LEAD FEATURE An Improbable Pursuit Introduction to the Current Thinking on Faster-Than-Light (FTL) Travel Dan Fries The enormous distances to even the nearest stars, coupled with the velocity limitation of special relativity, have challenged us since they were first measured in the early 19th century*. In this first of a series, Current Thinking on Faster-Than-Light (FTL) Travel, Dr Dan Fries, i4is Deputy Technical Director, introduces the FTL idea. References are at the end of the article. [Figure: The (logarithmic) scale of our interstellar neighbourhood. Credit: Based on work of JHU-APL (interstellarprobe.jhuapl.edu/)] The seemingly impossible has always captured human imagination, especially when the pay-off would change nearly every social and technological paradigm that we are working under. From fusion energy to the multi-verse, increases in our understanding of the universe have always given birth to fantastic ideas, some of which, against all initial odds, eventually become reality in one way or another. Since around 1908, when Minkowski and Einstein first introduced the idea that space and time are really not separate at all, but rather constitute a four-dimensional space-time fabric that makes up our universe, scientists, authors and dreamers have tried to push this idea to its limit, resulting in fantastic philosophical and technological prospects. And sometimes, in ideas for interstellar exploration, communication and civilizations spanning entire galaxies. * A history of astrometry, sci.esa.int/web/gaia/-/53196-the-oldest-sky-maps PRINCIPIUM | Issue 46 | August 2024 | 4 LEAD FEATURE One key aspect of Einstein’s theory of relativity is that no object can exceed the vacuum speed of light, ie the propagation speed of electromagnetic waves in a vacuum. In fact, this also implies that information can never travel faster than the speed of light. As a result, even individual photons, the field particles carrying the energy quanta of electromagnetic radiation, take a significant amount of time to travel between celestial objects emitting them. For example, it takes light approximately 8 minutes to travel from the surface of the sun to Earth, or 5 ½ hours from the sun to Pluto. At this point, we are still very much within our own stellar neighborhood. If we could hitch a ride on an electromagnetic wave, or a photon, for interstellar travel, reaching the nearest extra-solar star system (Alpha Centauri) would take about 4.3 years. Unfortunately, according to special relativity, even “just” reaching the speed of light is impossible for any object or particle besides photons. When an object with a finite mass accelerates, its kinetic energy increases. Approaching the speed of light, the particle would move at “relativistic” velocities. The total relativistic energy of that particle would be given by E=γmc², where m is its mass at rest, c is the speed of light, and γ is the Lorentz factor*. This factor corresponds to a transformation of time and space coordinates that ensures all physical laws are invariant with respect to arbitrary non-accelerating frames of reference†. In our day-to-day experience this effect rarely seems to play a role, but technologies such as the Global Positioning System (GPS) would not be as precise as they are if we did not account for time dilation (the apparent stretching and contraction of time in frames of reference moving relative to each other) in the signals transmitted by GPS satellites, due to the satellites’ significant orbital velocity relative to Earth. The GPS satellites’ position within Earth’s gravitational well introduces another correction, but this is related to general relativity and the warping of spacetime, which we will get to later. The Lorentz factor takes a value very close to one if the speed of an object is small (below a couple percent of the speed of light of 300,000,000 m/s or 83,333,333 km/h), corresponding to our everyday experience and explaining why we rarely experience time dilation effects when we drive on a highway or even fly on a plane. However, when approaching the speed of light, the Lorentz factor starts approaching infinity, initially slowly but then faster and faster. In the context of the equation mentioned above, this means that an infinite amount of energy, E, would be required to travel at the speed of light. And besides, if we want to build a galaxy spanning civilization, even the speed-of-light does not really cut it when we can’t even send emojis back and forth in less than a decade. Enter General Relativity: according to this macroscopic description of the cosmos, mass distorts the fabric of spacetime, resulting in effects that we perceive as gravity. And because mass is equivalent to energy according to special relativity, both mass and energy can cause local distortions in the spacetime continuum. One has to really sit with this idea for a moment and think about its implications to understand how monumental the impact of the theory of relativity is on our understanding of reality: space and time are parts of the same thing and can be distorted by the presence of mass and energy. Coming back to our simple example of GPS satellites, what this means is that, from our perspective deeper in the gravity well of Earth, ie in a region of larger spacetime distortion, the time on board of a GPS satellite moves faster. At the same time, an observer onboard a GPS satellite would perceive that clocks on Earth are moving slower than on the satellite. Of course, these effects still seem small, but they become extremely large near massive objects such as black holes or neutron stars, to the point that at a certain distance from a black hole time would seem to stand still to an outside observer. What else could such massive distortions in the