Space Game Theory and Space Stations

[speaker-to-trolls]

I assume many of you will be aware of what I call Space Game Theory (I don't know if it has a better name) but I'll run through it quickly anyway: The theory is that if two civilisations are aware of each other and able to send large craft at relativistic speeds to one anothers stars then the logical choice for each civilisation is to send a ship to the others home planet which doesn't slow down when it gets there. In other words a kinetic kill missile, or however many missiles it takes to take out the planet.
Now, putting the horrifying immorality of this prospect aside for a second, I have to wonder if it is really practical for advanced civilisations. See, when one is dealing with primitives like us, jammed as we are on to one planet, a single well placed salvo could probably finish us off forever. But when dealing with a more advanced culture, the kind which could build an interstellar missile, I think it's quite possible, probable even, that most of them wouldn't be on one planet, many of them could be dispersed around their solar system on space habitats of various kinds and sizes. And, of course, if they have the capacity to store their personalities in computers the prospect for the aggressors gets even worse, you'd take out a planet or habitat only to have its population upload into a new environment. What's more, if one civilisation is far enough from another, then it's possible that a potential aggressor will not know what the tech level of their target is when they launch, they could fire at primitive groundlings like us and hit the historic birthplace of an advanced posthuman civilisation, which might not take kindly to their bullshit.
I'm not sure if people have thought of this before, but it seems to me that these possibilities could curb the potential aggression of space-cold-warriors.

[Turin]

You're making one of the classic mistakes of people applying game theory to everything -- not examining the assumption that this is a game of Prisoner's Dilemma. Prisoner's Dilemma assumes that reward for mutual cooperation is less than that for sole defection. In many real-world examples (and I think this one should be included), this assumption fails to hold. The intrinsic cost of defecting (regardless of whatever the other person does) lowers the value of sole defection when compared to mutual cooperation. That changes it from a game of Prisoner's Dilemma (total relative rewards of DC>CC>DD>CD), which has no "evolutionarily stable strategy" to one of Stag's Hunt (total relative rewards of CC>DC>DD>CD), which has a stable strategy of mutual cooperation.

Civilizations who have the ability to send relativistic kill missiles to each other are relatively advanced, presumably. But the cost to launch of an RKV is non-trivial, while the costs to communicate with the other civilization (and open potential lines of cooperation) are trivial in comparison. The potential rewards for cooperation between advanced civilizations are immense.

[Darth Wong]

It's also worth noting that if you are paranoid, you would want to spend your limited resources to build early warning systems to detect and intercept an RKV with a long lead time, so that it can be safely diverted. That would be a much wiser use of resources than building RKVs and launching them on the assumption that the other party will be:

A) Unable to detect and deflect the RKV
B) Unwilling or unable to retaliate with an RKV (or worse) of his own

Who the fuck are these people who insist that the only logical course of action is to pre-emptively hurl RKVs at any alien civilization we discover?

[Illuminatus Primus]

Not to mention it suddenly alerts any third party you weren't smart enough to notice that there's a madman in the house. RKV-hurling is a one-track road to your own annihilation. Which should surprise no one.

[Admiral Valdemar]

What if you're not dealing with a logical foe? There's plenty of room for religious zealotry in space, and the idea of some species going out of its way to make sure no one rises to attack their status is interesting (although any elder species would probably erase or at least amend any such civilisation if in their locale).

Many instances of this scenario assume a species approaching a threat level, while the other one is already at least Level II on the Kardashev scale. In that case, it's fair to assume, given a more practical range from the target civilisation, that taking out the potential threat is much more enticing when they're unable to get off their planet en masse, never mind mount a counter-attack. Relativity factoring for time lag would be an issue, but no one goes half arsed with these kind of attacks. You either wipe them out to stone age level and send some probes to mop up later, or you face a very angry civilisation, united in their rage against you.

[GrandMasterTerwynn]

I assume many of you will be aware of what I call Space Game Theory (I don't know if it has a better name) but I'll run through it quickly anyway: The theory is that if two civilisations are aware of each other and able to send large craft at relativistic speeds to one anothers stars then the logical choice for each civilisation is to send a ship to the others home planet which doesn't slow down when it gets there. In other words a kinetic kill missile, or however many missiles it takes to take out the planet.

"Space Game Theory" is actually as stupid and empty-headed as it sounds. The logical choice isn't actually to try to kill other interstellar civilizations with RKVs, but to ignore them.

