in vacuum (very close to c), the average speed of all electrons in a metal wire without any electric potential (0), the average speed of all electrons in a metal wire with an electric potential (drift velocity, very small), and the speed of EM waves in a wire (60-80% of c in typical conductors).

Edit: one more note that complicates this picture, but the EM waves in a charged wire don't really move inside the wire, or not entirely - they move mostly around the wire - which means that their actual speed depends not (just) on the material from which the wire is made, but also the insulation outside the wire. That is, the EM field will propagate a different fraction of c for a copper wire than for an aluminum wire; but also for a copper wire wrapped in plastic versus one exposed directly in the air.

This brings me to a Veritasium video of a few years back that I didn't quite understand at the time. [1]

The claim being made was that if you connected a light bulb to a switch, with 300'000 km of wire left and right, and if the switch and the light bulb were 1 m away, the light would turn on in 1/c seconds.

But this would imply that the information travel is not along the wires, but straight from the switch to the light bulb?

[1] https://www.youtube.com/watch?v=bHIhgxav9LY

In theory the change in electric field will induce a small current in the other wire, and their magical science lamp turns on at any non-zero electricity. Whether the wires are connected or not at the far end doesn’t matter.

They never clarified how strong the other current would be.

Also, the phenomenon being discussed in the Veritasium video is slightly different, and that video sort of mixes up two things to make things more mysterious.

The simple explanation for what is going on in the video is that whenever you have a voltage change in a circuit, such as closing it with a switch, you get a tiny bit of radio waves being emitted radially outwards from that point out *.

In the Veritasium experiment, with a very precise measurement tool, they could detect the tiny radio pulse emitted by the switch at the moment it was closed, far before the main current reached the same point moving along the long wires.

The other thing he was mixing this up with is the Poynting vector, which is a mathematical object that represents the direction along which power (as in, worl, the thing you measure in Watts, not the actual current which you'd measure in Amperes) propagates in an electrical circuit. It's not clear at all that the Poyinting vector is a meaningful aspect of reality and not just some mathematical tool. It does happen to coincide with the direction that the radio waves propagate as described earlier, so some physicists do like to interpret it as a deeper, physically real, thing that is related, but you can just as easily ignore it.

Note that when I say that it's "not real", this is similar to how I would describe the Lagrangian and Hamiltonian of a classical mechanics system. It's an extremely useful mathematical tool and it predicts the behavior of the system perfectly well, and is mathematically equivalent to Newton's laws of motion. But while the laws of motion describe real direct aspects of reality, such as objects having mass and momentum, the Lagrangian doesn't really represent an actual thing in physical reality.

The above comes with a gigantic caveat: in QM, the Lagrangian and Hamiltonian correspond to the wave function, which is, to the best of our current understanding, the real underlying thing behind reality, with particles and waves and things localized being the artifical objects we introduce merely for convenience.

* This is normally completely negligible for DC current, but for AC current, where the current switches direction all the time, a relatively high amount of radio waves get generated radically put from the wires along their whole direction. This can lead to problems such as AC power lines causing significant radio interference. This is also normally described as "parasitic", since the power those waves carry is lost from the transmission line, which is designed to carry as much as possible of the power generated at the source towards the destination.