...after reading this whole thread, I've come to one conclusion:
We, as a Chrono fan body, have no idea what the floating images of the main party are. Our guesses have been clones and holograms, but usage is where we really disagree.
I personally think we take too many details too seriously. Chrono Trigger was made a decade ago, when games weren't nearly as deep as they are now, especially Chrono Cross. Chrono Trigger had alot of depth, but alot of it was comprised of gameplay, convenience, and other stuff. Seriously. I think we need to not look at so many minor details as if they really are important and planned that specific way, because they most likely aren't. It didn't take the developers more than a couple years to make this game, especially not the scenario people, etc.
Like with the Bend of Time. I'm convinced it's merely an easter egg where you can easily get shiny materials, fight characters from the first game for excitement value, and get the Dreamers Sarong, a kick-ass accessory. It doesn't need to have any importance/significane to the world and story because...it doesn't! It's a side place that offers nothing to the story. If we were to care about the actual existence of the Bend of Time, then we'd really need to take into account the realistic approach of EVERY possible ending in both games and where those dimensions went, the possibility of killing Magus, the possibility of not reviving Crono, the possibility of doing any combination of the side quests at the end of CT, etc.
Please, people. As deep as the Chrono world is, they're still a game, and being a game comes with those quirks of not being completely and totally detailed to make sense.
As far as I'm concerned, the doppelgangers are just there as a cool little "whoa, what ARE those?" I actually somewhat agree with the comment made that Square put it in so fans would argue about it for hours, haha.
And Zaper, where in the HELL did you hear they're remaking CT for PSP? I'd need to see proof of that. I check in on GameFAQs everyday, and that headline hasn't popped up yet that I've seen. Please, by all means, prove me wrong.