Definition: A channel is the hardware input on the scope a probe plugs into.
I understand professional oscilloscopes can accommodate this, what circuitry exists in oscilloscopes that allows referencing a seemingly arbitrary ground and comparing a signal to it?
No. Most scopes do not have isolated channels. Not even the $20k scope I have at work with 8 channels. And students blow scopes thinking they do by trying to measure across two different components simultaneously where they connect the probe ground clips to two different circuit nodes. The ground clip on all the probes is the same node unless you know otherwise.
So beware when connecting passive probes on a wall powered scope to a circuit powered from the AC mains that does not use a transformer. The reference node has already been decided for you since probe's reference clip is already connected to something in the circuit through the scope power supply.
What you are thinking of are either isolated probes or differential probes. Isolated probes actually do float.
Differential probes do not but instead amplify the voltage difference relative to the scope channel's reference and pass it on to the scope, often stepping it down first with a divider so high input voltages can be brought into range to be measured. So for my work scope we had to get a bunch of differential $4k differential probes for each channel we wanted to measure with a different reference. Ouch. This is what is inside a differential probe:
See link for circuit description. Enough is provided to build your own. Basically a symmetrical or balanced resistive divider in parallel with a capacitive divider of the same ratio for frequency compensation (so the R in the divider doesn't kill bandwidth by making an RC filter with parasitic and input capacitances) followed by a differential amp.
Or the scope power supply is outright isolated from the circuit supply so they can float to whatever you want for ONE reference among all passive probes since input channels still share the same reference. (Of course, differential probe or isolated probe connected still allow you to measure with different references).
- Either the scope or circuit is battery powered and the other is not
- Scope and circuit are powered from different batteries
- Either the scope or circuit is powered from an isolated supply and the other is not
- Scope and circuit are powered from different isolated supplies
Or, in the rarest of cases, the scope has isolated channels and each channel can be connected to a different reference node even if all passive probes are used. Battery powered, portable scopes have a higher chance of being this due to their expected usage.