I think we can also agree that there are many top secret projects which are completely unknown. Projects that are not part of some disinformation campaign involving the public, but real advanced military research completely hidden not just from the public but also from the rest of the military complex. Need-to-know-basis stuff.

Sure, I completely suspect that is absolutely the case, but you miss my point- see "part 2" above... The "It is classified technology" just won't fly, it requires a conspiracy of even greater magnitude than the conspiracy the "moon landing hoax" loons claim....

It requires that long ago an entirely new branch of physics forked off in secret and NONE of the unclassified scientists ever stumbled across it independently.

Perhaps highly advanced quantum entanglement experiments.

Quantum entanglement is weird, and allows some interesting applications, but it isn't magic, and there is not even the remotest hint that it could have an application that would in any way explain these phenomenon. Quantum entanglement is also heavily studied in the unclassified world by more scientists than all the secret organizations in the world could hire. We are working on it very publicly...

No... If these phenomenon are real, then its totally outside and beyond our physics and technology.

Here is the closest I could do using known physics and unknown engineering.

If you have an extremely powerful laser, and you focus it down in air you can create a ball of plasma that just floats there- the laser is intense enough to rip the electrons off of the air molecules and create a hot plasma.

If you have a large telescope you can use it to bring the laser into a tight focus at a great distance- the larger the telescope the longer the distance. (neglecting the complication of the turbulent atmosphere)

so theoretically you could create a ball of glowing plasma at a distance... if you slew your telescope pointing then that ball of plasma at a distance could have whatever velocity you like--it could seem to move at hyper-sonic velocity and stop in an instant- it would seem to be immune to gravity and inertia... it would show up on radar, giving the impression of a solid object... to make it vanish without a trace, simply turn off the laser...

But it would look like a ball of lightning- emitting brightly across the visible spectrum (and beyond), it likely would be HIGHLY elongated in shape- it would be VERY hot- thermal imaging would show super-heated air in it's wake...it would be loud... I have done this on a MUCH smaller scale many times- once with a 1500 Watt laser, THAT made everyone in the room jump... it sounded like a 2 ton angry bee.

The equipment to do this would be LARGE and not something that could be done in secret - especially not when you have fighter jets investigating. The engineering would be advanced beyond what we have now... but in terms of the physics, its the only way I can see to create some, but not all, of the behaviors these phenomenon supposedly exhibit.