Faster than light warp drives are now possible with known physics
A demonstration from classical physics shows us how.
This isn’t the first time that science has overtaken my writing here, but I didn’t think it would happen so quickly and on the topic of warp drives no less. I have long argued that Faster-Than-Light (FTL) travel is impossible with known physics because of “proofs” that warping spacetime in this way would violate a condition on all matter, including quantum vacuum energy, called the Achronal Null Energy Condition. This condition essentially enforces that the fastest path must be at the speed of light even taking wormholes and warp drives into account.
Nobody questioned these proofs and considered them a nail in the coffin of FTL travel, enforcing causal relationships in the universe to remain at light speed. That is, until a postdoc at Göttingen, Erik Lentz, published a paper just last week in a peer reviewed journal showing a counter-example. It has already received a lot of attention both in the news media and among scientists. In this article, I want to explore why Lentz’s solution doesn’t violate the proofs that have been published on this subject. Lentz doesn’t give them too much attention in his paper. After all, the proof is in the pudding. He constructed the counter-example, and the cleverest and most intricate proofs in the world cannot stand up to a good counter-example.
Counter-examples are a classic means of disproving theorems in mathematics, and in the case of Lentz’s demonstration, the counter example simply showed that the proofs all made an assumption that applied to all known warp drives including the famous Alcubierre drive, but not his.
Let’s back up. Up until 1994, warp drives were thought to be science fiction, a convenience invented for FTL travel in Star Trek and other movies, TV shows, and novels. In that year, a physicist named Alcubierre published a paper showing that Einstein’s field equations that describe the warping of space and time that generate the force we know as gravity have solutions, i.e., valid configurations, that allow for “bubbles” of warped spacetime to travel faster than light.
These bubbles can travel faster than light without violating the laws of physics because theoretically, in Einstein’s universe, space and time can warp at any speed. They do not exist in space and time but are, instead, like traveling waves of space and time. The speed of light, however, is only a law restricting the velocity of objects in space and time. They don’t apply to spacetime itself.
There were many problems with Alcubierre’s design. The first is that his design required enormous amounts of energy, more than exists in the universe. That turned out to be fixable. The other problem was that this energy was “exotic”. It required negative mass.
This requirement turned out to be more tricky because known physics has no concept of negative mass. There is such a thing as negative energy that we can generate out of the vacuum with things like the Casimir effect, but even that energy isn’t enough for faster than light travel. To go faster than light, you need a kind of energy that violates the Achronal Null Energy Condition, and Casimir does not violate even that.
Thus, one could say that, at least until Lentz’s paper, warp drives were beyond known physics.
I read through Lentz’ paper, which makes use of pretty standard geometrodynamics (the theory of curved spacetime changing in time given by what is known as the ADM formalism), and found his explanation for why Alcubierre’s and others’ warp drives violated this condition while his did not. It actually has to do with how many “fastest” paths you have between a point A and a point B.
The proofs ruling out FTL travel all assumed that you had a single fastest path. That means that it relies on the assumption of a warp bubble the size of a single point moving faster than light. Obviously, zero size is not an ideal sized warp bubble. So how is that even relevant? Well mathematically, Alcubierre’s warp bubble and all similar ones, it turns out, can have their interiors reduced to a point and still be an FTL warp bubble. Since they fail as point bubbles, they fail as larger bubbles as well. The energy requirements are always exotic.
Lentz’s solution, on the other hand, is “extensive” and cannot be reduced to a point without its vanishing completely. This means that you cannot have a single fastest path through a point bubble. Rather, you have many fastest paths through the bubble. This effectively redirects causal paths through the bubble, much as black holes redirect causal paths into their singularities. Paths that do not travel through the bubble at light speed are simply “slower” causal paths, much as light that gravity bends takes longer to reach its destination than light traveling a similar path by a straight line. Thus, there is no violation of causality. You are just speeding causality up.
If you think about it, Lentz’ warp bubble has to be very strange indeed to ensure that there are always multiple fastest paths. In ordinary geometry, including curved spacetimes, we are used to the idea of having a single shortest path between two points. This shortest path, called a geodesic, is usually unique, meaning that there is only one. On a flat piece of paper, a geodesic is just a straight line. On the surface of the Earth, the shortest distance between two points is called a great circle path. Unless your two points are on exactly opposite sides of the globe from one another, there is exactly one shortest path (if they are antipodes from one another, there are, of course, two).
All those who attempted such proofs, such as Tufts University professor Ken Olum who introduced his proof back in 1998, simplified them by assuming unique shortest paths. There was never a generalization to multiple fastest paths. Indeed, part of the reason for doing so is that it is hard, in a curved spacetime, to define what “faster-than-light” even means. Einstein’s physics always rules out the possibility, after all, that we can send a rocket faster than a beam of light if that rocket travels along the same path as the beam, all other things being equal. Therefore, one of the essential criteria for superluminal travel is that our rocket follows a path that is not the same as a beam of light that we are using as a measuring rod for speed.
One option for a definition is to say that, by faster than light, we mean that our rocket is reaching a destination before a beam of light sent through some ordinary space. Intuitively, this makes sense, but, from a causal perspective, as soon as you warp or bend spacetime you create the possibility of introducing new causal paths. The way out was, for Olum, to define superluminal as a path that reaches a destination before any neighboring path. In mathematics, a neighborhood is a word for some region that satisfies some definition of arbitrary closeness, i.e. the neighborhood is every path any small distance from the one that interests you. Therefore, the definition boiled down to defining a single fastest path.
Lentz’s paper explores warp bubbles where there is no superluminal path according to Olum’s definition. Rather, there is a region of paths that are superluminal with respect to paths outside of that region. If you look at Lentz’s bubbles, they look like tessellated rhombuses with various compartments segregated from one another. Each rhombus has a different energy source and they move in formation like a flock of birds to sustain the wave. He specially constructs them to have a central region where tidal forces are minimal, so that a ship could conceivably ride in the middle of it.
Lentz goes on to show that a charged plasma can generate the required warping of space and time to create the bubble. Unfortunately, the amount of energy required is equally as huge as Alcubierre’s original negative energy solution. Nothing we have now, not the Large Hadron Collider, or even a star can generate that amount of energy. Lentz leaves that for future work with the hope that, one day, such warp bubbles can be generated to allow travel to the stars. Since Alcubierre’s solution was improved by about 60 orders of magnitude since his original 1994 proposal, there is hope that with numerical modeling and a bit of ingenuity, Lentz’s requirements will be decreased as well. The rest is, as they say, all engineering.
I for one am more hopeful in the near term that such advances could revolutionize the future of communications. Being able to send tiny traveling waves at superluminal speeds would be a radical step towards creating an interplanetary communications network where distance is no longer a barrier to phoning home. While the energy required increases with the square of the velocity above light speed, it might be conceivable to achieve messaging that reaches Mars in seconds rather than minutes and the outer planets in minutes instead of hours. Likewise, any attempt to send probes to nearby star systems would also benefit from warp bubble communications where ordinary signals would take years.
I am also starting to wonder if such arguments might apply to wormholes as well, which suffer from similar problems as Alcubierre’s. Perhaps a wormhole that is not just a tubular region but some exotic, rhombus formation could be constructed and held open with positive energy density as well. I expect to see such results within the next few years.
Whatever the outcome, human ingenuity is always redefining what is possible and, while skepticism is always warranted, the word “impossible” should be a rare one indeed in a scientist’s vocabulary.
Lentz, Erik. “Breaking the warp barrier: Hyper-fast solitons in Einstein-Maxwell-plasma theory.” Classical and Quantum Gravity (2021).
Olum, Ken D. “Superluminal travel requires negative energies.” Physical Review Letters 81.17 (1998): 3567.
Graham, Noah, and Ken D. Olum. “Achronal averaged null energy condition.” Physical Review D 76.6 (2007): 064001.