Predictable Natural Law – Part 1By: FireTag
Mormonism comes with its own science. So does any brand of mainstream Christianity, but many such Christians are unaware of how their creeds embed the assumptions of the “scientists” and mathematicians of antiquity. They can consequently perform a mental jujitsu of preserving the religious idea as metaphor for modern times while ignoring the fact that the ideas were originally proposed and defended by ancients who were — literally — in error. Had the ancients known science better or cared more, they would have proposed different interpretations in the first place.
In the modern world, we care more about nature’s laws being expressed accurately, because doing so is more tied to survival and prosperity. I bet Governor Cuomo and Mayor Bloomberg of New York are wishing today they’d understood and believed what the meteorologists were telling them about storm surge about 48 hours sooner.
When scientists today look at the cosmos to which religious ideas of the nature of God have to conform in one form or another, one scientific touchstone is general relativity. One popular way to describe relativity is that “matter/energy in any location tells spacetime how to curve around it, and the curvature of spacetime then tells matter/energy how to move”. Matter/energy flows along the straightest, shortest possible path (the geodesic) through this curved spacetime, deforming spacetime as it moves, and the curved space is what we experience as gravity.
Since we don’t normally associate our experience of gravity with any such property of curvature, curvature in our three-spatial-dimensional world is clearly hard to picture. But we can picture two-dimensional spatial analogues of curved space more easily.
A globe is positively curved, or “closed”. If we expand the globe to infinite size, its curvature shrinks to zero. We call that space “flat”, and it is that geometry with which most of us are familiar in our daily lives.
However, spaces can also be “open” and have negative curvature. Over a certain range of smaller distances, these spaces can be called “saddle-shaped”, but viewed at larger and larger scales they have surprising and artistically challenging properties. The Escher interlocking fish motif above is one famous example. Another one, surprisingly, can not be easily drawn, but can be made with crochet needles and yarn and then photographed. A collection of such “hyperbolic planes” can even be staged to look like a coral reef. So, a space with negative curvature in three spatial dimensions behaves in ways that are extremely counter-intuitive.
The general relativity field equations that Einstein first derived are simply the mathematical expression of the idea that matter/energy flows along geodesics (i.e., straightest path) embedded in a standard technique (Lagrangian mechanics) for describing how you can identify minima in any mechanical system.
One can solve the Einstein equations for the universe as a whole under some widely believed simplifying assumptions (e.g., that the matter/energy distribution is generally the same everywhere if you look at large enough scales, and that spacetime is simply connected topologically — don’t ask unless you want to hear about dodecahedrons). The solution allows space that is open, flat, or closed. Space everywhere gets bigger forever, or it falls back into itself everywhere, or it hangs eternally on the knife-edge in between. The future is all baked in by how much matter/energy there is per unit volume and how fast space is expanding now. The past points to a time when all of the matter/energy was compressed to an infinitely dense state we refer to as the “big bang”, even if it offers no explanation (and lots of puzzlement) of how the big bang state came to be.
Scientists have believed this for a century, but within the last decade have come to realize that gravity, and the cosmology it implies, isn’t at all that simple. The universe also seems to contain matter we can’t see (“dark matter”) but that attracts things on the scale of galaxies. Further, at even larger scales, it contains a third element, a repulsive “dark energy” that overwhelms the effects of normal matter/energy and opens the universe into negative curvature, period.
Recently, two Chinese physicists ( Tian Ma and Shouhang Wang) came up with a fascinating new theory for explaining dark matter and dark energy as a unified phenomenon by changing only one idea about relativity and redoing the Einstein derivation. They asked, “What if something else besides matter/energy at a spacetime point affected the curvature of spacetime?” If that “something” made the curvature more positive (attractive) at some point, matter would behave like there was additional mass present, but we wouldn’t be able to see any mass. It would be dark matter. If the “something” made the curvature more negative (repulsive) at the point, it would seem that there was additional energy present that we couldn’t see. It would be dark energy.
Now, other physicists have proposed specific mathematical forms to write into the universe’s Lagrangian in order to mimic the behavior of dark matter/energy, but that ad hoc approach has been treated skeptically. Instead, Ma and Wang invert the process and solve for what “something” can be without it introducing any contradictions into the derivation. In other words, they redo Einstein’s derivation without formally assuming anything about whether there are other fields beside the matter/energy field to affect spacetime curvature, and without assuming that there is either dark matter or dark energy.
