Predictable Natural Law – Part 1

By: FireTag
November 10, 2012

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?

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13 Responses to Predictable Natural Law – Part 1

  1. AndrewJDavis on November 11, 2012 at 10:39 AM

    I love your comment about learning Tensor Calculus. I think I’m up to my 4th diet, and each time, I get it. Then I stop using it. And overall great analogy with cosmology and assumptions in life.

    I think a key point you have made in the past provides a great example. The CoC and LDS churches have slightly different assumptions about the eternal nature of families as taught by Joseph Smith. Let that small perturbation grow, and you get the Family Proclamation on one side, and a more open acceptance of gender/sexual orientation variations on the other. (Please don’t read into this comment any judgement on my part about which is more valid! That’s not the point!) The small assumption at the beginning (i.e. exactly which teachings of Joseph’s at the end of his life are doctrinal) can have very large differences.

    I think if we look deeply at our own individual assumptions about the Gospel we will come to the conclusion that we each have slightly differing ideas about some basic points (e.g. how repentance and grace work), and that can lead to many different ideas on how to act on our ideas.

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  2. FireTag on November 11, 2012 at 11:21 AM

    AndrewJDavis:

    Thanks for getting what I was leading toward. I felt from the sparse comments that I must have been too subtle with the theology, and too complicated with the physics.

    The issue about gender is relevant to this idea about predictable theology, as are many others. In part two, I’ll give an example of natural law and public policy that may be a little less grating on our nerves right now. :D

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  3. Hedgehog on November 11, 2012 at 12:59 PM

    First I have to admit that Fluid Mechanics was my worst undergrad subject, and back at A level Newtonian rotational dynamics (including planetary motion) was my worst bit in physics, I only ever had to do quantum mechanics in 1 dimension, and certainly didn’t go so far as introducing Einstein into anything more than passing trains… So I only sort of followed the physics example. The different ways physicists try to solve conundrums is interesting, but my Maths isn’t good enough to work through anything. It has taken me a while to think this post through before commenting.
    The thing that most struck me as an analogy was the difference between the larger universe-scale picture, compared to the very localised picture first envisaged by Newton. That’s probably because the thing I am most searching for at the moment is the wider context in which my/ your/ all religions fit. How does the gospel we teach, the history we have (both biblical and latter-day) fit into the world, and life, and everybody? The Bible relating to such a very small geographical area, and the NT really to quite a short period of time. The BoM similarly perhaps not referring to the entire American continent. Discovering more about the nature of the religious movements happening at the time of Joseph Smith and Brigham Young (much more than competition for members between Methodists and Presbyterians – again the impression I got growing up, not the whole Burned Over district thing – because this is afterall US history). That Mormonism wasn’t the only new religious movement emerging from that time period that is still around now (so no, just because the church survived is not what makes it the ‘true’ church). And I wonder if those things the prophets were forbidden to write – did they get to see the whole picture, the context, and so have a better understanding? At the moment I feel like Newton with the apple, but that it isn’t enough. And if I had the wider information, maybe my level of understanding would only be enough to appreciate the surface of how it all works, but not be able to work through the Maths for myself. And many people are very happy with the ‘Newtonian’ view of religion, which here and now for all practical purposes of where they’re aiming to go works well enough. But I don’t think that was where you were intending to go with the post.
    On your particular questions:
    I’ve recently been reading a book (aimed at the popular market, so not an academic tome) about the what the author describes as the ‘apocalypse meme’, which has been quite thought-provoking. I don’t know what the CofC view is (or indeed what a mainstream LDS view might look like now), but where I grew up the idea of 1000 year dispensations (equating to days), and the 7th day being the millenium was the view that held sway, and would appear to do so still. From where did the LDS get this view? The book I’m reading traces ‘dispensationalism’ back to the founding of the Plymouth Brethren in Dublin c. 1870 (but the author maybe wrong, perhaps it goes back earlier than that). But it’s interesting to see that all through time, there have been groups of people expecting a spectacular second coming (or similar) in the very near future – the Jews awaiting the Messiah, the early church of the NT, the early Mormon converts (in Utah and earlier), and so it goes on… I kind of got the impression that the church is sort of drawing back from the ‘Last Days’ rhetoric (at the April General Conference this year – was it Pres Packer?) if only by a smidgen. And you can only go on telling youth that they are a chosen generation for evil times of the last days for so long, because at some point, you then find yourselves saying the same thing to their children and maybe their children…, and presumably the post-NT early Christians found themselves having to make that kind of shift.
    On your comment #2, I’d welcome a change in precept regarding gender :-), if going in a less prescriptive direction.

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  4. FireTag on November 11, 2012 at 10:49 PM

    Hedgehog:

    Most people do quite well with a “Newtonian” form of religion — until they run into situations where the slight differences in perspectives between persons and cultures evolve into concrete issues large enough that a better theory that can explain more has to come forward lest the differences harden into schism and/or conflict. I think the West is entering such a period relevant to other world cultures as an inescapable part of economic and communications globalization.

