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Propose an implementation.
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rob ♦
rob ♦
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For what it’s worth, I did nearly this exact experiment (mostly by accident) back when I was a postdoctoral researcher. The context was sending pulses with a width of only a few nanoseconds down a cable with a propagation time of a few microseconds, to an LED next to a photomultiplier tube, then collecting a few-photon response from the detector a few microseconds later. My function generator output was connected by a “tee” to an oscilloscope; the cable to the scope was short, but still longer than the nanosecond rise/fall time of the brief pulse. So my setup was something like

   ,_________|f.g.|_____________________________,
|scope|                                       |LED|
   \_________|ground|___________________________/

One of the things I did as I was building this setup was to send long (millisecond) pulses, so that microsecond-scale transients had time to dissipate and the system entered a steady state. That’s roughly analogous to the Veritasium scenario of connecting the battery and waiting a year for the current to get to the end of the lightyear-long cable. If a millisecond-long pulse has a nanosecond rise (or fall) time, that leading (or trailing) edge and its reflections behave in the same way as the leading (or trailing) edge of the few-nanosecond pulse.

I might reproduce the thought experiment here by making the following changes:

  1. Introduce the battery in series with the center conductors of the coaxial cables, using a box like this one. A ground-isolated bipolar d.c. power supply might be easier to connect, but its complexity would distract a skeptical observer.

  2. In another box (or perhaps even the same box), put a small series resistance in series with the sheath conductors of the coaxial cables. Connect an oscilloscope (in its high-input-impedance mode) in parallel with this resistor. Ta-da, a fast ammeter.

  3. In a third box, perhaps with three inputs, an isolated transistor switch driven by the fast function generator between “conducting” and “insulating.”

  4. Complete the circuit by putting a zero-resistance terminator at the ends of the long cables. If I were actually doing the experiment, I’d also try swallowing the echos using an impedance-matched terminator, as well as leaving the cable ends open to demonstrate the current flows in both conductors until the reflection arrives from the open end.

The prediction in the video, as clarified by this question, is that if the resistor in series with the sheath conductor is near the switch, the current in that resistor will change when the state of the switch changes, in addition to when echos of the state change arrive from the ends of the long cables. Also, the timing of that current is essentially the same whether the switch interrupts the center conductor or the sheath conductor of the cable.

If I still worked at a place where I had all of these fast electronics lying around, I could probably put together a demo in an afternoon or two. (There would be some tedious issues related to the practice of fast electronics sharing a common ground.) Unfortunately I disassembled this setup a decade ago.

For what it’s worth, I did nearly this exact experiment (mostly by accident) back when I was a postdoctoral researcher. The context was sending pulses with a width of only a few nanoseconds down a cable with a propagation time of a few microseconds, to an LED next to a photomultiplier tube, then collecting a few-photon response from the detector a few microseconds later. My function generator output was connected by a “tee” to an oscilloscope; the cable to the scope was short, but still longer than the nanosecond rise/fall time of the brief pulse. So my setup was something like

   ,_________|f.g.|_____________________________,
|scope|                                       |LED|
   \_________|ground|___________________________/

One of the things I did as I was building this setup was to send long (millisecond) pulses, so that microsecond-scale transients had time to dissipate and the system entered a steady state. That’s roughly analogous to the Veritasium scenario of connecting the battery and waiting a year for the current to get to the end of the lightyear-long cable. If a millisecond-long pulse has a nanosecond rise (or fall) time, that leading (or trailing) edge and its reflections behave in the same way as the leading (or trailing) edge of the few-nanosecond pulse.

I might reproduce the thought experiment here by making the following changes:

  1. Introduce the battery in series with the center conductors of the coaxial cables, using a box like this one. A ground-isolated bipolar d.c. power supply might be easier to connect, but its complexity would distract a skeptical observer.

  2. In another box (or perhaps even the same box), put a small series resistance in series with the sheath conductors of the coaxial cables. Connect an oscilloscope (in its high-input-impedance mode) in parallel with this resistor. Ta-da, a fast ammeter.

  3. In a third box, perhaps with three inputs, an isolated transistor switch driven by the fast function generator between “conducting” and “insulating.”

  4. Complete the circuit by putting a zero-resistance terminator at the ends of the long cables. If I were actually doing the experiment, I’d also try swallowing the echos using an impedance-matched terminator, as well as leaving the cable ends open to demonstrate the current flows in both conductors until the reflection arrives from the open end.