spacetime continuum do? Already before 1950, John W Campbell and Issac Asimov wrote stories involving a “Warp Drive” to circumvent the speed and time limitations imposed on us during interstellar travel. The warp drive was subsequently popularized in a large number of shows, movies, and books, most notably Gene Roddenberry’s Star Trek. Inspired by this science-fiction idea, theoretical physicist Miguel Alcubierre showed in 1994 [1] that the Einstein field equations could, in principle, allow for a solution that produces such a warp drive. The underlying idea is deceptively simple: through a tailored distribution of mass and energy the spacetime fabric can be compressed ahead of a spacecraft and expanded behind it, allowing the craft to globally travel faster than the speed of light without ever locally exceeding it. * γ=1/√(1-v²/c²) where v is the speed of an object and c is the speed of light. † See also “Principle of Relativity” in special relativity. In the framework of general relativity, the laws of physics additionally have the same form in arbitrary frames of reference, see “Equivalence Principle”. PRINCIPIUM | Issue 46 | August 2024 | 5 LEAD FEATURE [Figure 1: Two-dimensional embedding diagram visualizing how the Alcubierre space-time metric would distort space and create a "warp-bubble". The opposing regions of expanding and contracting spacetime are what displace the bubble. Reproduced under CC BY-SA 3.0. Credit: AllenMcC. - Wikipedia] The spacecraft would be travelling in a “warp bubble”, as illustrated graphically in Figure 1. However, the solution initially seemed to require amounts of negative energy (or negative mass) exceeding the total mass of the known universe. Not only are negative energy densities a matter of ongoing speculation* and such extraordinarily large amounts of mass are an issue, traveling faster than the speed of light also poses potential problems regarding our understanding of causality. Using a flat spacetime diagram (Minkowski diagram), one can prove that an FTL spaceship could arrive at a point in time and space before its own construction, potentially leading to a time-travel paradox in which the traveler prevents themselves from journeying through space and time in the first place. Additionally, any observer travelling within the warp bubble would be causally disconnected to some extent from the surrounding universe and even from the bubble itself. Any light source that the superluminal (faster than the speed of light) observer moves towards would be infinitely blueshifted†, while anything the observer moves away from would be infinitely redshifted, meaning electromagnetic waves (eg light or radio transmissions) would be effectively undetectable. The observers would also not be able to send signals to the front of the warp bubble, preventing any attempts at steering or stopping their vessel [2]. Krasnikov tubes [3], permanent superluminal spacetime distortions, could potentially alleviate some of the navigation and causality issues but would still require negative energy densities to establish and stabilize them. Finally, researchers have been arguing that, even if an FTL warp drive could be realized, the effect of the warp bubble on particles encountered during the journey could have devastating consequences on both passengers and target destinations in the flight path. Passengers within the bubble could be exposed to dangerously blueshifted (ie highly energetic) particles, while “people at the destination would be gamma ray and high energy particle blasted into oblivion due to the extreme blueshifts for … particles” [4]. Another approach to FTL travel relies on a special type of black hole. We already mentioned black holes, regions in space of such extreme mass concentration that spacetime is distorted into a singularity from which not even light can escape. The singularity is predicted mathematically but probably exists physically, too, although we are currently unable to directly determine what lies at the core of a black hole beyond the Schwarzschild radius, ie the event horizon (The radius beyond which light cannot escape the black hole). The existence of singularities in solutions to the Einstein field equations was first shown by Karl Schwarzschild in 1916, when he derived the gravitational field around spherical distributions of mass and identified mathematical singularities at the so-called Schwarzschild radius and at the center of the mass distribution. For stars, the Schwarzschild radius always lies within the physical boundaries of the star or planet and, therefore, does not cause any issues for the description of the gravitational field. However, high-enough mass density can cause a situation in which the Schwarzschild radius lies outside the spherical mass itself. About four decades later, the Schwarzschild radius was clearly identified as a surface that can only be crossed in one direction, ie a region in space from which nothing can return. Additionally, researchers realized that the singularity at the center of such gravitational fields is most likely real, representing a physical feature of the general theory of relativity. * One of the proposed sources of negative energy relies on the exploitation of a quantum phenomenon called the Casimir effect. † Due to the Doppler effect: a change in the perceived frequency of a wave by an observer moving relative to the source of the wave. PRINCIPIUM | Issue 46 | August 2024 | 6 LEAD FEATURE [Figure 2: Two-dimensional embedding diagram of a wormhole. The green arrow indicates the path a particle, or light, might take through the wormhole, while the red arrow indicates the much longer path through undistorted space. Reproduced under CC BY-SA 3.0. Credit: T Samuel – Wikipedia] [Figure 3: Image of Saturn as seen through