How far do electrons physically move in a single clock cycle in a (theoretical) 4GHz processor?

It's not the speed of the electrons that matters, that's really slow, but the group propagation velocity of the electric fields that push them around, which is around 1/3 of the speed of light. Given that 2.4GHz has a wavelength of 12 cm roughly, the problem with 4 GHz chips is that the size of the chip die is pretty big compared to the wavelength of the clock, and so it starts to get way too hard to deal with the clock skew.

Also, the power consumption of a CPU increases really fast as the clock speed goes up, and at some point the thing overheats.

Each electron hardly moves at all in 0.25 ns, even with the tens of amps that flow in such processors.

"For example, in a copper wire of cross-section 0.5 mm2, carrying a current of 5 A, the drift velocity of the electrons is of the order of a millimetre per second."Wikipedia

Fortunately, we don't need the electrons to move very far to carry a wave that moves long distances very fast.