    I think the apocalyptic meme is really an interpretation of Scripture that is very natural, given that in pre-scientific eras we had no idea of how old the universe really is. The particular connection with 1000 year dispensations might be only 150 years old, and comes from taking “a thousand years” too literally when it seems more of a slang expression for “a very very long time”. (Notice in scripture people get lost in the wilderness for 40 days or 40 years, never 39 years — more symbolic slang.)

    But even when we consider the scientific era, there are only a few possibilities for the universe itself: everybody tends to come up with eternal life, repetitive cycles/generations, or finite death. For humanity, we imagine the same variations, at least in the spiritual realm. Human institutions (like nations and empires and churches) seem to have finite lifespans with large ups and downs.

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  5. Hedgehog on November 12, 2012 at 1:40 AM

    FireTag
    I certainly get that the use of numbers in scripture has more to do with poetic license than actual hard figures. According to the author, the earliest the ‘apocalypse meme’ can be found to dates back is to Zoroastrianism, and he suggest the Jews picked up the idea during their days in captivity. I mentioned the dispensationalism aspect as being an example of a ‘precept’ being introduced and then accepted in various denominations as an explanation of why a second coming hadn’t yet been seen, and also as something that (at the time) put it conveniently far ahead in the future. Of course other denominations took another view, and aren’t expecting a second coming at all. Those that adopted it are now having to deal with it as the ’6th day’ would appear to be up sort of soonish even accounting for a semi-literal view on 1000 years (meaning not exact, but a close approximation). For myself I find it little bit odd that on this view the ‘Meridian of time’ isn’t in the middle, though why I’d be more comfortable if it were I don’t know…
    (The book itself is more for this year – to answer ‘why the world probably won’t be ending on 21 December 2012′, but is interesting none the less.)
    Lots to think about still, and I shall probably add more later today.

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  6. AndrewJDavis on November 12, 2012 at 1:48 AM

    @Hedgehog —
    I think describing a ‘theory of everything’ vision of the Universe would be really really hard. I think that, more than anything else, makes it hard for Nephi or the people at the Temple of Bountiful in the Book of Mormon, or Joseph or anyone else to actually describe what they saw, heard and felt.

    Gospel wise, our final Theory of Everything will have to include all of what I just described, but all of biology, all of theology, inter-personal relations, and all of the Gospel as we know it, and more. To me, the small glimpse that I have, is every now and then interspersed with a fleeting awesome view of how life just might be so much grander than I thought. And maybe it’s one of my assumptions at the beginning holding me back.
    I look at it in terms of astronomy, which is what I do for a living. Put me back in Galileo’s time, when he had for the first time ever, turned a telescope to the planets, and saw the moons of Jupiter for the first time – the first objects ever shown to not orbit the Sun ( or Earth, depending if you believed Copernicus at the time). Now, come with me on a vision of the whole Universe, looking at binary stars, zoom-ins of hot Jupiter planets, planetary nebula, pulsating stars, supernovae, accretion disks around black holes, galaxies, colliding galaxies, merging galaxies, massive stellar winds destroying the birth clouds of young stars, and so on. Then, receive a brief glimpse into understanding Gravity (and a bit of Nuclear Physics) so well that you *know* exactly how all those processes happened. I just don’t see how Galileo could have put all that into words. I think one would be hard pressed to one-up Moses, who said, “Truly, now I know man is nothing.”

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  7. Hedgehog on November 12, 2012 at 6:30 AM

    Andrew,
    Well my training is probably more engineering than science (although we did some science: elements of both physics and chemistry, hence the 1D quantum mechanics), and engineers do tend to deal with the everyday practicalities, as opposed to the grand unifying theories. And mostly the gospel is the everyday practicalities: love God, love your neighbour. And I’m fine with knuckling down and serving. I do like to think about the bigger view though, and sometimes find that LDS theology as often presented, or perhaps understood by many, can kind of get in the way. Galileo and others certainly had far greater problems with the Catholic church in that regard than I do now with mine. But in my own little microcosm one of my enduring memories of feeling the conflict occurred when I was about 9 years old. My sister, two years behind me in school had come home from school wondering how could the world have come from nothing, and surely we weren’t all descended from monkeys. This was pre-national curriculum days, and I hadn’t been taught anything of the sort back when I was 7. In my experience a primary school teacher isn’t the best qualified to explain either the Big Bang or Evolution anyway. But what sticks in my mind is that the following Sunday my father stood up in fast and testimony meeting and bore testimony that little children (my sister) were better able to discern the nonsense of these ideas that ‘educated’ adults were teaching. I didn’t know anything about any of it, but I felt dismayed and somehow flat. It wasn’t an uplifting testimony, and because it was my father who was saying those things it remains imprinted on my mind. ( I suppose it was a first intimation to me that a testimony can be more subjective in many ways than absolute. In fairness to my dad, he left school at 16, he was barely 30 years old, and he’s much more nuanced now, so its not like his mind was closed. I grew up in a home where my mother read popular science, and listened to science on the radio.) Maybe the particular LDS theologies we grow up with are influenced by where in the world we are, which leaders are responsible for that area and what their particular views might be… As for my testimony, I suspect when I say I have a testimony of Joseph Smith and the restoration of the gospel (a la the TR interview), I probably don’t mean quite the same thing as the majority of members.

