A Universe is More than it Contains

In order to move on in my work, I’m studying advanced physics and mathematics, concentrating for now on general relativity — broadly speaking since I have to take various diversions to refresh my old knowledge or to acquire new knowledge in basic physics and matrix algebra and differential geometry and so forth. One of the books I’ve been struggling through is Principles of Physical Cosmology by P.J.E. Peebles, a distinguished authority in the field of general relativity. He has various interesting comments and insights, but one insight is particularly fascinating to me since I wish to better understand modern physics so that I can better understand God’s Creation. In the following quote, square brackets are used to include my explanatory insertions.

We see that the faster decrease of [the radiation density of a relativistic universe modeled as a gas] compared to the mass density of a nonrelativistic gas is the result of the pressure work done by the expanding radiation. However, since the volume of the universe varies as [the third power of the expansion factor of the universe], the net radiation energy in a closed [and expanding] universe decreases as [the inverse of the expansion factor of the universe] as the universe expands. Where does the lost energy go? Since there is no pressure gradient in the homogeneously distributed radiation, the pressure does not act to accelerate the expansion of the universe. (The active gravitational mass due to the pressure has the opposite effect, slowing the rate of expansion…) The resolution of this apparent paradox is that while energy conservation is a good local concept…and can be defined more generally in the special case of an isolated system in asymptotically flat space, there is not a general global energy conservation law in general relativity theory. [Principles of Physical Cosmology, P.J.E. Peebles, Princeton University Press, 1993, page 139.]

I have to make an important disclaimer: we don’t yet know the exact geometric properties of the universe, or rather — the region of the universe which is visible to us. It’s not even certain we have a complete inventory of types of matter and forces in this universe. It might be that we do live in a universe that conserves energy at the ‘global’ level, but there’s no ‘law’ mandating such and a good chance that we live in a universe where certain types of energy can go away at the level of the universe.

Given that disclaimer but remembering that there is no “general global energy conservation law in general relativity theory,” we can see that a universe can be described in which all localities do have an energy conservation law while that universe doesn’t. While those ‘conserving’ localities make up the universe in some strong sense, the universe as a totality can have properties different from what would be implied by an effort to construct the universe using only its localities. In other words, the universe as a totality is itself an entity and may have properties not found by assembling it, tinker-toy fashion, from its ‘pieces’.

There is an element of weirdness here, a seeming violation of our understanding of the ways in which larger and more complex entities are ‘built-up’ from their components. It almost seems as if there’s an analogy between the universe and a living creature, especially a social creature. We don’t have any ‘common-sense’ intuition that a man or an elephant can simply be built out of its components but that’s potentially a misleading insight because much of the individuality which is striking in man and elephant comes from the historical nature of such creatures, from their context in a greater world. We human beings, along with at least social creatures, exist more as boundary phenomena where our organ-based physical selves interact with our environments and perhaps more. If that’s true of the universe, what is its greater context? My worldview provides some ways of answering that since I speculate that the universe is only one phase of a far greater Creation, but that’s a vague claim and would require a major effort to develop — perhaps an effort beginning with years or even decades of study.