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Science fiction has entertained and inspired millions of people and we should all be grateful for that but it has also distorted what people think space really is.

When you consider the scale of space it becomes pretty understandable why the Milky Way isn't teeming with civilizations sending large amounts of mass all over the galaxy. A realization one comes to despite the facts that it has taken humans a blink of an eye (on a galactic timescale) to go from tools to rockets and the Milky way is billions of years older than the entire history of the Earth.

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I blame Star Wars, kinda. Watching it with my kid, I can't help but notice that everywhere they travel in space -- even by accident -- they end up by a planet that can support human life in terms of temperature, atmosphere, and gravity. Mandalore (the Mandalorian home planet, natch) has a moon that doesn't only support life; it also has the exact same gravity as Mandalore!

Sentient life in hospitable environments is as unavoidable in the Star Wars universe as it is absent in ours.

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Seriously even the nearest star is 6,200+ years at Parker probe speed.
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If we’re talking about human technology available in a few hundred years, don’t discount far more exotic options. I’ve heard people talk of theoretical terrestrial lasers pushing on tiny probes. With an absolutely gigantic laser and magical material at the back of the probe that won’t instantly vaporize there’s enough energy to get something the size of a smartphone up to a reasonable proportion of the speed of light.

I can’t prescribe this theoretical technology to the problem. But I also think it’s unreasonable to set the limit using known technology and then discount the idea altogether. We have no idea what will be possible in 300 years.

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Exactly. Imagine what would be possible after a billion year of technological evolution, heck even just 100'000 years. We already know that space time metric engineering is theoretically possible within our current understanding of physics, we don't have either the technology or access to energy density necessary to do it. And that's only within our limited understanding of how the universe works.
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Note that you can't use these lasers to slow down the probe, which will dramatically limit the things the probe can do at the destination. I'm not even sure what kind of interesting things a probe the size of a smartphone could do, let alone phone home.
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