Am I insane to question that only with a closed path can electrons move?

You are completely right.

The "closed loop" rule comes from a simplification that we often use in circuit analysis called the "lumped component model". This model provides a good approximation to actual circuit behavior at DC and low frequencies, where the effects of parasitic inductance, capacitance and the speed of light can be ignored.

However, these factors become significant at high frequencies and can no longer be ignored. Any circuit of nonzero size has inductance and capacitance, and is capable of radiating (or receiving) an electromagnetic wave. This is why radio works at all.

Once you start considering parasitic capacitances, you'll discover that everything is connected to pretty much everything else (moreso to nearby objects), and there are closed loops where you wouldn't normally expect to find them.

Responding to your title:

Am I insane to question that only with a closed path can electrons move?

Currents usually* travel in loops. However, the loops need not be entirely made of conductors (ie, copper). Current is a flow of charge. Therefore, all the following physical phenomena represent current:

• Electrons flowing in a copper wire
• Ions (which are charged) moving between the electrodes of a battery (or an electrolytic capacitor)
• Electrons flying through vacuum (ie, thermionic valves, cathode ray tube)
• And, last but not least, displacement current

The last one answers the question "how can a current pass through a capacitor's dielectric?". A quick summary is that charges accumulating on one plate of your capacitor will push the charges on the other plate away, and give the illusion that electrons are flowing through the cap's dielectric, while in fact they are not. One plate is filling up with electrons, while the other is getting drained of electrons.

... * Yes of course! You can have currents not travelling in loops: simply shoot an electron beam into deep space, with enough speed to escape the solar system. Obviously, this is not applicable to everyday electronics design.

Also, it has a drawback: you only have a certain number of electrons to shoot... and the more electrons your "gun" shoots away, the more positively charged it becomes, making sending electrons away progressively harder.

Whereas your usual circuit, which is a loop, recycles the same electrons (if DC) or just wiggles them around (AC), and will run as long as the battery / nucular power plant / solar cell has available energy.

Rule #1. There is no such thing as an open circuit except under DC steady state conditions.

Between every wire, every part and even every atom, there is capacitance, resistance and inductance to some other wire, part and atom. Microscopic as it may be, it is there. Even within the wire or part itself.

However, if the circuit you are testing is in a steady DC state, the capacitance and inductance present no load, only the resistance does, and that is high enough not to matter. For current to flow in that "Circuit" it has to have a path from it's start point to it's end point.

Rule #2. There is no such thing as DC Steady State conditions.

We are swimming around in a sea of electromagnetic waves. As such, a steady state DC circuit is actually impossible to achieve. Further every current in your circuit is producing it's own electromagnetic field that interacts with each other AND with those outside fields. There will always be what we call "noise" in your circuit.

Rule #3 : The faster you modulate a voltage / current the more potential circuit paths you need to worry about

Those little invisible circuits I mentioned in Rule #1 have impedances that change as the frequencies you are trying to pass increase. As such the higher we go the more we have to deal with strange effects like signal loss, reflections, and noise emission to name but a few.

Fortunately:

For the most part we can dismiss most of these effects because, at the frequencies you are using, they produce little disturbance.

A 60Hz AC circuit works basically the same as the circuit diagram indicates if the connections are not lengthy. We can safely make the bold statement that circuit needs to be complete for current to flow because the current that is actually flowing is basically not measurable enough to matter.

However, if you are trying to pass a 100GHz signal round the same circuit, you will find the numbers no longer make any sense.

As for broken loops... See Rule #1

Are you insane to question that?

No, actually quite the converse. It is always good to think deep and ask questions like that. However, the answers may drive you there.