There is a problem with that analogy: if you only apply pressure to a single marble, the marble at the other end will not be pushed out instantly. In fact, the 'signal' will travel with the speed of sound in the material of the marbles and you can measure the time difference it takes for the last marble to move after the first one has moved. The marbles will be slightly compressed and decompressed while moving, accounting for the extra length needed to accommodate the 'not moving instantly'. [1]
A better analogy would be one where all marbles are pushed simultaneously. That is more like what happens in logic circuits.
[1] People doubting relativity often try this thought experiment: I have an incompressible metal bar of a lightyear long. I press on one side. The other side must move instantaneously and not after 1 second (or longer). In fact, this proves the reverse: relativity is incompatible with the existence of incompressible metal bars. As we know, all metal bars are in fact compressible, so that is not a problem. And with compressible metal bars, the thought experiment fails, because the push will travel with the speed of sound.
That's true, but it is only an analogy, and like every other analogy it breaks down at some level (after all, it isn't the 'real thing').
The fact that there is a pressure wave set up in the materials is possible because marbles are made of some material (glass, stone, metal, whatever). If you wanted a 'perfect' picture you'd have to explain about electron migration in detail and then we're looking at a completely different picture.
You'd not have a pressure wave in an electron to begin with, and they're not 'pushing' against adjacent electrons either.
But it serves well to show how a slow move can have an apparent instantaneous effect at a distance.
Edit: I had a thing written here, but I figure I'm not understanding what you mean by 'all marbles are pushed simultaneously'. Can you elaborate? Other than the conflation of the speeds of light and sound (which is not such a big deal, really), it's a good analogy.
As for the 'all marbles are pushed simultaneously': a key characteristic of useful transistors is that they operate as amplifiers[1]. This is possible because effectively, every transistor has its own power source. As such, on each clock cycle, then can all get a simultaneous push from their power sources.
BTW, I'm not conflating the speeds of light and sound. If you bang on one side of an iron bar, a wave travels through the material, quickly compressing and decompressing the bar where the wave passes. Such waves travel at the speed of sound in that material, no at the speed of light. That makes sense, because sound is nothing more than the physical modulation of the density of a medium, most commonly air.
You're not, the person you're replying to was. I find it odd that you would object to an analogy where the signal propagates through the marbles at the speed of light (i.e. 'instantly'), and offer up instead one where each marble moves simultaneously. If the exit event is simultaneous to the entry of the other marble, they are separated by a spacelike interval despite the causal relationship between the two events. This violates relativity.
On the other hand, in the original analogy the two events are separated by a lightlike interval, which while impossible in the case of marbles, at least does not violate relativity when the two events are causally linked. This is what I meant when I said the conflation of the speed of sound and the speed of light is not such a big deal, in this case.
Anyway, it's perfectly reasonable to talk about light traveling instantly and it's time that has propagation delays. The idea being what separates the present from the future is the ability to interact with each other.
The electrons are only moving at ~ mm/s. With an AC current, the net effect is that they're not moving at all. Electrical power is not provided by the movement of electrons. The force carriers of the electrical field, the particles responsible for actually exchanging energy, are photons.
I initially was mostly interested in the word instantly, but if we're going to analyze this analogy further, I'd have to say you just can't treat electrons inside bulk materials as particles. It may sound sensible and give you the idea you understand what's going on, but it's just not even wrong.
Umm, yea just like the marbles in the example. If you have a marble pushed into a pipe with 1,000 marbles the one popped out at the end is pushed out a lot faster than any single marble moves.
Ummm... no? It'll come out at roughly the same speed (less if the moment it came out there was still energy trapped in the form of compressed marbles when it emerges). Why would it be otherwise?
Have you ever seen those desktop toy's where steel balls 10+ steel balls are strung up next to each other. You drop one and it fall hit's one end of the chain and in less time than it would have taken the first ball to move that distance the last one pops off the end? Same concept the final ball moves a little slower than the first ball that hit the chain, but it start moving sooner than it would have taken the first ball to move the distance of the chain.
Ok that's true, but not how I read your post. Yes the energy is transfered at the speed of sound in the material, but I read your post as saying the velocity of the marble on the end is greater than the velocity of any other marble, including the one you push in, which is certainly not true.
A better analogy would be one where all marbles are pushed simultaneously. That is more like what happens in logic circuits.
[1] People doubting relativity often try this thought experiment: I have an incompressible metal bar of a lightyear long. I press on one side. The other side must move instantaneously and not after 1 second (or longer). In fact, this proves the reverse: relativity is incompatible with the existence of incompressible metal bars. As we know, all metal bars are in fact compressible, so that is not a problem. And with compressible metal bars, the thought experiment fails, because the push will travel with the speed of sound.