Especially Einstein’s general relativity and quantum theory lead to a large number of proposals for time travel, in a certain sense, into the past, i.e. also to proposals for superluminal transmission of classical information. However, the step from theoretic proposals to a realization will be hard and expensive, if it can be achieved at all. Sending classical information into the past would create a problem that one could try to create an inconsistent history. A simple conceivable proposal for a solution is sketched, an exclusion principle which would exclude all inconsistent histories, i.e. they would not occur in reality, and instead one of the remaining conceivable consistent histories could occur, e.g., with correspondingly increased probability, i.e. the probability of all consistent histories would be enlarged by a factor which is described in the present text. The exclusion principle, and, e.g., alternative versions could be tested by conducting such experiments in future, however, such principles remain to be analysed, e.g., according to quantum field theory. For the conceivable case that transmission of classical information with the exclusion principle could be realized reliably enough over suffiecient distances, a large number of ideas for applications are presented, e.g., to solve hard computational problems extremely fast, applications within future computers, quantum teleportation, quantum machines, expensive machines, and robots. Different forms of exclusion principles are described and they could be tested by conducting these experiments. Detailed and, e.g., quantum field theoretic computations of corresponding experiments remain to be conducted in future.