Now, putting the horrifying immorality of this prospect aside for a second, I have to wonder if it is really practical for advanced civilisations. See, when one is dealing with primitives like us, jammed as we are on to one planet, a single well placed salvo could probably finish us off forever.

Cavemen like us are the only civilization this strategy would work on. But you'd have to invest lots of time and effort sniffing cavemen out in order to kill them. Barring some bizarre, hitherto unknown, new physics, we'll be several thousand years building up the infrastructure and energy reserves needed to send an RKV any appreciable distance. Blink of an eye to a civilization 10 million years old, to be sure, but plenty of time to properly evaluate us.

But when dealing with a more advanced culture, the kind which could build an interstellar missile, I think it's quite possible, probable even, that most of them wouldn't be on one planet, many of them could be dispersed around their solar system on space habitats of various kinds and sizes.

This is precisely what makes the idea of the interstellar RKV so singularly retarded. A sufficiently sophisticated and aged civilization will have virtually all its population in a Dyson swarm. They will probably be hacking apart their terrestrial planets for more orbital habitat material. Shooting those planets with RKVs will only be doing them a favor.

What's more, if one civilisation is far enough from another, then it's possible that a potential aggressor will not know what the tech level of their target is when they launch, they could fire at primitive groundlings like us and hit the historic birthplace of an advanced posthuman civilisation, which might not take kindly to their bullshit.

There is a very simple game that you play when dealing with interstellar civilizations. It's called "Angels and Cavemen" and it works thusly:

A) Assume that habitable stars have lifespans of billions of years, and there are stars that have had habitable zones for billions of years before you came along, and stars that will have them for a trillion years hence.
B) Assume that the evolution of life on planets orbiting these stars can be tremendously affected by both cyclical repetitive, and low-probability singular events.
C) Given A and B, the time which a given planet will produce a sapient species will vary by tens or even hundreds of millions of years, even for star systems which formed at the same time.
D) Thusly, any sapient life-form you encounter will either be astoundingly primitive Cavemen, or Angels tens of millions of years older than you.
E) Given all of the above, the probability of encountering Angels is 100%, no matter how powerful you think you are.

To play the game: In a given encounter between two civilizations, each party should assume that they are the Caveman and act accordingly. And that is to say, extremely politely.

Unless the beings you meet are definitely cavemen. In which case, you leave them alone, because launching RKVs and smashing planets are energy-intensive affairs and will be visible from light-centuries away to folk who will view this sort of behavior as being very impolite. In a game that's all about being extremely polite.

[Admiral Valdemar]

A better idea would be an army of von Neumann machines instead a la the Inhibitors. You don't risk the less subtle and quite obvious signs of wiping out (or attempting to) another race via powerful RKVs which is like chucking ICBMs around on Earth. It's not the best way to make friends or peace. Tweak their prime directive to focus on assessing any intelligent signs of life, and carry out any actions if needed. If the species is looking especially barbaric and advancing with gusto technology-wise, then corrective measures are taken.

You simply have a great many such probes replicate, branch off and hide away in various sectors of space. Perhaps, also, forming oddities in interstellar space to attract such intelligences for assessment.

[cosmicalstorm]

Isnt the idea of RKV's idiotic to start off with?
Those things would be turned into clouds of plasma by the ISM in no time.

As others have mentioned you would probably be better off building unmanned Von Neumann probes, even with todays crude tech we are able to build some fairly dangerous stuff that does most of the work on its own such as Tomahawk missiles, UAV's, ICBM's etc.

Once you get your space industry up and running it would be easy for an automated system to build absolutely massive amounts of defensive and offensive probes and drones that could be scattered about around your solarsystem/systems silently scanning every nearby star within a hundred lightyears and the space between them for threats, ready to retaliate with many different weapons on their own if something was to happen to their homeworld.

[Sarevok]

This is something I had been wondering for a while regarding the "2 star systems and lots of hate inbetween issue"

RKVs are extremely dangerous. But only to planet dwellers. Could it be possible the threat of these weapons could force a civilization to complete space based existence ? Imagine nomads in space travelling from system to system in generation / sleeper ships. They occasionaly make stops to mine asteroids, moons etc then move on quickly. Individual moving targets are much hard to hit than a planet in a predictable orbit. Plus if one ship is destroyed there is still an entire fleet which in time could build a new replacement ship.

Thoughts ?

[Admiral Valdemar]

Isnt the idea of RKV's idiotic to start off with?
Those things would be turned into clouds of plasma by the ISM in no time.

