Giving life to Schrodinger?s cat
Mathematician Roger Penrose on the joys of Escher, the tyranny of PowerPoint and the universe in between, writes Amitava Sanyal.india Updated: Nov 21, 2006 03:04 IST
Can the explanation of life, universe and everything lurk in a curiously kaleidoscopic image of angels and demons? Mathematician Roger Penrose certainly thinks so. Sitting in his hotel room in Delhi, the Emeritus Rouse Ball Professor at Oxford University burrows over ‘Circle Limit IV’, a woodcut by Maurits Cornelis Escher. This is what Penrose is using to explain his theory of the Big Bang, that grand moment of expansion. “I wonder why some artists considered him a good draughtsman, something less than an artist.”
Penrose’s fascination with Escher began around 1954 when he, as a graduate student in Cambridge, went to Amsterdam to attend a congress of mathematicians. There was an Escher show at the Van Gogh Museum. It inspired Penrose to produce the ‘tribar’, something he has described since as “impossibility in its purest form”. He showed it to his father, Lionel, who then produced some drawings of buildings with impossible steps that can go on ascending or descending, depending on the way you look.
“We wrote an article on it and sent it to the British Journal of Psychology, simply because we didn’t know what the subject was and my father knew the editor,” says Penrose. “We made a reference to Escher and sent him a copy. He was stimulated and produced the ascending and descending stairs.” Penrose will use some of the Dutch master’s ‘impossible pictures’ as a lead-in to mathematical ideas in a forthcoming book.
The fine art of science
Art has coloured the Penrose family line for long. The 75-year-old traces his formidable lineage: “My father’s father, James Doyle, was a painter. One of his four sons was Roland — a Surrealist painter who was friends with Picasso and Man Ray. My father would sometimes go out into the country and sketch.”
“I occasionally used to do that, but not any more,” says the man whose only patent is on a tiling pattern. The pattern took forward Robert Berger’s mathematical proof that it is possible to tile a plane aperiodically, without repetition. Berger took 20,426 different tile patterns to do it; Penrose did it in two. Nobody has done it with one pattern yet.
But Penrose attracted some funny faces later when he sued Kimberly-Clark UK, the manufacturers of Kleenex toilet paper, for embossing a line of their TP with his patterns. He settled the case out of court.
About the same time four decades ago, Penrose was also working on what may have happened some five billion years ago, during the Big Bang. His work on the singularity theorems arising out of Einstein’s general theory of relativity, along with work by his collaborator Stephen Hawking, proved, among other things, the existence of black holes.
So, it was only fitting that this year, the centennial of the theory of relativity, Penrose delivered one of the Annus Mirabilis lectures that the Centre for Philosophy and Foundations of Science had organised to celebrate Einstein’s path-breaking work.
At another lecture, Penrose again uses ‘Circle Limit IV’ to illustrate. “You take the smaller angels and demons towards the edge,” he says, wielding a tong. “You make them bigger and they become similar to the ones near the centre. The hyperbolic plain is represented in totality within (the rim). But then, if you are only interested in the conformal geometry — one that knows angles, not sizes — then you can continue beyond the rim.”
The cosmological equivalent is that our Big Bang, any Big Bang, can “join on” to the next Big Bang without a Big Crunch, or a grand moment of contraction, in between. One problem is, such a theory would sit oddly with the well-respected Second Law of Thermodynamics that says entropy — roughly, the measure of disorder in a system — should increase with volume. So, if the current universe’s point of greatest expansion has to morph into the beginning of the next, the entropy at that point would be very high and very low at once. How to reconcile the two? Let us say it would just go on expanding by giving rise to another universe. What happens to our universe then? “This is where black holes come in.”
A brief bit about Stephen
“Stephen had this wonderful idea about the temperature of black holes with the implication that that it would radiate out. The information would be gone from the universe. Lots of people didn’t like the idea. A couple of years ago, Stephen recanted and agreed with them. I thought he was right earlier. The new scheme I have here really needs black holes to swallow up the information,” says Penrose. So that’s where parts of our universe go.
“The trouble with Stephen is that he is too wedded to conventional quantum mechanics,” says the Oxford professor of his Cambridge compatriot. “Since I am not, I always thought black holes were a part of the argument why we need a revolution (in physics).”
Penrose has been talking about the revolution for a long while. He has often quoted physicist Paul Dirac in calling quantum mechanics “a provisional theory” and underlined the doubts two other founding fathers of the theory, Einstein and Erwin Schrödinger, had about it. In the current entanglement, people have been mostly trying to apply the quantum idea to relativity, and the two often do not agree. Penrose would like “a more even-handed marriage”.
He believes the next Big Shift can come from observation, rather than theory. “If it’s a purely intellectual thing, then you need someone with the insights of Einstein. But if it’s experimentally driven, it can come about like how quantum mechanics came about — through curious observed facts.”
Dirk Bouwmeester and his team at the University of California , Santa Barbara are observing some such curious facts. They are proposing to put a very tiny mirror in two positions at the same time. It would be something akin to Schrödinger’s cat, which could theoretically be alive and dead at the same time.
After a while, the sketch-pen colours of the slides start swimming. Why take the trouble of drawing them? “Something is lost in PowerPoint,” he says. “If you ask me what, I might say something simplistic like ‘the personal touch’. But I am sure something is lost.” Lost like information through a black hole? Lost like me listening to Sir Roger talk about life, the universe and everything?
First Published: Nov 21, 2006 03:04 IST