The probe would be silent and would not create a sonic boom
Inertial problems are almost nonexistent because of extremely low mass.
Shape could be flexible.
A radar signature is probable.
Descent and ascent at steep angle is to be expected (along the carrier beam).
It could leave behind evidence of its presence such as burn marks or wilted vegetation. It might even kill the engine of a car by inducing a current in the circuitry with polarity opposite that of normal operation.
The short duration of presence may result from difficulties maintaining entangled coherence near Earth's surface. This may also explain the preference for desolate locations as the avoidance of excessive electromagnetic radiation in more urban settings. Or . . . they may just wish to remain covert as much as possible.
Changes in intensity could be the result of variations in beam energy all the way down to zero (disappearance).
Finally, there is the question of human-like creatures. Already described is what the earthbound observer might see from a close encounter distance, but should the probe actually envelope the observer then both ends of the probe would be seen simultaneously. The observer would see the target environment because that is his/her locale, and superimposed on this would be the source end, observed via a holograph, of the inside of the storage ring chamber. Should there be autonomous creatures present in the chamber at that time then they might be apparent to the earthbound observer. This would explain events like the classic Kelly-Hopkinsville case (1,3) where glowing creatures appeared to float and suggests that the beam in that case originated from somewhere with a very low gravity.
Major Question Marks
I feel this scenario is conceptually plausible, but I admit that technological unknowns abound:
How do you make the huge numbers of entangled particles required?
Can the coherence of entangled particles be made to last for long periods of time instead of the microseconds we now experience?
Can particles (electrons?) be put into a stable orbit around a carrier beam with wave characteristics and moved along the beam by adjusting the phase velocity?
Does synchrotron emission carry information about the state of particles in a storage ring and can that information be used to produce a holographic image?
These are a few of the questions that need answers, and I assume that a highly advanced technical civilization would have ironed out these wrinkles long ago. The part I am most confident about is the involvement of some kind of particle beam that could enable remote sensing via entanglement and moves as described by Dr. Hynek.
Notes and References:
1) Calamia, J.R. "August 21, 1955 - Shots Were Fired" MUFON UFO Journal 483 July 2008
2) Einstein, Podolsky & Rosen "Can Quantum-Mechanical Description of Physical Reality Be
Considered Complete?" Physical Review 41,777, May 15, 1935
3) Hynek, J. Allen 1972, The UFO Experience: A Scientific Inquiry. Henry Regnery Co. p. 150,
plate 6
4) Jacobs, David M. 1975 The UFO Controversy in America. Indiana University Press, p. xiii
5) Mahood, Tom 1998 "Particle Beams and Saucer Dreams" http://www.serve.com/mahood/probeams.htm
6) Mason, R.L. 2008. The UFO Experience Reconsidered*. Schooner Moon Books
Available at http://stores.lulu.com/smbs