. “…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.
ADDITIONAL READING
“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.
Wheat & Tares 
I am impressed with how many physics related posts are posted on this blog. Keep up the good work.
And I found it a very interesting idea to relate the path integral to the church needing people propagating along every path to reach it’s destination.
Sort of a more sophisticated form of: The head should never tell the foot I have no need of thee? 🙂
You might want to add that the path integral includes all possible events as well as all possible paths, including multi-particle creations and annihilations. If you feel like you’ve gone to pieces, don’t worry, we all do this all the time. It’s all part of the big equation and it all comes back together and contributes to the big summation.
FireTag:
Great post – I really liked it.
I do think there is something relating time to mortality. Time is talked about throughout the scriptures and forms a fundamental part of mortality. We are born, we grow, we die. There is a time to everything under the sun. Our time is not God’s time. Etc.
I like how you explained the collapse of paths into a 3-D space with the addition of time. It helps with a possible reason of “why” we see what we see and why mortality has to be what it is.
And, importantly, I really like your analogy about different paths to God. I’ve expressed my opinions on here quite a bit, and they certainly differ with other people’s opinions, but I really am convinced (for no real reason perhaps than hope) that God is successful. I think the vast majority of people going through mortality will ultimately end up in the highest level of being in God’s presence, whatever any particular religions wishes to call that. I think it will be FAR more than the 0.1% who are active LDS Mormons in mortality.
This concept will be absolutely foreign to traditional LDS teachings – with the “one true Church” paradigm and the missionary program to help people join and therefore be able to have the only valid ordinances done which will allow them to return to God. But quantum physics was also absolutely foreign when it first came out. Einstein had a hard time accepting the implications of the uncertainty principle. And there are quotes that there are fewer than 10 people in the world who TRULY understand string theory.
Thank you. Great post.
Paul 2:
I decided to refer vaguely to the “evolution” of the particle and leave creation and annihilation operators out of the discussion for simplicity. CDT is an empty space theory as yet, with work just starting in 2-D systems to incorporate massive particles.
Joseph Smidt:
I wish I’d have thought of that scripture when I wrote the post.
Mike S.
Your comments in this area were one of the inspirations for the post, so I’m glad you liked it. Of course, that and the fact I’m outside the TBM definition by a lot myself.
“I think it will be FAR more than the 0.1% who are active LDS Mormons in mortality.”
All believing Mormons believe this in various ways. It makes little sense to say this to a Church that believes in vicarious ordinances.
By the way, FireTag, this post does a good job of explaining why something close to universalism must turn out to be true for a perfectly loving God.
Bruce:
Although the Community of Christ tradition treats ordinances as more of a “natural law” than “administrative law” in terms of their saving power and does not perform them vicariously, we certainly share the notion of near-universal salvation.
In fact, as I have discussed in a few places, I think a human actually realizes a “sum of all paths” in which we have duplicates and variants of our physical existence naturally recurring throughout an infinite spacetime. The spirit is the result of collective behavior of all of these individual lives, IMO. So. we all have “evil twins” and “saintly selves” and the proportions determine what spiritual glory we come to inhabit.
It’s a lot like brain development, too. Neurons strengthen or weaken their connections, and some are even culled, but the formation of the brain is far more important than the individual neurons.
#5: Bruce
All believing Mormons believe this in various ways. It makes little sense to say this to a Church that believes in vicarious ordinances.
Then why do we devote so much time to missionary work? Why is it so important try try to get people to be LDS IN MORTALITY, if for 99.9%, it really doesn’t matter? Wouldn’t we be better off spending the time and money on helping people more directly?
Just as an example: The Peace Corps directly does work to help people around the world improve their lives. They currently have around 9000 volunteers. Imagine what we could accomplish if we had 50,000 volunteers doing that for 2 years each.
#7 FireTag:
I really like the idea of an “evil twin” 🙂 The idea makes a lot of sense, actually. I think things are much deeper than we typically talk about.
Interestingly, the people who have explored a lot of this in much more detail than us are the Eastern religions. There is a lot in there that hints at what you are talking about.
Mike S:
“Then why do we devote so much time to missionary work? Why is it so important try try to get people to be LDS IN MORTALITY, if for 99.9%, it really doesn’t matter?”