No. The ISM is still extremely empty and any decent civilisation will make an RKV that is essentially a crowbar of kilometre length or more. A very small cross-section means little ablation to the mass and practically no detection and prevention without solar system scale defences, and even then you can throw up spoofs.

This is something I had been wondering for a while regarding the "2 star systems and lots of hate inbetween issue"

RKVs are extremely dangerous. But only to planet dwellers. Could it be possible the threat of these weapons could force a civilization to complete space based existence ? Imagine nomads in space travelling from system to system in generation / sleeper ships. They occasionaly make stops to mine asteroids, moons etc then move on quickly. Individual moving targets are much hard to hit than a planet in a predictable orbit. Plus if one ship is destroyed there is still an entire fleet which in time could build a new replacement ship.

Thoughts ?

Yes. If you're trying to attack another race that can also potentially use RKVs, then you must accept that they likely have space colonies and interstellar ships too, by virtue of the technology demonstrated already. This is why it only really makes strategic sense to take out a species that is nearing space flight capability, not one that is near your tech level and can more than likely stage a retaliatory strike by tracing the impact of the RKV. Hence, either use the aforementioned von Neumann machine concept, or stage your RKV launch from elsewhere (which is even more horrendously energy intensive).

[Ender]

Yes. If you're trying to attack another race that can also potentially use RKVs, then you must accept that they likely have space colonies and interstellar ships too, by virtue of the technology demonstrated already. This is why it only really makes strategic sense to take out a species that is nearing space flight capability, not one that is near your tech level and can more than likely stage a retaliatory strike by tracing the impact of the RKV. Hence, either use the aforementioned von Neumann machine concept, or stage your RKV launch from elsewhere (which is even more horrendously energy intensive).

Or use a "long gun" concept to launch it. No gamma flux to give away your position, and even harder to detect. With a self powered R-bomb you might be able to detect it as it accelerates up to speed. It's a low probability thing, but you might pick it up. If it gets launched by something that uses a lower power density and doesn't release a huge signature like that, even that low chance goes away. With the long gun your only hope for seeing it is picking up the emissions from the rare impact in route to target and maybe as it heats up from solar flux as it comes in system (though that would be an after the fact "so that's where it came from!" by anyone in a space station that survived)

Of course, all relativistic concepts are based on the assumption that you can get up to those kinds of speeds, and without knowing more about dark matter and how it interacts, that isnt' a given. My understanding is that recent calculations of the dark matter concentration based of newer observations means that while it isn''t dense enough to obscure anything we are looking at, there is enough to make high relativistic flight a no-go.

[Ender]

It's also worth noting that if you are paranoid, you would want to spend your limited resources to build early warning systems to detect and intercept an RKV with a long lead time, so that it can be safely diverted. That would be a much wiser use of resources than building RKVs and launching them on the assumption that the other party will be:

A) Unable to detect and deflect the RKV
B) Unwilling or unable to retaliate with an RKV (or worse) of his own

Who the fuck are these people who insist that the only logical course of action is to pre-emptively hurl RKVs at any alien civilization we discover?

I'm almost troubled to ask - what could be worse then an R-bomb? I mean I came up with that massive grazer on a lark, but that was almost a James Bond supervillain type over the top planet killer. What is there realistically that could be deployed to top an R-bomb in terms of destruction?

[Admiral Valdemar]

Or use a "long gun" concept to launch it. No gamma flux to give away your position, and even harder to detect. With a self powered R-bomb you might be able to detect it as it accelerates up to speed. It's a low probability thing, but you might pick it up. If it gets launched by something that uses a lower power density and doesn't release a huge signature like that, even that low chance goes away. With the long gun your only hope for seeing it is picking up the emissions from the rare impact in route to target and maybe as it heats up from solar flux as it comes in system (though that would be an after the fact "so that's where it came from!" by anyone in a space station that survived)

I was assuming that anyway, since Reynolds uses the concept of a linear accelerator several thousand klicks long with a single projectile propelled along via fusion detonations. One shot device, but one shot, one kill. There's no way to use a rocket anyway, without some really quite exotic physics getting around the lack of propellant and energy issues.

Of course, all relativistic concepts are based on the assumption that you can get up to those kinds of speeds, and without knowing more about dark matter and how it interacts, that isnt' a given. My understanding is that recent calculations of the dark matter concentration based of newer observations means that while it isn''t dense enough to obscure anything we are looking at, there is enough to make high relativistic flight a no-go.

