Put another way, the main reason this effect is observable in the way shown in the video is because the light and battery, and the wires between them, are so close together. Move them further away, and, per the inverse square law, you'll start seeing a much lower induced current-- the effect may still be there, but it won't be measurable over the noise floor of the experiment setup.
What's happening is that you are straying further and further from the "impedance matched" condition (the inductance per unit length stays the same but the capacitance goes up with the separation--however, being "too close" will also cause similar behavior). Consequently, the energy transmitted per reflection gets smaller and smaller.
Part of the problem in this whole discussion is using a "light" as a "threshold detector" where the threshold is effectively microamps. A microamp threshold detector is not what people think of as a "lamp".
If the original Veritasium video had showed the current flow via meter, oscilloscope, etc. nobody would be terribly surprised as it would show small flows getting bigger upon each reflection until it built up to the full current.
Question: At which point does the influence reach actual zero? If it doesn't, does that mean the coffee in front of me is being influenced by Jupiter, however minuscule?
What happens when they are not close enough for any meaningful electric field interaction?
The voltage/energy transmitted becomes vanishingly small, and smaller than the thermal noise of the electrons in the other antenna, and undetectable. https://en.wikipedia.org/wiki/Johnson%E2%80%93Nyquist_noise
- Different sized loops
- Wires closer together / farther apart
- Wires on the ground instead of in air
- Current on both sides of switch
- Wires in two big spread-out loops
- Different strength resistors
The other issue with the Veritasium "setup" was that he specified that the wires had no resistance. That being the case the RC time constant would be 0 and thus you wouldn't see that initial charging of the capacitance (and associated current flow) because it would happen instantaneously under those assumptions.
I also wonder what would happen if, instead of a setup like this:
You did something like this: That is, battery (and switch) and light at opposite corners of a large square, instead of on the middle of a long double-line. Veritasium video implies the current will start flowing at sqrt(2) * width, instead of at 2 * width. Would these effects really work over longer distances like this?