For a while now, I've been "working" on a story where mankind begins to set out towards the stars; and in my procrastination I started to get hung up on something.

In the universe I'm working on, there are actually TWO different ways to travel to other stars: traveling the long way, and "going hyperstellar" (a form of FTL travel).

In the story's timeline, hyperstellar travel was discovered first. By opening a tear in space time called a "rift" a ship could access a higher dimension where distances in space are compressed down from normal; and the farther you travel, the shorter your trip is. By going hyperstellar, a ship traveling at today's interplanetary speeds could reach stars light years away in anywhere from a few months, weeks, or even days.

But, because the trip gets shorter the farther you go, this creates a narrow band of reachable stars between two "jump horizons"; where either the journey will take too long (inner) or the trip becomes too short for the drive to operate (outer).

In order to reach stars within the inner jump horizon, colony ships have to take the long way to get there. Using antimatter-ramjet hybrid engines, immense "Arkships" are built fly to nearby stars directly. By burning constantly these ships reach nearly 70 percent the speed of light, with their frozen crews eventually reaching their destinations over the course of a few decades.

Here's where I got stuck on a thought. On one hand, a hyperstellar vessel can cover lightyears of distance in less than a year, but because the distance is shortened, it is only traveling as fast as a modern day space probe. On the other hand, an Arkship is traveling at a very hefty portion of the speed of light, but it takes decades for it to get there.

So, with one ship having a faster absoulute velocity, and another having a faster relative velocity, which of these two ships is the fastest?

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    $\begingroup$ What this boils down to is a poll of people as to which definition of "fastest" they prefer. I really don't see how this can be transmogrified into anything else. $\endgroup$ – Mark Olson Jun 5 '18 at 1:06
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    $\begingroup$ If the FTL drive can be controlled, why can't you just make two long jumps in order to make a short jump? Analogy: Fly from New York to Philadelphia by way of Los Angeles in order to get the frequent flyer miles for each leg. $\endgroup$ – manassehkatz-Moving 2 Codidact Jun 5 '18 at 1:08
  • $\begingroup$ Ask this on the Philosophy.SE, I'm sure they'd love this question. $\endgroup$ – Sydney Sleeper Jun 5 '18 at 1:55
  • $\begingroup$ "Absolute velocity" is an expression with no meaning in either special or general relativity and mixing that with FTL makes the whole thing pretty meaningless, as you will break causality. "Fastest" is entirely observer dependent here - different observers will see different things. $\endgroup$ – StephenG Jun 5 '18 at 6:41
  • $\begingroup$ I bet people in this world would argue for decades, so how could we know? Outcome depends on their culture more than any technical detail here. $\endgroup$ – Mołot Jun 5 '18 at 6:59

There is no reason why a hyperstellar ship cannot jump far away and then jump back close. IF there is a minimum jump distance you could simply make a route that looks like an Isosceles triangle where the trip is the two longer lines instead of the one shorter one, because it would still be faster even though it takes more distance.

This already happens in real life when an area takes longer to traverse due to certain areas not being crossable without using a slower transportation method, such as a plane taking the long way around a no fly zone, instead of landing, having everyone disembark and go by bus instead.

  • $\begingroup$ Nice lateral thinking there! Also, welcome to the site. You've given a fantastic first answer there, I might add. $\endgroup$ – Sydney Sleeper Jun 5 '18 at 2:08
  • $\begingroup$ We routinely encounter this in everyday life. Note how often your phone gives you something other than the absolutely shortest route. $\endgroup$ – Loren Pechtel Jun 5 '18 at 4:56

If you really insist on comparing the two, the hyperstellar vessel is faster because it can travel further in less time and can also do two long jumps to get a short jump.

However you would likely classify them differently because the way they travel is different. It doesn't make sense to compare the speed of FTL travel to conventional travel. Especially with your restriction, the hyperstellar vessels mode of travel must either require a huge amount of space and/or fuel otherwise there shouldn't be a reason you couldn't use the same engines to move the ship on both vehicles.

  • $\begingroup$ Thanks, I probably should have brought up the fuel requirement. The FTL drive isn't an engine because it doesn't move the ship. It needs to open two rifts to enter & exit the higher dimension. Each rift requires so much energy to open that it actually offsets the mass of the ship; along with using up a meta-material crystal that is really expensive to produce. In fact, the ships that have the drive are a lot like heighliners from Dune, since it's cheaper and safer to strap a bunch of smaller ships onto one big carrier than multiple smaller vessels sporting their own drives. $\endgroup$ – Mattias Jun 5 '18 at 3:12
  • $\begingroup$ @Mattias If a Rift can be opened in both places from 1 end (the ship) why not just use massive planetary platform or stationary ones to move ships far distances, or maybe use a very small version to be able to send messages FTL when you need to get out of an area really fast (They receive the message and co-ordinates and open a rift for you). $\endgroup$ – Shadowzee Jun 5 '18 at 4:14
  • $\begingroup$ You can't open a rift remotely because you have to launch the crystal into it directly (ie, fire it out in front of the ship with basically a high tech cannon). It isn't like a wormhole where you have to open both sides at once. The transition between dimensions is more like traveling through a more gentle black hole. You can only go through it one way, and it's direction depends on which dimension the rift is opened from. That is why it has to fire twice: Once to enter the higher dimension, and later on to return back to normal space. $\endgroup$ – Mattias Jun 5 '18 at 14:30

Well, it's hard to really make a concrete determination without a more precise mathematical description of how your rifts work and what you consider to be velocity, but the most probable answer is: there isn't really a consistent way to compare their velocities.

