When I'm floating in air (no gravity involved), I can imagine that when I blow out air, I will move in the opposite direction to the air I blow out. I will move because of the asymmetric air pressure on my body.
But what will happen if I suck in air? The air I suck in will hit me and send me backward. At the same time, total momentum should be conserved. So if I suck in air, my body just has to move forward, to conserve total momentum. So how does sucking in air produce forward momentum? Is the outside air pressure involved (which is not the case with blowing)?
Now imagine that I magically can inhale air for an indefinite time. Will this be the reverse process of blowing? Clearly not, because the air I blow out will be free, while the air I suck in will end up in my lungs. Only the time-reversed blowing out (which looks like inhaling) will be the same. I give a velocity to the air I suck in, but at the same time (or somewhat later) it stops in my lungs. So in total, I give no momentum to the air. Does this mean that I can't accelerate? Or maybe only at the moment I suck the air in?
This is what I think: At the moment I start to suck the air gets momentum which is directed towards me. As a result, I have to get momentum in the opposite direction. How?? I'm not sure, but I have to acquire it, in accordance with the conservation of total momentum. So initially I get some small velocity (ignoring air friction). If the suck is stationary, there is no net increase of air momentum, so I will keep my initial momentum.
What would happen if I could suck the air in at an increasing rate (or, more realistically, if I stop the suck)? Will I accelerate (or will I have zero velocity after the suck, to be left with a displacement only)?