What is a Capability

Computer science has no theoretical foundation within which there is a concise definition of a capability. Here are some short attempts and dissections thereof.
  1. In a computer system, an unforgeable ticket, which when presented can be taken as incontestable proof that the presenter is authorized to have access to the object named in the ticket.
My description of capability and object: This is not very satisfactory. One can speak of call or sending a message. The message primitive demands describing how the reply is made. This differs in good capability systems. A call primitive looses the similarity between the messages involved with the call and with the return. Further not all messages are part of either.