Actually, as a sci-fi fan, it was the Synergy Machine that first piqued my interest in the show...

That said, since I'm an evil genius, I actually 'reverse-engineered' Synergy for use in another RPG. My findings:

Synergy did NOT produce holograms. PERIOD.

Why call them 'holograms', then?

Easy, in the 80s, laser applications were becoming commonplace, including laser reactive image creation - commonly known as holograms. It was a buzzword, plain and simple. A hologram is a single object read by lasers and then written to a film element with varying degrees of intensity to produce an illusory three-dimensional image. With Synergy light was used, but in a much less obvious way. This is why things are easier to create than explain, or why so few creative types are scientists - but I digress...

So what is the nature of the beast?

Synergy produced and projected both aureal and visual components, which leads to the conclusion that all holograms were created through something I've come to call 'resonance binding'; which is to say, the vibration of air through ultrasonic frequency to the point it will 'solidify'. Through variance of the frequency, one could foreseeably project varied frequencies in order for the surrounding air to refract/reflect light. Since an objects perceived color is the product of it absorbing the electromagnetic spectrum and reflecting only a certain part, it stands to reason that one could vary the resonance to emulate that effect.  But it gets deeper...

Now, the interesting part... In THEORY, since these 'holograms' were the result of solidified air, it stands to reason that one could INCREASE the frequency modulation to the point of actually HARDENING the air to a 'solid', or 'solidogram' (Suh-LID-o-Gram) as I've dubbed it. That given, the weapons-use applications become obvious, and thus distasteful to our Mr. Benton, who 'limits' Synergy to a maximum range/degree of resonance - in effect allowing its projections to become only 'hard' enough to reflect light as a solid, but not enough to have 'substance' in the standard sense.

THIS is where it gets REALLY interesting...  Observe: In order to be effective, each 'hologram' would not be a single image. It's not feasible. Otherwise, Jem and the girls would 'step out' of their clothes whenever they moved. Rather, each image would have to be made up of BILLIONS of 'pixels' which would have to be calculated and rendered *on the fly* for EACH projection - providing for each individual pixel having a separate 'color' and thus frequency. Logically, this data would have to be gathered by a broadbeam, perhaps even a radial, field of effect that would have to 'read' where *each* band member was, track their motion, and react to it with a change in the projection in REAL-TIME. This would have to occur THOUSANDS, if not MILLIONS of times per SECOND. This field would be basically ultrasonic resonance, which explains a 'tingle' each of the girls experience when the field activates. They can feel the air humming around them like a living thing, which no doubt lends to the 'energy' they have when they perform. (Minds out of the gutter, please.)

The nature of Synergy's illusory applications are mind-numbingly complex, and when you consider that the transceivers/sensors were miniaturized to the size of EARRINGS, it's even MORESO amazing. Not even today, with Moore's Law in effect, can such a machine possibly exist. It's frightening how much processing power would be required to make a stationary 'hologram' the size of an APPLE, and Synergy created 'dynamic/reactive sheathings' for FIVE WOMEN AT ONCE. When you consider that its stated limit before appreciable power-loss was SIX-HUNDRED 'holograms' (presumably entire images) per SECOND, it's dizzying.

Further, one could modulate the resonance with enough force to create AUDIBLE SOUND, which would have to be digitally rendered and projected to a certain 'source', much like ventriloquism. This all but demands, logically, that the Synergy Effect was a radius field rather than a beam, as it could render sounds from any of its projections - and some (the flying dragon in The Princess and the Singer, the roc in The Music Awards, etc) were as far away as three hundred yards! Further, it helps explain how Synergy could project around corners, in other rooms, and in the midst of milling crowds of people - all of which it did repeatedly in the show, despite claiming to be a light-based medium...

And speaking of RANGE, let's examine the JemStar earrings... No matter where Jem/Jerrica is - Paris, Las Vegas, Philadelphia, Greece, Alaska, China, and a dearth of other remote areas (even fabled Shangri-La) - the link with Synergy in California is constantly active. Talk about some wireless broadband, eh? Apple AirPort my Aunt Fanny. When you consider the thousands of TERABYTES per second that was being read, transmitted, computed, rendered and then projected every SECOND.... Well, that expensive Pentium III and cable-modem seems a little chintzy, don't it?

Many fans speak about Jem/Jerrica's love interest Rio Pacheco being such a dunderhead that he couldn't tell Jem and Jerrica were the same person, even after hugging and kissing them both. Allow me to clear that up (no, he's not retarded)... If we agree that the ultrasonic field/sheathing is the only possible explanation, and that it resonates to the point that the girls 'feel' it when it kicks in, then it is logical to surmise that when he embraced Jem - who had MUCH more big 80's hair than Jerrica - he felt the resonance of the 'hologram' of Jem's hair, and basically just equated it with actual hair. Never in the show did we see him run his hand through her illusory hair, as lovers do, but when he actually TOUCHED her hair, it was nearer to her face, which was where Jerrica's actual hair was... As for the kissing, again assuming that the dynamic/reactive sheathing is the correct explanation, then he would feel the resonance of the illusion when he kissed her - and equate THAT with Love's Fireworks. So you see that Jerrica and Jem did NOT kiss the same, as Jerrica does not have the 'shimmer' that Jem does. Doesn't look so stupid anymore, does he? Good. Though he does seem a little more naughty in that light, I digress...

Regarding Synergy's ONE weakness, transmitting through water, this is easy to explain. Water, being liquid, is denser than air and refracts light. While able to sustain the sheath for short periods, the constant shifting of the water through the ultrasonic field 'confuses' it, and makes it unable to accurately project illusions. In response to the wildly inaccurate data, as well as light displacement inherent to the medium, it aborts the projection. Fairly akin to dividing by zero, for all intents and purposes...

Christy Marx, creator of Jem, said this about my theory:
That's a fascinating alternative for what Synergy does.  Let's face it, the earrings were magic.  No way could any technology, even today, match that.

This leads me to a side theory. Emmett Benton supposedly built Synergy BY HIMSELF with mid-80s technology and materials, but I think logically that considering the technology involved that is not feasible. How to explain it, then? Well, I think that Synergy was probably alien technology, possibly crash landed and salvaged by him. It's known that things are easier to repair than create, so that explains alot, such as how Jem can repair the earrings when they're damaged (like in The Last Resort episode when she caught an elbow from Roxy). Logically, with the proper materials, Synergy can self-repair - it's the only explanation that makes any sense.

So possibly Emmett provided the needed materials for Synergy to repair itself, plus enough data about earth to make itself viable (like a personality template - that of his wife, Jacqui). And since it clearly shows itself capable of emotive response (hell, it shows itself capable of INTUITIVE CREATIVITY, like when she fooled Jerrica herself in the Midsummer Night's Madness episode), in gratitude it opted to accept him, and later Jerrica as its operator. What choice did it have, really? Obviously, none of its original owners survived the theoretical crash, so it would have to accept SOMEONE in order to be useful...

That about sums it up. If anyone uses this information in a fanfic or similar, I'd appreciate a credit to the effect of 'With Thanks to SinUrge for hashing out the mad science of Synergy'.