a wormhole. Reproduced from [5] under Creative Commons CC BY-NC-ND 3.0.] Using the Kruskal–Szekeres coordinate transform to obtain a well-behaved solution everywhere except for the singularity itself, it can be shown that in addition to the black hole there could be a white hole, a region from which no particles can escape and a region into which no particles can return, respectively. Graphical representation of this solution results in an object that looks like a tube connecting two outside regions, as shown in Figure 2. This was first discovered by Ludwig Flamm shortly after the publication of the Schwarzschild black hole solution, and then rediscovered by Albert Einstein and Nathan Rosen in 1935. The resulting object is nowadays called an Einstein-Rosen bridge or a Wormhole, after an article by John Wheeler and Charles Misner in 1957 [6]. In principle, such a wormhole could connect two regions of space, that are lightyears away from each other, almost instantaneously. What a traveler might experience on their journey through a wormhole has been impressively visualized in the movie “Interstellar” with the help of leading researchers in the field of general relativity*, see the example shot in Figure 3 and the paper by James et al. [5]. Unfortunately, a wormhole-like structure would also present a potential for causality violations, time-travel like phenomena, and it would again require negative energy densities to stabilize the connection [7]. Clearly, interstellar travel and efforts to build a galaxy spanning civilization, capable of meaningful commerce and information exchange, are severely hamstrung by limitations imposed on us by the finite speed of light and our understanding of the theory of relativity. Nonetheless, as we learn more about the implications of the four-dimensional spacetime continuum and possibilities to manipulate its geometry, ideas have arisen that might allow us one day to circumvent these limits. Past efforts in this direction have yielded deep insights into the physical theories describing our reality and have sometimes hinted at missing links between our macroscopic (general relativity) and microscopic (quantum mechanics) description of the universe. However, these efforts have also shown that realizing faster than light travel often requires a theoretical violation of physical constraints. This has not stopped researchers from considering creative ways to bypass obstacles and to come up with novel solutions that are more likely to work within our current understanding of the natural world. With this article laying the groundwork for the discussion of space-warping FTL propulsion technologies, we will take a deeper dive into more recent developments in this area in a follow-up article. * See the front cover image of this issue and details with references on page 83, Cover Images. PRINCIPIUM | Issue 46 | August 2024 | 7 LEAD FEATURE References 1. M Alcubierre, “The warp drive: hyper-fast travel within general relativity,” Class. Quantum Grav., vol. 11, no. 5, pp. L73–L77, May 1994, doi: 10.1088/0264-9381/11/5/001. 2. J Natário, “Warp drive with zero expansion,” Class. Quantum Grav., vol. 19, no. 6, pp. 1157–1165, Mar. 2002, doi: 10.1088/0264-9381/19/6/308. 3. S V Krasnikov, “Hyperfast travel in general relativity,” Phys. Rev. D, vol. 57, no. 8, pp. 4760–4766, Apr. 1998, doi: 10.1103/PhysRevD.57.4760. 4. B McMonigal, G F Lewis, and P O’Byrne, “Alcubierre warp drive: On the matter of matter,” Phys. Rev. D, vol. 85, no. 6, p. 064024, Mar. 2012, doi: 10.1103/PhysRevD.85.064024. 5. O James, E Von Tunzelmann, P Franklin, and K S Thorne, “Visualizing Interstellar’s Wormhole,” American Journal of Physics, vol. 83, no. 6, pp. 486–499, Jun. 2015, doi: 10.1119/1.4916949. 6. C W Misner and J A Wheeler, “Classical physics as geometry,” Annals of Physics, vol. 2, no. 6, pp. 525–603, Dec. 1957, doi: 10.1016/0003-4916(57)90049-0. 7. M S Morris and K S Thorne, “Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity,” American Journal of Physics, vol. 56, no. 5, pp. 395–412, May 1988, doi: 10.1119/1.15620. References free access: 1. www.researchgate.net/profile/Miguel-Alcubierre/publication/1963139_The_Warp_Drive_Hyperfast_Travel_Within_General_Relativity/links/09e4150be3bde39e78000000/The-Warp-Drive-Hyper-fast-Travel-Within-General-Relativity.pdf 2. web.archive.org/web/20110823164109id_/http://omnis.if.ufrj.br/~mbr/warp/etc/CQG19.1157.2002.pdf 3. arxiv.org/abs/gr-qc/9511068 4. reprints.gravitywaves.com/Warp/McMonigal-2012_TheAlcubierreWarpDriveOnTheMatterOfMatter.pdf 5. pubs.aip.org/aapt/ajp/article/83/6/486/1057802 6. citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=84d94d614aedb00b22f3e9e97c1c869fa2c3a2d4 7. pages.jh.edu/rrynasi1/spacetime/eprints/Morris+Thorne1988WormholesInSpacetime+TheirUseForInterstellarTravel.pdf Dan Fries Bio Dan Fries is a researcher at the University of Texas at Austin, Deputy Technical Director of i4is and a board member of the Initiative for Interstellar Studies. He received his PhD in Aerospace Engineering from the Georgia Institute of Technology (USA), and Master’s degrees from both the Georgia Institute of Technology and the University of Stuttgart (Germany). Starting in 2025, he will be a professor at the University of Kentucky (USA). His research interests include high-speed fluid mechanics, aerothermodynamics and aerothermochemistry, plasma and combustion chemistry, reentry, and propulsion systems. As an experimentalist, he uses and develops advanced optical and laser diagnostics, spectroscopic techniques, and methods for uncertainty quantification and the inversion of measurement models. He is also intrigued by the possibilities of breakthrough propulsion systems and the possibilities of interstellar exploration. PRINCIPIUM | Issue 46 | August 2024 | 8