Hi,
imagine a wire to be a rope. There are short and long wires and narrow and thick wires. Now imagine dancing on a rope.
The shorter and the thicker it is the more solid or stable it is.
But a GND plane is like a solid floor. It doesn´t move, you can rely on it.
Like a rope moves, similar the voltage moves on a thin wire.
And like a solid floor the voltage of a GND plane is reliable and doesn´t move.
Now there are electromagnetic waves (EMC) in the environment. It is like wind when you dance on a rope. It will make you dangling.
But if you stand on solid floor (GND plane) the wind won´t harm you that much.
*****
I don´t know where you measure (and to what reference) the 0.5V, but it is very likely, that with a GND plane you will see only some mV.
Klaus