For starters:
http://www.projectrho.com/rocket/rocket3v.html
So many people can't seem to let go of the idea of a warp drive, but it can't happen.
If we ever do find a way around the speed of light, it won't look like Star Trek.
I tend to agree with you, but Trek certainly doesn't violate the "FTL, Relativity, Causality, pick any two" rule. They've obliterated causality enough times...
"All of the above".
I do, however, see certain technologies being developed that resemble their fictional counterparts, such as the tricorder and the cellphone.
Alcubierre drives and wormholes are (AFAIK) mathamatically possible, but they run into little problems such as requiring masses more then that of the entire universe to power them. They are not "FTL" in the strictest sense, but they allow far faster travel through space then would be allowed otherwise.
Alcubierre runs into problems with requirements for extreme amounts of negative energy. Wormholes require negative energy, but I think the amounts involved are "relatively" minor (as in measured in masses on planetary or stellar scales for wormholes that are actually human traversable, rather than on universal scales).
Mathematically possible is not the same as physically possible. AFAIR, the Albuquierre paper assumed the existence of a material that has a negative distortion of space-time, roughly equivalent to negative mass.
Physically, this is unobtainium and a violation of thermodynamics in many places (basically you gain negative entropy by it).
No, negative energy doesn't violate thermodynamics. Its physical implications would almost be less scary if it did. It has the potential to obey thermodynamics as far as the numbers are concerned while creating a lot of effects that *look* like they violate thermodynamics.
As far as I know, physicists don't quite know yet whether negative energy is or is not possible, but it makes them uncomfortable (as in "if it is possible, certain types of very weird things could happen, and we wonder why we aren't seeing those things"). There are some observed effects that do suggest it, though.
It's got to be possible one way or another. Our science might look solid now, but in a hundred years we're likely will be laughing at how ignorant our predecessors were at the start of this century.
It doesn't have to be possible.
Our science isn't entirely solid now, but we do have a fairly good idea of where it is and isn't solid, and what new theories could or could not say to be consistent with the observations that led to the current theories. It's at least as likely that in a hundred years they'll be laughing at us for thinking that wormholes *were* possible as that they *weren't*.
And even if FTL is possible, the methods that are most consistent with current theories would require some fairly massive engineering projects, involving gathering and doing strange things to amounts of matter at least on the asteroidal, if not on the planetary or stellar scale. Then it would require moving a large portion of that mass a few light years at sublight speeds. At the end you'd end up with either a wormhole or something like a
Krasnikov tube.
The wormhole allows FTL travel between the mouths once they've been manufactured (probably in the same general area of space) and then the mouths have been transported to the places they're supposed to connect.
The Krasnikov tube allows FTL travel along its length, but AFAIK has to be constructed by STL means, and can't be cheap to build.
In the case of the wormhole, you have to be careful what you do with the mouths, or with multiple wormholes, lest you create a time machine, which, if wormholes are possible, will lead in the best case to some sort of event (likely the destruction of one or more of the involved wormholes) which unmakes the time machine before you get to use it, and in the worst case will lead to the creation of a time machine that you actually get to use (along with all the horrors *that* would cause).
With a Krasnikov tube you'd have the same problem with multiple tubes, though I don't think you could get it with just one.