I assume that by 'the world' you mean humans in the world and by 'owing something to you' you mean to be obliged to provide you with something? Or nothing, in this case.
Let's say I approach a stranger on a street and say: "You owe me 20$." Without any intention of harming another person if I won't get my way. Would the stranger be obliged to provide me with 20$?
Let's say I drive a car and... the policeman stops me to chat and fines me with 20$. Let's say I broke some law or rule, there is a recording with the clear evidence of it; there might be the consequenses if I would refuse to pay. Would I be obliged to provide the policeman with 20$?
A group of strangers approaches me and say: "You owe me 20$." They look like they wouldn't shun of hurting people, judging by their tattoos, quasi-gangsta clothes, and a knife casting its edge on you. Do I owe them 20$?
I think that obligation has sufficient weight if it's warranty succeeds to enforce this obligation. The warrant here is anything that forces obligation. A brute force, a fancy document, a keen mind, an ingrained belief... And what makes us follow the obligation is a personal benefit, I think. We see its worth to follow if we gain something from it, or trust the authority, retain personal integrity, suchlike.