The prediction in the video, as clarified by this question, is that if the resistor in series with the sheath conductor is near the switch, the current in that resistor will change when the state of the switch changes, in addition to when echos of the state change arrive from the ends of the long cables. Also, the timing of that current is essentially the same whether the switch interrupts the center conductor or the sheath conductor of the cable.

If I still worked at a place where I had all of these fast electronics lying around, I could probably put together a demo in an afternoon or two. (There would be some tedious issues related to the practice of fast electronics sharing a common ground.) Unfortunately I disassembled this setup a decade ago.

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rob ♦
rob ♦
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This is a transmission line problem. Transmission-line problems can be counterintuitive for people who are used to thinking about the moving charges in circuit but are used to ignoring the fields. (One example here).

Let’s imagine that the long cable to nowhere is not pair of parallel wires, but instead that the "outgoing" and "return" wires are wrapped around an iron core, like a transformer. In the approximation that the freshly-connected battery is only pushing current along the outgoing wire, this high-inductance makes it a little more obvious that the current cannot instantaneously start moving down the entire outgoing wire. The basic principle of an inductor is that the magnetic field has some intrinsic "inertia." If the magnetic field through some loop isn't constant, an electromotive force develops around the boundary of the loop; charges which are free to move under the influence of this e.m.f. will generate a current which tries to prevent the magnetic field from changing. If you treat the outgoing wire, wrapped around an iron core, as a single solenoid, each coil in the solenoid will be fighting the changing magnetic fields as the current changes in the neighboring coils.

But if the wires for the "outgoing" and "returning" currents are wrapped around the same magnetizable core, there's a much easier way for the entire system to fight the changes in the magnetic field: the outgoing current can induce a current in the return wire. (Of course I already gave away the game by talking about transformers.) Note that the direction of the return current, in this transformer-transmission-line model, depends on whether the two coils are wound with the same handedness or not. But the current in the outgoing wire will unquestionably induce some nonzero current in the return wire.

Now let's unwind our two wires and return to the parallel-cable setup from the video. Unwinding the wires from the imaginary transformer, and removing the imaginary magnetizable core, dramatically reduces the mutual inductance between them —— but that inductance is still nonzero. Pick any two points along your lightyear-long cable, and the gap between the two wires makes an Amperian loop:

                           A        B
,_____|L|__________________⋮________⋮___________,    _
|                          ⋮        ⋮           |    | 1m
\_____|B|_/ _______________⋮________⋮___________/    -
                           ⋮        ⋮
                           C        D

If the battery changes the current along the segment $CD$ from zero to not-zero, the magnetic flux changes in the loop $\mathit{ACDB}$, and the electromotive force associated with this changing flux will induce an opposing current in the segment $BA$. This is happening in both arms, and the induced current flows through the lamp, which illuminates.

Now the amount of current that flows through the lamp, and the time it takes to reach a steady state, will depend in a complicated way on the transmission-line characteristics of the cable: its inductance, capacitance, series resistance, and shunt conductance (all traditionally measured per unit length). The point of the linked video is to remind you (or teach you) to think about these circuit properties in terms of their fields, rather than only in terms of the motions of charges.

but if you move the switch so it's an equal distance from the light source and battery?

I'm not 100% sure I understand your proposal here. But suppose there is a second switch, which is also initially open, located many light-seconds down the transmission line:

,_____|L|_____________________________________,    _
|                                             |    | 1m
\_____|B|_/ _________________________/ _______/    -
          S1                         S2

If we close $S_1$ and leave $S_2$ open, the signal will propagate down the cable as before until it reaches $S_2$. The open switch $S_2$ will effectively function as a series capacitance, which will change the impedance of that section of cable. At an impedance mismatch in a transmission line, part of the signal is transmitted and part of it is reflected. However, the signal that "$S_1$ has been opened" has already been propagating down the cable, with current in both wires, and the lamp has already illuminated.

Likewise if we close $S_2$ but leave $S_1$ open, that signal will propagate to the left down the cable from the location of $S_2$. In this geometry, the lamp will be illuminated by the part of the signal transmitted through the impedance mismatch at $S_1$.

Electromagnetism is local. Think about the fields.