While chatting with one of the players in my Superhero campaign yesterday, the subject of FTL travel in superhero and sci-fi games came up in the course of the conversation. Since I’m always on the lookout for good subjects to write about for Campaign Mastery, and this is a problem that’s come up in many games, I thought I’d take a moment to fill our readers in concerning some of the problems, solutions, and hand-waving that’s necessary to accommodate FTL travel, using the solutions that have been put in place in the Zenith campaign. And, to wrap the subject up into a tight little bow, I’ll discuss how FTL is a concern for straight fantasy games like D&D – and what the solution is to THAT problem.
Furry Thimbles Of Lethargy? – The Einstein Problem
Let me state at the outset that I don’t believe in the Speed Of Light limit. In my opinion, it has no more reality than the Mach 1 limit – the solution is a matter of insight and engineering, and the problem will eventually be cracked. Of course, this might be wishful thinking on my part. If you aren’t interested in the physics of FTL, feel free to skip down to “Fanciful Theory Leftovers? – The Inertia Problem” below.
Before the speed of light was measured, it could be considered instantaneous – a term for which physicists have an irrational dislike. The physical world was divided into physical phenomena, that move at some measurable speed, and energy phenomena, that moved with (effectively) infinite speed. Galileo was the first to attempt to measure the speed of light; he failed. In 1676, Olaus Roemer, a Danish Astronomer, became the first to successfully measure it, having noticed that the intervals between eclipses of Jupiter’s moons varied with the relative motions of Earth and Jupiter – he got a speed of 132,000 miles a second, a very good first estimate.
Einstein once said that every time he considered the possibility of moving faster than light, he found himself caught up in paradoxes, and it was this that led him to develop the Special Theory Of Relativity. Every high school physics text attempts to describe those paradoxes, and all of them are flawed, because they all operate on the assumptions that (1) there is some absolute limit to the propagation rate of information, and (2) that because light is the fastest thing we know about, it is the fastest thing that we CAN think about.
But here’s the problem: if you exclude light as a means of information transmission – assume that it has not been discovered yet – the next fastest phenomenon known to physics becomes the limiting velocity. Prior to particle physics and particle accelerators, and the invention of electrical current, that was the speed of sound. Every one of Einstein’s Paradoxes hold true for the slower ‘ultimate speed limit’ – and the same chains of logic lead to the development of Lorentz-type transformations of length, mass, and time, just using that lower speed limit in place of the speed of light in the formula:
The obvious implication is that the speed of light is only a speed limit if we can’t conceive of anything faster.
Let me put it in even plainer English. Let’s assume that we are looking at a clock that is some distance away, and that this clock is in a room where there is an observer who is watching or measuring some phenomenon – rolling a dice, let’s say. Each time he rolls the dice, he sends us the results using the fastest means of communications possible, whatever they might be. Einstein contended that if some means of FTL communications existed, we would receive the results of the die rolls before they happened, because our visual reading of the clock on the wall was limited to the speed of light. In other words, because Light could not travel faster than the speed of light, nothing could.
Is the hole in the logic clear now? I hope so, because I can’t put it any more clearly.
Those Pesky Transformations
And yet, the Lorentz-FitzGerald transformations are clearly valid. Not only have they been tested and found to measure up, but if they were wrong, everything from the design and manufacture of modern computers to particle accelerators would be completely different. They’ve been verified using everything from atomic clocks to astronomical phenomena. And they only work if the speed of light is the limiting speed of the universe.
Or do they? Is it possible that they only refer to what a stationary observer perceives, and not what really happens? That would account for the fact that they seem to work, and are factors that have to be taken into account – without saying anything about an ultimate speed.
The Transformation Of Mass
The transformation of mass is the one that has the greatest impact in terms of forbidding FTL travel. The theory goes that the faster you go, the more any acceleration is diverted into increasing the mass of the object that’s accelerating; hence it gets harder to accelerate the object any further. Like Xeno’s Paradox, you can get ever-closer to the limiting speed, but never quite get all the way.
Sorry; like that same Paradox, it’s an interesting thought experiment, but has no bearing on reality. For example, if our object was a missile using a conventional rocket engine, the mass of the exhaust would also increase, so the drive becomes more efficient by exactly the same ratio as the purported increase in inefficiency due to the mass of the payload.
