Thinking back to my pirate radio days got me thinking about various oddities that happened at that time. One of those things was a phenomena known as "Long Delayed Echoes". This is a phenomena whereby when someone who is transmitting a radio signal hears their own signal echo back with a delay that is not explainable by common sources.
For example, HF amateur radio operators will sometimes hear a very quick echo that results when the signal propagates all the way around the world via multi-hop skip, that is multiple reflections off the ionosphere and ground. The delay of such an echo is about 1/7th of a second, so this sort of echo would not be considered a long delayed echo. A long delayed echo will have a longer value, which might range from a larger fraction of a second to tens of seconds and only very rarely much longer echoes have been reported.
The echoes that I experienced where fairly short, perhaps 1/3rd of a second, and I only heard it a couple of times, but in both cases it was after powering down the transmitter late at night, catch a last little blurb of was just transmitted. We weren't running enough power nor were we on a frequency to allow around the world travel to be the explanation. We were only running about 100 watts on 1200 Khz on the AM broadcast band. With our long wire antenna, that amount of power would provide us with a signal that was intelligible on a good communications receiver with a box-loop antenna for 10-20 miles. It would produce a good signal for a normal receiver for only 3-4 miles. There was just no way this signal could have made it around the world.
I've heard all sorts of theories but I don't really find any of them acceptable. People have suggested alien probes intercepting and retransmitting the signal back. I would think such a probe would be more deterministic. If it were intelligent enough to recognize such a signal from noise, I would think it would also be intelligent enough to generate a more recognizable response. Also, with some of the reports I've read from amateur radio operators, it seemed to be a phenomena that propagated west to east slowly which seemed to point to a natural phenomena. If there is directivity, then it can't be far from the ground, and if it's not far from the ground, then the delay can't be explained by a more distant alien probe.
One suggestion I've read is that an electromagnetic wave is being converted into an acoustic wave in the ionosphere, transmitted some distance acoustically, then reconverted back into an electromagnetic wave. I think this is perhaps the most plausible theory, that doesn't invoke totally new physical phenomena, for all but the very rarest and longest long delayed echoes. Still, it's hard to believe the path loss for such a double conversion and re-radiation to be detectable with a low powered transmitter. The only time I did experience it was during early morning hours, 3-4AM local time during the summer. One thing that comes to mind is that is close to the time when the day/night boundary was approaching. Other reports I've read though have been various hours.
I also wonder though if there aren't unknown physics that this is hinting at. A lot of things about radio and high frequency high voltage electricity is just weird. Sometimes I wonder if our straight-line concept of time isn't wrong, if time isn't some kind of spiral and adjacent loops influence each other. Everything in nature seems to be cyclical, everything seems to have spin. Maybe it relates to the geometry of time.