Assuming it affects us that much, otherwise the ISM is practically empty and it should offer hope for at least fractional c speeds for an unmanned projectile, if not a ship. The bigger issue here is the game theory over whether to go along with such attacks, which would be favoured by Berserkers and warmonger species.

[Admiral Valdemar]

I'm almost troubled to ask - what could be worse then an R-bomb? I mean I came up with that massive grazer on a lark, but that was almost a James Bond supervillain type over the top planet killer. What is there realistically that could be deployed to top an R-bomb in terms of destruction?

Using stars as weapons. Far more adventurous, but being able to get a GRB focused on an enemy system is not something for the faint of heart. Or go through ways of killing stars, rather than just take on the planets (more a terror tactic of permanence than quick and easy).

[Ender]

I was assuming that anyway, since Reynolds uses the concept of a linear accelerator several thousand klicks long with a single projectile propelled along via fusion detonations. One shot device, but one shot, one kill. There's no way to use a rocket anyway, without some really quite exotic physics getting around the lack of propellant and energy issues.

Ah, I was adapting real plans for interstellar travel, use a multi AU railgun to send canned primate at .5C and cargo at .1C. Only they were EM rather then bomb pumped, so nothing to give it away.

Assuming it affects us that much, otherwise the ISM is practically empty and it should offer hope for at least fractional c speeds for an unmanned projectile, if not a ship.

My understanding was that the latest estimates on the amount of it and its concentration throughout the galaxy (figured by the viral theorem) was enough to make it unlikely. Previous evaluations of the ISM hadn't factored it into account. If that's been redacted, cool, but do you have a link?

The bigger issue here is the game theory over whether to go along with such attacks, which would be favoured by Berserkers and warmonger species.

Long haul it's gonna end with one kind of intelligence being on top and the others extinct. Whether it is through out competing or wars of xenocide, it's gonna happen.

Using stars as weapons. Far more adventurous, but being able to get a GRB focused on an enemy system is not something for the faint of heart. Or go through ways of killing stars, rather than just take on the planets (more a terror tactic of permanence than quick and easy).

The key word there was "realistically". Yes, popping stars would be worse. So would causality violation weapons, or inertia manipulation weapons. But none of them are realistic. In terms of bound by the laws of physics and engineering, what could really top an R-bomb?

[Admiral Valdemar]

Ah, I was adapting real plans for interstellar travel, use a multi AU railgun to send canned primate at .5C and cargo at .1C. Only they were EM rather then bomb pumped, so nothing to give it away.

You could do it either way. That idea is not as simple, but is reusable.

My understanding was that the latest estimates on the amount of it and its concentration throughout the galaxy (figured by the viral theorem) was enough to make it unlikely. Previous evaluations of the ISM hadn't factored it into account. If that's been redacted, cool, but do you have a link?

No link. Going by the assumption that the medium isn't as cluttered as it may be. We shall hopefully know for sure in the near future, not that it changes our plans for space travel anyway.

The key word there was "realistically". Yes, popping stars would be worse. So would causality violation weapons, or inertia manipulation weapons. But none of them are realistic. In terms of bound by the laws of physics and engineering, what could really top an R-bomb?

For species that are able to produce RKVs, I'm not ruling them out either. We're talking a species that is easily millions of years ahead of us, and we're nowhere near understanding what composes most of the universe. It's Clarke tech territory beyond there.

[Covenant]

What's an R-Bomb?

Also, dump Game Theory, pick up Drama Theory. People are quite often willing to do things that hurt them personally just to punish an aggressor, and it matches more closely the few real-life instances we have of this, like that Russian Hero-of-Earth refusing to fire his missiles despite the computer telling him to.

[Surlethe]

No. The ISM is still extremely empty and any decent civilisation will make an RKV that is essentially a crowbar of kilometre length or more. A very small cross-section means little ablation to the mass and practically no detection and prevention without solar system scale defences, and even then you can throw up spoofs.

Do you have any calculations to back this up? When you're dealing with interstellar precision bombs, how much do you have to take into account the various influences of nearby stars, the influences of the planets in your system and the system you're shooting for, the shockwave at the edge of the system you're shooting for, etc.?

Also, in case anyone is interested, the formula for how much time you have after detecting the launch of an RKV aimed in your direction is d(1/v - 1), where v is the fractional speed of light of the RKV (e.g., if it's traveling at 0.95c, v = 0.95) and d is the distance to the aggressors in light-years. So if you detect someone 350 ly away shooting an RKV at you at 0.98c, you have all of seven years plus change to get ready.

