David Deutsch, Julian Barbour, and Roger Penrose have each spent the last few decades thinking very deeply about the nature of time, and have come to some very counter-intuitive conclusions.

David Deutsch, a physicist, is known as a pioneer in the field of quantum computers. His 1997 book The Fabric of Reality explores multiple universes, causality, free will, and time travel. For Deutsch, the "flow" of time is an illusion. Sure, there is a moment we call "now" and later another "now" that takes its place - but the old now did not evolve into, or move toward, the new one. Both moments, Deutsch insists, are quite static. Physics, he says, tells us nothing about time's "flow." "I think time has quite a reputation for being mysterious," he says. "There just are a few common-sense facts about it that we think we know. And the funny thing is, is that it's those facts that are wrong."

Julian Barbour is an independent researcher, a freelance theoretical physicist who also happens to have settled in Oxford. In his 1999 book The End of Time, he goes even farther than Deutsch, arguing that time itself does not exist - that it is merely a construct of the mind. The quantum universe, he insists, is static; only timeless "nows" exist. We have no evidence for the past, Barbour argues, other than our memory of it, and no evidence for the future other than our belief in it. All those nows, he says, are not a "sequence in time" within our universe - rather, they represent an array of universes, all of them frozen and unchanging. And what of time? It is "a mistake the mind has made," he says. "I would say of time what Laplace said to Napoleon about God: 'I have no need of that hypothesis.'"

One of the implications of this "timeless" perspective is that we are all, in a sense, immortal. Each stage of a person's life, Barbour argues, exists permanently in some particular universe. "You" as a young child co-exists with "you" as a young adult and "you" as a senior citizen, simultaneously, somewhere in this vast set of universes. Julius Caesar, he says, is just as alive as you are.

Roger Penrose is a mathematical physicist; he's known for establishing the existence of black holes, and for suggesting a link - however controversial - between quantum mechanics and consciousness. He is also the author, most recently, of The Road to Reality: A Complete Guide to the Laws of the Universe, a hefty tome of 1,000-plus pages.

For Penrose, as for Deutsch and Barbour, the flow of time is illusory. In relativity, Penrose reminds us, "one has just a 'static' four-dimensional space-time" - three for space and one for time - "with no 'flowing' about it. The space-time is just there and time 'flows' no more than does space." It is only our conscious experience that seems to impose a flow onto this entity that we call time; our theories of physics make no mention of it. In other words, says Penrose, the puzzle of time is caught up with the puzzle of consciousness. And consciousness, at least for Penrose, is something we are not yet equipped to tackle. We'll only come to understand the mind, he argues, when we develop a more complete theory of physics - that is, when we finally unify quantum theory with Einstein's theory of gravity, known as general relativity. In the meantime, he can only muse that time "is not what we think it is... It's not a steady progression - certainly not a sort of universal steady progression."