The

**Alcubierre warp drive**

Guan Yuanhao

Duke university

Math 89s

Professor Hubert Bray

The Alcubierre drive (Alcubierre warp drive or Alcubierre metric) is a fascinating idea that would allow a spaceship to travel faster than light which seems to violate Einstein’s law of relativity. The fun part is that this idea and proof is actually driven from a solution of Einstein's field equations in general relativity. Proposed by theoretical physicist Miguel Alcubierre, Alcubierre drive is the idea that in order to travel faster than light, you don’t really have to exceed the speed of light within a local reference frame (which seems to be impossible, says Einstein). Instead, it’s more like a shortcut: this method stretches the space in a wave form to make the space ahead of the spacecraft to contrast and the space behind it to expand. In short, instead of spacecraft moving in space, it’s more like the space moves and takes the spacecraft with it.It is mathematically valid because the model it built is consistent with the Einstein field equations. Alcubierre drive is still one of the central topics today in the field of physics even though Alcubierre proposed it 2 decades ago. The main reason is that even though this idea is rather practical compare to traversable wormholes, the problems that it brought up still trouble physicists today.

**How to Travel Faster Than Light**

When thinking of Albert Einstein, people usually relate to two things: His famous mass-energy equation E=MC^2 and his conclusion: “Nothing can travel faster than light”. Actually, a more formal and accurate expression would be something like this: “Information and energy can’t travel faster than light in a local reference frame”. Special relativity restricts the velocities of all objects with mass in all reference frame. People would generally think of a question though: what if we have two photons travel at the speed of light in opposite directions? Does that mean if we set one photon as the reference point, the other one would travel at the speed of 2c?

If that’s really the case, it would bring today’s topic a lot simpler. If we set one photon as the reference point, the other photon would still be traveling at the speed of light. The mean problem is that time flows differently for objects with different speed. Just think of it this way: if you are running in the night and holding a flashlight which emits a ray of light, does this light ray travels at the speed of light plus your running speed relative to the ground? Clearly no. So how could it be? The only solution would be the time flows at a differently rate for the objects involved at this problem. As a result, it is clearly not that simple to travel faster than light (At least definitely harder than simply picking a reference frame).

There are things growing faster than light, though. I am not talking aboutpseudoscience likewaving a laser emitter toward the sky to make the laser ray travels faster than light (the laser ray is actually a consecutive array of photons, so it just creates the illusion that it travels faster than light). I am talking about the expansion of universe. Contrary to a lot of people’s ideas of “expansion”, galaxies are not inside the “blowing balloon” universe. Rather, galaxies are on the surface of this balloon. (Vsauce, 2012) No matter where you are in the universe, you would see everything else moving away from you, expanding at the same rate. (This is known as Cosmological Principle, which scientifically proves that anyone can be the center of the universe)As a result, if you choose a galaxy that is enough far from us, we are actually ‘moving’ away from it at a speed that is FTL.

This phenomenon seems to be contradictory to Special Relativity at first. However, we are not actually ‘moving’; instead, as universe expands, new space is being created between any two objects. Although Earth and the galaxy we chose may be at rest with respect to the cosmic microwave background, the distance between those two object may grow at a rate that is FTL. Since light speed is still the local speed limit here, the expansion of universe doesn’t violate special relativity.

**The Science Behind Warp Drive**

Warp Drive uses the same idea to circumvent the law of special relativity, but on a more local scale. Alcubierre gave a solution to the Einstein field equation and built this beautiful ‘metric’ to represent the curvature of space.

