FTSE 100
Dow Jones

Saturday, 4 September 2010

Clarification: the origin of the universe

The papers are full of stories about Steven Hawking denying that God created the universe, not that even Steven Hawking knows the answer to that. Of course, none of this is new, and the scientific theory behind it dates back to earleier work by Hawking and James Hartle, but there is now a book; hence the fuss.

Going back to the post war years George Gamow first proposed the big bang theory that is now widely accepted, but one of the problems with the theory is that it does not explain what may have occurred before the inflation of the universe. In an attempt to resolve this issue, Hartle and Hawking proposed another theory for the creation of the universe in 1983. The theory was based on the idea that the universe did not have a boundary, just as the earth does not have a boundary. For example, one may travel around the earth and not come to a boundary or fall off. In addition, the theory was based on quantum theory, a superset theory encompassing general relativity and quantum mechanics.

Quantum theory defines a wave function that describes all of the possible states of a quantum particle, such as an electron. The values of the wave function indicate the probabilities of the particle being found in the various states. For example, if the value of the wave function is high for a particular state, then the particle is likely to be found in that state. Conversely, a low wave function value suggests that the particle is less likely found in that state.

Hartle and Hawking's theory treated the universe like a quantum particle. As a result, they created a wave function that describe all possible universes. The wave function is assumed to have a large value for our own universe, and small, non-zero values for an infinite number of other possible, parallel universes. The other universes are expected to have different physical constants from those in our universe and are quite probably devoid of life.

The wave function of the universe in Hartle and Hawking's paper gives a probabilistic and noncausal explanation of why our universe exists. More precisely, it provides an unconditional probability for the existence of a universe of our sort (i.e., an expanding [and later contracting] universe with an early inflationary era and with matter that is evenly distributed on large scales). Given only their functional law of nature, there is a high probability that a universe of this sort begins to exist uncaused.

This can be explained more exactly. In their formalism,y[hij, f] gives the probability amplitude for a certain three-dimensional space S that has the metric hij and matter field f.

A probability amplitude y gives a number that, when squared, is the probability that something exists. This is often put by saying that the square of the modulus of the amplitude gives the probability. The square of the modulus of the amplitude is |y[hij, f]|2

In the case at hand, the probability is for the existence of the three-dimensional spatial slice S (the "three-geometry S" in Hartle and Hawking's parlance), from which the probability of the other states of the universe can be calculated. The three-dimensional space S is the first state of the temporally evolving universe, i.e., the earliest state of the temporal length 10E-43 second (the Planck length). S is the state of the universe that may be called the "big bang"; it precedes the inflationary epoch and gives rise to inflation.

The metric is the degree of curvature of spacetime; the metric hij Hartle and Hawking derive is that of an approximately smooth sphere (like the earth) that is much smaller than the head of a pin.

The matter field f is equivalent to an approximately homogeneous distribution of elementary particles throughout the small sphere S.

Hartle and Hawking derive the probability amplitude by adding up or summing over all the possible metrics and matter fields of all the possible, finite, four-dimensional spacetimes which have a three-dimensional space S with metric hij and matter field f as a boundary. The square of the modulus of the amplitude, |y[hij, f] |2, gives the probability that a universe begins to exist with a three-dimensional space S that possesses this metric and matter field. The probabilities for the history of the rest of the universe can be calculated once we know the metric and matter field of the initial state S.

Since the wave function includes the three-dimensional space S as the boundary of all merely possible four dimensional, finite spacetimes, we can calculate the "unconditional probability'' of the 3-space S, in the sense that we do not need to presuppose some actually existent earlier 3-space S* as the initial condition from which the probability of the final condition S is calculated. The probability of the existence of the 3-space S is not conditional upon the existence of any concrete object (body or mind) or concrete event (state of a body or mind) or even upon the existence of any quantum vacuum, empty space or time; the probability follows only from the mathematical properties of possible universes. The probability of S is conditional only upon certain abstract objects, numbers, operations, functions, matrices, and other mathematical entities, that comprise the wave-function equation. This gives us a probabilistic explanation of the universe's existence that is based solely on laws of nature, specifically the functional law of nature called "the wave function of the universe."

One problem with this theory is that the authors do not say who defined the "wave function of the universe". They do not eliminate the possibility that it might have been God.

I hope that sets things straight.

No comments: