For me, this is the most interesting technology in the Star Trek universe, so I'm going to discuss it in some detail. Along the way, I'll show how the technology has "evolved" over the years, as the writers attempt to keep up with known science.
In the summer of 1964, Gene Roddenberry, in a meeting with his newly formed Art Department, issued the following instructions to Pato Guzman and Matt Jefferies:
According to Matt, the Enterprise design was arrived at by a process of elimination. Matt and Pato would create a pile of sketches, Gene would be called in, he would pick a few elements he liked from the sketches, and the process would start all over again. By the third time around, they were down to about two dozen sketches, one of which was the beginning of the design that was finally chosen for the Enterprise.
Eventually, the design became quite specific. The following is from "An Official Biography of a Ship and It's Crew":
The "Unofficial Starship Design Rules" as told to Andrew Probert by Gene Roddenberry...
Evolution, Or Just Confusion?
In Star Trek: The Motion Picture, we see for the first time fractional warp factors. For me, this was a big change. In TOS, warp factors were always whole numbers, which implied at least to me, that velocity changes were accomplished by shifting the entire fabric of the ship and it's contents from one quantum state to another. As an example, think about your typical kitchen blender. If you push button one, you get speed one. If you push button two, you get speed two, and so on. There is no speed 1.7.
The creation of Star Trek: The Next Generation, brought us an entirely new engine room layout complete with a "warp core," and a far more critical role for the now famous dilithium crystals. This was actually a gigantic step forward, and it has had a profound effect on the entire series ever since. Strictly speaking, the warp core doesn't create the warp field, it is the matter-antimatter reactor, the "prime mover" that generates the power needed by the engines. The warp core is a type of particle accelerator laid out vertically, with matter being fed in from one direction, and antimatter from the other. The dilithium crystals now sit in the center of the reaction chamber, where their position is controlled by an "articulation frame." If even a few atoms of antimatter missed their target and impacted on the reactor housing, the result would be catastrophic. The structure of the crystal creates atomic scale channels so narrow, the antimatter cannot help but impact the target matter being fed in. The articulation frame is used to make microscopic adjustments to the orientation of the crystals so that the channels line up with the particle streams. This type of reactor would produce huge bursts of gamma rays, and I do not know if these streams of gamma rays are supposed to be the warp plasma itself, or if the gamma rays would be used to generate / energize a more exotic form of plasma.
We also learned in ST:TNG that the engine nacelles contain Warp Coils. Apparently, these coils are made up of conduits that carry warp plasma, just as the wire coils of electromagnets act as conduits for electrons. What happens to the warp plasma after it passes through the coils is so far, a mystery. In electromagnets, the electrons circulate in a complete circuit. In nuclear reactors, the primary coolant is also recirculated. We do know that venting warp plasma is a bad thing, but the writers have never needed to tell us what normally happens to "used" warp plasma.
When electrons circulate through a coil of wire, they generate a magnetic field. I'm going to assume for the moment that plasma circulating through a coil will also produce a magnetic field, perhaps an extremely intense one. If those coils are arranged into an advanced form of Halbach array, with the magnetic field being projected out rather than in, the result would be an axial field with a magnetically neutral core. Place two of these axial arrays in parallel, and I'm speculating here, the two fields should merge into one, with a large neutral void in the middle.
Now we jump into the fiction part with both feet: As the field strength builds, the spacetime inside the field begins to decouple from the spacetime outside, thus becoming it's own sub-section of spacetime. (Subspace for short.) As the bubble around the ship decouples, the mass of the ship relative to the external frame of reference decreases. At Warp One, the ship has completely decoupled. Within the bubble, the ships mass has never changed, and the ship remains stationary relative to the internal inertial frame. (This is why the crew is never crushed by the acceleration. Within the bubble, the ship never moves.) Furthermore, the crew is free to move about within the inertial frame, so they can go about their duties completely unaffected. The warp bubble, now at zero mass, moves at the speed of light through the rest of the universe. In ST:TNG we observed the Enterprise using it's warp drive to reduce the mass of a stellar core fragment. We also saw Dr. Crusher trapped in a "static warp bubble" created by her son.
If we extend our extrapolation just a little further, A warp field of sufficient intensity will "fold over" on itself, (develop a strong harmonic,) so that it appears to have a negative mass in the external frame. It would then behave much like a tachyon, and travel faster than light.
This is all pretty good stuff. Why in the world then, are we made to suffer with shuttlecraft that are little more than empty boxes, but still manage to be warp capable, boast phaser weapons, and even transporters? I'd love to have the writers for Next Generation or Voyager explain to me where the power source is located, let alone the rest of the equipment that would have to be there for the other functions.
