You will have had enough time for that before you start moving really fast. (Also, philosophizing is usually a very slow process anyway.)
(Some people don't even believe the Earth is round. They think that their local tangent space is all there is too it! That's how small we are.)
The equivalence principle is the opening from special to general relativity, I don't think ajconway was confusing the two at all!
But then I got to wondering if our bodies aren't critically entangled with our Earth ecologies in various time sensitive ways, and realized that I don't know the answer to this question.
(I.e. https://arxiv.org/abs/quant-ph/0004105 )
So my second question is treating the human body as being meaningfuly physically entangled with it's environment and as being in some sense unified with it. Accelerating a body away from Earth at 1g might be akin to cutting off a limb and expecting it to survive on its own. I don't know if this is the case, but it seems possible.
From the point of view of conventional, reductionist models of human biology, the only basic physical health effects, given a reasonably humane spaceship life, would be the risks of collision.
Otherwise, I'd think 1 g would actually make a space journey more livable!
(Velocity is entirely relative, so traveling near the speed of light really doesn't mean much of anything in terms of basic physics/chemistry in the traveling frame. Physics undergrads are told that: light/physics under 1g of acceleration, by the theory of general relativity, is going to behave in exactly the same way as light/physics under 1g of gravity from mass.)
Now, as far as psychological/spiritual/emotional health are concerned, that's another matter. Relativistic effects would extract you from the context of time that gives meaning to all of your relationships with other Earth life, and with Earth itself. It'd be very deep.
Okay but now I'm remembering the article recently shared about Posner molecules and the possibility of meaningful quantum biological organizations in the body.
If our bodies physically depend on, in some yet to be articulated way, quantum information being exchanged/entangled ecologically, and if we depend on the synchronicity of these exchanges (say for example to inform some deeper biological sense of meaningful time)... Well then moving close to the speed of light would take those processes to a different tempo. To what degree are our physical bodies in temporally dependent relationships with their environment or ecologies? How critical are these relationships to basic functioning?
Now I have to agree that we don't know what effects on physical health might be!