Warp drive is a theoretical method of propulsion which may be capable of achieving speeds faster than the speed of light by means of manipulating space-time. The idea is to contract the space in front of you while expanding the space behind you, effectively moving your vessel from one point to another while not actually moving at all relative to your immediate surroundings. However, this is, so far as can be determined, something that can only exist as a math equation. One of the key components of such a drive would be what is called ‘exotic matter’, matter which demonstrates abnormal physical properties, specifically, matter with negative mass. This is something we can describe with numbers and use in math equations, but which, so far as we can determine, does not actually exist anywhere in the universe and perhaps cannot exist at all in physical reality. Its a bit like saying “I have two barrels of apples, one which has ten apples in it and one which has negative seven apples in it. So my total number of apples is three apples.” Except that you cannot actually have a barrel filled with a negative number of apples. Since this seems to be impossible, many physicists who like the idea of faster than light travel have been trying to find ways to make it work without the exotic matter, but their solutions to the equations involved have not all been proved. Even if we did find such a solution, that still doesn’t mean it would be at all possible to build such a drive.

When it comes to the ‘energy’ required by such a drive, we are talking about mass-energy, which is what causes the bending of spacetime. Even in the best theoretical models you need a lot of energy to bend space like this (as well as the exotic matter). Some of the solutions to the equations suggest you might need to convert something like the entire mass of Jupiter into energy that you could move around in order to make this method work.

To understand warp drives, you have to understand spacetime.

In general relativity (our best, but still not perfect or totally correct, since it’s in fundamental discord with quantum mechanics), all objects move through spacetime, a 4D hypersurface which is hard to visualize, because we live in a 3D world, perceived through 2D. But the idea is that space and time are interconnected in a single surface that cannot be further decomposed into a combination of anything simpler. Since it’s so hard to visualize a 4D hypersurface, for the rest of this explainer, pretend spacetime is only a 2D surface, with 1 spatial dimension, and 1 temporal dimension.

GR comes in the forms of field equations (partial differential equations) that relate the distribution of matter and energy on the one hand, and the curvature of this spacetime surface on the other. In other words, spacetime is non-Euclidian (think of a warped or stretched sheet, e.g., with a depression or mountain in it), but can warp and bend and stretch and bend in untold number of ways

In GR, many kinds of geometries are *permissible* (meaning the equations *allow* it)

Your 2D spacetime sheet:

1. Could be flat everywhere

2. Could be curled up onto itself so that it forms a sphere. Like an ant walking around on a ball: they are traveling along a 2D surface, but the surface they move on is curled up on itself so by traveling straight the ant ends up where it started.

3. Could be flat everywhere but with a depression, a valley in a particular spot

4. That valley could be “infinitely steep” to the point where the fabric pinches off

5. Could have a mountain, the opposite of a depression / valley

6. Could look like a sheet of paper folded over itself with a “tunnel” that connects two distant parts. This is [the classic “wormhole” visualization](https://c02.purpledshub.com/uploads/sites/41/2021/12/F0113300-Wormhole_in_outerspace_illustration-0bc04e0.jpg), e.g., as described in Interstellar.

These are all what we call “solutions” to Einsten’s field equations, in that they are geometries that satisfy the field equations.

(1) is what’s called the Schwarzschild solution when there’s no matter or energy present.

(2) would be a spherical spacetime universe: if you traveled far enough in one direction long enough, you would end up back where and *when* (that’s right, you would arrive back at your own past) you started. These are so-called “closed time-like curves.”

(3) describes the same as (1) but with some mass or energy.

(4) describes what happens when you compact enough mass or energy into a small enough mass and energy into a sufficiently small space—this region of spacetime is called a “black hole.”

(5) Is what happens when you have negative mass or negative energy density.

(6) Describes a wormhole, an Einsten-Rosen bridge.

It’s important to note these are merely geometries the maths of pure GR allows. Just because you can dream up a geometry that satisfies the equations doesn’t mean they have to exist. In fact, many of these probably either outright can’t exist, or at least can’t in our universe, for many good reaons we suspect.

But the point is you can envision all sorts of theoretical exotic geometries given the correct mass and energy distribution that satisfy the equations of pure GR.

Now we get to warp drives. Imagine an ant walking on an apple. It has a speed limit: it can’t walk faster than a certain speed no matter how hard it tries. But what if you picked up the apple and threw the apple, with the ant still on it, super fast to a distant region. Then, though the ant obeyed its walking speed limit, because the surface it was on was moved super fast to somewhere far away, it could travel an immense distance very quickly. That’s what a warp drive wants to do.

GR descirbes not only how space looks statically given mass and energy, but how it evolves over time, how it evolves from one geometry to the next. A warp drive is a theoretical mechanism by which you could stretch and/or contract space to allow some observer in that region of space and who is therefore comoving with that space to enjoy the benefits of the space’s transformation. Some have tried to do this by relying on the Alcubierre metric, which describes how spacetime behaves when you have negative mass / negative energy density in the right configuration so that you get a mountain on one side and a valley on the other. The resulting spacetime would contract in front and expand in a way that propagates through spacetime. Any vessel on the interior of this spacetime region would come along for the ride. Now here’s the problem. The Alcubierre metric only describes a theoretical geometry that requires the presence of negative mass or negative energy density, and for various reasons, physicists are convinced those things can’t exist. So just because some theoretical arrangement of mass and energy can give you a certain spacetime geometry in pure GR doesn’t mean it can exist in our universe.

But some new papers have proposed subluminal warp drives that don’t rely on negative energy density, but instead propose another arrangement of positive mass / energy (which we do have lying around) that can cause spacetime to stretch / contract in a way similar to Alcubierre but not exceeding lightspeed.

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