Charging a Capacitor Using Only One Pole of a Transformer Secondary—Is It Possible?

By definition, voltage requires two points with difference in electrical potential. Usually these points are two wires or one wire and earth/ground.

But it doesn't seem to have to always be true since you can connect both sides of capacitor the same wire via diodes and charge the capacitor as in the circuit attached image (source: www.youtube.com/watch?v=ApAn0VlXXrs).

Another example would be the aftermarket cell-phone antennae that were around a decade or more ago with an LED connected to two different points of the cell phone antenna wire. During transmissions, the LED lit up (and probably ate half of the RF budget).

My question: is it possible (and how) to draw power (e.g. charge a cap) from only one pole of a low-voltage transformer secondary and leave the other pole floating?

In quirky terms, how does one borrow from the first half of the AC wave and sell it back to the second half without using a real ground?

It looks feasible. Energy would be transferred into the capacitor, but the external charge would be moving "in and out", effectively moving around the electrons in the capacitor/diodes circuit, but the total (average) charge would be constant in that part of the circuit.

I think it is analagous to the single wire of a radio aerial receiving an electromagnetic signal.

Capacitive charging base for mobile phone ?

Thanks for responding.

"I think it is analagous to the single wire of a radio aerial receiving an electromagnetic signal."

Exactly what I was thinking. Do you know of a source of formula that would help me establish what I need to do this. I'm not sure what elec laws govern the charge/current/energy that I can gather in the cap. In my case, the other end of the transformer has to be left floating and not sure how that affects things.