I'm unsure about the 'ownership' of such a device. If someone denies ownership of something, do they loose all rights to it? "Is that your $20? No? Ok, must be

I'm unsure about the 'ownership' of such a device. If someone denies ownership of something, do they loose all rights to it? "Is that your $20? No? Ok, must be mine." Furthermore, if you trespass upon someone's property and leave something that you feel is important ($20) while trespassing, can you demand it back? Also proof of ownership is something I wonder about. Surely the FBI has serial numbers, but the person with the 'device' could deny them to enter their private property to inspect such. If i haven't done a crime, then you can't get a warrant to search my place for such a device. Should i find such on my motorcycle, I'll simply attach it to the nearest 18-wheeler I find, or mail it around the country.