I love the smell of wrong Physics in the morning.
Signals propagate differently when wires are set up as transmission lines - they propagate at much closer to the speed of light, because you're actually sending a wave down the line (imagine creating a ripple on a trough of water, instead of actually filling and emptying the trough).
Last time I checked, speed of electron flow is only based on the material around it. Higher dialectric constant = lower speed of propgaition. Transmission lines aren't voodoo science, they are a property of the electrical length of the line and the rate of change of the signal on that line. It does not change the rate of propagation at all. Whether a given wire is 1" long, or 200 miles long, it will not change the speed of propagation.
I recently attended a seminar where the presenter talked about clocking based on LRC oscillations and he had actually fabbed chips that worked. The basic idea was to put an inductor on the die, and set up oscillations between the inductor and the clock load capacitance, which results in a ticking clock. Of course, you get a sinusoidal clock instead of a nice almost-square-wave, so your circuits have to be designed a little bit differently, but the point is, it works and is doable.
Not to be cheeky, but it's quite easy to change a sine wave into a square wave: Schmidt trigger. While I can't rule this out entirely, I would imagine that if it was more economical to produce an LRC resonator, it would be built into devices already. These circuits have been around for decades. It's very difficult to beat quartz crystals in terms of stability, ease of use, and power consumption.
You're half right. You're right that what's going on is a charging and discharging of a cap, but you're wrong that the charge can't be recycled. A conventional clock works by connecting the gates of a bunch of devices (i.e. capacitance) to Vdd, then after a little time connecting it to ground instead. Wait a little bit, then repeat. What effectively happens is that you dump some amount of charge from Vdd to ground each switch, and it's gone (i.e. it's heat now). A water analogy would be a tub of water above you (Vdd), a bucket in your hand (the capacitance), and the ground (gnd). You pour some water from the tub into your bucket (charge the cap), then dump it on the ground.
Wrong. The clock drives into a high impedance node. (The CMOS receivers on the other side of the clock line). CMOS drivers do have the problem of connecting to ground temporarily during switching - more akin to spilling some of the water out of the bucket as you pour it, not pouring it entirely on the ground. This can be overcome using clocks that are 90deg out of phase. And if the cap that you're talking about is the 10pF or so that is on the gate of the reciever CMOS - there are larger fish to fry power wise than this minimal capacitance. Try taking on the bulk leakage at 90nm before taking on this minimal source of power dissipation.