The Transformation Of Time
Which brings me to the Twin Paradox, in which Time Dilation leads to a twin moving at close to the speed of light aging more slowly than one who isn’t.
The explanations for this paradox all stem from the concept that one twin has undergone acceleration and one hasn’t. How does the universe know which is which? Isn’t it just as accurate to say that the planet with the “reference” twin on it has accelerated away from the twin in the space-ship? So far as one twin is concerned, the other has aged more slowly, no matter which twin we are talking about.
It’s easy to construct thought experiments to demolish any arguements based on time dilation as proof of the limiting speed of the universe. Twins accelerating to something close to the speed of light (say 90%) in different directions, for example – if the speed of light is the ultimate speed of the universe, then their speed of separation can’t be 180% of the speed of light. When they turn around, decelerate, accelerate back the way they came from, and again accelerate, they will both have experienced the same amount of time dilation, i.e. that their speed of separation was zero throughout.
Paradoxes, Paradoxes Everywhere
Which brings me back to that statement attributed to Einstein: “every time I consider the possibility of moving faster than light, I find myself caught up in paradoxes.” In terms of proof against FTL speeds, this is a washout – because (as shown), every time I consider the possibility that nothing can travel faster than light, I find myself caught up in paradoxes!
A Question Of Physics: The Propagation Of Electric Current
When the poles of a battery are connected by a wire, a current flows. One electron is pulled along the wire from one atom to the next, creating a void that a neighboring electron is pulled into, creating a new void. Or maybe one electron pushes into an atom, which gives it too many, so another electron of that atom is pushed into a neighboring atom. Or maybe both these descriptions are oversimplifications of events in a subatomic realm where normal physics doesn’t obtain.
I remember reading that the actual speed of electrons within a current flow was relatively slow, but the propagation rate of the existence of a current is ‘virtually instantaneous’ – but can’t remember where I read that. The source then went on to assume that the propagation rate was the speed of light, or slower, because nothing can travel faster. I wonder how long it takes for the middle of that length of wire to “realize” that there is an electron current flowing?
A Question of Physics: Quantum Tunneling
Another question posed by modern physics concerns the phenomenon of Quantum Tunneling. During the “tunneling” phase of the phenomenon, speeds exceed the speed of light (1.5 to 1.7 times c. Currently, there’s a lot of scrambling going on amongst physicists to try and reconcile this and related phenomena with their old theories, such as postulating “Vacuum Energies” and “Virtual Particles” – in effect, trying to show that even though a phenomenon can travel faster than the speed of light, this doesn’t violate relativity. To quote from the last page of the excellent Wikipedia overview of Faster-Than-Light,
It was… claimed by the Keller group in Switzerland that particle tunneling does indeed occur in zero real time. Their tests involved tunneling electrons, where the group argued a relativistic prediction for tunneling time should be 500-600 attoseconds (one attosecond is 10e-18 seconds, or 0.000 000 000 000 000 001 seconds). All that could be measured was 24 attoseconds, which is the limit of the test accuracy… other physicists believe that tunneling experiments in which particles appear to spend anomalously short times inside the barrier are in fact fully compatible with relativity, although there is disagreement about whether the explanation involves reshaping of the wave packet or other effects.
This sounds an awful lot like making weasely excuses to a layman. “Your honor, my client committed the misdeeds of which he is excused, but technically he did not break the strict letter of the law.”
There have been suggestions made that this result is meaningless, because no information can be conveyed by these means; but last year (or possibly in 2009) I remember reading reports that a series of pulses had been transmitted via Quantum Tunneling all the way across Boston Harbor (I wish I had the reference handy to link to it). And if FTL communications is possible, then according to science, so is time travel.
And if you can travel in time, then you can arrive at a destination before the speed-of-light limit says you should be able to – in other words, travel at (effectively) FTL speeds (for that matter, you could arrive before you left).
A Question Of Physics: The Propagation Of Gravity
Gravity is a continuous, non-electromagnetic phenomenon – at least, no-one has ever detected a particle of gravity, a Graviton. Science postulates that such a thing exists, simply because everything else that science has discovered operates through fundamental particles.
