The Alcubierre Drive — Is Faster-than-Light Travel Possible?

The fastest spacecraft we have created is the New Horizons Probe, an interplanetary spacecraft that reached speeds of 16 km/s as it passed Pluto in July 2016 [1]. Travelling at less than 0.00005% of the speed of light, it would take this probe over 81000 years to reach the nearest star to the Sun. To travel to the nearest galaxy it would take over 47 billion years (the universe has existed for about 13.7 billion years) [2]. To put it simply, travelling interstellar distances will clearly require a much faster spacecraft. The Alcubierre Drive is a potential solution, allowing hyperfast travel within general relativity.

In 1915, Einstein published his gravitational field equations of general relativity [3]. These equations relate the geometry of spacetime with the distribution of matter within it. As demonstrated below, the left side of the equation represents how matter should curve spacetime while the right side illustrates how matter moves through this curved spacetime [4].

In 2000, Miguel Alcubierre, a Mexican astrophysicist, published a solution to Einstein’s field equations that would allow for the contraction and expansion of spacetime to create a “warp drive” similar to the one seen in Star Trek [5]. This solution is shown in the equation represented below, where a is the lapse function that gives the interval of proper time between nearby hypersurfaces, βi is the shift vector that relates the spatial coordinate systems on different hypersurfaces, and γij is a positive definite metric on each of the hypersurfaces [6].

Proven mathematically, the Alcubierre Drive can allow for faster-than-light travel without breaking any relativistic laws. A bubble of spacetime can hypothetically be created around an object where spacetime ahead of it contracts and spacetime behind it expands [5,6]. In theory, a spacecraft could sit inside of this bubble and “legally” travel faster than the speed of light [6]. Since the craft itself is not moving — only a region of spacetime itself is travelling faster than light — no relativistic laws are broken and the effects of time dilation do not apply [5]. However, to an observer outside of the disturbed region, the spacecraft would appear to be moving faster than the speed of light.

The Contraction and Expansion of Spacetime in the Alcubierre Drive. Credit: Phys.org

While this technology might seem promising, there are some major challenges to overcome. General relativity states that matter distribution is related to the geometry of spacetime [4]. In theory, you can take any geometry of spacetime that is twice differentiable, plug it into Einstein’s field equations, and find the matter distribution required to create it [3]. When the geometry of spacetime required for the Alcubierre Drive is plugged into the equation, the resulting matter distribution required to create it is quite interesting. It would require negative matter, a hypothetical substance that generates a negative gravitational pull, to create the necessary distortion of spacetime [5,6].

How Negative Mass Particles would interact with spacetime. Credit: Quora

Even if we have obtained this hypothetical negative matter, we still have no way of constructing a bubble of spacetime in a region of space that does not already contain one. Further, there is no known way of exiting this bubble once inside [6].

Since an Alcubierre Drive would be capable of faster-than-light travel, the drive would also enable time travel [5]. However, this contradicts the Chronological Conjecture Theory which asserts that quantum mechanics will always prevent causality-breaking actions [7].

Although it seems impossible now, this might change over time. As history has shown us, the impossible often becomes reality. NASA’s Eagleworks has continued to research the Alcubierre Drive and has constructed a “microscopic instance of the phenomenon” [8].

While we have not observed it in the universe, negative matter is mathematically possible under the geometry of special relativity. I am a firm believer that if something is mathematically possible, then its existence is likely true. Who knows? We might detect negative matter or find a way to synthesize it this century. With future research and funding, this seemingly impossible feat could become a reality.

The Warp Drive. Credit: JSTOR Daily

References

1. NASA, New Horizons. Available from: https://www.nasa.gov/mission_pages/newhorizons/main/index.html
2. NASA, Timeline of the Universe. Available from: https://www.nasa.gov/mission_pages/spitzer/multimedia/timeline-2006121889912.html
3. Warwick Department of Physics, Einstein’s Field Equations. Available from: https://warwick.ac.uk/fac/sci/physics/intranet/pendulum/generalrelativity/
4. S. Walters, How Einstein Got His Field Equations. Available from: https://arxiv.org/pdf/1608.05752.pdf
5. M. Alcubierre, The warp drive: hyper-fast travel within general relativity. Available from: https://arxiv.org/pdf/gr-qc/0009013.pdf
6. M. Williams, What is the Alcubierre warp drive?. Available from: https://phys.org/news/2017-01-alcubierre-warp.html
7. S. W. Hawking, Chronology protection conjecture. Available from: https://journals.aps.org/prd/abstract/10.1103/PhysRevD.46.603
8. S. White, Daydreaming beyond the solar system with warp field mechanics. Available from: http://www.icarusinterstellar.org/daydreaming-beyond-the-solar-system-with-warp-field-mechanics/