(originally posted here)
Very often I see people confidently think or claim that the Star Trek warp drive works like the warp "drive" first proposed by physicist Miguel Alcubierre in 1994. Unfortunately, this is in error (I put "drive" in quotes because Alcubierre apparently dislikes calling it a drive, preferring to call it a "warp bubble"). As Alcubierre himself says, it was Star Trek that gave him the inspiration for his metric, not the other away around.
Why there is this conflation may be because people desperately want to think that Star Trek is based on hard scientific principles, or that the same principles in Star Trek are actively being worked on in real life. I don't propose to speculate further. There are also several fan ideas and beta canon ideas in licensed fiction about warp drive (notably in the excellent novel Federation by Judith and Garfield Reeves-Stevens) but for the sake of brevity, I'm limiting my discussion to what we see on-screen and related behind-the-scenes documents.
Background
The basic obstacle to superluminal or faster-than-light travel is Einstein's Theory of Special Relativity. Special Relativity says that as the velocity of an object with mass accelerates towards the speed of light (c), the mass of that object increases, requiring more and more energy to accelerate it, until at c, that object has infinite mass, requiring infinite energy to push it past c. In fact, Special Relativity says that nothing with mass can reach c - photons are massless and can only travel at c. From there, it follows that theoretical objects with negative mass can only travel above c, hence given the name tachyons, from the Greek tachys, or “fast”.
Alcubierre wondered: if you can't move the object/ship without running into relativistic issues, why not move space instead? Alcubierre's idea was to warp space in two ways - contract space in front of the ship and expand space behind it, an effect he compares to a person on a travelator. So while the ship itself remains stationary in a flat area of spacetime between the two areas of warped space (the whole thing being the "warp bubble"), that flat area gets moved along like a surfboard on the wave of warped space. Of course, warping spacetime in this manner involves incredible amounts of negative energy, but that's another discussion.
So this is how the Alcubierre metric circumvents relativistic issues. Because the ship itself remains essentially motionless, there is no acceleration or velocity and thus no increase in inertial mass.
But that's not how Star Trek’s warp drive works, and has never been.
Warp Drive pre-TNG
There is no description on how Star Trek warp drive works on screen in TOS except perhaps for a vague pronouncement that the "time barrier's been broken" in TOS: "The Cage" (in the episode Spock also calls it a "hyperdrive" and refers to "time warp factors").
During the production of Star Trek: The Motion Picture (1979), science consultant Jesco von Puttkamer, at the time an aerospace engineer working at a senior position in NASA, wrote in a memo to Gene Roddenberry dated 10 April 1978 (The Making of Star Trek: The Motion Picture by Susan Sackett and Gene Roddenberry, 1980, pp153-154) his proposal for how warp drive was supposed to work, in a way eeriely similar to Alcubierre's metric:
When going “into Warp Drive,” the warp engines in the two propulsion pods create an intense field which surrounds the entire vessel, forming a “subspace”, i.e. a space curvature closed upon itself through a Warp, a new but small universe within the normal Universe (or “outside” it). The field is nonsymmetrical with respect to fore-and-aft, in accordance with the outside geometry of the Enterprise, but it can be strengthened and weakened at localized areas to control the ship’s direction and apparent speed.
Because of the its non-symmetry about the lateral axis, the subspace becomes directional. The curvature of its hypersurface varies at different points about the starship. This causes a “sliding” effect, almost as a surf-board or a porpoise riding before the crest of a wave. The subspace “belly-surfs” in front of a directionally propagating “fold” in the spacetime structure, the Warp - a progressive, partial collapse of spacetime caused by the creation of the subspace volume (similar to but not the same as a Black Hole).
But there's no evidence that Roddenberry actually used this concept. In fact, Puttkamer said further in the memo that at warp, Enterprise would have "little or no momentum", which we will see is not how it's portrayed. Puttkamer was even against the now famous rainbow effect of going into warp:
The effect should not be firework-type lights but a more dimensional, geometric warping and twisting, an almost stomach-turning wrenching of the entire camera field-of-view.
So while an interesting document, there's no evidence that Puttkamer's ideas made it into any on screen incarnation of Star Trek.
Warp Drive in TNG and beyond
In TNG, the first publicly available description of how warp drive is supposed to work came from the licensed Star Trek: The Next Generation Technical Manual (1991). At page 65:
WARP PROPULSION
The propulsive effect is achieved by a number of factors working in concert. First, the field formation is controllable in a fore-to-aft direction. As the plasma injectors fire sequentially, the warp field layers build according to the pulse frequency in the plasma, and press upon each other as previously discussed. The cumulative field layer forces reduce the apparent mass of the vehicle and impart the required velocities. The critical transition point occurs when the spacecraft appears to an outside observer to be travelling faster than c. As the warp field energy reaches 1000 millicochranes, the ship appears driven across the c boundary in less than Planck time, 1.3 x 10^-43 sec, warp physics insuring that the ship will never be precisely at c. The three forward coils of each nacelle operate with a slight frequency offset to reinforce the field ahead of the Bussard ramscoop and envelop the Saucer Module. This helps create the field asymmetry required to drive the ship forward.