[Darth Ruinus]

What's an R-Bomb?

Relativistic bomb?

[GrandMasterTerwynn]

The bigger issue here is the game theory over whether to go along with such attacks, which would be favoured by Berserkers and warmonger species.

Long haul it's gonna end with one kind of intelligence being on top and the others extinct. Whether it is through out competing or wars of xenocide, it's gonna happen.

Competition? There are a minimum of one-hundred billion stars in this galaxy. Most of which are red dwarves, and will serve as inhabitable space for the next trillion years. Even if, for some bizarre reason, everybody insisted on having planets to colonize, most planets would be hard-pressed to develop life more sophisticated than lichens, and there ought to be tens or hundreds of millions of suitable planets in the galaxy. Even when you encounter another civilization in this context, their biochemistries will likely be seriously incompatible with yours, and you'll be spending a few thousand years after each conquest dropping large rocks on their planets and waiting for your newly seeded ecologies to take when the dust settles.

Arguably, the fact that we exist is evidence against Berserkers, Inhibitors, Mulkari, and other such sapients or sapient-smashing technologies. The best time to smack a planet is not when it develops technology, but when it develops multicellular life. If you're trying to kill potential competitors at the stage when they're right at the cusp of becoming a planet-independent civilization it's xenocide and invites flash-back. If you're doing it when they're trilobites, it's a terraforming exercise.

Using stars as weapons. Far more adventurous, but being able to get a GRB focused on an enemy system is not something for the faint of heart. Or go through ways of killing stars, rather than just take on the planets (more a terror tactic of permanence than quick and easy).

The key word there was "realistically". Yes, popping stars would be worse. So would causality violation weapons, or inertia manipulation weapons. But none of them are realistic. In terms of bound by the laws of physics and engineering, what could really top an R-bomb?

Directing the energy output of your primary star at your opponent. All you need is a lot of mirrors and a reasonably sophisticated intelligence to handle the pointing and orienting of them.

[Ariphaos]

No. The ISM is still extremely empty and any decent civilisation will make an RKV that is essentially a crowbar of kilometre length or more.

If by decent you mean retarded. To get something a meter wide and a kilometer long up to relativistic speeds you'd need light-years of coil.

I still haven't had the time to properly work through the equations Kuroneko tried to explain, but even the absolute upper bound makes RKVs completely impractical.

A very small cross-section means little ablation to the mass and practically no detection and prevention without solar system scale defences, and even then you can throw up spoofs.

The ISM does impose a speed limit..

Prevention is just sunshine and happiness. Rather trivial for any type II civilization. Even only assuming a 1 ly radius sphere of influence (ridiculously tiny), a 99% of c projectile (rather near said limit) gives a response time of ~44 hours. More than plenty of time to vaporize it.

RKVs are extremely dangerous. But only to planet dwellers.

If by dangerous to planet dwellers you mean to cavemen sitting within ~10 ly of a type II civilization to whom they pose no threat whatsoever, and are willing to dedicate a significant fraction of their solar output in the attempt.

Past a hundred light years, it's absolutely insane.

Could it be possible the threat of these weapons could force a civilization to complete space based existence ?

No, the realization that other race's homeworlds are only around for sentimental value and trying to expend such immense resources to destroy one is only probably going to piss them off and leave the vast majority of their industrial capacity intact means that the race that actually goes through with one of these is going to be rather rare.

Imagine nomads in space travelling from system to system in generation / sleeper ships. They occasionaly make stops to mine asteroids, moons etc then move on quickly. Individual moving targets are much hard to hit than a planet in a predictable orbit.

If by predictable you mean a tiny gravity tug will throw Earth's orbit completely off their path. There are moons that qualify by the time you get out to the 100ly range.

Plus if one ship is destroyed there is still an entire fleet which in time could build a new replacement ship.

The paranoid nomads will quickly become overwhelmed by those willing to tap the power of the stars themselves.

Yes. If you're trying to attack another race that can also potentially use RKVs, then you must accept that they likely have space colonies and interstellar ships too, by virtue of the technology demonstrated already. This is why it only really makes strategic sense to take out a species that is nearing space flight capability, not one that is near your tech level and can more than likely stage a retaliatory strike by tracing the impact of the RKV. Hence, either use the aforementioned von Neumann machine concept, or stage your RKV launch from elsewhere (which is even more horrendously energy intensive).

