Expanding on my earlier look at one of the motives that might (but probably won't) impel human beings to colonize the galaxy, I'd like to examine a second colonial motive – the acquisition of scarce resources – and the reasons why it will probably not create a galaxy-spanning human civilization.
We can certainly find plenty of valuable resources beyond Earth's atmosphere: precious metals like iridium, germanium, osmium, and platinum, and “volatiles” (to use John Barnes' term), particularly water ice, which miners can use to generate water, oxygen, and rocket fuel. Pace television shows like V and Battlestar Galactica, water abounds in our Solar System: most asteroids are comprised of ice and carbon, as are the rings of Saturn and other gas giants, as are the countless comets that drift in the Oort cloud and occasionally fall sunward. Meanwhile, the asteroid belt offers mineral resources beyond the dreams of avarice. The hard SF writer and physicist Stephen Baxter estimates that even a fragment of a mid-sized asteroid (over 500 meters in diameter) could yield a trillion dollars' worth of rare and precious elements, and NASA estimates that our asteroid belt contains over one million asteroids of one-kilometer size or larger, of which 20-25% are of the nickel-iron and silicate variety likeliest to harbor more valuable metals. Other asteroids one may find in the Trojan Points (where Jupiter's and the Sun's gravity counter-balance one another) and in various solar orbits in the inner Solar system.
I think it very likely that other star systems also feature abundant resources. Earth-like planets might prove rare (depending on how broadly one interprets “Earth-like”), but as Norman Spinrad recently reminded SF readers, the Solar System is far from unique in its diversity of elements and ices and worldlets. Even interstellar space is “full of icy and rocky comets...Oort Clouds and Kuiper Belts...even free-floating organic molecules.” However, while one can imagine a future human civilization burning through 250,000 asteroids' worth of industrially useful metals, and a few thousand comets' worth of water, I find it much harer to imagine that civilization spreading at an exponentially increasing rate through the galaxy in search of new stellar systems to suck dry.
What will dramatically slow expansionist space miners is another concept developed by John Barnes: "you can't outrun compound interest." It takes resources - spacecraft building and maintenance, fuel and provisioning, crew recruitment and training, vacuum construction work, etc. - to set up extra-terrestrial mining operations and ship the end product to Earth. Those capital resources are not limitless and one could profitably employ them in other ways; using them to mine asteroids and comets incurs an opportunity cost, which (very roughly) equates to the interest rates that capitalist economies charge for the hiring of capital. Interest rates in 21st-century industrial economies are low and I suspect they will remain so in a space-faring civilization. However, interest payments grow and compound over time; even at one percent interest per annum, a loan will double in size in 75 years.
In the early-modern epoch, companies could profitably undertake trading missions (like voyages to China) that took several years to complete. But a multi-decade interstellar voyage needs to generate much higher profits to justify tying up resources for so long a period of time. At light speed*, spacecraft will take decades to travel between even relatively close star systems. A 50-year voyage would cost 165 percent of its initial investment cost after one factors in interest payments (or opportunity-cost-equivalents) of one percent per year. A longer voyage, say from Earth to the vicinity of Betelgeuse, would take over 500 years and require a return of more than 10,000 percent on the original investment to break even. A flight across the Milky Way would take 50,000 years and require a return on investment of 6 * 10 ^200**, assuming anyone at the bank will still care by then. (Note: they will.)
John Barnes, The Man Who Pulled Down the Sky (1986)
Stephen Baxter, Manifold: Space (2000)
Arthur C. Clarke, The Songs of Distant Earth (1986)
Norman Spinrad, “Very Hard Science Fiction,” Asimov's, June 2016 (quote 110)
* Interstellar spacecraft won't be able to travel at lightspeed, or anything close to it. Remember that Norman Spinrad quote about interstellar space? A spaceship traveling at a significant fraction of lightspeed will suffer ablative damage from hitting particles as small as hydrogen and helium atoms. One traveling at close to C will lose most of its hull before it finishes its voyage, especially if it hits something larger than a helium atom.
** The current gross world product of Earth is about $80 trillion, or 8 * 10^12 dollars. If every star system in the Milky Way had an Earthlike planet with the same economic output, they would generate approximately 8 * 10^23 dollars. Just sayin'.