Remembering Muhammad Ali allegedly claiming to switch off the light in his room and getting into bed before the room went dark I wonder how fast the effect of interrupting an electrical circuit travels down a conducting line. So, to put it in concrete terms: if I have a battery and a 300,000 km cable with a light bulb at the other end and I switch it off, how long would it take for me to see the light go out?
Assume that the switch is instantaneous and that the light bulb (or LED or whatever is best for this thought experiment) goes off immediately and completely with no dimming transition when the power does not reach it, or explain why those are not valid premises.
What is it that keeps “flowing” (I suspect that this a just a colloquial language metaphor and that nothing really flows) through the wire during the time lag before the light goes out?
The important thing isn’t the electrons themselves. It’s the electromagnetic waves. The electrons mostly just serve to keep the waves guided along the path of the wires.
As such, you’re looking at the speed of light. Depending on the precise setup, it might be the speed of light through the metal, through the insulation around the metal, or through the air around the insulation. But in any event, it’s going to be very, very fast.
So in the sketched setup (300,000 km wire) it would be two seconds, one second for the electromagnetic wave to stop reaching the light bulb, one second for noticing that the light emmited is no longer reaching me? Where does the energy for the first second come from? Is it already in the wire?
Yup, or more precisely it’s traveling the path of the wire.
Thank you, I will let that information settle for a while, but it feels clearer now.
You are right, what I sketched is a telegraph! It’s been a long time since I last solved any differential equations like those in your links, but I’ll give it a try. I am not very confident that I still can gain useful information from that, but let’s see…
According to this, it could take as long as three seconds:
So if my link is correct, and it seems plausible to this non-physicist, the signal is not quite as fast as light through a vacuum. But I still can’t credit Ali’s tall tale.
He was good at bragging, that much is sure 
I see in your link a distinction between the speed of the electrons and the speed of the “wave” or “signal”. I think that is relevant to the doubt I had, thanks for the article!
The propogaton velocity of the E and M fields around the wires is always less than c, and depends on a number of variables. For most pairs of wires, the velocity is somewhere between 0.4c and 0.8c:
He wasn’t the first.
https://quoteinvestigator.com/2013/06/12/before-dark/
I should have seen that coming, this being the Dope 
So the thread is hereby officially solved? Fast as was to be expected. Kudos to all!
Huh? When you switch off a circuit, the interruption is almost instantaneous. This is AC if we’re talking household light bulbs, so there are induction and capacitance issues with the circuit too. (Above my math grade)
With most electronics (TV, stereo, computer, etc. but not old bulbs) , of course, the power supply splits the AC into DC using rectifiers (or nowadays, switching) including capacitors to smooth the result. So turning off the power allows the power to slowly drain out of the capacitors. (and electronics like computer that reboot have an RC circuit to hold down the “reset” line on chips until the power turned on is at a decent level, a second or so. If you are rebooting electronics, pull the power, count to 10, then power on again. If the power is not completely drained from the supply, the chips could be enabled without a reset, possibly freezing it.
Electricity in even low-resistance wiring travels substantially slower than EM waves in a vaccum. (I recall doing the interferometer test to determine the difference in wavelengths between a laser in an almost vaccum vs. atmospheric pressure. Do it slowly and count the wavelengths. )
I’m surprised nobody stated the obvious - back then, they would have been incandescent light bulbs, so turning off the power could mean it take a second or two for the bulb to stop glowing.
Well, I stated in my OP that the light goes on and off instantaneously, with no dimming transition, and that you could take an LED or whatever if this was helpful, I also wrote that I was using a battery (DC) and a cable, no rectifiers needed, and the physical switch is also ideal (thought experiments allow this, IMO). But of course in real life your objections are relevant. Specially concerning Mr. Ali I strongly suspect that the afterglow you mention plays a role, as does image perduration on the retina.
I’m starting to think he also maybe couldn’t sting like a bee either. Humans have no venom glands, nor any way to inject it in a victim.
It takes a lot less than a second for an incandescent filament to cool down enough that it’s no longer visibly glowing. It’s much longer than the lag time due to the speed of signal in the wires, but still too quick for any human to perceive.
That’s not true, especially for high-power halogen lamps.
An electric stove burner, OTOH, takes quite a few seconds.
It an take a very long time. The first transatlantic cables were failures. When they finally go one working well enough to use, it took two minutes to transmit a single character. The key to getting it to work well, was the understanding of the correct differential equation, the solution of those equations, and Heaviside’s proposal to distribute extra inductors along the length of the cable. He was ridiculed for this suggestion, because everyone “knew” that extra inductance would make things work.
The problem was due to electrical resistance. In the limit of large enough series resistance or small enough shunt resistance, the differential equation is the diffusion equation, the same one that describes heat conduction; in the opposite limit, it is the classical wave equation, which describes dispersion free propagation with a velocity somewhat smaller than the speed of light.
In diffusion, the time scale goes up with the square of the distance, while in wave propagation, it goes up linearly with distance. Also, in diffusion the signal is stretch out in time.
Sorry about all the typos.