# Small universe - is there any point in interstellar communication?

Everything on Earth and in the Solar system is as we know it. However it is discovered that we live in a small but unbounded universe. That is to say if we travel far enough in a straight line we will return to Earth.

You may be familiar with the classic Asteroids game that can be played here. If you fly off one side of the screen then you reappear at the other side.

Scientists have discovered that we live in a cube-shaped universe. It is just like Asteroids but in three dimensions.

We know that other versions of Earth (or rather Earth itself) are 1 light year away because we receive radio and TV broadcasts that were transmitted a year ago from the six different directions.

Question

We can see these 'other' worlds tantalisingly close but in fact it's like looking at the back of our own heads.

Is there any use that humanity can find for this phenomenon or is there nothing to gain at all?

What does it mean for science and space-travel?

• What about all the other stuff we see in the sky? (ie stars and stuff?) This is going to run into a lot of physics related problems I think.
– Erik
Aug 13 '15 at 17:58
• As Erik said, In this universe, no point in the universe is more than half a light-year away. Modern estimates put the outer edge of our Solar System's Oort Cloud at 0.79 light years away. There's really not space for the rest of the universe. Is the an understood tenant of your universe? No galaxies...just a predictable pattern of stars that are composed of us seeing outselves Aug 13 '15 at 18:02
• Well, it will be just like asteroids again. There are only a few stars in the universe. We'll just see repetitions of the same ones receding infinitely into the distance. Aug 13 '15 at 18:04
• @guildsbounty - Yes, that's it. Rather like holding two mirrors facing each other and the reflections go on for ever. Aug 13 '15 at 18:07
• This is a very thought provoking question, well done. Aug 13 '15 at 18:31

As has been mentioned in the comments, in a universe like this, there is no room at all for other astronomical bodies. There are no galaxies and no other solar systems. Just our own. So, this leads to some interesting points that I'll mention before I get into why interstellar communications would still be a thing...assuming some magical system saved us from being vaporized by pouring massive amounts of energy into a tiny box.

Weird Sky

Given that, because of the 'loop' formed by our small, enclosed universe, 'Earth' appears to be repeated every 1 light year... we are going to have a very odd looking night sky. Because every time you see the sun, you can see another one beyond it...it's like looking into mirrors that face each other.

Weird Orbits

We have some stuff that passes more than half a light year away from our sun as part of its orbital path...these things may find themselves instead being tugged into orbit around multiple iterations of the sun

Thermal problems

In an enclosed space like this, the heat shed by the sun would start to build up. Averaging things out, there are no points in the universe more than half a light year away from the sun. Given a cuboid shape, as you described, we have 1 cubic lightyear of space to deal with. Or $9,460,528,400,000,000m^3$.

The sun operates at $3.8 * 10^{26}$ watts. Multiply this out and our enclosed universe sees an average increase of unleashed energy (radiation, infrared, visible light, etc) to the tune of 40.17 Gigawatts per cubic meter, or roughly twice as much power as you'd see on the Space Shuttle's pad during launch. Due to conservation of energy, this power isn't going to go away. Not all of this power is thermal in nature, but a lot of it is. Our little box universe is going to get very hot, very fast. Or the compounding radiation would kill us all. One of those. See here for what happens when you apply gigawatts of power to a cubic meter of space.

But, assuming we can survive that (somehow?) because some system is in place to handle that energy safely...there could be a really cool effect that we get from this small universe, and is plenty of motive to look to the skies.

We can look into our own past

Because the Earth is one light year away from itself, that means that we can see another copy of ourselves, one year ago. Obviously, a light year is too far away to visually see details by looking with an optical telescope, but we can take scientific readings on the past state of our planet.

There would be a huge challenge to this though. Because every light year is another copy of Earth, there is going to be a tremendous amount of Noise (in the form of radio, light, etc) the further back in history we try to look. We are going to need exceedingly advanced systems to be able to look through all that noise to look back any distance...but if we pull it off...

If we look far enough, we could see the dawn of Earth...and the birth of our little universe. By studying the Past Earth, we could collect a much larger sample size of climate information and build more advanced and accurate weather prediction systems. Questions of Origin would be non-existent...we could just point our equipment to the skies and check.

Conclusion

Most likely, nothing would survive in this universe long enough before the thermal buildup sterilized/vaporized everything. But if we could survive...and somehow see through all the noise...you could look into the past and see the origin of Life and your own Universe.

