Griffiths Much of modern technology, including computers, lasers, and magnetic resonance imaging, utilizes the principles of quantum mechanics, the physicist's most fundamental theory of nature, and would not be possible if this theory had never been invented. Given this success, one might suppose that quantum mechanics would by now be as well understood as other foundation stones of modern science, such as thermodynamics and relativity theory. On the contrary, as Richard Feynman, one of the great physicists of the 20th century, once put it, "Nobody understands quantum mechanics." The lack of a clear understanding, to which Feynman was referring, has not, obviously, prevented quantum mechanics from being applied to a vast range of technological devices. But students are frustrated when they try and learn the subject from teachers and textbooks whose lack of clarity illustrates the truth of Feynman's remark. Clearing up the conceptual mess in its foundations would certainly not detract from, and might even assist in, the technological applications of quantum mechanics, and could well prove important for future developments in areas such as quantum computation and quantum cryptography, where impressive advances are accompanied by equally spectacular gaps in our current understanding.
This research project, as indicated in the title, has a double focus. One is the use of quantum histories - a promising approach developed by various people including Murray Gell-Mann, a Nobel laureate who at one time was Feynman's colleague at Cal Tech - for addressing and clearing up the conceptual difficulties in the foundations of quantum theory. Several major paradoxes, including the famous double slit, have been resolved using the histories approach, and this method gets rid of mysterious long-range influences that are present in some older interpretations of quantum mechanics, and which are hard to reconcile with relativity theory. However, up till now these new developments have been confined to the technical literature, and they need to be moved into classrooms and textbooks if they are to make the subject more accessible to the next generation of scientists. There is plenty of work to be done, both in making abstract mathematical formulations more understandable through simple physical examples, and in convincing teachers and textbook writers that students deserve something better than the traditional ("Copenhagen") approach, the one Feynman could not understand.
The second focus of this research is quantum information theory, the fundamental science behind both quantum computing and quantum cryptography. Classical information theory was developed half a century ago by Claude Shannon, and plays an important role in the modern theory of communication, as in the efficient use of weak radio signals to transmit information from distant space probes to the earth. Quantum information theory generalizes Shannon's ideas to situations where quantum effects are important, and while it has had some notable successes, it has also run into the following difficulty: Shannon's formulation is based on the use of probabilities, but incorporating probabilities into quantum mechanics in a consistent way is the source of many of the conceptual difficulties that troubled Feynman. The histories approach resolves the problem of quantum probabilities in a consistent manner that allows an immediate extension of many of Shannon's ideas into the quantum domain. Whether this provides a satisfactory foundation for quantum information theory remains to be seen, but it looks promising. If it succeeds, there will be a double benefit: a clearer understanding of what quantum computing and cryptography can and cannot do, and a new way to think about quantum mechanical processes in terms of the generation and transmission of information.
