. “…Because strait is the gate, and narrow is the way, which leadeth unto life, and few there be that find it.” Matt. 7:14 KJV
Well, that’s the way it works at the macroscopic level, anyway. When you get down among the weeds, things are a lot more complicated. However tight the fit at the endpoint of your journey from point A to point B, the way that you can travel there is very broad indeed, and the journey you experience macroscopically is really composed of a sum of every possible journey microscopically.
In his interesting series on Science and Religion, Mike S. has been connecting one approach to Mormon theology to ideas of modern physics such as higher dimensional spaces and string theory. To date, he has not addressed why there are three macroscopic dimensions when ideas such as string theory allow for nine or more spatial dimensions.
No one really knows the answer to that yet, but in the last five years, some real progress has been made. The results are not that surprising to experts, but the reasons for the outcome are surprising, and those reasons may address some ideas of “the strait and narrow” that trouble many liberal Mormons.
The new results build on a formulation of quantum mechanics associated with the work of Richard Feynman shortly after World War II. All formulations of quantum mechanics interpret reality as a “superposition” (summation) of multiple “states”; they differ mainly in how reality goes from that superposition to the single reality we experience. Feynman found a way to reorganize the summation so that it became far more tractable to handle in important fields such as particle physics.
Physically, the various terms in the summation can be interpreted as all of the possible evolutions a particle can undergo, or, when applied to a particle going from point A to point B, as all of the possible paths between the two points. It is, thus, often called the “path integral”. It is symmetric in respect to time: the paths from A to B are the paths from B to A as well.
A key difference between quantum mechanics and relativity is that in the latter, time is not part of the stage (the “background”) that’s built for the play of life; it’s in fact a dynamic actor (as is space itself) whose character development is central to the plot. When you try to extend Feynman’s method to how space and time evolve, the sum of all paths must be replaced by a “sum of all histories”, and the sums produce crazy results.
To create even a single history to sum, you have to first break spacetime down to mathematical pixels, much the same way images in these blogs are created from pixels. Physicists started out with training wheels by making the spacetime pixels four dimensional (3 space and 1 time) by fiat. They also wanted something that could easily produce curved spaces (since space, in general relativity is not flat) and packed together well, so they chose pixels that were hyperpyramids — the 4-D analogue of an equilateral triangle.
So the procedure is to use a computer to start out with one of these pixels of edge length x and glue another pixel against a 3-dimensional “face” at random — a process referred to as Dynamical Triangulation — and keep doing that a few thousand times until an approximation of one history is created. Then you repeat from a one pixel start to produce a second random history, and so on. Eventually, you get a good approximation of what the sum of all histories is going to look like, especially if you use smaller and smaller values of x in the process (which should further reduce artifacts of choosing a particular shape for the pixel).
But, surprise, surprise! Even though you cheated by starting with 4-D pixels, your runs never end up with four dimensional histories. They either line up in a branching tree arrangement like a polymer, or they crumple into infinite dimensional wads like the Creator was having writer’s block. The same thing happened when they tried pixels of different dimensions. That’s embarrassing for the method.
So physicists tried another trick: they imposed an additional restriction that the pixels were glued together so that, whatever their spacial orientation, their time histories had to point in “parallel” so that vertices always had to be at the beginning or end of fixed slices of time. When they did this and studied what happened as the pixel size shrank toward zero, they hit a jackpot.
When small numbers of pixels were connected with time edges in parallel, the structures tended to form a one dimensional space (i.e., a 2-D spacetime). However, as these “Causal” dynamical triangulations (CDT) continued to evolve along the time axis and more connections were added, the dimensionality of space gradually rose to three and stayed there. (For more on the idea of dimensions that are not integers, see here.)
Thus, to summarize, merely (but only) selecting a direction for time forced space to have three dimensions at a macroscopic level. Furthermore, the space was recognizable as a known solution to the equations of general relativity called a Friedmann cosmology. At scales where quantum mechanical effects would become important, there was a transition to a single spatial dimension. Indeed, one could picture at even smaller scale a “pre-geometric” state where pixels of spacetime are unaligned or unconnected at all.
Now, back to that scripture at the top of the post. It seems that this notion that reality is a superposition of all possibilities — with very few restrictions imposed on how we get where we’re going — has more explanatory power than we thought. Maybe alignment of the time axes of the pixels isn’t really important. Maybe “unaligned” pixels form part of timelines running “perpendicular” to ours and, thus, not further interacting with us. Who knows?
But if God really likes this feature of superposition, maybe He applies it to our spiritual development as well. And, if so, that has some interesting implications toward the issues discussed in a previous thread about whether there is really a “cultural” Mormonism.
For example, when the path integral is analyzed rigorously, the “classical” straight-line path contributes to the sum with “measure” (probability) zero. The paths that contribute significantly are paths like those shown in the top figure of the post — paths that are made up of all sharp corners that spend relatively little time anywhere near the classical straight line. Remove these radical “departures from the truth”, and the sum of all paths ends up, not at point B, but somewhere else entirely.
In other words, if point B is where God wants us to end up, we can’t get there without either the wandering Mormons, the disaffected, or the never converted. They are contributing, unseen, to where the future goes. Indeed, we don’t know where the strait and narrow gate is until the final swerve. Even if we limit consideration to the Judeo-Christian tradition (and there’s no reason to do so in this context yet since we are still mid-path), Isaiah, Paul, Martin Luther, or Joseph Smith would have projected the location of Point B very differently from each other.
To get to the one true faith, we may be expected to take different paths — not just for our sakes, but for the sake of the true faith itself.
“The Universe from Scratch”, J Ambjorn, J Jurkiewicz, and R Loll; arXiv: hep-th/0509010 v3 14 Oct 2006.
“The Emergence of Spacetime”, R. Loll; arXiv:0711.0723v2 [gr-qc] 16 Apr 2008.
Link to arXiv.org search page at Cornell University Library for the above papers and related citations.