In his model, space curves in a really peculiar way. At the front of the warp volume, space is being contracted and annihilated, and at the back of the warp volume, space is being expanded and created.It is still consistent with special relativity, since the light emitted by this spacecraft is still going to travel faster inside the warp volume. (John G. Cramer, 1996)

Although warp drive seems to be a perfect solution for FTL and circumvents a lot of problems liketime dilation, it still has some bizarre properties. In particular, a ship using warp drive would always experiences free-fall no matteraccelerating and decelerating. The crew on the ship would feel no acceleration force at all. In addition, an enormous tidal force would be present at the edge of the warp-volume due to large space curvature, thus tear apart anything that happens to lie in the path in to fundamental particles.(Cornell University Library, 2015)

**Observe Alcubierre Drive at Home**

Actually, you can even see how an Alcubierre drive ship work at home. Cut a small piece of soap and stick it to the back of a small paper boat. Put it in your bathtub, and you will see the boat moving really fast in water. What’s just happened is that the soap dissolves in water and creates a film of oil and bubbles which sabotages the surface tension of water behind the boat, so the surface tension of water ahead of the boat drags it to travel forward. To imagine Alcubierre Drive visually, you just have to constitute water with space, and paper boat with spacecraft. We just need to curve the space in front of the spaceship and the space behind the spaceship differently so that the space will drag it to move, although it is much harder to do than it sounds. Space is not like a usual object which we can see, feel, touch and, of course, bend really easily. In order to bend or curve the space around the spaceship, a few hardcore problems arise.

**Building USS Enterprise in Real Life?**

Let’s not be so optimistic for now. Although Alcubierre Drive does possess fascinating properties, huge barriers still lie ahead of us. Despite our difficulties in economy of building a warp drive spaceship this scale, there’s mainly three problems in this theory.

The first problem, and maybe the biggest problem is pointed out by Alcubierre himself. Although Alcubierre metric is a valid solution for Einstein's equations of general relativity, his solution needs an energy field that has the expression like this:

It is easy to tell that this expression has to be negative since all the variables here are been squared. Negative energy? Although quantum field theory permits the existence of regions of negative energy density under special circumstances, Casimir effect for example, (in fact, we can create negative energy in lab today for a really short period of time) we don’t know if we can create a stable negative energy field.Some quantum physicists even stated that there would be no stable negative mass-energy in the universe due to uncertainty principle. Honestly, physicists today would expect there’s no such thing, because negative energy would suggest the existence of particles with negative mass (‘exotic matter’, if you prefer), which would distort all our conceptionswe built on fundamental particles. Although the Casimir effect and the accelerating universe both support the existence of such matter, there’s still no evidence or theory to convince us that such thing exists. Without exotic matter, as physicist Low has argued, it would be impossible to construct warp drive within the content of general relativity. (Dr. David Lewis Anderson,2011)

What’s even worse, not only this energy is negative, it is also proportional to the square of Vs, the velocity of this ship.This means, in order to travel FTL, we would consume incredible amount of negative energy for warp drive ship to work.If certain quantum inequalities conjectured by Ford and Roman was true,the energy that is equivalent to -10^67 gramsof mass might be required to transport a small spaceship across the Milky Way galaxy. It is orders of magnitude greater than the mass of the universe.If they are wrong, according to Chris Van Den Broeck’s work in 1999, we can reduce the energy we need by contracting the surface area of the 'bubble' being transported by the drive in 3+1 dimensions. Later, Krasnikov reduced the necessary total amount of negative energy we need to transport small atoms to a few milligrams.(ClaraMoskowitz,2012) Although it is a big progress we have made, it still seems impractical to construct warp drive due the amount of negative energy we need and the uncertainty that exotic matter exists.

The second problem is based on the assumption that we have successfully create sufficient amount of exotic matter in our lab. The problem is, even we got what we need, what should we do next?What should we do with negative matter in order to create warp-volume? Science today didn’t provide any effective way to curve the space except for using mass. However, the mass we used for experiment creates negligible space curvature. The space curvature we need, however, is close to that of a mini black hole. Even we can easily create black hole safely and manipulate them in the future, it remains unclear how to generate a “warp bubble”.

