I’ve wondered since I was a kid how it could be impossible for something to travel beyond the speed of light. Given an infinite, expanding universe, galaxies are receding from us faster the farther away they are. There has to be a distance at which they would be receding as fast as the speed of light, relative to us.
Mathematics tells us anything beyond that is impossible. We live in the center of a knowable sphere, beyond which time as we know it has stopped.
I used to think our knowable sphere must be the roughly 3 kelvin background radiation we call the Big Bang. At some particular time perhaps it must, but I doubt this is that moment. I think probably the edge of our sphere lies somewhere farther than the Big Bang as we know it. Still, for all we can see, they might as well be the same.
Probably there is, or will be, an inhabited galaxy on the very edge of our knowable sphere. People in that distant galaxy perceive they are standing still, and we are the ones receding at the speed of light. What is more, they can turn around and see a vastness of rapidly receding galaxies beyond what we can.
As I understand it, mathematics tells us they and the galaxies beyond are all really at the same distance from us, in what I presume is an infinitely dense surface where relative velocity has collapsed all the space beyond into what we can know only as a singularity. Even that, time and space being what it is, we can see only in the glimmer of its most distant past.
Likewise, I presume mathematics tells people in that oh-so-distant galaxy that we are on the edge of their sphere, amidst their own Big Bang, most of which lies outside ours. They can barely know us, and yet they can also know another galaxy on the opposite side of their sphere from us. As inhabitants of that farther galaxy can know them, and another galaxy beyond, and so on, and on…
Each of us has our own knowable sphere, and each can surmise an infinity of knowable spheres beyond, like I just did. But each can only know its own.
That’s relativity (i.e., special relativity). At least, I think so. Often I wish I had the math skills to work it out for sure. (But not enough to actually learn how.)