FTL speed, Replicators,Holodecks,and Transporter Technology.

[farntfar]

It seems to me that it mostly all boils down to one problem to solve: The organised and controlled conversion of mass to energy and back again, along with one hell of a lot of computing and memory power. And, of course, the ability to do this at a distance. (the surface of the planet for instance.)
The original process, transporting, was explained that way pretty much right from the beginning, and the memory issues were dealt with in the throw away phrase "Pattern buffers".

Replication is just doing it on a smaller and more localised level and with stored patterns of steak and chips, romulan ale and earl grey tea.

And holodecks, the same thing. (I'm fairly sure someone explained to someone else, at same stage (*) that only the close up things were produced physically. More distant things were merely images, in order to save energy. (* How to be vague: 101)

So once the principle of very fine tuned matter/energy conversion is mastered (it shouldn't be difficult. Right? (sine qua non)), the rest is just playing about.

As for internal gravity, this is just a tractor beam spread thinly all over a ship. So again just a specialised projection of energy, at a distance.

The real question is why, with all this remote control of these vaste amounts of energy, anyone is bothering to use phasers or photon torpedoes any more.

 

[Wayne Mack]

The one challenge beyond the decomposition, transmission, and recomposition of physical matter is translation of life force to information and back. The implications of creating or recreating a living organism from an information stream extend far beyond a transporter. Why not simply mass produce a clone army (think Power Rangers' putties)?

 

[Vladd67]

I seem to remember in Star Trek the animated series it was a common solution to run someone through a transporter to cure a disease as the transporter had healthy versions of the crew stored in it.

 

[Cydramech]

I'm going to say, absolutely not. Why? Because damn it, that's the answer needed to make these things happen!