There are several reasons for this. The first one is very basic and comes out of special relativity, and it's simply the question "faster from whose point of view?" After all, if I'm sitting in one of the ships, the other ship is automatically going at least as fast as mine from my point of view, since I'll always see my own ship as sitting still. Now we can "fix" this problem by arbitrarily declaring some reference frame to be the one we measure velocity relative to (say, the Earth's frame), but we're still left with another problem from general relativity.

You see, in general relativity, velocity is an inherently local measurement; spacetime needs to be "flat" like that of special relativity in order to compare it. But the mechanics of general relativity dictate that space time need only look flat in small patches; overall it can have much more exotic composition-- much like how the Earth looks flat on a human level but if you walk in a straight line you eventually come back to the point you started at! This weird "bendy" global behavior makes it impossible to consistently compare velocities of separated objects.

As a more concrete example, imagine a pair of two dimensional beings that live in a world that's topologically a sphere. If it helps you visualize it, you can picture the sphere in three dimensions, but keep in mind access to a third dimension is not a luxury afforded to our flat friends-- the words "up" and "down" have no physical meaning to them. Now, say that they are at opposite poles of their sphere, moving at equal speeds along the prime meridian such that they will collide at the equator. What's their relative velocity? One approach is to say "why not look at their relative velocities in 3-D space?"

The answer is: many reasons. Now, there's actually a theorem called Whitney's Embedding theorem that guarantees we can always put this kind of locally flat, globally wonky type of object (called a manifold) into a higher dimensional flat space. But although the flat space allows us to consistently define velocities, it has drawbacks:

  • Embeddings can get tricky to calculate for non-trivial space-times
  • Most importantly, the velocities you obtain from this method have no real physical interpretation, because the 2-D creatures don't have access to a third spatial dimension. In fact, if you think about it, this method tells you that the relative velocities of the beings is zero, which seems like the least correct possible answer!

So, what if we give up on trying to use the global structure and instead concentrate on patching together local properties, much like how the manifold itself is intrinsically defined? Well, that's fine and dandy, but despite having a more physical interpretation, we run into the problem of multiple answers. For instance, imagine we set our reference frame to be that of the being on the north pole. If that creature is looking at the other along the prime meridian (which to him looks like a straight line), he'll see it moving towards him. But if he turns around and looks the other direction, he'll see it moving away from him! If you're into math, this is an example of the notion of parallel transport along a smooth manifold, which is a long winded way of saying that we're SOL if we want to compare velocities of distant objects in General Relativity. If you want to throw an even bigger wrench into the idea, just imagine what you would do if the sphere's radius was increasing with time.

The only reason we can talk about the speed of various space probes in our solar system is because on that scale, space is very nearly flat so acting like special relativity applies is a good approximation. But zoom out far enough and you can see weird things like galaxies receding faster than their light reaches us. This is often misinterpreted as them moving faster than light, but by now hopefully you've gleaned that such a phrase is utter nonsense since velocity and restrictions thereof are local notions.

Finally, to actually address your specific question:

Now, you may wonder why I spent so long talking about the problems of measuring relative velocity in general relativity. The answer is that it's even worse in the situation you describe! Like I said before, it kinda depends on the mathematical nuances of your rifts. But, as described, accessing additional spatial dimensions means that we don't even have the luxury of our spacetime being a manifold anymore, since its 3+1 dimensional spacetime abruptly glued onto a higher dimensional spacetime. So we no longer have even the notion of parallel transport to help us. Long story short, your question doesn't really have a well-defined answer.


Let's think of it another way;

The problem with comparing subluminal travel with FTL travel is really that you're thinking of 'speed' as displacement over time. That works in a Newtonian framework but when we look at it through the lens of relativity, we see that the universe is really made up of 'spacetime'; a 4D framework in which time is just another spatial dimension.

I could explain that FTL travel really breaks relativity which is why it's impossible yadda yadda yadda but that's not in the spirit of the question. Instead, I'm going to propose a different (FTL compatible) way of looking at speed;

Kinetic Energy.

Kinetic Energy is basically the integral of momentum - e(k) = 1/2 MV^2. What that means is that if you think of spacetime as being spatial then ultimately, the measure of speed is to reverse the equation;

v= sqrt(e(k) / 2M) (sorry if I've got the equation formatting wrong, happy to address typos as well)

The trick here is finding a reliable way of measuring kinetic energy output. But, let's say (for the sake of argument) that your ship is fitted with a new 'energometer' that tells you your kinetic energy at a given point. You already know the mass of your ship so you can plug both these values into the formula and you have your 'velocity', the scalar version of which is your speed.

For FTL speed ratings, this might be the only way to truly measure your speed as velocity is a vector, and at FTL (even relativistic to some degree) speeds, one of the 'directions' you're travelling in is time. So, if your kinetic energy is actually lower while folding space, it means you're travelling slower than the subluminal speeds, but you're doing so partially backwards in time which facilitates the FTL effects.

In that sense, E(k) may be the only way to reliably compare speeds of ships travelling via different FTL approaches AND ships that run in a subluminal manner. If we take it that the relative time that one arrives is no longer relevant because subjective time on the ship is going to be different to observations outside the ship anyway, then it just makes better sense to consider 'speed' as applying to all 4 dimensions, and it being a measure (along with mass) of a more objective (true from many perspectives) form of velocity, and therefore speed.

  • $\begingroup$ Really nifty concept of comparing their values of kinetic energy. You could do the same with momentum. On a side-note: FTL motion doesn't break relativity. Superluminal velocities can fit within special relativity. It just looks very strange. Relativistic mass increase makes crossing the lightspeed barrier impossible, that's the real difficulty. with FTL travel. $\endgroup$ – a4android Jun 5 '18 at 13:04

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