If an object – let’s say a planet around Alpha Centauri – is exerting a gravitational field that is affecting, however slightly, the orbit of Earth around the Sun, and that gravitational field changes, how quickly does that gravitational field change become detectable on Earth, assuming instruments of sufficient sensitivity?
‘Changing gravitational fields?’ you may ask; ‘Is that even possible?’. Well, yes – an orbit is an ellipse, and as an object orbiting the sun approaches perihelion, it travels faster, according to Kepler’s Second Law. That means that it accelerates, and – according to the Lorentz-FitzGerald transformation – it increases its mass (or, as I contend, its apparent mass).
If the mass actually increases, that should have an impact on the shape of the orbit, as shown by Kepler’s Third Law – either the Period of the orbit (the length of time it takes to complete an orbit) should be reduced, or the size of it (as measured by the semimajor, ie long axis) should be increased, or both. The first means that the object will accelerate more than expected, producing an even bigger distortion, and so on – ad infinitum – or, at least, until escape velocity is achieved. The second means that the orbit will decay outwards – until the orbiting body is thrown free of the sun altogether.
Yet, we still have a solar system. That means one of two things: either the effect hasn’t had long enough yet to fling all the planets of the solar system out into the depths of space, or the mass increase of the Lorentz-FitzGerald equation – which relies on the speed of light being an absolute limit to how fast things can travel – is an illusion, an effect of perception; in which case the speed-of-light limit itself is also an illusion.
Conclusion: FTL is possible – we just haven’t figured out how, yet.
Fanciful Theory Leftovers? – The Inertia Problem
So, for game purposes at least, there’s plenty of room for FTL travel to exist. But is it practical? There’s still a major hurdle to be overcome before the answer can be ‘yes’: Inertia. And it arises because people don’t really appreciate how fast the speed of light is.
Ignoring the Lorentz-FitzGerald effect, if you can accelerate continuously at one gravity (i.e. you would weigh as much as you do on the surface of the earth), it would take a whisker under 30,559,884 seconds to reach the speed of light. That’s 8,448.856 hours – call it 8449 hours for convenience – or 353.7 days. That’s right, less than a couple of weeks short of a year.
To halve that, we need to double the acceleration. Most humans black out at a sustained G-force of 5 Gravities – which would cut the acceleration time to a little under 71 days, or a bit more than 10 weeks. But no-one has ever been subjected to that sort of G-force for anywhere NEAR that length of time.
Modern pilots, with training and special exercises, and G-suits, can reportedly sustain up to Nine G without blackout – a little under 40 days of that would get you to light-speed.
Sixteen gravities, sustained for more than about 1.1 seconds, is generally considered to be lethal, according to Wikipedia. It would take 22 DAYS of such acceleration to achieve light-speed.
Game Scale Numbers
In order to achieve FTL speeds in an hour, we’re talking 8449 G’s. At that acceleration, the pressure of air on the body would be more than 124,000 pounds per square inch. That’s the same as having a battleship’s main gun or a locomotive on top of you – for each square inch of exposed skin. Our pilot would immediately assume the thickness of tissue paper, or less.
Champions has a combat turn of 12 seconds. To go to FTL in that span of time would subject the character to more than 2.5 MILLION G’s. At more than about 10,000G’s, the pressure would compress the character into Neutronium, or worse yet, into a black hole.
These numbers are blatantly ridiculous.
The Acceleration Interval
The problem is that this acceleration is not instantaneous, it takes time – and because it occupies duration, inertia has to be overcome. The results are in keeping with physics as we know them – but are inconvenient in game terms.
It follows that if the acceleration is to be experienced in real time, it is going to take REAL time to achieve the speed in question – I would not be comfortable suggesting any figure short of 6 months, ie an acceleration of 2G maximum if any sort of realism is to obtain.
Unless, of course, your game is going to utilize one of the “cheats” to avoid this difficulty. They make the game more science fantasy than science fiction, but so what? Superpowers are already more science fiction than science fantasy anyway!
The following mechanics are designed for use with the Hero System, but are easily adaptable to any appropriate game system – since they are mostly a table of results from a set of calculations, with virtually no game rules involved. The universal “mechanics” are beneath the table below.
