Junior Ganymede
We endeavor to give satisfaction

Diversity of perfections

July 19th, 2009 by Vader

One of the distinctive features of Mormonism is the doctrine of the diversity of perfections.

But, being a Dork Lord and all, I’m going to make a long digression into theoretical physics before returning to the theological point.

Most theoretical physicists now agree that, at the heart of the physical laws making up our universe, there is a collection of symmetries. Each such symmetry has associated with it a conservation law.

For example, suppose God instantaneously moved the entire Universe a few million light-years to the right. How would we know? We wouldn’t. Moved relative to what? All points in space are alike to Him, unless there is some substance at that point in space to give it a distinctive character. The laws of physics, so far as we mortals have been able to determine, reflect this sameness. When you formulate the laws of physics to explicitly display this sameness, you can extract from those laws, by a straightforward mathematical analysis, the law of conservation of momentum.

Suppose God put the Universe in suspended animation for a few million years. How would we know? We wouldn’t. Suspended relative to what? All of time is present before Him, and the laws of physics, so far as we mortals have been able to determine, reflect this sameness. When you formulate the laws of physics to explicitly display this sameness, you can extract the law of conservation of mass-energy from them.

Suppose God took the Universe and instantaneously gave it a spin around some axis. Ditto, ditto. The isotropy of the laws of physics translates into conservation of angular momentum.

These are the classical symmetries of physics. In addition, we have more subtle symmetries not corresponding to anything directly visible in our time and space. In particle physics, the known symmetries are described as U(1)xSU(2)xSU(3), which is precisely what it looks like — jargon all but incomprehensible to anyone but a mathematician or mathematical physicist. The SU(2) and SU(3) parts represent rotational symmetries in complex multidimensional spaces that even mathematicians have some trouble visualizing, so I’m going to stick with the U(1) part.

U(1) is the mathematical label for the symmetry of the circle. You can rotate a circle by any angle you like and it remains unchanged. It’s a very pleasing symmetry — so pleasing, in fact, that until the work of Kepler, it was assumed to be the basic symmetry of the physical heavens. Any point on the circle is the same as any other. It’s as good as any other. It’s as perfect as any other.

At least until you have some outside point of reference, such as another nearby circle.

In modern physics, it’s the same way. There is a U(1) symmetry at the heart of the physical universe. You can think of it as a little clock dial with a single hand that is duplicated at every point in space and time. Or you can think of it as a circle in an internal space not directly visible to our senses. That makes it no less physically real. This space is duplicated at each point in space and time and has real physical effects.

If God came and simultaneously advanced all the clock dials by the same amount at every point, we wouldn’t know. The Universe would be left unchanged. The laws of physics, so far as we can tell, are the same for any orientation of this set of clock dials. A straightforward mathematical analysis of the laws of physics produces the law of conservation of electric charge, of all things.

There’s nothing to make one orientation of the U(1) clock dial any less perfect than any other — until you can make reference to the U(1) clocks at surrounding points in space and time. Advance the hand on just one clock, and it is suddenly out of step with surrounding clocks. You can tell that the one clock has been advanced.

When you take the mathematical expressions describing the Universe, and allow the position of the U(1) clock hand to vary in time and space, you get a bunch of mathematical terms that violate the U(1) symmetry. The perfection seems to have been lost. But it’s possible to restore the symmetry by introducing a field that accounts for the variation in the positions of the clock dials. In effect, this field transfers the rotation of the clock dials into the curvature of the internal space in which the clock dials live. They then all line up again. The perfect U(1) symmetry of the laws of physics is restored. When you work through the math do this, you discover that this so-called gauge field is mathematically identical with the electromagnetic field — light.

I think some of you will have guessed where this is going by now.

Restoring a broken symmetry

Restoring a broken symmetry

There are some rather important distinctions between the gods of the Greek and Roman pantheons and the community of Persons we Mormons call God. The Greek and Roman gods were big, bad, and immortal. Big and bad as they were, however, they were not omnipotent. They were constantly checking each other’s power. They also seem to have not been omniscient, judging from Hera’s inability to catch Zeus in his numerous infidelities. Nor does it seem like all Time was before them, judging from their need to consult the Fates from time to time. In fact, they sound a lot like Congress.

