While doing my research I read about the Hackaday Component Abuse Challenge. While I am not really "abusing" components here, It feels "Bizarro World" enough to fit into the challenge and I submitted! YouTube Video linked below!

Fig.1: No Power source needed!

Two experiments

In my first experiment  I used two LEDs with 10MΩ - resistors in series and a power source (see circuit diagram 1 in images) that kept the LEDs right at the breakthrough voltage, so that they emitted a small amount of light. My "antenna" is placed between the LEDs. In that experiment I could see that the LEDs  were very sensitive to any potential change close by, be it me touching any part of the circuit or just moving cables around. 

Because the antenna is between the LEDs, a charge change influences them differently. When it is charged positively, the potential between that point and "+" decreases, and it increases compared to circuit ground. Thus, the LED between "+" and the antenna darkens, and the other one gets brighter. A negative charge change has the opposite effect.

Then I realized that the LEDs emit light even without any power source, just by picking up the electromagnetic fields. 

Experiment two explores that phenomenon. Here, I get rid of the power source altogether (see circuit diagram 2) and the LEDs are simply in a loop with the resistors and the antenna. The LEDs still light up visibly because of the fields around us caused by the mains voltage, by switchmode PSUs and by anything that creates static charges. 

All experiments can be seen here: