It has been determined that when accelerating a mass towards light speed it gains mass, experiences length contraction, and time dilation. During such a period of special relativity what would a person feel with regards to length contraction? Other than the normal acceleration to propel them towards light speed would they feel their body being crushed in the direction of motion because of length contraction? Or would they feel nothing at all because all molecules and atoms remain in their same relative positions functioning normally as they would have done if nothing were occurring at all?
Basically, no, you wouldn't experience length contraction or time dilation or increased mass or any effects like that. You'd feel acceleration, like you feel when a plane takes off, but acceleration and effects from close to light speed velocity aren't related.
At .86 of the speed of light - time dilation would be 50%, So, lets say, You're traveling to Alpha Centauri, To people from earth observing you, it would take 4.3/.86 or about 5 years. But on the ship, it would appear to you that Alpha Centauri was 2.15 light years away and so, it takes you 2.5 years to get there. To the observer traveling at near light speed, the universe they observe changes, not them.
There's other effects like light would be blueshifted infront of you, redshifted behind and you'd get that weird warping effect where you'd actually see things that are behind you when you look ahead. Also, traveling that fast, hydrogen atoms in space become effectively radioactive and bits of space dust could do pretty significant damage to the ship, so in the reality, there would be noticeable effects, but theoretically in pure empty space it would be completely unnoticeable.
I think that's right, anyway.
You may feel the acceleration, but if you're not accelerating you won't notice anything.
Other people may see you moving and observe you contracting, however, from your reference frame, you are not moving at all, and hence you won't notice any length contraction of yourself.
If a "person" is a single entity with bodily integrity, then it follows that a person will never experience length contraction of any part of their own body, because the body parts do not move relative to one another at any great speed.