Champions charges 10 character points for a base level of FTL travel, which gives a maximum speed of 1 Light Year per Year. Each 2 additional points doubles this value:
|Champions FTL Table|
|10||1 LY per year|
|12||2 LY per year||2 LY per year|
|14||4 LY per year||4 LY per year|
|16||8 LY per year||8 LY per year|
|18||16 LY per year||1 LY per month|
|20||32 LY per year||2 LY per month|
|22||64 LY per year||1 LY per week|
|24||128 LY per year||2 LY per week|
|26||250 LY per year||4 LY per week|
|28||500 LY per year||1 LY per day|
|30||1,000 LY per year||2 LY per day|
|32||2,000 LY per year||4 LY per day|
|34||4,000 LY per year||8 LY per day|
|36||8,000 LY per year||1 LY per hour|
|38||16,000 LY per year||2 LY per hour|
|40||32,000 LY per year||4 LY per hour|
|42||64,000 LY per year||8 LY per hour|
|44||128,000 LY per year||16 LY per hour|
|46||250,000 LY per year||0.5 LY per min|
For these numbers to be of much use, outrageous accelerations have to be used – or travel takes a very long time. For those who want their ships to accelerate to FTL speeds from rest, I have put together a PDF (link above). For each of 24 different acceleration rates, ranging from 0.1 (Light-sail) to an unbelievable 16000 Gravities, it gives two critical numbers: how long it takes at that acceleration to achieve the maximum velocity from the table above, and how far the character/ship will travel while doing so.
At 1 G, for example, and a top speed of 16 Light Years per year, it will take 15,500 years to achieve top speed – at which point the character/ship will have travelled 248 million light-years. And it then has to decelerate, taking another 15,500 years and covering another 248 million light-years.
The table is useful, because if you don’t want to travel such an outrageous distance, you can locate half the total distance you DO want to travel, determine the peak velocity from it and half the travel time.
For example, at 1G, if the character/ship only wants to travel 10 light-years, look for a distance of 5 light-years. The closest values are 3.9 light years and 15.5 light years, so the answers will be somewhere in between, and rather closer to the lower value. Nevertheless, the character will have had to pay for a top speed of 4 LY per year. The times that go with those values are 1.9 and 3.9 years, respectively, so a rough guesstimate is that each half of the trip will take about 3 years.
If the character/ship had only paid for the 2 LY per year top speed? The acceleration to that speed at 1G takes 1.9 years and covers 3.9 light-years; deceleration takes the same; so for the rest of the trip, the character/ship will be travelling at their top speed of 2 LY per year. Ten light-years is the total distance to be travelled, less 3.9 while accelerating and another 3.9 while decelerating leaves 2.2 to be covered at full speed (2 LY per year), so that takes another 1.1 years. The total travelling time is 1.9 (accelerating) plus 1.1 at full speed, plus 1.9 decelerating = 4.9 years.
The tables make it easy to work with constant acceleration drives – provided that the problem of Inertia is dispensed with, or ignored.
Friskier Than Logic? – Warp Drive: The Star Trek solution
That’s where the Star Trek solution comes into play. The theory behind Star Trek’s warp drive – as determined in between the show’s original airing and the writing of Star Trek II: The Wrath Of Khan, and implied in several of the original Star Trek novels of that period – is that the Warp Drive creates a “subspace bubble” around the ship and accelerates this inertial reference frame relative to the rest of the universe. The ship itself – and the passengers within it – don’t experience inertia because they aren’t moving, relative to the space around them.
The result is that a ship or character that uses this type of FTL can accelerate to whatever speed it/they are capable of in whatever time frame the GM considers reasonable.
Although the Hero Games rules never come out and say so, the description of the power clearly implies that this is also what the authors had in mind.
The Star Trek Scale
According to the writer’s guide for the original series, the velocity of a ship or object travelling at warp N was N³ or N×N×N times the speed of light. In the Next Generation, this was tweaked to a more complex formula that give slightly higher speeds for a given Warp Factor. Both guidelines were regularly ignored and abused during production.
For what it may be worth, the following table permits conversion between the Hero System FTL scale and Star Trek’s Original Warp Factors:
Show Me The Way To Go Home
A problem they never really address in Star Trek or the Hero system is how to navigate in such an inertial subspace bubble. Direction control is easy, but how do you know where you’re going?