I can think of several answers to that in this kind of model, assuming that free will is real and that we have any choice at all.
From the point of view of the individual experiencing a single macroscopic reality, we want the best for ourselves and are striving to get to whatever point B WE desire. We don’t want to be the copy that is culled (“cast into outer darkness” is so much more poetic) or to achieve less than the best possible outcome for ourselves and others. We aim as best we can, even knowing we will not hit the mark by our own efforts. Unlike the individual neurons in our brain, we are conscious of our own self-interest.
From the viewpoint of the ensemble of copies, it works out whether we try or not — because there will be variants of us elsewhere/elsewhen that make the opposite choice.
But I also think we need to keep in mind that Mormon thought expands the concept of spirit more broadly if we apply it to this kind of physical model. The establishment of the Kingdom is for humanity, but not JUST for humanity. Consider Enoch’s vision in Joseph Smith’s elaboration of Genesis in this context. The Kingdom is perhaps also for the fulfillment of the Earth’s spiritual creation, and perhaps part of still larger spiritual structures.
” I think the vast majority of people going through mortality will ultimately end up in the highest level of being in God’s presence, whatever any particular religions wishes to call that”
Hogwash. This is in direct contrast to human nature; and, is in direct contrast to what is found in the scriptures. Most notably, the 88th section of the D&C. Those who cannot live the Celestial law, will not receive Celestial glory…those who cannot abide the Telestial law, will receive NO glory. The Lord then goes on to discuss how the above mentioned are the degrees of glory. There are an infinite number of Kingdoms. As he said, where there is space there is a kingdom (see versus 22-36).
I do agree this distribution is not isolated to the LDS faith. Few will find Celestial glory. Most of the inhabitants (in and out if the Church) will fall somewhere in the middle like with any other
significant test.
With that said, it is the ONLY faith with a true Prophet; and, is the ONLY faith with all the restored truths necessary for salvation.
Will:
If I can go completely nerdy for another moment, I’ve sometimes wondered whether the glories of the sun, the moon, and the stars, with outer darkness might correspond to the four categories of unbounded good, bounded good, bounded evil, and unbounded evil, in that order. It’s really hard to become infinitely good, and really hard to become infinitely bad, so most of us end up somewhere in the middle as you say.
Firetag,
That us exactly what was being said in the 88th section. I don’t know where our version and your version start to differ, but I think that section is in your version of the D&C.
By the way, great post. I always find your posts intellectually stimulating.
Will:
I believe your 88 is our 85. They don’t “start” being different anywhere; there is a different judgement after the 1835 Book of Commandments.
I usually have to go to the Wiki article chart on the D&C to sort it out, which is why I tend to use scriptural quotes in my posts a lot less often than I could. I think our church has gotten rid of all the quill pens by now 😀 , but we just lack manpower and money to do a good job of putting scriptures online.
Re: #11 — Not to be nitpicky, but I think it is important if you’re using this to argue for why most people won’t get to the Celestial Kingdom. There are plenty of distributions that are not Gaussian! There is no reason why it couldn’t be a power law distribution. We have NO IDEA what the final distribution will be.
Andrew:
I don’t think anybody said a Guassian, but there is that part of the scripture in the OP “few there be that find it”. 😀
Maybe it’s a one-tailed distribution.
My own opinion is that it’s NOT ultimately Gaussian. Perhaps it might be if we truly relied on ourselves, but I think that Christ’s atonement skews things. It is an “infinite atonement”, so there it theoretically the power to shift the ENTIRE curve, except for those who totally reject Christ and refuse to be shifted. So I still stick with my original statement that the vast majority of people will ultimately be saved at the highest level.
Interestingly, this problem is one of the things that is really appealing to me about reincarnation (I know, it is difficult to reconcile reincarnation with my previous paragraph, but like this post, I can actually accept that BOTH are true – maybe my mind is warped). The chance of achieving nirvana in this life is actually very, very small. But, if you don’t make it this time, you have another go at it. In this way, EVERYONE will ultimately achieve the highest reward. And the idea of a bodhisattva is amazing. This is someone who has achieved nirvana, but who has voluntarily delayed going there until they have helped every other sentient being also achieve nirvana. This is beautiful to me, taking “Love thy neighbor” to the nth degree.