Well, when the ‘leading authority’ in a field is Thomas Bearden, who’s not only a noted over-unity kook, but also believes lots of funny things like the KGB engineering the USA’s weather since some time in the late seventies using those elusive ‘scalar weapons’, Chernobyl just being a Russian cover story to hide the truth of an experiment involving standing electrogravitational waves gone wrong, and far more wackiness than I’m willing to confront myself with now, you can probably tell that the whole field is a bit questionable…
But, two answer your question as best as I can, there seem to be two things at the heart of the matter: longitudinal EM waves and vacuum energy.
A longitudinal wave is a wave where the oscillating quantity varies in the direction of the wave’s propagation – for instance, a sound (or any other pressure) wave. Picture a slinky, laid out horizontally, you give a shove on one of it’s endings: the displacement will travel through the slinky, varying the distance between single windings.
Electromagnetic waves are generally transversal, meaning the oscillating quantity varies perpendicular to the direction of the wave’s propagation. Picture a rope that’s bound to something, and shake it up and down. That’s the picture for all electromagnetic fields in free space, i.e. a vacuum, as given by Maxwell’s equations; it’s probably noteworthy that the oscillating quantity, in this case, is a vector.
Now, the (supposed) longitudinal EM waves of scalar weapon fame do differ from those familiar waves in that they apparently have a scalar quantity oscillating parallel to the direction of propagation; this presupposes the existence of a so-called ‘scalar field’, not to be confused with the electrostatic scalar potential (the latter being actual science), that permeates all of space and gives rise to both the magnetic and electric fields.
There’s no experimental reason to assume the existence of such a scalar field, and it’s at odds with current understanding of electrodynamics – since charge gives rise to electric fields, and moving charge gives, via relativistic transformation, rise to magnetic fields, any time variant electric/magnetic field will also have a corresponding magnetic/electric field.
However, in this supposed scalar field theory, it would be possible to create a scalar wave via manipulating a purely magnetic field, which would have no electric component – the picture, essentially, is that magnetic attraction creates a scalar ‘void’ between two magnets, and magnetic repulsion creates a scalar ‘bubble’. Switching two magnets back and forth from mutual attraction to repulsion thus creates ‘ripples’ in the scalar field in a similar manner to pressure variations in air, and it is thus possible to create a device that emits no measurable EM field, while yet, via those ‘scalar ripples’, having the ability to influence attraction between two magnets a distance away, something not possible in classical electrodynamics (the whole thing, emitting no EM field, would only heat up).
Now, closely interconnected to this notion of scalar field (somehow, I don’t know the specifics), is the quantum mechanical zero-point energy associated with vacuum fluctuations – to gloss over the details a bit, uncertainty permits the spontaneous generation of virtual particles, provided they annihilate again in a reasonable amount of time. This leads (via some complications due to the quantization of fields and the associated necessity of renormalization) to a non-zero energy value for empty space.
Which then, somehow, leads to the scalar field outlined above. I didn’t really find anything explaining that somehow, though – basically, most of the texts on the matter amount to random tossing out of pseudo-scientific buzzwords, that basically use them with so much equivocation and implicit re-definition that it’s near impossible to make out any coherent concepts (even more so than this very post ;)).
So, to sum up: someone dun made it up.
