- View SourceTheory of Everything does not Exist?

Hawking gives up on there being a Theory of Everything. The way that the mainstream tries to understand things just does not work.

Article below from New Scientist 5 April 2003

THE IMPOSSIBLE PUZZLE:

How much can we ever know about the Universe? The world's most famous living physicist has had a change of heart, as Michael Brooks reports.

On the closing page of his famous book A Brief History of Time, Stephen hawking celebrated the idea of a theory of everything that could unify all the forces of nature. He argued that it would be the ultimate triumph of human reason: "for then we would know the mind of God".

The controversial statement gained the author great notoriety. It read like a declaration of science's supremacy over religion and philosophy, while many critics saw it as a sign of supreme arrogance. Perhaps they were right. Today, 15 years after Haw king's book was published, it seems the Cambridge cosmologist has changed his mind.

"Up to now, most people have implicitly assumed that there is an ultimate theory that we will eventually discover. Indeed, I myself have suggested we might find it quite soon," he told an audience this week in Davis, California. But now he has doubts. "Maybe it is not possible to formulate the theory of the Universe in a finite number of statements." If this is true, we can kiss goodbye to the idea of a theory of everything.

Hawking's turnaround has been prompted by his work on one of the most advanced ideas in physics: a would-be theory of everything called M theory. This monolith is not so much a single idea as a basket of string theories, all of which build on the idea that matter and energy arise from the vibrations of tiny subatomic strings.

String and M theories were created to tie together Einstein's thinking on gravity with quantum theory, the description of how matter and energy interact on tiny scales. But although individual string theories are successful in limited conditions, they cannot deal with all eventualities. Even together, they do not truly describe reality.

The problem physicists face with M theory is one that we might have seen coming for decades, Hawking says. It comes from the work of the Austrian - born mathematician Kurt Godel, who in 1931 proved that there exist true but unprovable mathematical statements. And, Hawking believes, the same may well be the case in physics.

Godel's work blew mathematicians off their feet. The prevailing notion at the time was that in formal mathematical systems - which are built up from a handful self- evident statements, or axioms - a mathematician could prove any theorem true or false simply by the reasoning from the axioms.

In 1900, the renowned German mathematician David Hilbert had set out a list of 23 problems as a challenge for the new century. He argued that every mathematical problem had a solution: be clever enough, look hard enough and everything would be tamed. For thirty years, mathematicians celebrated the supremacy of their discipline. Then Godel came along. He showed that not every theorem could be proved from the axioms: mathematics was "incomplete."

Although this result might sound depressing, it has stimulated mathematics ever since, spawning a wealth of new understanding about the limits to what we can ever know. The British mathematician Alan Turing used Godel's finding to show that there are things a computer can never do. And IBM mathematician Gregory Chaitin used it to show that there exists a number, called Omega, that is real but utterly incalculable. Now Hawking thinks that Godel's result, or at least its analogue in physics, signals that the mind of God may stay hidden forever.

Godel's master stroke was to create the arithmetical equivalent of a sentence that refers to itself, such as "This statement cannot be proved true." If the statement is false, then it can be proved to be true, and there's a contradiction. So it must be true, but then it cannot be proved. The statement, then produces inconsistent results.

Hawking has a direct physical analogy for this problem. In days gone by, Newtonian reasoning told us that we could calculate the future, such as the position of a car racing along a road, simply by extrapolating from our understanding of the present. But these days of certainty are no more: modern notions of gravity and quantum theory show that this approach is inadequate. "We and our models are both part of the Universe we are describing," says Hawking. "We are not angels who view the Universe from outside."

This means that these physical theories are self-referential, as in Godel's theorem, so we shouldn't be surprised if they are inconsistent or incomplete. "The theories we have so far are both inconsistent and incomplete."

[[ME - I cannot resist a 'dig' here. It used to be that if a theory was inconsistent and /or incomplete, then this meant that the theory was wrong and needed to be replaced as per Kuhn's Structure of the Scientific Revolution. Now that the existing theory (and its variations) is found inconsistent and wrong, we are now expected to believe that 'it' is supposed to be like that, by what appears to be some 'bodged' reasoning.]]]

M theory is incomplete in a very real sense. It assumes that we can define the Universe's "wave function" - the full quantum description of its properties - at each and every point in space. In an infinite universe, this would require an infinite density of information, but there's a fundamental problem with that idea.

In their work on black holes, Hawking and Jacob Bekenstein of the Hebrew University of Jerusalem have shown that the amount of information contained in a black hole is not proportional to its volume, as you might expect, but to the area of its boundary - the event horizon, inside which the black hole's gravity is so strong for anything to escape. This fact rules out any possibility that M theory can utilise an infinite density of information. "What we need is a formulation of M theory that takes account of the black hole information limit," says Hawking.

But Godel's shadow will loom large over that model. The information the model itself contains has to be represented by something - the arrangement of particles on magnetic tape, for example. After all, as the IBM physicist Rolf Landauer famously remarked, "information is physical". Arranging these particles costs energy, so the model will change the energy - and information - in the very system it is trying to represent. Just like Godel's arithmetic statement, it refers back on itself. So a theory of everything may be out of reach for ever.

Once again, you might find this conclusion depressing. But Hawking is sanguine. "Godel's theory ensured that there would be a job for mathematicians," he says. "I think M theory will do the same for physicists."

Stephen Hawking first presented these ideas in his lecture "Godel and the end of physics" at the Dirac centennial celebration at the University of Cambridge.

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