Minimum speed required for a galaxy spanning empire

Question

The dawn of the Galactic Empire!

Assume that FTL travel and communication is possible, for simplicity we say c is the speed of light.

Assume any speed of travel and communication < c*2^100 is achievable given research time.

For example, in the year 2100 ftl of c*2 is possible, in the year 2110 ftl c*3 is possible in the year 2150 c*4 is possible.

Assume that people will attempt to make a "Galactic Empire" before that is possible, possibly leading to fragmentation of the Galaxy.

Assume that a Truly Unified Galactic Empire is a galaxy ruled by a central authority, with some delegation of authority. Similar to how American democracy has State representatives, but on a planetary scale. For example, It is ok if there is a planetary president that makes most of the day to day decisions, but those decisions must be overridable by the central government.

Assume that if any planet is not affected by anything coming from the central government directly for long stretches of time, it is not technically in the Galactic Empire, but is instead a separate sovereign state, technically only allied with the empire.

Assume that a for a Truly Unified Galactic Empire to exist has least 95% of all habitable stars in the galaxy only have the Galactic Empire as their government.

At what speed is it possible to have a Truly Unified Galactic Empire?

Is it not possible at any speed?

Answer 1

Someone who's done more than 15 minutes of googling will probably have a better response, but here's what I came up with....

As a starting point, we need to know what length of travel time is an acceptable maximum. I settled for an easy and well-known example: the ancient Roman Empire. It turns out there's a source available -- an interactive map -- for travel times throughout that region of the world in the first century:

https://www.livescience.com/20211-google-maps-ancient-rome-shows-travel-times-2000-years.html

The results also show how much it would have cost to travel or to ship a kilogram of wheat that distance, at that time of year. For example, the fastest possible July trip between Rome and Londinium – or modern-day London – would have taken 27 days.

Hadrian's wall, the uttermost limit of Roman occupation in that direction, is roughly 300 miles (about 480km) further north from London. The ORBIS site which hosts the map doesn't offer Hadrian's wall as a destination but it does cite 30km/day as a reference speed for foot travel, so let's add [ 480km / 30km/day ] = 16 days to that total... it comes to 43 days.

So to keep control over the galaxy, the outermost systems & planets need to be within 43 days' travel of the capital -- which, for simplicity, we'll put more or less at the center of the Milky Way.

Now the full diameter of the Milky Way is 105,700 light years. Divide it by two and we get a maximum travel distance from the galactic capital of 52,850 light years.

So to keep things in line from rim to rim, we need to be able to travel 52,850 light years in 43 days:

(..drum roll, please...)

[ 52,850 light years / ( 43 days / 365 days/year ) ] = 448,610 c

So we need communications and/or physical FTL travel that moves at nearly 450K times the speed of light.

EDIT:

Fels' comment (thanks, good additional example) notes that a longer timeline (2-4 months) could still potentially work. Applying that range lowers the bar a bit:

60 days (2 months): 321,504 c

120 days (4 months): 160,752 c

Answer 2

First order estimate: The Horse

The Roman Empire at its peak (117 A.D.) is estimated to have encompassed 5 million square kilometers. Now, the Mediterranean sea was in the middle of it, so the speed of an early ship is also involved, but let's be generous and stick with the horse. The average top speed of a horse (because there are many breeds and they don't all do the same thing) is about 88 kph.

OK, so our goal is to visit the center of each and every one of those square kilometers on the horse at top speed. No, you obviously can't do that in reality as some kilometers would need to be passed over again to get to others, but bear with me, it's a simplistic way of analyzing the scope of this baby. Please keep your hands and feet inside the ride at all times.

5,000,000 km² / 88 kph = 56,818 hours to visit each square kilometer or about 6.5 years.¹

Let's test our theory

The U.S. had the Pony Express, but it really didn't hit its stride until the Railroad! The area of the continental U.S. is 8,080,464.3 km² and the average top speed of the rail in 1860 was 80.5 kph.

8,080,464.3 / 80.5 = 100,378.4!

OK! Our solid two points of experimental overly-simplified data suggests that the railroad would be slower than the horse — except — that assuming the horse could actually hold out at 88 kph all that time is really stretching reality!

So I humbly declare that these numbers are on the right track (ah-ha).

One more check: From the Earth to the Moon

So, the volume of the Earth is about 1 trillion cubic km and the volume of space described by the orbit of the moon in three dimensions is V=4𝛑r³/3 where r=385,000 km so V=477,874,465,321,626,227 cubic km (yeah, 4.8 quadrillion...) and we remove the Earth's volume from that to get 477,873.5 trillion cubic km and Apollo 10 was booking through space at a top speed of 39,897 kph... and we want to visit each and every one of those cubic kilometers!

