Starting with 7.4 billion people in 2016 and a population growth rate of 1 % per year we will reach the carrying capacity of Earth in less than 1400 years - the body heat alone will raise the surface temperature above the boiling point of water.
Once we reach the carrying capacity of Earth - no matter when that is - and decide to move into space we have 2685 more years until we run out of places to live in the Milky Way assuming 400 billion stars and one Earth-like colonizable planet per star.
Unfortunately 2685 years is not nearly enough time to reach all the stars in the Milky Way even if you would be traveling at the speed of light, you could cross just about 2 % in that time.
There are very real limits to the possible growth and we are talking about centuries or a few millennia. With a growth rate of 0.1 % per year one can push that to tens of millennia but that is still the blink of an eye in the grand scheme of things. And while I used population growth, things of course don't change if you substitute energy consumption per capita.
It is very unlikely the population of earth will continue to grow at 1%. In the best scenario, we will have worldwide development followed by a fall in fertility that it inevitably brings. In the more morbid ones, climate change, wars etc. will result in a large amount of the population getting destroyed.
Once we reach the carrying capacity of Earth - no matter when that is - and decide to move into space we have 2685 more years until we run out of places to live in the Milky Way assuming 400 billion stars and one Earth-like colonizable planet per star.
Unfortunately 2685 years is not nearly enough time to reach all the stars in the Milky Way even if you would be traveling at the speed of light, you could cross just about 2 % in that time.
There are very real limits to the possible growth and we are talking about centuries or a few millennia. With a growth rate of 0.1 % per year one can push that to tens of millennia but that is still the blink of an eye in the grand scheme of things. And while I used population growth, things of course don't change if you substitute energy consumption per capita.