A laser beam consist of photons. Space is almost empty but not completely empty. There are a few atoms per cubic meter in interstellar and intergalactic space. So your beam gets eroded when your photons collide with some atoms. Eventually photon count on your beam reaches to zero and you have no longer have a laser beam.
If it does not hit *anything*, yes.
It does not need a solid object, even a gas molecule could take out energy from a light wave.
That said, it actually takes no energy at all. It’s pretty easy. The conservation of energy says, that as long as you do not have any force counteract, there is not energy needed to continue whatever you are doing.
It doesn’t take more energy to go further because it doesn’t use any up traveling. It’s just a clump of energy that happens to be moving in the same direction.
Same as how you can see stars for a super long distance, but it requires less energy because it’s only moving in a specific direction instead of everywhere.
If you were to remove Earth’s atmosphere and assuming that space is a perfect vacuum, which it is definitely not, and there were no obstruction to absorb the photons, then yes, it would continue to infinity. However, due to the inverse square law, the light would spread out over the vast distance to the point where it wouldn’t be detectable in a meaningful way. The individual photons coming from your laser would still continue though until something stopped it.
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