Here’s where the magic happens, and it seems magical because I can’t imagine what would make anyone think to try this. They take a bunch of recent work in the mathematics of the dynamics of incompressible fluids like water and start mimicking those mathematical proofs to prove a bunch of theorems applicable to Einstein’s view of spacetime — page after page of specialized proofs that I can kinda-sorta-not-really follow (learning tensor calculus is like dieting; I myself have successfully done it at least six times) — about properties that these “other fields” have to have to be consistent with the Einstein derivation. Eventually, although I can’t check them, they succeed in deriving enough properties and symmetries and conservation laws to prove that there is always and only one such additional field, and it exists everywhere in spacetime just like gravity does. I have no idea why spacetime should act like an incompressible fluid, and I doubt they do either, but that is what the math seems to say.
They can solve for the field values in certain simplified cases, and this allows them to derive its physical significance. They call it the scaler potential energy. When the normal matter/energy is uniform everywhere in spacetime, one of the conservation laws says that the scaler potential must be zero everywhere. On the other hand, another conservation law says the average value of the scaler potential over all spacetime must be zero, and a third law says that if there is zero matter/energy in any location, than the scaler potential must be non-zero at the same location. Together, these two laws imply that the scaler must contain both a positive (repulsive) and negative (attractive) term in order for cancellation to be possible. (I’ll come back to this in a moment).
Another simple case they can solve is that of the field of a single spherically symmetric mass like a star or planet, but of any finite size. In this case the solution is the normal attractive 1/r^2 gravitational field + an additional attractive 1/r term + a repulsive term that is linear in r. So, at small distances, everything looks like normal gravity, but on the scale of galaxies, it looks like there is more mass present (dark matter), and on the scale where r becomes very large (like the large scale structure of the universe) it looks like gravity has become repulsive — dark energy. Everything seems to pop out from the math of the one assumption that something else than “normal” gravity might affect the curvature of spacetime.
In fact, the physical interpretation of the scaler potential is that it is a potential energy arising from the inhomogeneous distribution of matter/energy throughout spacetime. Remember, a uniform distribution of matter/energy, as I noted above, requires that the scaler potential be zero everywhere, so it exists if and only if there is an inhomogeneous field of real matter/energy. The scalar potential tells matter/energy to move in a way that makes its distribution less homogeneous while normal gravity tells matter/energy to clump together until some other force (like the atomic electrical forces of solid matter) stops it from clumping further.
And this, in connection with any theory of quantum mechanics, the other pillar of modern physics, seems to make spacetime unstable to expansion.
Theories of quantum mechanics always allow random fluctuations in energy (a statement of the “uncertainty principle”). So, imagine that there is a positive energy fluctuation somewhere in spacetime. Then the scalar potential requires that an expansion occurs everywhere far away from that point because of the r term in the potential. That then produces scaler potential energy from which more quantum fluctuations can arise at those points, etc., in a positive feedback loop. If the initial fluctuation was negative somehow, then the 1/r^2 and 1/r terms would automatically become infinite and switch sign to repulsive. Either way, space blows up large very fast. A big bang is unavoidable. In fact, a big bang or multiple big bangs are the only things except nothingness that seems possible.
So, let’s recap with an eye to my original observation about Mormonism coming with its own science. Mormon cosmology postulates generations of divinity of which Heavenly Father (and by inference Heavenly Mother) and Jesus Christ are the generations relevant to humanity’s past and future. The Divine exist within a framework of spiritual natural laws that They may fully understand, but are not free to ignore. Humans certainly do not fully understand those laws, yet Mormons are confident humans are even less free than Divinity to ignore them. The laws have real consequences, we are sure.
But are we so sure we can predict what those consequences are? If we are taught that the spiritual and the physical are inseparable, can physical nature be contradictory to spiritual nature in something so fundamental as the ability to make reliable predictions about how much “theology” changes under even small new revelation?
After all, Ma and Wang have just shown how taking a tiny “precept” from fluid mechanics and suggesting that space behaves like an incompressible fluid changes something in the physical realm as all-encompassing as the “big bang” from the category of mysterious to compulsory. If they are right, space “bangs” and becomes ever more inhomogeneous for the same reasons apples fall.
How big a difference might tiny precepts added to Mormon science make in our understanding of Mormon theology?