I have an Arduino Uno and what it does is simply output an oscillating signal of 1 MHz on PIN11. I measured the signal using a oscilloscope and a probe with a ground clip. First, I connected the probe to a wire which is plugged into PIN11 and the clip to the wire connected to GND. The oscilloscope showed me the expected signal.
Then, I connected the probe to the GND wire and removed the ground clip from the probe while an open wire is plugged into PIN11. The oscilloscope showed me a weakly oscillating signal of 1 MHz. I extended the open wire which is connected to PIN11 and the signal got stronger. Then I removed the wire and the oscillating signal disappeared. My first guess was that the open wire is acting as an antenna.
I also tried to connect the ground clip to the GND while the probe stayed disconnected. Also, an open wire is plugged to PIN11. I expected a weak reversed oscillating signal but the signal was flat.
Now I am not sure again if the weakly oscillating signal is caused by the open wire which I thought it acts as an antenna.
Best Answer
I don't think your ground rail is oscillating. You may be able to test whether it's oscillating relative to the voltage rail by connecting the ground clamp to ground and the probe to the 5v or 3v rail for your Arduino.
Voltage isn't like current: you can't measure it at a point, it's almost always the difference between two points in the circuit. When you remove the ground what exactly you're measuring becomes somewhat ambiguous. What you're most likely to see is the distorted AC component of the signal at the probe mixed with a weak 60Hz (or 50Hz in some places) distorted sine wave from the mains power in the building and any other AC signals near the probe.