• WRT thermal problems - You would expect the same to be the case with our present universe. Let's say the real universe that we live in is infinite. Then whichever way you look, you should see a star. How come the night sky isn't just a blaze of light? Why aren't we already cooked? There are infinite stars pumping out energy. Where is it all going? Aug 13 '15 at 18:44
• @chaslyfromUK We still aren't sure that the universe is closed. Or infinite. Or...well, much of anything. But, the unfortunate thing about plugging 'infinity' into any equation is that it breaks the equation. If there are infinite stars, then the universe must be infinite as well. So, an infinite number of stars pumping out an infinite amount of energy into an infinitely large space equals.... $\frac{inf*inf}{inf}$ Which equals...."UNDEFINED." Which one is more infinite? Stars or Space? As it is...we figure that space is simply too big for stars to heat up that much Aug 13 '15 at 18:52
• Ref here for why $\frac{inf}{inf}$ is undefined: math.stackexchange.com/questions/181304/… In your closed universe, we aren't dealing with infinity...we are dealing with a single star in a finite space. Aug 13 '15 at 18:54
• Okay, here's another argument. I read somewhere that in terms of physics, the sun is a perfect black body. That is to say it absorbs light that hits it and does not reflect any. If I look towards the nearest 'sun' in one of the six possible directions, it will hide the next furthest sun behind it. I will only ever see the nearest one. The rest form an infinite queue in its shadow. If we combine this with simply making the sun a weaker radiator, won't that do it? Aug 13 '15 at 18:58
• Unfortunately, nope. The sun may shield us when it is currently between us and the next iteration of it. But shift to the side, and the massively long conga line of stars are now visible peeking around the side of the sun and all of its copies. But even beyond that is the question of Conservation of Energy. The sun is a Fusion Reactor, converting the stored energy in atoms into thermal, electromagnetic, and radioactive energy. Energy cannot be destroyed. Thermal energy cannot be reclaimed (ref: Entropy). There is no way to make that energy go away. It is being released, it has to go somewhere. Aug 13 '15 at 19:07

Resonance

Eventually, we'll be a mature civilization, with a far better grasp of physics. At that point when can use the nature of our universe to create some unique effects.

Most importantly, because it's a closed loop we can create a resonance feedback loop using gravity or light waves. Anything we send off will show up again in a year, at which point we can re-enforce it by repeating the event. Eventually this will allow us to build up massively huge energy or space-time distortions that we wouldn't be able to create in a normal universe.

Now, it's impossible to tell what we could do with these effects, since we're not at that point yet. It could be anything from an energy source to scientific experiments, or even potentially creating a new universe if we can force a big-bang type event. Surviving it might be trickier, though...

I can see one direction to explore for a reason, and one concrete reason.

The direction to look at is communication delays. My first instinct is that there's no advantage to doing something to transmit a message over a year when the same message can be delivered by fiberoptics in milliseconds, but there's at least one case where this could be beneficial: commitments.

Right now we have this idea of cryptographic commitments, which are like a magician having the audience member sign a card. A real life example of using this is rolling a virtual die by having each party pick a number, add them, divide by 6 and return the remainder. Clearly whoever provides their number second can lie to get whatever roll they want. Cryotpgraphic commitments are the equivalent of handing the other guy a box saying, "In here is the number I will announce. I hold the only key, so nobody can forge that number... it's mine. We trade boxes, then trade numbers, then trade keys. That lets us both verify that the other didn't cheat." If you sit down and try to figure out how to cheat the system, you find there's no way to fudge your number, because the boxed commitment is basically a verifiable promise that you will use the given value.

Cryptographic commitments depend on cryptography, and there's always the question of whether someone has broken an algorithm without anyone knowing. A toroidal universe like you describe would offer a physical alternative: beam a message into space, towards other-earth. A year from now, the message will be received (on the other side of the earth). If its hard to fake signals like that, this could be a powerful signing measure.

The other reason is concrete: are we 100% proof-positive-swear-on-God's-name sure that the universe is simply toroidal? Science is never that sure. One might send messages out this way or that way, and listen for responses, just looking for anomalies which may suggest the world is even stranger than we thought it was.

• WE can tell it's toroidal (at least to a good degree of certainty) because the nearby reflections of the Sun appear only in the 6 faces of the cube. North, South, East, West, Up and Down. We'll see other Suns in other directions but they will be further away according to the angle we look. Aug 13 '15 at 18:50
• @chaslyfromUK "to a good degree of certainty" has rarely ever actually held up as "truth" for too long. Newtonian physics is a good example. Sure the regions where it doesn't apply don't appear in every day life... or do they? GPS depends on adjustments for relativity to work. You never know what science will come up with if they keep poking and prodding. Aug 13 '15 at 18:57

No, there is only one star, so no "interstellar" anything.

Communication within the solar system is useful, so we'll do that for certain.

Is there any use that humanity can find for this phenomenon or is there nothing to gain at all?

We can see one year into the past and theoretically beyond that. That might come in handy.

What does it mean for science and space-travel?

It's going to be a really hot little universe. The energy of the sun is not going to be pouring out to infinity, it's going to be coming right back around constructively and destructively interfering with itself. I don't know how to calculate how this would look, but I suspect life would not exist in such a universe.