Introduction
Have you ever envisioned yourself sitting alongside Han and Chewie in the Millennium Falcon travelling through hyperspace seeing the stars form streaks across your windscreen? Or do you rather fancy yourself on the USS Enterprise and its iconic warp drive? Worry not, because as I am about to explain in this blog, warp drives and faster-than-light (FLT) travel might actually “be possible” according to physics with some caveats.
Image depicting travel of a spaceship through a wormhole by curving spacetime around it . Source : [4].
It is quite well-known that given our current technological limitations, that feasible interstellar travel is impossible. One of the reasons for this is the large amount of fuel required to carry out these journeys which we simply do not have or have an efficient source of. Another reason is special relativity which states that the faster an object travels, its ‘relativistic’ mass or mass due to an object’s motion increases tremendously and becomes infinite at the speed of light. This has the effect of requiring more and more energy as the spaceship is to go faster and faster, finally needing an infinite amount of energy to get the spaceship to the speed of light! With these in mind, let us see how a hypothetical warp drive would work
General and special relativity
Special relativity forms a subset of general relativity which holds under very small regions of 4D spacetime that can be considered to be flat[2]. Thus, general relativity does not impose restrictions on the speed of light, only that special relativistic restrictions must hold ‘locally’ including the limit on the speed of light[2].
Warp drives and general relativity
In 1994, theoretical physicist Miguel Alcubierre published a paper based on his work on general relativity proposing a solution to Einstein’s field equations of general relativity. According to Einstein’s field equations, one can calculate the deformation of the 4D spacetime, that Einstein predicted we live in, by a ‘distribution of mass and energy’[1]. Alcubierre did the reverse and, using a particular configuration of spacetime, was able to figure out the mass and energy distribution that produced it. The configuration he proposed was that of a bubble of flat spacetime containing the spaceship with a region of compressed spacetime in front of the ship (which can be thought of as spacetime being destroyed similar to the Universe collapsing in the Big Crunch) and a region of expanded spacetime behind the ship (which can be thought of as the spacetime being created just as the Universe expands with the Big Bang)[2]. This “warped” region can push this pocket of flat spacetime containing the spaceship to arbitrary velocities including faster than light without the spaceship having to move.
Image depicting the warped spacetime as proposed by Alcubierre. The region dipping down as shown compresses spacetime and is felt as the force of gravity, known by us all. The region projecting up is more unusual and expands spacetime as described and can be thought of as “antigravity”[1]. These two regions work together to push the flat region in the center, containing the spaceship, forward at any arbitrary velocity .Source : [5]
Thus, for a spaceship at the center of this bubble, it would find itself at rest or even moving slightly with respect to a relatively flat portion of spacetime, thereby having its velocity less than the “local” speed of light within the flat region of the bubble. Moreso, the spaceship being at rest or close to it in the flat spacetime region, it would not experience any of the relativistic effects such as length contraction, time dilation or mass expansion. So, the spaceship stays at rest within the pocket volume of flat spacetime, but this pocket moves as it is pushed by the “warped” region of spacetime.
Too good to be true?
Although the warp drive configuration of spacetime or known as the “Alcubierre metric” is a valid solution of Einstein’s field equations, to produce it is to open up a whole new assortment of problems.
One of the major problems is that the Alcubierre metric requires negative energy density to produce it[2]! This seems impossible to produce, however, there have been observed effects in quantum field theory that gives rise to negative energy densities under certain scenarios such as the Casimir effect[2], but what is this Casimir effect?
In quantum vacuum, quantum field theory predicts there are fluctuations in electromagnetic energies that produce electromagnetic waves at all wavelengths[3], but if two perfectly conducting, uncharged plates are brought close together, only those waves having nodes at either plate will fill the space between similar to standing waves on a guitar string[3]. This reduces the number of possible waves compared to that in free vacuum which reduces the energy density inside the cavity compared to outside[3]. With the energy density outside being close to zero, there is a small negative energy density created inside the cavity that results in a negative pressure inside that cavity which results in the plates being pushed together or attracted to one another. This is known as the Casimir effect.
Image depicting the Casimir effect with limited number of electromagnetic modes inside the cavity due to constraints resulting in a negative energy density with respect to the surrounding, producing a force on the plates. Source : [6]
As shown with the Casimir effect, negative energy densities do exist on a quantum scale, however, this is way too small for the amount of negative energy we require. Another viable solution of Einstein’s equations is a wormhole (also called Einstein-Rosen bridges) that require the same negative energy constraint in order to work[2]. In order to produce stable wormholes, “exotic matter” having negative energy density is required but this is completely hypothetical[2].
Another problem that Alcubierre warp drives brings is that it creates the possibility for making “closed time-like curves” which open up violations of causality[2] (such as effect happening before cause!). A well-known example is the grandfather paradox: if you travel back in time and kill your grandfather before your parent was born, they never would have been born and neither would you so who went back in time to kill your grandfather?
Conclusion
Thus, it can be seen, no matter how exciting building a warp drive to cruise by countless galaxies we can only dream of visiting may seem, we are still limited by our current technology. And although the need for the impossible negative energy can be overcome by using positive energy instead and with a slightly modified spacetime metric[1], the amount of energy required would be still phenomenal. Moreover, care must be taken to ensure that the spaceship and its inhabitants do not fall prey to the massive tidal forces at the boundaries of the moving “bubble” of spacetime.
So, to conclude, although warp drives still seem like they belong on our television screens and on the pages of our books, the promising physics behind it give us hope that somewhere a long time from now, we may visit a galaxy far, far away.
REFERENCES:
[1]: Gast R, Spektrum. Star trek ’s warp drive leads to new physics [Internet]. Scientific American. [cited 2022 May 13]. Available from: https://www.scientificamerican.com/article/star-treks-warp-drive-leads-to-new-physics/
[2]: Alternate view column AV-81 [Internet]. Washington.edu. [cited 2022 May 13]. Available from: https://www.npl.washington.edu/av/altvw81.html
[3]: Stange A, Campbell DK, Bishop DJ. Science and technology of the Casimir effect. Phys Today [Internet]. 2021;74(1):42–8. Available from: http://dx.doi.org/10.1063/pt.3.4656
IMAGE SOURCES:
[4]: https://commons.wikimedia.org/wiki/File:Wormhole_travel_as_envisioned_by_Les_Bossinas_for_NASA.jpg
[5]: https://commons.wikimedia.org/wiki/File:Alcubierre.png
[6]: https://commons.wikimedia.org/wiki/File:Casimir_plates.svg
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