We believe that God is omnipotent and omniscient, and that all Time is before Them. We believe that They are completely united in purpose and power, so that we can speak of Them as One God. One wonders, then, at the redundancy. And yet God is continually reproducing Himself: “For behold, this is My Work and My Glory, to bring to pass the immortality and eternal life of man.” One thinks of all those U(1) clocks, which must be synchronized to maintain the perfection of the U(1) symmetry. What’s the point?

In the physical universe, the electromagnetic field provides the counter terms that make possible a diversity that does not violate the perfect U(1) symmetry. Each clock has its own orientation, but they are reconciled to each other by the electromagnetic field.It’s a dynamic perfection: The counter terms appear in the parts of the laws of physics that represent changes in space and time.

So it is with God. It would be redundant and pointless for every Person of the community we call God to be in lockstep with every other. Yet if God did not have a perfect unity of purpose and power, God would cease to be God. The perfect symmetry would be broken. It is the power of the Redemption and the Restoration, brought about by the Atonement of Christ (the Light of the world), that makes it possible for there to be a diversity of perfections.

God knew Adam would partake of the forbidden fruit in the Garden, thereby violating the perfection of Heaven. Yet God allowed the drama to proceed. One is forced to conclude that God considered the agency of man — the potential to create a diverse and dynamic perfection — to be worth the cost paid at Golgotha, where God Himself was tortured to death under the hands of the Romans.

Does this justify an antinomian approach to ethics? To quote Paul, God forbid. There is more than one way to preserve the symmetry of Heaven. Those who will not be reconciled to God by the Atonement will be reconciled by justice. Those who refuse to be reconciled at all, either by the Atonement or by justice, will be cut off from this universe. At least, that seems like a good description of outer darkness.

All analogies are imperfect. But I think there is some deep truth in the seemingly silly analogy between God and the Atonement and the U(1) symmetry of theoretical physics and the electromagnetic field.

Comments (10)
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July 19th, 2009 22:26:07

Bruce Nielson
July 20, 2009

This is a facinating post, Vader. I would like to learn more about the physics you discuss. First of all, how did you learn it? Is this part of a degree? Or are you just a reader? If a reader, what do you recommend?

As I just mentioned in a post a just put up, I am reading Physics of Immortality out of interest because I just read Fabric of Reality and it reference it. Strange book, but facinating ideas. I have no basis, however, to assess his arguments. I am — no really — thinking of going back to school and taking a Calculus class or Physics class so that I can understand arguments like this better.

July 20, 2009

Let’s just say that, as a Dork Lord, I have a professional interest in forces.

Bruce Nielson
July 20, 2009


Gee, thanks Vader. :)

Guess I can’t count on good ole’ Darth for future career advice. :P

July 20, 2009

I find your lack of faith disturbing.

I don’t think you can learn this stuff rigorously from a book unless you already have a fair amount of formal education in the field, or are really really bright.

There may be some good “flavor” books out there. Let me think about it.

If you have some background in calculus, Roger Penrose has a pretty good book out called The Road to Reality.

Ben Pratt
July 20, 2009

I just took a graduate Group Theory course in the physics department (see http://www.phys.washington.edu/users/sharpe/507/course.html).

The symmetries that observed particles mostly obey really are amazing and beautiful, and I enjoyed your thoughts, Vader.

Bruce Nielson
July 21, 2009


Actually, what I am saying is I want to take some classes in my spare time. :)

Is a “group theory” class the right one?

Then, obviously, I’ll have to take all the prerequisites first. So, er, I guess that means I need to get a degree in Physics. :)

August 11, 2009

[troll post removed]

August 11, 2009


You’re no longer welcome here, as far as I’m concerned. There’s honest disagreement (see: Agellius) which we can handle just fine, and then there’s bitter trolls.

You are a bitter troll, and I see no reason whatsoever to supply with a soap box.

Adam G.
August 11, 2009

Do we supply gleeful trolls with a soapbox? Besides ourselves, I mean.

August 11, 2009

I would just as soon not. Besides the irritation, it’s precious seconds out of the gift of time God has given me he’s wasting.

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