477,973,465,321,626,227 / 39,897 = 11,977,679,156,869

Yup, that's 11 trillion hours of watching Gilligan's Island! And we've also lost our working theory with the horse that can't actually keep up that long. What we have proven is an axiom from Douglas Adams: "Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space."

But, to be fair, there's a whole lot less to see in space. I mean, what's the point of visiting all those cubic kilometers?² Let's assume that railroad number is absolutely spot-on,³ which means we really don't care about 99.999999% of the volume of space.⁴

But what speed are we talking about on a galactic scale?

OK, so our magic number is 100,378 and we're ignoring 99.999999% of the volume of space and the estimated volume of the Milky Way is 6.65X10⁵¹ cubic kilometers. So, the speed you need is:

.00000001 * 6.65x10⁵¹ / 100,378 = 6.625x10³⁸ = 614x10²⁷ times the speed of light

or approximately warp factor 8,499,379,494. (AKA warp factor 8.5 billion.)

Which absolutely proves Mr. Adams' axiom and demonstrates that trying to match reality with your fiction is frequently a waste of time.

Why on earth should I trust this number?

Because the Romans didn't use horses to visit every square kilometer of their empire. What I did was use an arbitrary ratio⁵ that compared two very real and very practical numbers in such a way that I could try to normalize the effects over time.

If anything, what this proves is that humanity must move at exponentially faster speeds to manage growing empires.

The surprise in all this to me was that the railroad actually slowed down compared to the horse. But what I'm not comparing is the ability of the railroad to carry vastly more goods than the horse could. So while my magic number increased, a heretofore unknown ratio describing the increase in logistics vastly improved.

My conclusion? You're looking at the wrong number. Speed isn't that relevant. Logistics is. You should be looking at the ability to haul a boatload of freight between solar systems. Because in the end, far flung islands of the empire will rule themselves more according to how well the government was set up than how fast communication (and assassins investigators) can travel.

---

_{¹ *And to make that work you had to urinate from the back of the infinitely enduring horse while eating Ofellas thrown at you by vapid admirers. but hey, it's just a first-order estimate.*}

_{² Other than bragging rights. NEVER underestimate the value of high-quality bragging rights.}

_{³ Stop laughing, my number is just as good as yours! My momma can kick yo momma's butt, too! And yours wear combat boots! Yeah! Yo momma so ugly the TIDE won't take her out! What were we talking about...? Oh, yeah, angels weeping over the ridiculous number. Yo momma still ugly....}

_{⁴ And I dare anybody to prove that number wrong! Hah!}

_{⁵ A remarkably arbitrary ratio.}

Answer 3

It seems quite unlikely that anything resembling democratic government as we understand the concept is possible.

You speak of 95% of the stars in the galaxy being part of the empire. I assume you mean "habitable planets", since it seems likely that "only" a few percent of the stars will have a human-habitable planet. That's still a lot of planets! There are several hundred billion stars in the Milky Way, so we're talking about several billion inhabited planets.

First problem: Assuming that each planets has a single representative, that's a legislature of several billion people. "My Chairman! Mr. Chairman! I request the floor to make a speech on an issue of grave importance to my constituents on Delta Leonis IV." "Certainly. There are six million, three hundred and forty five thousand, seven hundred and six representatives ahead of you. You can expect to get the floor in about 103 years."

Whatever the legislature of the GE is like, it could not possibly be anything like what we understand.

Possibly you could have a hierarchical system: a few dozen nearby planets having a local legislature. A few hundred local legislatures each electing a delegate to a sub-regional legislature, and few hundred sub-regional legislatures banding together in a regional legislature and a few hundred regional legislatures creating sector legislatures which elect delegates to the GE's legislature. It's not clear that the GE thus constituted would be democratic in any meaningful sense.

A second issue is more fundamental: What would this GE do? It's silly to think of it making laws which regulate individual people -- countries of a few hundred million humans are big enough that many feel that the central government has lost touch with them. And our one measly world of only six billion people is far too diverse for a central government to do much other than prevent wars -- what few world-wide thing that matter which actually exist were built from the bottom up, and all the effective ones are independent of the UN. (This isn't because the UN is weak -- the UN is weak because we don't know how to have a democratic government fr many billions of people, many of whom don't even share democratic values.) How would the GE be any different?

