static methods & instance variables in an interface
An interface is meant to be a contract that is to be followed by a sub class. A contract is meant to be something like a rosetta stone which classes can look up to, to make their own interpretation of what that contract should do.
Static methods cannot be 'overridden' as such, so inheritance would not work. Instance variables do not make sense since there is only one interface. You cannot instantiate an interface, so there is no question of using instance variables.