edit: this is probably bullshit. since I have a few topics I've used his blog for that I care about, and this is not one of them, I will leave this as deprecated.
A pretty cool and very basic phenomena in electricity is that components that oppose the flow of electricity can be neutralized by other components that oppose the flow in the reverse way. You can add two components together, that individually would increase the resistance in the current, and get zero resistance. This phenomena is frequency dependent, the components have to be selected to neutralize resistance at a specific frequency.
Assume the Earth is a conductor, and the ionosphere is a conductor, but the air between them is a dielectric. The two also act as a capacitor, and there might be inductance property too. Like with any other capacitor, if you inject alternating current into the Earth "plate", the current will propagate across the dielectric to the ionosphere plate. And since both the Earth and ionosphere are also conductors, the injected current would be able to reach any point on Earth, but it has no reason to prefer any point over any other.
If it were possible to find the right components to neutralize the resistance for a current between the Earth and the ionosphere, then it would be possible to transmit current into the Earth and ionosphere at one point on the Earth, and then receive that same current at any other point on Earth. The current would choose to travel between the transmitter and receiver, since they were the path of least resistance, and not between any of the infinitely many other points.
This seems like one possible mechanism for the "Tesla Tower" or Wardenclyffe tower. I don't know at all if it is possible to create low impedance paths using some kind of tool like Wardenclyffe tower, it just seems to me that the only way to avoid "inverse square law" loss of energy is if the current takes a direct path from sender to receiver, like, when transmitting a signal with laser or through a wire.
This idea fits with basic electrical science, except the issue of if it would be possible to form a low impedance path somehow. It does not require any new wave forms or anything like that, since it just relies on transmitting the current like in a capacitor.
The circuit can be simplified more or less to the schematic below.
And further, to this, sort of.
And that last circuit can be seen here as a simulation on Falstad.com, with the LC filters tuned to resonate.
Have you heard of mad.energy who are building these towers?
Check this video especially around the 27 minute mark:
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