Several Star Trek novels get around this by postulating that energy striking the “bubble” can be detected as – effectively – tachyons, which the ships computer can detect and interpret into an appropriate viewscreen image, showing stars streaking by as though the ship were really travelling at Warp Factor whatever.
Well, that’s all well and good – but how about for the ordinary (or extraordinary) super-type who can travel at FTL speeds?
The Zenith-3 campaign house rules resolve this by stating that an external gravitational field distorts the shape of the bubble, and that characters / ships travelling using warp drives are able to detect these distortions as feedback. In effect, they can “see” the density of matter in the local space around their subspace bubble. Using these masses (after recognizing and excluding those caused by nearby planets – not an easy task) permits significant masses to be used as navigational beacons.
The strength of a beacon is the product of its mass and its proximity – a smaller mass relatively close by is just as strong as a really big mass (supergiant or black hole) that is a long way away, and therefore difficult to distinguish. And, of course, the closest masses are those of the local star and its solar system.
The practice is therefore to locate all the relevant masses using conventional celestial navigation techniques, so that you know what to avoid. In the directions of those planetary and solar objects, they drown out the starfield in noise, but by knowing where these celestial objects are not you can determine where to get a clear view of the sky.
The other factor that is useful in Warp Navigation is that apparent motion has a greater effect with local proximity. So by “tagging” the most significant mass-objects in the vicinity and watching to see how they shift position as you travel, you can identify what is local, what is remote, and what is in between.
Gas Nebulae show up as fog, as does a galactic centre.
I would love to do an illustration of it for you – I have designed one, but have run out of time. Maybe I’ll come back and add it afterwards.
Freakish Thin Legalities? – Jump Drive & Warp Points: The Traveler/Mote In God’s Eye solution
The third approach to FTL in the Zenith-3 campaign is modeled on another classic science-fiction approach – jump points. These are curdles in space-time that appear naturally near large masses provided that the mass does not have all its energy locked up in fusion reactions. In effect, a concentration of potential energy too great for the local space-time to accommodate creates a warp point.
Warp Points are massless, because their mass has been shunted out of this space-time to form a conduit into another realm, known as Hyperspace or Otherspace or by various other names. When a ship passes through a warp point with sufficient energy, it exits from another warp point elsewhere in space-time. One warp point connects to anywhere from one or two to dozens of others, each with a different quantum temporal energy level; navigation is achieved by matching the spacio-temporal energy level of the desired exit gate.
The connections between Warp Points are distorted by significant gravitational forces and by other phenomena. What’s more, with only a limited set of possible energy quantum states, nearby gates with similar energy levels will take precedence over more distant jump points with the same signature. A ship or character will always emerge from the closest jump point that matches the quantum state of the energy it has built up at the moment of transition.
It follows that navigating to a particular destination may require a very roundabout path, avoiding various dangers and hazards. Consider the diagram: A ship wants to jump from A to E, but B has roughly the same energy potential as E, and is much closer. The only way to reach E is to follow the line A – B – C – D – E, five jumps.
Some ships can generate enough energy to make multiple such jumps in succession; others can only make a single jump at a time. Some energy differentials between warp points are so high that transiting from one to another counts as multiple jumps in and of itself; these routes are not accessible at all to lesser ships.
Warp Points, by their natures are both unstable and prone to being temperamental; many change size and shape, or even open and close irregularly, and some often have jarring gravitational discontinuities. They are not permanent, and can evaporate or dissipate at any time; every ship that passes through one equalizes the potential differences between two warp points just a little, contributing to the erosion. All of these problems can be controlled to some extent by the creation of Stellar Gates, also known as Jumpgates and Warp Portals – artificial mechanisms that act to stabilize, control, and advertise the presence of a jump point.
Jump drives are often preferred over warp drives because, while the initial energy expenditure of a jump may be higher than that used over a period of time by a Warp Drive, once this expenditure has taken place the universe itself provides the energy to complete the FTL transition, whereas a Warp Drive is a constant ongoing expenditure. Overall, it takes a lot less energy and effort to use a warp point.
