Can you accelerate forever and never achieve the speed of light?
Can you get in a spaceship and achieve gradual acceleration so that the people inside would experience 1G. Perpetually?
Just imagine. A tall spaceship, many floors, all experiencing “gravity” like at Earth. Forever.
That’s 1G. To achieve it you have to accelerate the spaceship, and that would, over time, require more fuel than you could carry.
Still, is it possible to accelerate gradually, given unlimited or even an unknown fuel source, so that everybody on board experiences regular Earth gravity type experience?
Logic will tell you no. Eventually you are going to reach the speed of light.
You’d be wrong.
Your speed is relative to where you are now. That’s why it’s called relativity.
For example. You are already going fast. You’re not standing still on Earth by any means. The Earth is rotating on its access, and then it’s going around the sun in an orbit, and the sun is going around the center of the Milky Way Galaxy.
That being said, you’re accelerating a spaceship in relationship to what?
The answer is relative. Try to get your head around this. You are accelerating in relationship to yourself.
In that sense, there is no speed limit of light because everything is relative.
No matter how fast you are going in relationship to your starting point, if you turn on a flashlight and point it ahead, the beam will leave your flashlight at the speed of light. If you point it backwards, it will do the same.
Given that you had unlimited fuel, you could accelerate so that you have 1 G forever.
Problems happen if you were trying to arrive somewhere, it would be a real difficult thing to slow down.
Going back to the original premise: A tall spaceship, many floors, all experiencing “gravity” like at Earth. Forever.
Wait for it… wait for it…. Flat Earth society.