Illustrated Theory of Everything: The Origin and Fate of the Universe by Stephen Hawking Page A

the right size of variations of the microwave background. The infla-tionary model showed that the present state of the universe could have arisenfrom quite a large number of different initial configurations. It cannot be thecase, however, that every initial configuration would have led to a universelike the one we observe. So even the inflationary model does not tell us whythe initial configuration was such as to produce what we observe. Must we turnto the anthropic principle for an explanation? Was it all just a lucky chance?That would seem a counsel of despair, a negation of all our hopes of under-standing the underlying order of the universe.
QUANTUM GRAVITY
In order to predict how the universe should have started off, one needs laws thathold at the beginning of time. If the classical theory of general relativity wascorrect, the singularity theorem showed that the beginning of time would havebeen a point of infinite density and curvature. All the known laws of sciencewould break down at such a point. One might suppose that there were new lawsthat held at singularities, but it would be very difficult even to formulate lawsat such badly behaved points and we would have no guide from observations asto what those laws might be. However, what the singularity theorems reallyindicate is that the gravitational field becomes so strong that quantum gravita-tional effects become important: Classical theory is no longer a good descrip-tion of the universe. So one has to use a quantum theory of gravity to discussthe very early stages of the universe. As we shall see, it is possible in the quan-tum theory for the ordinary laws of science to hold everywhere, including at thebeginning of time. It is not necessary to postulate new laws for singularities,because there need not be any singularities in the quantum theory.
We don’t yet have a complete and consistent theory that combines quantummechanics and gravity. However, we are thoroughly certain of some featuresthat such a unified theory should have. One is that it should incorporateFeynman’s proposal to formulate quantum theory in terms of a sum over histo-ries. In this approach, a particle going from A to B does not have just a singlehistory as it would in a classical theory. Instead, it is supposed to follow everypossible path in space-time. With each of these histories, there are associateda couple of numbers, one representing the size of a wave and the other repre-senting its position in the cycle-its phase.The probability that the particle, say, passes through some particular point isfound by adding up the waves associated with every possible history thatpasses through that point. When one actually tries to perform these sums,however, one runs into severe technical problems. The only way around theseis the following peculiar prescription: One must add up the waves for particlehistories that are not in the real time that you and I experience but take placein imaginary time.
Imaginary time may sound like science fiction, but it is in fact a well-definedmathematical concept. To avoid the technical difficulties with Feynman’s sumover histories, one must use imaginary time. This has an interesting effect onspace-time: The distinction between time and space disappears completely. Aspace-time in which events have imaginary values of the time coordinate issaid to be Euclidean because the metric is positive definite.In Euclidean space-time there is no difference between the time direction anddirections in space. On the other hand, in real space-time, in which events arelabeled by real values of the time coordinate, it is easy to tell the difference. Thetime direction lies within the light cone, and space directions lie outside. Onecan regard the use of imaginary time as merely a mathematical device-ortrick-to calculate answers about real space-time. However, there may be moreto it than that. It may be that Euclidean space-time is the fundamental conceptand what we think of as real