Adding to the complexities of Warp Point navigation is the fact that entry speed and direction contribute massively to the travel time by dictating the orbital path within the warp connection that a vessel or character will follow. While the average time will be the same as if the journey from Warp Point to Warp Point was conducted at the maximum FTL speed of the vessel, with no acceleration or deceleration time, it can be anywhere from 90% shorter to more than 3.5 times as long, per jump. (To determine the transition factor, roll d6+1 and multiply the results by a roll of d6+2, then divide by 10).
Successful navigation rolls can reduce the results of one die roll by up to 3 (to a minimum of 1). Successful piloting rolls can reduce the results of the other by a similar amount.
Some energy configurations do not lead from one warp point to another, but deposit the ship/traveler in the Hyperspace medium (called the Astral Plane by the players of the game) through which the connections between warp points travel. Since the conduits maintain an inertial frame that is coupled to the frames at both ends but separated from them by the jump point barrier, ships travelling between jump points continue to experience time and gravity and related phenomena exactly as they would in normal space; that is not the case when a ship or traveler leaves a conduit and passes into hyperspace proper.
Hyperspace is a strange realm in which velocity is proportional to determination and will, and is the home of many strange phenomena. Inertial frames are not maintained within this realm, and hours, days, weeks, months, or even years can pass with no awareness of them being experienced by the individual. In terms of space-time, the individual is decoupled from their time-frame of origin and while their personal entropy arrow maintains the inertial state that it possessed prior to departure from normal space-time for the individual, it is decoupled from the space-time of origin of the character.
All this enables an individual reenter the time-space of their primary realm at any point in time or space, or to enter instead a parallel world to that of their origin, or an even more divergent reality.
Navigation is especially difficult, as perceived time is measured in hours plus, and every stray thought draws the individual in the direction of a space-time that resonates with that thought and its historical or emotional content. Think of escaping a repressive regime and you may find yourself entering a space-time in which that regime never existed; thing of the regime from which you are fleeing and you may find yourself entering a space-time in which they or an analogous group are even more powerful or dominant. There are no fixed landmarks, adding to the challenge.
Hyperspace can take you places Warp Points and Warp Drive can’t – but it is far more dangerous because of that capability.
Further Than Limbo? – Extra-Dimensional Movement: The Stargate solution
The last type of FTL that is available in the Zenith-3 campaign are artificial portals such as stargates, fairy circles, rainbow bridges, and the like. Regardless of their appearance, topology, and nature, these can all be essentially summed up as artificial temporary warp points, created to bridge point A to point B. With all EDM there are issues of accuracy, and the potential of bridging from one space-time continuum to another through hyperspace. If the energy is supplied to them, some of these constructs can be semi-permanent.
Like the other types of FTL, Portals can encounter unusual phenomena and hazards that are unique to this mode of travel, such as bifurcating transit conduits, gravity snarls, and reality shock.
Navigation poses an interesting problem when it comes to portals, since – like jump points – all navigation must be done in advance of the actual travel; no correction or adjustment is possible en route. Unlike jump points, which can be stabilized and explored on a long-term and consistent basis, portals only exist long enough for the traveler(s) to transit through them, plus a few seconds.
They also tend to be more direct than other forms of FTL which involve interstellar travel at the very least; most portals are point-to-point operations from the surface of one world to the surface of another, or something very close to it.
Fairytale Twisted Locii? – FTL in Fantasy Gaming
What’s that? FTL in D&D? Well, why not?
Portals exist in most games – if you know where to look for them. There are spells that let you travel from one plane to another. There’s a spell called Teleport that you might have heard of.
Any of these can constitute FTL travel. Sufficiently creative PCs can attempt to exploit any of them for the purposes of quick travel from A to B. And this can pose problems in D&D that are unlikely to arise in more science-oriented (including superhero) campaigns, simply because the science gives a context and framework to FTL – that’s what this article is all about, after all.
In fantasy gaming, most of that context and framework, and the protection from abuse that they carry with them, are absent. There are multiple vectors into the FTL-travel realm – and they are all in something approaching a state of anarchy, ripe for exploitation.
The solution: think of them in Science-Fiction terms, but without the restraints on your imagination. Decide how they work, and come up with complications that you can spring on over-clever players. The interpretations of FTL-capabilities described in this article would make an excellent starting point – the only differences are that access to “FTL” might require a flying carpet, or a sea voyage, or an overland trek, instead of a starship, and that the means are magical rather than technological.