I - the loose ball you see pictured before you - am a fumble.
I know this because I was jostled from the arm of one young Ben Rapistberger (I believe that is his name) prior to him crossing the plane of the goal line. By my very definition, I exist when Player A - in complete control of me - loses grasp of me, by sheer force or stupidity, which causes me to become possession-less and open to recovery by players from either Team A or Team B. Naturally, since I exist in a possession-less state, SOMEONE must recover me. I do not simply exist on a possession-less plane, infinite in my unrecovery by either party for an interminable amount of time. I do not simply UNexist?? Heavens, even the great cosmologists - your Carl Sagans or your Stephen Hawkings (though he IS a randy fucker) - would hardly agree! In fact, I have taken the liberty of computing an algorithm for you that would yield such impossible results. I call it the "Steratore Theorem". Please. Allow me:
Here, r = the ball, N = the force with which said ball was removed from the ballcarrier's arms and ∑= the sum of gofuckyourselfbecauseyourteamisnotwinning. Naturally, the answer to this equation is undefined.
So as you can see, it is hardly possible that the ball cannot belong to SOMEONE after a play is completed - one or the other team must retain possession regardless of the ruling on the field. Particularly under review, a play must occur in at least two ways: Option A - say the original ruling on the field or, Option B - an alternate ruling that sheds light on what REALLY occurred on the field, and as a byproduct, who retains possession.
For a final example, let us say that Team A throws a pass into the endzone to an open receiver. As the receiver reaches for the ball it appears as though he has narrowly managed to include both feet within the plane of the endzone. However, just as he is doing this a defender hits him, knocks the ball out of his hands and it is caught by another defender for an interception. The ruling on the field is that the receiver had both feet down and was within the touchdown plane. However, upon further review it is apparent that the receiver had only ONE foot down, thus making the now loose ball recovered in air by the defense an interception.
Just because you originally ruled the play a touchdown, would that make the alternate reality (that really actually happened) null, void and moot? Would you simply 'do over' and give the offense back the fucking ball? How is that much different than our player coming up with the ball after a crucial fumble, supported by several refs calling 'white ball' and admitting we came up with it? Why does the poor officiating of one play negate the reality that existed LIVE on the field??
The world may never know....