Using https://en.wikipedia.org/wiki/Nuclear_pulse_propulsion we could, with currently conceivable technology, build spaceships that travel at several percent of the speed of light, and decelerate when they reach their goal. At 1% of the speed of light, we can cross go 100,000 light years in 10 million years. This is sufficiently short relative to the time that it took intelligent life to evolve that it would be a pretty good coincidence if there were two that just happened to reach that stage that close together.
Note that with the magic of exponential growth, a few probes sent long distances and then spreading out locally should be able to reach every star in a galaxy with surprisingly little extra time over simply making the trip.
Nuclear pulse propulsion might be possible and it might approach the initial assumptions, but unless your talking ounces of cargo reaching and slowing down from 1% light speed is not feasible. We can’t rely on hand waving science fiction, they would need to send enough infrastructure to booststap manufacturing of a replacement probe. Let’s lowball that at 1 Billion tons of cargo and run through the rocket equation for 10,000 ISP.
Even hand waving that we don’t have force fields to survive single gram impacts at 1% light speed. At those velocities anything is going to act like a massive shaped charge. Space is fairly empty, but when you start talking about the volume swept up across light years that’s really not a safe assumption.
70 years ago people generally assumed fusion was right around the corner. It’s only when you start building these things you get some idea of all the real limitations.
Sanity check. https://en.wikipedia.org/wiki/Project_Longshot was a NASA design that could use nuclear pulse propulsion to deliver 30 tons of payload from here to Alpha Centauri at an average speed of 4.5% light speed. That is with acceleration and deceleration. The same technology could let us go much farther - just with coasting in the middle.
Now it is absolutely true that we could not survive any significant impacts at that speed. However we also have data indicating that the interstellar medium is essentially empty.
Here is a sanity check. Per http://cdms.berkeley.edu/Education/DMpages/FAQ/question36.ht... the density of dark matter (that is, all the stuff that we can't see) is around 6x10^(-28) kg/cm^3. Since you arbitrarily said a gram, let's switch that to g/m^3, and we get 6x10^(-19) g/m^3. The distance to Alpha Centauri is on the order of 4x10^16 m. So a 1000 square meter surface should run into about a gram of "stuff". According to our best theories, most of it is currently unknown stuff, 99% of the rest is single atoms, and the vast majority of the rest is dust particles with sizes on the scale of waves of blue light.
Dealing with that dust and hydrogen is a serious issue. But the odds of running into pebble sized objects at random are pretty low. Heck, even microbe sized objects will be vanishingly rare. True, it will be a disaster if we do. But that translates in practice into, "There will be a failure rate for probes."
The size of a probe to bootstrap manufacturing seems likely to be a lot smaller than a billion tons of cargo. Don't forget, this is going to be encoded using technology that is as far beyond us as we are beyond building the pyramids. I think we can assume rather efficient storage/bootstrapping mechanisms to be available for us.
Work out the kenetic energy of a 0.0001 gram strike at 4.5% c.
Ignoring relativity it’s 9 x 10 ^6 J. By comparison, one kg of tnt is 4.184×10^6 J so that’s over 2.1 kg of TNT. Now reolize it’s much worse than that much TNT as it’s penetrating into your shield before releasing that energy. Even atom sized impacts are an issue at those speeds https://en.m.wikipedia.org/wiki/Sputtering
As to your sanity check, Alpha Centauri our closest star, if we are sending multiple probes then you need to targets much further out. Especially if we are trying to get somewhere approaching a straight line in 3D space. The 20th closest star system is 12 light years from earth and on the order of distances we need. Though this gets worse if you need specific kinds of star systems.
That’s pushing 3+ grams under your estimate and your 30 ton payload would need truly massive shielding. Or, you can have a 30 ton shield being activly maintained in front of a postage stamp sized cargo and possibly survive the trip.
As to that billion tons of cargo, it’s almost unimaginably better than current tech could do. We are talking either self sustaining habitats for hundreds of people or safe replicating near full AI on million year timescales. It’s got to gather energy and resources, build CPU’s, engines, etc to gather even more resources. It’s got to travel hundreds of years meaning redundancy and self repair on all critical systems etc etc the list just keeps going.
In terms of engendering from ancient Egypt to now the tallest structure is just under 6x as tall. Some things have improved vastly more and others even less. We simply can’t assume magic even on 10,000 year time scales.
PS: Longshort also used intercial confinement nuclear Fusion which we are no where near getting to work even in ideal laboratory conditions. It’s got a host of it’s own issues and is well into sci-fi territory, as in it might be physically possible but it seems unlikely.
Note that with the magic of exponential growth, a few probes sent long distances and then spreading out locally should be able to reach every star in a galaxy with surprisingly little extra time over simply making the trip.