Languages. Ah, yes, languages. Even if every single colonist spoke English with a classical Brooklyn accent when they left Earth, long before the Galaxy was settled, millions of mutually unintelligible languages would evolve. (Languages evolve fast in isolation.) Communication would be an utter nightmare.

And then there's communications lag. Even if you could send messages at a light year/second, we're still talking about 25 hours to get a message one-way across the Galaxy. (This is the only objection that's merely difficult and not utterly insurmountable!)

So my answer: The Galactic Empire is unsafe at any speed.

(My guess is that the most workable answer is something planets acting like the modern concept of Westphalian states who interact mostly with their neighbors and then mainly to keep the peace and facilitate trade and tourism. Lots and lots of little overlapping treaty organizations with no overarching organization whatsoever.)

Answer 4

AI Technocracy

It's not about speed but the type of government.

Human run government would need FTL travel and communication. There is no point sending out laws and decrees when the person you address to will have died of old age before it arrives. No point sending out soldiers to quell a rebellion if all they can do is chat to the grandchildren of the rebels after the fact.

Now if the government was AI controlled, the AI can duplicate itself and copies running in every town/city/planet/space habitat, the government would be the same and cohesive. The AI would run continuous streams of updates to it's copies to keep everything synchronised. It really wouldn't matter if a copy is 100 years out of date. Everything would keep running.

AI gets a bad rap from Hollywood but an AI government and legal system would be free of corruption, impartial, efficient and consistent. It will do it's job to the best of it's ability and isn't looking to throw off the yoke of humankind by building a army of terminators. It's more likely to be a super nanny than an evil robot overlord

Answer 5

No need for FTL travel whatsoever. We'll organise our state like a religion.

The top layer near the center of the galaxy only bothers with the core rules - similar to the 10 commandments or the UN charta of human rights. They regularly send generation ships (large armadas) to the regional governments to keep them in line. They also broadcast their ideology through the whole galaxy at the speed of light, using some inclusive populism to keep people united. They also transmit technological and other information, some of it encrypted, so they stay relevant and so only the star systems which cooperate with the delegations sent from there can access the information. Some information is also transferred in just selected directions. They are on fast moving star systems closer to the center and make up a very large population cluster. They also demand access to technologies from all the further away systems, so they are usually more advanced in all areas, while they share the less important technologies with the rest - enough to keep up the flow of information their way. While there is always a central organisation in charge, the planet hosting it is flexible, and if the organisation fails, it can easily be renewed somewhere else - similar to how large religions and populist movements are organised.

20 or 30 regional governments control their parts of the galaxy and provide constitutions for the other systems in their region. They relay the broadcasts from the center to further away places and to places with less large radio dishes. They are usually on clusters of star systems with very large populations, reserving some space for delegates and missions from their region and other needed representatives, including some from the center.

The next level down provides basic laws and structures, then come important laws, then standards, norms and more specific laws, and then finally the planetary specific legislation.

A special role comes to star systems and clusters of star systems moving in and out of the center, in opposite direction to the other stars or such. They are obviously of very high strategic value, as they can move very large armadas quickly through the whole galaxy and control or upset a lot of what's going on. They also get regular visits from the center, and from nearby regional governments. They are used as a glue to keep up the order and the motivation for it - trade, common ideals, common legal standards and so on.

Every planet sends delegates to the star systems responsible for them - all the way up to the center. They travel on generational ships, and will act as representatives of their race and their branch of the populist ideology the galaxy unites under. They will also relay necessary changes of their local laws to their home planets, even if those take thousands of years to reach their target. They will also provide some of their encryption systems or keys to the center and other organisational levels for targeted messages, while keeping others for themselves.

That obviously means billions of representatives in and close to the center star systems. They take part in elections similar to our elections in large democracies, and thus keep the central government in line with the rest of the galaxy.

Atrocities against traders, generation ships, representatives and so on are punished very heavily - even if it takes a few thousand years for that to happen and the people don't even clearly remember what happened. The absence of delegates which should be there is usually enough reason for a punitive mission.

Typically, a planetary system has a moving star system within reach (a few dozen light years) every hundred or so years (more often near the center) and uses the opportunity for large exchanges of know-how, representatives, norms and so on.

Generation ships (sometimes asteroids or even rogue planets) come by very often near the center and every few years near the outskirts of the galaxy. They usually get to drop some colonists or representatives and can choose whether to let some locals hike a ride in exchange for more supplies.

I expect all of them on a technological level far beyond ours - with bodies which are artificial in nature and can be adapted to needs, which also meanst that exchange of technology also includes exchange of useful properties of their bodies. Not to mention adaptions to fashions.