Wait, does this apply to AC too? I always believed AC can create current even if the loop isn't closed. Say you have an exposed AC wire and touch it; I'd expect you to get a burn at the place you're touching, as the electrons from your finger at the contact point are pulled into the wire and pushed back to the finger, at 50 or 60 Hz. In general, isn't this how RF burns work?
However, RF is more complicated. The difference between "RF" and "AC" is a matter of what materials and frequencies are involved and how you are using them.
Terrestrial RF systems rely on the Earth as a ground conductor. It becomes more complicated because the impedance (like an AC version of resistance <waves hands>) of a material (such as your body between the antenna and ground) will change depending on frequency. Once a circuit it in place, the impedance mismatch between your finger and the thing it is touching will cause energy to build up at that interface.
This is similar to how light diffracts when it moves from one material to another and you can see the boundary because some energy builds up there and is scattered.
You won't get a burn if there is no circuit.
...but if you are fully enclosed in an RF field, you may get little circuits forming because your body is in contact with that field, and therefore referenced to it, and the potential of the field might vary across your body.
Your body also has a little bit of effective grounding just by existing inside a room, but that's modeled as "a 100pF capacitor in series with a 1.5kΩ resistor". Charging a 100pF capacitor to 120 volts 120 times a second comes out to 0.2 milliamps, which is not going to burn anything. 0.6 milliamps on a 240 volt 50Hz supply. And that's only if your current source is badly isolated. The better it's kept away from the local ground, the less flow you'll see.
Maybe what I've failed to make clear is that my real question is about the relative difference in safety of the isolated transformer as used in a "razors only" plug and the normal breaker protected outlets used in US houses. For both of them, you could stand on a dry wooden ladder and momentarily grab either wire. But the focuses on the increased safety of the isolated transformer. I'm trying to understand what exactly about this system provides for the increased safety.
From what I can tell, everything in your answer applies to both systems. It's the difference in safety between the systems that I don't feel I understand.
An isolating transformer is a 1:1 transformer where the input can be referenced one way and the output another. The output is not connected to ground on either side so when you grab one of the sides, that's the first time it gets referenced to ground. ...and then the explanation continues as per my previous post.
When you have a power source it needs two wires to make a current flow: a wire "out" and a wire "back". You're only part of the circuit if you're connected to both sides.
When the two wires are not connected to anything, there is infinite resistance between them.
If you grab one side then there's no path through you to the other side so no current flows: the resistance between the two wires is still infinite.
Due to Ohm's law, (V=IR), if the current through you is zero then the voltage across you is also zero. The hand touching the wire is at the same voltage as the rest of your body.
So you "float up" to whatever voltage the wire you are touching is at.
If you complete the circuit then current starts to flow. The shock you receive is related to the current that flows through you. However, even tiny currents cause a big shock because humans are quite sensitive to currents in the micro or milliamps range as that's more than our nervous system uses to move our muscles.