The third problem arises because of the way that Alcubierre solve the problem. Usually, when someone wants to come up with a solution to the equations of general relativity, he/she would usually first come up with the distribution of matter and energy, and then finds out the geometry of the space-time associated with it; but it is also plausible the other way around, you can first come up with a metric and then find the energy-momentum tensor associated with it, which is what Alcubierre did. (Miguel Alcubierre,1994) However, this way of solving the equation does generate some side effects like it may need some bizarre things in order to work, like exotic matter. In addition, it may violate various energy conditions, and may even need tachyons in order to prevent a naked singularity appeared at the front of bubble.

**The Best We Can Get: Latest Warp Drive Model**

Yet, Harold White has proposed the best model we can have for Warp Drive.A ring-shaped warp drive device could transport a football-shape starship (center) to effective speeds faster than light (Harold White, 2012). This ring, an accelerating device that is made of exotic matter, would effectively curve the space around the ship. This ring actually has the shape of a round donut rather than a flat ring, which would oscillate while working to make the ship steady and reduce the amount of energy needed at the same time. (Diaz, Jesus,2012)

A project has been set up by White and their colleagues and they have done a series of experiment in their laboratory. (He named the project “humble experiment” comparing to what would really be needed for a real warp drive) In short, they are trying to create alaser interferometer that instigates micro versions of space-time warps. (Harold White, 2011)

Harold Whiteand his colleagues have this crazy idea: All progresses that have been made on Alcubierre drive so far are all trying to reduce the amount of negative energy (or exotic matter) we need. What if we can replace exotic matter with something that has similar properties to solve the problem once and for all? From 2006 to 2016, they are trying to use a toroidal positive energy density to create a spherical negative-pressure region, thus eliminates the need for exotic matter. Unfortunately, although they have already made some progresses in this field, these progresses have been criticized to be meremeasurement errorcaused by the interference of people walking outside the room.Now they are trying to increase sensitivity up to one hundredth of a wavelength and implement the oscillating field in order to get definite results. (Harold White, 2013)

**Conclusion: Still a Fantasy for Now**

Clearly, we have made a lot of progresses along the way. However, it is still too early to say that warp drive is practical in the future. Same as warm-hole, Alcubierre drive is still being classified as one of the physics problem that has a valid solution in math but is impractical in physics. Alcubierre drive is a cool thing to mention in sci-fictions and movies, no doubt, but will it successfully makes the transition from a science fantasy to a necessity that our everyday life relies on? Let time be the judge.

Works Citied

"Faster than Light: Warp Drive 013." YouTube. Ed. Space Conferences. YouTube, 08 Nov. 2013. Web. 19 Sept. 2016.

Cornell University Library, “Einstein-Maxwell Equations for Asymmetric Resonant Cavities”

(Submitted on 26 May 2015 (v1), last revised 5 Sep 2016 (this version, v2)) Web. 19 Sept. 2016.

Diaz, Jesus. "NASA Starts Work on Real Life Star Trek Warp Drive." Gizmodo. N.p., 17 Sept. 2012. Web. 19 Sept. 2016.

ClaraMoskowitz. "Warp Drive More Possible Than Thought, Scientists Say." Space.com. N.p.,September 17, 2012. n.d. Web. 19 Sept. 2016.

Dr. David Lewis Anderson. "Alcubierre Warp Drive Time Travel." Alcubierre Warp Drive Time Travel. N.p Sept, 2011., n.d. Web. 19 Sept. 2016.

John G. Cramer. "The Alcubierre Warp Drive." N.p Apr. 1996., n.d. Web. 19 Sept. 2016.

Vsauce. "Center of the Universe." YouTube. YouTube, 09 Sept. 2012. Web. 19 Sept. 2016.

Miguel Alcubierre, Classical and Quantum Gravity, v. 11, pp. L73-L77, (1994).

White, Harold (January 2013). "Warp Field Mechanics 102: Energy Optimization". NASA Johnson Space Center. Web. 19 Sept. 2016.

Dr. Harold White (2011-09-30). "Warp Field Mechanics 101" (PDF). NASA Johnson Space Center. Web. 19 Sept. 2016.