Thanks for the response. I would like to understand Einstein's theory of relativity better. Asking these questions is helping me to understand it better. (I think/hope.)
But the way I see it now, if the speed of light is some finite distance per unit of time, and the earth is infinitely accelerating, it seems inevitable that at some point the speed of light will be exceeded. (Infinity > x where x is a finite number)For sure from the perspective of a fixed position in space. I too believe that the velocity would be limited to c. Which is why it does not seem to me that infinite acceleration is possible. At any rate, if that was the case, I guess the sun moon and stars would also be infinitely accelerating in the same direction or we would soon leave them in the space dust.
Also, doesn't this just create a bigger problem? What is causing this acceleration? it seems like it would be something as hard or harder to believe than the theory of gravity.
I'll answer the last part first. You ask
"Also, doesn't this just create a bigger problem? What is causing this acceleration? it seems like it would be something as hard or harder to believe than the theory of gravity."
About all I can say is, in my humble opinion, yes, "dark energy", whatever that is and yes, I find gravity much easier to believe.
But (there's always a
but) gravity caused by a finite diameter (24,900 miles) flat earth would point down in the centre (their North pole), but as the edge was approached it would start to point not quite down, but have component pointing in towards the centre as well. On earth gravity is always down, at right angles to to the surface.
So flat earthers have to deny gravity, even though in my opinion it is well supported by evidence and measurements. So, Newton, Cavendish and others often get demonised.
As to explaining relativity, it's a big topic.
The need for something like relativity probably arise with James Clerk Maxwell's claim that the electromagnetic properties of "space" were independent of location and (uniform) velocity.
Since the velocity of light (electromagnetic radiation) is determined by these properties (magnetic permeability and electrostatic permittivity), the velocity of light must be the same for any observer, no matter what their (uniform) velocity.
Rather than makin a long post I will give a few references. See what you make of them.
Special Relativity SimplifiedSPECIAL RELATIVITY EXPLAINED BY THOUGHT EXPERIMENTSSpecial relativity.
There is also this video, I have no idea what it is like, here's hoping it helps
Best of luck! Then there's General Relativity, but that's a whole new ballgame.