The Future of Quantum Cosmology by S.W. Hawking
The Future of Quantum Cosmology by S.W. Hawking
Department of Applied Mathematics
and Theoretical Physics,
University of Cambridge,
Silver Street, Cambridge CB3 9EW,
United Kingdom.
August 1999
Abstract
This is a transcript of a lecture given by Professor S. W. Hawking for the NATO ASI conference.
Professor Hawking is the Lucasian Professor at the University of Cambridge, England.
In this lecture, I will describe what I see as the frame work for quantum cosmology, on the basis of M theory. I shall adopt the no boundary proposal and shall argue that the Anthropic Principle is essential, if one is to pick out a solution to represent our universe from the whole zoo of solutions allowed by M theory.
Cosmology used to be regarded as a pseudo science, an area where wild speculation was unconstrained by any reliable observations. We now have lots and lots of observational data, and a generally agreed picture of how the universe is evolving.
But cosmology is still not a proper science, in the sense that, as usually practiced, it has no predictive power. Our observations tell us the present state of the universe, and we can run the equations backward to calculate what the universe was like at earlier times. But all that tells us is that the universe is as it is now because it was as it was then. To go further, and be a real science, cosmology would have to predict how the universe should be. We could then test its predictions against observation, like in any other science.
The task of making predictions in cosmology, is made more dicult by the singularity theorems that Roger Penrose and I proved.
The Universe must have had a beginning if
1. Einstein’s General Theory of Relativity is correct
2. The energy density is positive
(1)
3. The universe contains the ammount of matter we observe
These showed that if General Relativity were correct, the universe would have begun with a singularity. Of course, we would expect classical General Relativity to break down near a singularity, when quantum gravitational e ects have to be taken into account. So what the singularity theorems
email: S.W.Hawking@damtp.cam.ac.uk
1
are really telling us is that the universe had a quantum origin, and that we need a theory of quantum cosmology, if we are to predict the present state of the universe.
A theory of quantum cosmology, has three aspects.
Quantum Cosmology
1. Local theory – M Theory
2. Boundary conditions – No boundary proposal
(2)
3. Anthropic principle
The rst is the local theory that the elds in spacetime obey. The second is the boundary conditions for the elds. I shall argue that the anthropic principle is an essential third element.
As far as the local theory is concerned the best, and indeed the only, consistent way we know to describe gravitational forces is curved spacetime. The theory has to incorporate super symmetry, because otherwise the uncanceled vacuum energies of all the modes would curl spacetime into a tiny ball. These two requirements seemed to point to supergravity theories, at least until 1985. But then the fashion changed suddenly. People declared that supergravity was only a low energy e ective
theory, because the higher loops probably diverged, though no one was brave (or fool-hardy) enough to calculate an eight loop diagram. Instead, the fundamental theory was claimed to be super strings, which were thought to be nite to all loops. But it was discovered that strings were just one member of a wider class of extended objects, called p-branes. It seems natural to adopt the principle of p-brane democracy.
P-brane democracy
We hold these truths as self evident:
All P-branes are created equal
(3)
All p-branes are created equal. Yet for
1, the quantum theory of p-branes diverges for higher
p
< loops. I think we should interpret these loop divergences not as a break down of the supergravity theories, but as a break down of naive perturbation theory. In gauge theories, we know that perturbation theory breaks down at strong coupling. In quantum gravity, the role of the gauge coupling is played by the energy of a particle. In a quantum loop, one integrates over all energies. So one would expect perturbation theory to break down.