The von neumann concept only works
1: If you're already there or
2: The race hasn't achieved sentience yet. See 1.

Getting a VN swarm safely to another star system is going to take much, much longer. If you want to do it stealthily, it's going to take millennia.

Any civilization approaching the Type II scale is already going to have a pretty solid stock of its resources, and those of other nearby systems.

[Ender]

Competition? There are a minimum of one-hundred billion stars in this galaxy. Most of which are red dwarves, and will serve as inhabitable space for the next trillion years. Even if, for some bizarre reason, everybody insisted on having planets to colonize, most planets would be hard-pressed to develop life more sophisticated than lichens, and there ought to be tens or hundreds of millions of suitable planets in the galaxy. Even when you encounter another civilization in this context, their biochemistries will likely be seriously incompatible with yours, and you'll be spending a few thousand years after each conquest dropping large rocks on their planets and waiting for your newly seeded ecologies to take when the dust settles.

I regard planet habitation as foolish for a number of reasons, so lets stick with stars. There are ~200 billion of Which sounds like a lot. Until you consider exponential growth. Then they run out really fast. And this is just considering the number of stars, it isn't subtracting those that fall in the extinction zone or whatever it is called (those within a certain radius of the galactic center that get sterilized by GRBs every so often). It isn't taking into account the differences in size, spectrum, elemental composition, etc that will make some undesirable. But even if tech advances to the poitn where anything is a good home to us, it still comes back to exponential growth. Each star will have a given carrying capacity, which puts a cap on the total number of beings. Even if you go the dyson sphere-quantum computer-upload route, eventually you hit a cap on space and power. And then you need another one. And so it goes.

You can argue that "a species will be smart enough to curb its own growth". And perhaps some will. And that will go along swimmingly, until another one comes along that doesn't.

Arguably, the fact that we exist is evidence against Berserkers, Inhibitors, Mulkari, and other such sapients or sapient-smashing technologies. The best time to smack a planet is not when it develops technology, but when it develops multicellular life. If you're trying to kill potential competitors at the stage when they're right at the cusp of becoming a planet-independent civilization it's xenocide and invites flash-back. If you're doing it when they're trilobites, it's a terraforming exercise.

You don't have to be a murderous civilization to wipe out another species. Our history with the Neanderthals is a good example of that - we just out competed them, and history took care of the rest. Frankly, I think making sure no one can take us out is a far more pressing thought experiment than figuring out how to take them out.

Directing the energy output of your primary star at your opponent. All you need is a lot of mirrors and a reasonably sophisticated intelligence to handle the pointing and orienting of them.

What, to disrupt the energy/gravity balance in their star? I would think it would be to diffuse for anything else.

[Darth Wong]

I'm almost troubled to ask - what could be worse then an R-bomb?

Something that is easier to aim or more difficult to deflect or destroy, I'd imagine. The difficulty of accurately aiming and accelerating a sizable RKV is immense, thus necessitating similarly elaborate support technologies and investment in equipment. The difficulty of lasering the RKV and gradually evapourating its surface so that its particles scatter far beyond the aiming cone is relatively small. A huge laser or light beam would be much more of a problem, since you wouldn't even see it coming until it's on top of you.

[Surlethe]

What does the interstellar medium look like from the perspective of an RKV? The density in its rest frame is ρ = 1 atom/cc. Suppose the RKV has cross-section A, and will trace out a path of length L (in the rest frame of the ISM). There will be AρL atoms in the way. From the perspective of the RKV, the path will have length L' = L/γ, and thus volume AL' = AL/γ. The density from the perspective of the RKV is ρ' = AρL/[AL'] = AρL/[AγL] = ργ.

If the RKV is traveling at 0.98c, it will be plowing through an interstellar medium with a particulate density that has increased by six orders of magnitude, not taking into account mass dilation that accompanies the speed of the atoms.

[Ender]

Also, in case anyone is interested, the formula for how much time you have after detecting the launch of an RKV aimed in your direction is d(1/v - 1), where v is the fractional speed of light of the RKV (e.g., if it's traveling at 0.95c, v = 0.95) and d is the distance to the aggressors in light-years. So if you detect someone 350 ly away shooting an RKV at you at 0.98c, you have all of seven years plus change to get ready.

Yes, but will you be able to see it? The problem is the sheer area of space you have to sweep and the resolution of your telescopes. Further out you place it, the more time you have to respond, but the lower the probability detecting it. Its a losing probability, since the time to see it increases linearly and the area to cover increases exponentially.