One could assume that the Federation has/will find technological wonders on the sphere, but in line with the usual "reset button" philosophy of Trek I have assumed that the discoveries so far have been mostly of interest to archaeologists.
Almost all of the technology mentioned towards the end of the specs page is my own invention, and is an attempt to apply the basics of trek science to make the sphere work. That the sphere is made of 'carbon-neutronium' is mentioned in the Encyclopedia (2nd edition, page 126) - that carbon-neutronium has the density of carbon (diamond) and the strength of neutronium is my own invention, because with neutronium density the sphere would mass thousands of times more than the rest of the galaxy put together.
The idea of a sphere as a 'greenhouse' seems fairly obvious from basic physics - ultimately the sphere must radiate as much energy as is incident on it, or it will heat up. By how much I don't know, but I imagine it would be a lot. The idea of the gravity generators radiating the energy away as technobabble "gravimetric interference", mentioned at the start of the episode, is intended to explain both this problem and the presence of intense gravimetric interference in one go - on the 'keep it simple' premise.
My last comment on this subject is that I sure hope that the Federation has claimed the Dyson sphere and is working like mad to try and work out a way to stabilize that star. If they could do this, they would at a stroke have more living area than they could ever dream of; even as scrap the sphere would yield up a practically inexhaustible source of ready-refined materials. Providing the owners don't turn up and demand it back, of course...
This episode has two rather famous nits. Scotty seemed to think Kirk was alive when he was revived despite seeing him apparently die in "Generations" - which was made after this episode. Various theories have been offered for this, including gimmicks like time travel. Of course, Scotty is a little old by this time and there was a slight degradation in his stored pattern. Either one could account for a faulty memory. Yeah, I know, it's cheesy isn't it... but better than time travel.
Secondly, the makers forgot to have the Jenolen lower its shields so that Geordi and Scotty could be beamed out by the E-D. Again, there are explanations - we've seen that it is possible to beam people out sometimes, if you know the characteristics of the shield system (see "The Wounded"). This would be especially so in this case, as Geordi and Scotty actually want the transporter to be able to beam them out. They could transmit shield info - which the E-D would have on record in any case - or set the modulation frequency so it matched the E-D's transporter system, etc.
Incidentally, I gather that serious scientist types aren't especially
impressed with this representation of a Dyson sphere. I can't say as I
blame them, but whatever the flaws it is nice to actually see something
this cool on TV at last, rather than just reading about it in a book. I
wonder if we'll ever see a Niven-style Ringworld...
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