    I like your suggestion that maybe Moses et al were told not to write it down because if they’d tried they could only have made a hash of it :-).

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  8. Hedgehog on November 12, 2012 at 6:51 AM

    FireTag,
    Continuing from my earlier comment, I did last night finally get around to listening to the fMh podcast interviewing the CofC women seventies. It was very interesting. I can’t see the LDS church making such a move for a long time yet however. I gather you lost a fair number of members because of it, and the current LDS certainly seem to be very conservative when it comes to not upsetting the existing membership by introducing that kind of change (the 1978 change would indicate this). It is an issue in the CofE here as well, with many prominent Anglicans including clergy – the only married Catholic Priests being those who used to be Anglican, converting to Rome when the ordination of women was introduced. I do wonder why equalising the position of women in society (throughout the world), and in religion is such a hard change to make.

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  9. FireTag on November 12, 2012 at 11:20 AM

    Andrew and Hedgehog:

    I’ve been of the opinion for a long time that the Book of Moses in LDS Scripture (and the CofChrist includes the same directly in the D&C and in Genesis) depicts PARALLEL UNIVERSES — and that has even more profound implications for Christian theology than anything discussed in this post. There appear to be physical copies of earth all around us, and that is a robust prediction of most competing modern theories of cosmology. That means that there are multiple copies and variants of each of US wandering around, too. So, I think the one body, one spirit, one eternal fate concept that undergirds Christian teaching and that of many other religions is itself too simple to be right.

    Hedgehog:

    One of the things my own research on the CofChrist has shown is that our membership size is controlled by the inability to recruit new members fast enough to sustain our leadership base. So, I think it’s more a case that decline leads to quarrels over the direction of the church than that quarrels over the direction of the church lead to decline. In fact, the leadership base of the RLDS/CofChrist reached saturation as long ago as 1880, so modern issues weren’t even in play then.

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  10. Hedgehog on November 12, 2012 at 2:34 PM

    FireTag
    Interesting view re. the parallel universes. Are these the same as a multiverse, or this there some subtle difference? For now, I take the view that it is all a simulation, and a ‘program’ which has to allow for any possible act/decision, well that’s going to look like an infinity of universes, but that we are each only an individual entity outside of that simulation. But I’m not the physicist, and that may look totally loopy from where you’re standing. I often feel I only know enough about most things to be dangerous.
    On your comment re. CofChrist (apologies for my earlier abbreviation), are you saying that there are too many leaders for the number of members, or not enough new members to fill the leadership positions? I’m assuming the latter, extending ordination to half the population wouldn’t make sense otherwise. I didn’t pick up on the lack of growth from the interview, but it’s not something they’d want to advertise I suppose.

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  11. FireTag on November 12, 2012 at 5:14 PM

    Parallel universes form the multiverse, although there are several different ways the parallelism can arise.

    As to the growth of the CofChrist, I believe leadership resources have had to be split among all of life demands because we were never isolated from society sufficiently (no Utah) to establish alternative economic or political systems after the Reorganization. I can show an economic growth/decline model based on predator-prey relationships to show that by about 1880 we could not recruit members and develop them into leaders any faster than old leaders had to divert their own resources into professional, family, or other demands. Our growth was “saturated” for about a century until societal changes made it harder to recruit members. At that point, we could no longer quite keep up, and started to decline.

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  12. FireTag on November 12, 2012 at 5:35 PM

    I should add that I wrote about the decline of the CofChrist here

    http://www.wheatandtares.org/2010/10/23/middle-day-saints-or-church-mortality/

    and linked there some charts (below the hour glass) that show the CofChrist entering the “stochastic phase” of decline, where its survival in North America becomes basically a random process. Whatever the merits theologically or ethically, ordination of women didn’t change the trend; open communion didn’t change the trend; accepting baptism by other Christian denominations didn’t change the trend, and I have no reason to believe that endorsing same sex marital relationships or ordinations will either.

    We did not thereby open up the church so much as move its boundaries and exclude a different group of people.

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  13. Hedgehog on November 13, 2012 at 8:11 AM

    Thanks for the link FireTag. And the discussion too. I’ll take a look at that.
    I guess my discovery of the Bloggernacle is attributable to the 2011/2012 ‘mormon moment’, since I started off just reading the US newspapers online.

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