Creatio ex nihilo, creation from nothing, is a fundamental doctrine of Catholicism. Furthermore, it is the position of Catholic theology that the Big Bang theory does not contradict the doctrine of creatio ex nihilo as long as the BB theory implies an absolute beginning.
The Big Bang theory states that not only did matter, time, and energy emerge from a singularity, but so too did the space that gives dimensionality to the universe.
How “space” emerged from whatever the singularity was immersed in can only be imagined by assuming two modalities of space.
This is not a problem because we can identify two modalities of space: the continuous and the discrete, both of which can be modeled mathematically. The Cantor-Dedekind axiom states that that the real numbers are order-isomorphic to the linear continuum of geometry. In other words the axiom states that there is a one to one correspondence between real numbers and points on a line. Cantor also showed that there are as many points on the real number line as there are in two or three-dimensional space. Hence all points in 3-dimensional space can be associated with the real numbers.
The real numbers, hence continuous space, are described by the second transfinite number, aleph-1. The rational numbers also lie on the real number line, are denumerable, and are described by the first transfinite number aleph-0. Rational numbers define discrete space.
The two modalities of space, discrete and continuous, allow us to explain the duality nature of reality. Objective reality, consisting of space, time, matter, energy, is constructed from discrete space, while continuous space provides a spiritual aspect of reality.
Thus, the mathematical properties of the infinite allow us to describe a scenario in which discrete space is crunched into a singularity and is caused to emerge from continuous space.
Because [aleph(1) - aleph(0) = aleph(1)] an infinite amount of discrete space can be removed from an infinite amount of continuous space without changing continuous space one iota; God can create the universe (or an infinite number of universes) from Himself without change. That is the nature of God, the Infinite.
Relative to God, aleph(0) is nihilo. And even more so, God does not require an infinite number of “points” to create the universe, some large finite number will do.
To those skeptics that may bridle at the thought the matter is composed of some form of space, consider what string theory implies. Also consider that the typical atom whose material size is determined by the position of “point-particle” electrons, is 50,000 times the size of the nucleus and the nucleus is composed of “point-particle” quarks. In other words, matter is mostly empty space.
I contend that the empty space that provides the materiality is the continuous space that provides the spiritual aspect of reality. I call, the continuous space from which the universe emerged, infinite nothingness. It is the Mind of God. We are immersed in the Mind of God.
I contend that what I have presented may not be the truth; I offer it as a plausible “philosophical” explanation for the doctrine of creatio ex nihilo.
Yppop