Faster than Light
Faster than Light is a common concept in modern SciFi storytelling. The hint lies in the unit with which we measure the distances to star - the lightyear. Although it has “year” in the title, it is not a unit for time at all: it is the distance light can bridge in a vacuum over the time of a year. One lightyear is a vast distance for our everyday life proportions and equals about 5,908,909,347,180 miles, yet not a single other star is in the vicinity of our sun with one lightyear range. It is pretty clear why SciFi invokes faster-than-light travel. If a space shuttle flies through space with about 5 miles per second, it will take 37,000 years to travel the distance of 1 lightyear. An action-packed story, playing out over interstellar distances, would grind to a hold. There are many versions of faster-than-light travel: the recent “Another Life” SciFi series invokes the FTL drive, as does the “Dark Matter” series. Star Trek made familiar the “warp drive”, which cloaks the spaceship into a warp bubble, allowing the ship to move with a multiple of the speed of light. It is time to address the question: what is preventing us from moving faster than light?
Before doing so, it might be interesting to look a the scale of the issue, i.e., the distances between stars and points of interest in outer space.
Alpha Centauri - 4.4 lightyears
Our immediate cosmic neighbourhood hosts a double star system - Alpha Centauri AB. The brighter one of the two stars is more extensive than our sun but emits light in the same spectrum. The other star is a cooler K-type star producing an orange type light, which might be even more suited to host a habitable planet and life than our sun (see here).
Vega - 25 lightyears
Vega is the brightest star in the northern hemisphere. It has about twice the sun's mass, has about a tenth of the sun's age, and has almost twice the surface temperature of our sun. Vega predominantly emits light in the blue spectrum. Vega is surrounded by a disk of debris (as is our sun - the Kuiper belt). It might have a hot Neptune orbiting Vega in close proximity. It is doubtful that conditions around Vega are suitable to sustain life as we know it. (Artist impression BelleDeesse)
M35 cluster - 3870 lightyears
M35 is a cluster of about 300 - 400 stars relatively close to our sun compared to the diameter of our galaxy of 100,000 lightyears. Its core has a diameter of about 11.4 lightyears with 1600-3200 solar masses. An alien life-form inhabiting a stellar system inside the cluster must have a spectacular night sky. If those aliens looked to Earth now (with a hypothetical super telescope), they would see humankind at about 1900 BC. They would see the end of the early Helladic culture in Greece and the rule of the 12th dynasty in Egypt. Still, 1849 years to go to watch the birth of Christianity.
Quite naturally, humankind does its best and wants to explore these regions and realms of potential life and that in a few years. Many SciFi novels see a new home in an interstellar system as a last resort to escape an exhausted and polluted Earth. What cruel twists of the laws of nature are preventing us from inviting faster-than-light propulsion systems? Ok, we saw in my last blog that we cannot reach the speed of light by conventional means, but what if we develop a device that let us jump over the light barrier?
It is the structure of space-time itself and the arrow of time, dictating a causal order of events. Let us understand these concepts better.
Coordinates help us to locate things. Two coordinates - longitude and latitude - are sufficient to find any point on Earth. The number of coordinates you need to map the space entirely is called dimension. The surface of the Earth is thus a 2-dimensional space. Two dimensions are not enough to find my car keys: I need three - length, width and height (on the table). In fact, I need four numbers: let's add time since at 1 pm the car keys were at the table but at 2 pm not anymore. Mathematicians call this a 4-dimensional vector space: we call it space-time.
We want more. So far, the vector space is a heap of points telling us when to find things where. We would like to measure angles and distances between points. Mathematically, we upgrade the vector space to a metric space. We use those all the time: the cup of tea is about 90cm above the floor on the table; the corner of my room has an angle of 90 degrees, well, almost. Metric spaces differ by how they measure distances and angles. For instance, the space in my room is called a Euclidean space, and it has the property that the distance between two points is always positive: we would not know what it means if the distance between my cup of tea and the floor is minus 2m. There are other spaces where the length can be negative.
We are perfectly able to see three dimensions with our eyes. We sometimes call them length, width and height. We cannot see time. We still could accept this - maybe our brain in com pelt enough at add 4th direction - and have 4-dimensional Euclidean space with time bolted on to the three other directions. However, this would not match our observations: foremost, the constancy of the vacuum speed of light.
This is a prime example of Mathematicians discovering new abstract structures - here spaces where distances can be negative -, working with them and leaving it later to physicists to find them as the structure of this universe, if at all. The space that we need to reconcile our desire to locate objects in space and time and at the same time incorporate the universal speed limit of the universe was discovered Hermann Minkowski, and space-time is now called Minkowski space.
It is not only the space-time structure where time is different from the other three coordinates. It is also that time is constantly on the move. Even if you stand perfectly still, your wristwatch ticks away, and you are moving from the past into the future. You can also move 1m to the left or the right. You can move 5 minutes into the future, but you cannot move 5 minutes into the past. There is a constant flow of time, which can pass at different rates (as we discovered in my earlier blogs), but it always points from the past to the future.
This is imminently important not only for all physics processes but also for all life in this universe. All life is subjected to a rhythm of cause and action: we eat, and then we are not hungry anymore. We sleep, and then we are rested. It is not possible to be rested because we sleep later.
Let us now come back to why we cannot move faster than the speed of light. It is due to the structure dictated by the Minkowski space, i.e., space-time itself. Let us assume Albert is on Earth and plays darts: the dart leaves his hand and misses the bullseye by an inch a split second later. The cause 'the dart leaves Albert's hand' precedes the action 'the dart hits the target'. Neil is flying by in spacecraft with some significant speed, but still slower than the vacuum speed of light. He watches the dart leaving Albert's hand and, indeed, sees the dart missing the bullseye a bit later in his own time. It does not come as a surprise to you that how long the flight of the dart takes is different for Albert and Neil. The critical point is, however, that also for Neil, the cause always precedes the action. This changes if Neil is flying with speed faster than light. Neils observes the dart missing before Albert throws the dart. He sees the game's outcome and could use his faster-than-light radio to warn Albert that he is going to miss. Albert then never throws the dart. However, Neil has seen the dart already hitting the target - a contradiction! You cannot jump over the barrier of light since the universe would not make sense anymore.
Of course, there are many attempts in research and SciFi literature trying to avoid paradoxes that arise from upsetting the arrow of time. Neil needs to enter a parallel universe where the dart is not hitting the target. They all go to great lengths to avoid giving up on the FTL technology, which is not just for now. I might blog about some of these ideas later in a separate blog. These ideas ask a lot from the universe to be true, and for what reason? Humankind's lifespan hardly exceeds 80 years - a fact for which we hardly can blame the universe.
Should we not accept that the technology that gets us off Earth and allows comms and trade over interstellar distances over the course of decades on Earth will not happen? It is our short lifespan that glues civilisations like us to the planet, not technology. This span confines us to a bead of time, and travelling to another solar system would foremost imply crossing the rift of time that this journey would take.
Are there any interstellar space farers then at all? Of course, we do not know, but we can ask what it takes. The lifespan needs to be longer: if we lived for 300,000 years, we would make it to Alpha Centauri and back in a space shuttle from the nineties. Changing the lifespan would most likely also change how we perceive the flow of time. Everything that we achieve in a lifetime is happening in about 80 years. This sets the pace of our actions. Interstellar space farers either slow down how they perceive time flow or naturally have a different rate for their causes and resulting actions. If they sense a millennium as we do an hour, the journey across the rift of time might not be so dull.