As described here, Star Trek warp drive gets around Special Relativity by using the warp field to distort space around and lower the inertial mass of the ship so that the shaping of the warp fields and layers around the ship can push and accelerate the ship itself towards c with reasonable energy requirements. The stronger the field (measured in units of millicochranes), the lower the inertial mass gets and it becomes easier to accelerate. When the field hits a strength of 1000 millicochranes, the ship pushes past the c barrier. Presumably at this stage it's in subspace, where Relativity no longer applies, and can accelerate even faster to each level of warp until the next limit at Warp 10 (TNG scale), or infinite speed. I'm not getting into how warp factors are defined (but see here for a discussion on the change between TOS and TNG warp scales, which also goes into the definition of warp factors, if interested).
The Technical Manual was written by Rick Sternbach and Michael Okuda, who were both technical consultants behind the scenes, and evolved from a document prepared by them in 1989 (3rd Season) to aid writers on the show in writing the technobabble in their script. (See also the history here.)
Here’s what the first, 3rd Season edition says about the way warp works, which is simply that the drive “warps space, enabling the ship to travel faster than light,” and that the ship is “‘suspended in a bubble’ of ‘subspace’, which allows the ship to travel faster than light”. This description also shows up in the 4th Season edition, and the Star Trek: Voyager Technical Guide (1st Season edition) in identical form.
While the actual text of the manual never made it on screen, there are several pieces of on-screen evidence that tell us Sternbach and Okuda's description of warp drive is followed: warp fields lower inertial mass, and the ship experiences acceleration and inertial forces during warp.
Evidence of warp fields lowering inertial mass
In TNG: "Deja Q" (1990), Enterprise-D uses a warp field to change the inertial mass of a moon:
LAFORGE: You know, this might work. We can't change the gravitational constant of the universe, but if we wrap a low level warp field around that moon, we could reduce its gravitational constant. Make it lighter so we can push it.
Later in that episode, we see the effect the warp field has on the moon:
DATA: Inertial mass of the moon is decreasing to approximately 2.5 million metric tonnes.
At the time "Deja Q" was broadcast, all that was said about warp drive in the technical guide was that warp drive "warps space" and the ship is in a subspace bubble with no mention of lowering inertial mass. Yet "Deja Q" shows warp fields doing exactly that, which tells us that either the writer gave Sternbach and Okuda that idea or they already had their ideas in place behind the scenes. The latter is more likely, given that the Technical Manual was published the following year.
In DS9: "Emissary" (1993), O'Brien and Dax use a warp field to lower the mass of the station so they can use thrusters to "fly" the station to where the wormhole is.
DAX: Couldn't you modify the subspace field output of the deflector generators just enough to create a low-level field around the station?
O'BRIEN: So we could lower the inertial mass?
DAX: If you can make the station lighter, those six thrusters will be all the power we'd need.
Evidence of inertia during warp
We've known from TOS on that during warp speed, inertia still exists. If it didn't, then there wouldn't be the bridge crew being subjected to inertial forces when maneuvering at warp speeds and being tossed around the bridge (TOS: "Tomorrow is Yesterday", when Enterprise slingshots around the sun at warp - with the last reported speed being Warp 8 on the TOS scale).
In TMP (1979), we see Enterprise accelerating to warp speed before the engine imbalance creates a wormhole.
KIRK: Warp drive, Mr Scott. Ahead, Warp 1, Mr Sulu.
SULU: Accelerating to Warp 1, sir. Warp point 7… point 8… Warp 1, sir.
As noted, a ship using the Alcubierre metric doesn't need to accelerate, because it's space that's moving, not the ship. Additionally there'd be no need for an inertial dampening field (as we see in TNG and beyond) that is supposed to protect the crew when accelerating to superluminal speeds. From VOY: "Tattoo" (1995):
KIM: Could we go to warp under these conditions?
PARIS: The ship might make it without inertial dampers, but we'd all just be stains on the back wall.
In the 2009 Star Trek movie, Enterprise was unable to go to warp unless the external inertial dampeners were disengaged.
SULU: Uh, very much so, sir. I'm, uh, not sure what's wrong.
PIKE: Is the parking brake on?
SULU: Uh, no. I'll figure it out, I'm just, uh...
SPOCK: Have you disengaged the external inertial dampener?
(Sulu presses a couple buttons)
SULU: Ready for warp, sir.
PIKE: Let's punch it.
If there's no acceleration or inertia, there's no reason why them being on would impede warp drive operation.
Closing Remarks
Taking all these pieces into account, I hope I've shown convincingly that the way the show treats Star Trek warp drive is consistent with a drive system that involves acceleration and inertial forces, and with warp fields that lower inertial mass - just like Sternbach and Okuda describe in the Technical Manual, and definitely not consistent with way the Alcubierre metric is supposed to work.
For those who want a deep dive into Star Trek warp physics, some canon and some speculative, I heartily recommend Ex Astris Scientia's series of articles on warp propulsion. I also recommend Jason W. Hinson's series on "Relativity and FTL Travel". Hinson was a regular participant in rec.arts.startrek.tech in the 90s and educated us on how Relativity worked and how it applied to Star Trek.