In 1993 I published a novel kind of theory of psychic phenomena in a book entitled 'Shadow Matter And Psychic Phenomena'. Although I devoted a whole chapter to the issue of possible survival of the human personality after bodily death, I did not go remotely far enough. Contrary to common-sense, it seems physically quite possible that an important component of each of us survives death. It is a part of this component which during life and death carries our memories and our ability to think, feel etc., Perhaps a valuable guide to the possible machinery of death and dying might be obtained by attempts to elucidate the conceivable mechanisms of Near Death Experiences (NDEs). Various people have studied these for many years. My own theorising begins with a critical reappraisal of some of these ideas on NDEs. In the course of the argument I hope to persuade the reader of the advantages of a theory based in the new physics of shadow matter.