Ah well I can't help myself... actually you CAN send a radio signal to the other side of the world.
Whether your viewpoint is that the earth is Flat or Spherical, Anyone with a 10 or 15meter rig, about 100watts (heck 50 will do it in perfect conditions) a good high-gain antenna, and some patience behind the key... you can bring up stations all over the world inside your bounce.
Which is basically wherever your signal lands on the earth, then bounces back up again to the atmosphere, and back down again. Any time it makes a hit on the earth, you can communicate in that area (assuming some is there with equipment to respond with) until your signal decays beyond reception.
Anyway, had to stick up for the radio waves there...

later...