If you have many of them in parallel too, then the velocity of each individual marble is low, but the number of marbles pushed in and out huge. If you knock one marble in, it takes only a tiny fraction of a second for the outermost marble to ping correspondingly, even though the velocity of any individual marble is very low. (Consider, in particular, how the length of the marble chain doesn't really affect much how long that takes.)
I don't think that's correct.
It is a horribly crude and not very apt comparison, because marbles (or ball bearings or anything similar) behave very differently than delocalized electrons.
(I was considering an analogy with springs already a bit compressed, but not everyone has played with those. The springs would better represent the interactions between electrons, instead of trying to represent individual electrons.)
I
obviously don't have the excellent popularization skills of famous physicists like Feynman; I just decided to try.
The motion in a cat's cradle is propagated via a shockwave, which presumably would be the speed of sound in the material. It just looks instant because the line of marbles is so short.
In conductors, the propagation is via the electromagnetic field interactions, which occur at
c.
The reason the current signal is slower is due to those same interactions, causing things like very-shortlived excitation states (femtosecond-attosecond time scales or faster, not even bothered with in simulations). I think that in the "spring model" those could be modeled with baffles of some suitable material (foam rubber in slight compression?) between springs. The best analog for a shockwave might be those exitation states, because in a very short pulse they'd progress through the conductor in a similar fashion (at the speed of 2/3
c or so).
If you consider a signal in a coaxial cable, those EM fields are mostly in the insulator between the core and the shield.
In a rather real sense, it is important to remember that electrons in conductors like metal atom lattices are not at all localized, but really spread over many lattice points, and they do overlap a bit. They are also in constant motion, because the atoms they share are in constant motion; the density of that spreading out varies all the time. Even "balloons" in slight compression might be better analog than marbles, but then one must remember that those "balloons" would be filled with electromagnetic fields, and not air...
To me, it is clear what Feynman is saying here, and it is exactly the reason that I quoted him in the first place. He is warning us that knowing the name of something and knowing how it is represented and modelled in some mathematical space, is not understanding the reality of it. Trying to form a visual image of it as something that can flow from place to place will very likely lead one astray. As has been amply demonstrated in this thread.
Yes; I am in full agreement. (I have people with significant skills and knowledge in visual arts in my family; me, uh, not so much. Matisse's was one that bridges art and how I see physics myself, modeling and predicting the universe, but not trying to explain it.)
This is also why I try to make it clear that these (as above) are
analogs, that should help one build an intuitive picture of the model we have, but not an exact description that can be used to extrapolate other behaviour and properties from.
How does a wave propagate slower in a stripline than in a microstrip?
Very good (rhetorical) question! It is also the key to why I consider the entire question (of this thread) unphysical: it is like asking whether it is best to wear a parka or just a swimsuit, without specifying
where: Antarctica, or a beach in Hawaii.
It is the geometry of the system that determines where the energy flows. We measure current as the amount of electrical charge through a surface or into a control volume, but that does not mean that the
energy keeping the charge carriers (electrons and ions) moving is charge carrier kinetic energy. No, it is the electromagnetic field interactions between those charge carriers where the energy is. We just cannot extract it directly, so we use the flow of the charge carriers, which we can exploit easily. (Even with antennae, we first convert to charge carrier movement, and then exploit those. EDIT: Rather like gravity, which we cannot exploit directly, but is easy to indirectly exploit by moving masses up and down.)
(And all that ignores all the weird stuff that happens when the energy
starts flowing, a very non-equilibrium state, where we'd really need to apply quantum electrodynamics to understand all that happens.)
Now, if the conductor is a straight line/cylinder/rod, with no other conductors nearby, a direct current will flow in it. An alternating current will flow mostly near the surface. Add another hollow cylinder, "ground", around the first one, and now most of the energy is in an EM field between the two, even if you stuff some suitable insulator, dielectric material, between the two. While we say current flows in even such a coaxial cable, in reality, in any cross section not at the ends of the cable, most of the energy is in the EM field between the two.
The same applies to striplines, which can be considered a 2D wave guide: only the outer hollow cylinder, and a short length of the initial rod to get the EM wave going in the "cavity". And to microstrips, where instead of having the ground surround the wave guide, you only have it on one side, with the other exposed to air or similar insulator/poor conductor with sufficiently different properties to the waveguide dielectric.
Hell, even on a plain PCB, if you make a very sharp angle, you can leak EM radiation from the bend, if the voltage or current has suitable frequency components!
To be useful, the question should be completely rephrased in terms of observed phenomena, or a very specific circuit or transmission line setup. The geometry is
that important here. As it is,
any argument in any direction can be countered by very slightly modifying the geometry of the system.