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All for the cinematography :) I will say that there's a small caveat in really extreme situations like close to a black hole. Spacetime gets so warped there that your head and your feet take very divergent paths through spacetime, enough to stretch you out and even break you apart at the atomic level. You'd definitely notice that...
Oh boy, special relativity is another fun one. So here's the thing: there's no "universal speed" that you're moving so you're never any closer to c no longer how long you accelerate for. To accelerate is to change your reference frame and there are no special reference frames.
Which is to say that any physical test you could run inside your ship will give you the same result, always. Accelerate for 13 billion years at any rate and check the the how fast light moves within your ship, the answer is always c.
This is where the name relativity comes in. You have to think in terms of relative speed. Your speed relative to earth will indeed advance closer and closer to c but never reach it. There's a bunch of really wild and crazy implications behind this.
Like that acceleration doesn't change the relative speeds of things uniformly. Keep accelerating at 1 meter per second per second and every second Earth's relative speed changes by less than 1m/s. And look up relativity of simultaneity, another consequence of special relativity. It's fascinating stuff.
ah, right. In a ship travelling with c, for someone outside the ship, I turn on the lights and observe the light to travel with c. For that external observer the light from my lamp travels at the same speed as my ship
My mind was already bent! ;)