This is an area that's been abused by the writers right from the start. I've noticed that the staff of Enterprise have attempted to improve things, but some temptations are just too great.
Very early on in TOS, ships' phasers emitted blobs of light. I suppose someone must have pointed out that directed energy weapons must emit beams, since the energy MUST travel at the speed of light. So the blobs of light became Photon Torpedos, and for the rest of the series, phasers were beam weapons.
This always made sense to me, in a weird sort of way. When two ships are travelling at Faster Than Light (FTL) speeds, what kind of weapon can one ship use against the other? Taking my cue from the name Photon Torpedo, I always imagined that the ship must be shooting out packets of actual photons, wrapped in a warp bubble so they can travel FTL, since photons have no mass to begin with, it seemed reasonable to me that you could push them to a velocity higher than that of the ship itself. One can only imagine the amount of energy that would be dumped into a target.
Quoting once again from "The Making Of Star Trek":
So photon torpedos were supposed to be pure energy weapons, that nevertheless could be detonated by electrochemical fuses. It seems that even the writers and producers were confused on this point. In the movies, the issue was resolved when we finally got to see one before launch. We were shown a fairly conventional looking torpedo which presumably carries a small warp drive and a matter-anti-matter warhead. They have remained pretty much the same ever since.
My pet peeve when it comes to weapons, is that we're always seeing the phasers being used at FTL speeds. When are the writers going to get it though their heads that you can't catch a ship moving at 700 times the speed of your weapon? This is like mounting a water pistol on a car, and trying to shoot another car while traveling at 100 mph.
In Deep Space 9 and Voyager, we saw the introduction of "Quantum Torpedos" . How these are supposed to work has never been explained, but I'm going to go ahead and make a few guesses. First, let's assume that "quantum" is as meaningless as "photon" has been. Second, since there is no theoretical basis for an energy source more powerful than a matter-antimatter reaction, we'll assume that the warhead is still powered by antimatter. What's left then? Let's look at lasers for a little inspiration. Lasers are powerful because you have photons triggering the emission of additional photon in a cascade, with all of the photons in phase with each other, so they act like one giant high energy photon. If you could construct a weapon with thousands or millions of concentric shells of matter and antimatter, a trigger detonation in the center would create a cascade of shell detonations, and hopefully, a coherent energy wave of extremely high density.
DS9 also gave us pulse phasers on the Defiant. These looked great on screen, but until the writers can come up with some kind of explanation, they're scientific garbage.
I was rather surprised when I learned that the NX-01 Enterprise has Transporters, but not shields. Compared to the Warp Drive, shields should be a fairly simple technology. Credit is again due to the writers of Enterprise, who elaborated on this technology when they showed it in it's infant form. Essentially, you have a thin sheet of particles (one assumes charged particles, i.e. plasma) suspended between a pair of fields. This part is simple enough. As far back as 1980, I remember seeing a loudspeaker that worked by suspending helium plasma between two magnetic fields. Modulating the fields caused the plasma sheet to vibrate, thus moving the air and creating the sound.
The fiction part of all this is finding a particle that's a perfect energy conductor. What you definitely don't want, is a shield that absorbs energy. Such a shield would be overwhelmed in nanoseconds. Just as the space shuttle heat shield is made up of heat conductors that re-radiate the heat almost instantly, the shields in Star Trek would have to dump the energy directed at them very quickly. You would also need a particle that works across a wide range of frequencies, or a blend of particles to achieve the same result. In order to break through a shield, an enemy is forced to pump in energy at a high enough density that it destroys the particles, and does so at a faster rate than the target is capable of replacing them.
The navigational deflector is the giant dish on the front of all Starfleet ships. to be consistent with other Trek Tek,, this deflector would operate at sublight speeds by sweeping space in front of the ship with an E-beam to charge everything from atoms to small asteroids, then use a magnetic field to sweep this debris aside long before it poses a danger to the ship.
By the way, I think there's room within physics for an entirely different shield technology, and not that multiphasic crap they came up with on TNG. I've named this new type a spawning shield, and the theory goes something like this: Hadrons (protons, neutrons, etc.) are subatomic particles made up out of quarks. (true science) Scientists can't produce isolated quarks, because the energy required to smash hadrons apart winds up as new quarks, which combine with the originals so that you just wind up with extra hadrons. (also true science) Now, IF you found a hadron that absorbed energy across a wide spectrum, they would make a very interesting shield. As energy is pumped in, the particles would break apart and spawn additional particles. Enemy fire would strengthen a shield, rather than weaken it. Indeed, the problem might very well become one of how to shed surplus particles fast enough.