# Reflections on the World-Crystal

**In which I roughly gesture at some out-there ideas — mostly due to others, with some modest unique Goertzelogical variations — that could possibly, maybe, conceivably hold some keys to unifying physics and forming a scientific partial-explanation for psi phenomena.**

# In Praise of Wacky Out-There Fundamental Physics Theories

A half century past the concretization of what is now called the “Standard Model” — quantum field theory plus quark theory, handling electromagnetism and weak and strong nuclear forces — the theoretical physics community still has not come up with an accepted way to unify the Standard Model with General Relativity (our best current theory of gravity).

Meaning: there is no empirically-demonstrated unification of the two physics theories, and also no theoretical formal unification that is sufficiently elegant and compelling that everyone in the field accepts its correctness.

String theory and loop quantum gravity, themselves complex sub-fields full of. multiple overlapping and competing theories, have been the main contenders here for some time, but they both present complex issues and problems that are keeping brilliant theoretical physicists busy and probably will be for some time.

Concurrently with research on these major contenders, there is a constant flow of “out of the mainstream” ideas on unified physics — mostly not getting much love from the high-prestige core of the theoretical physics community. Yet given the difficulties with the more commonly endorsed approaches, it’s hard (for me) to dismiss these out-of-the-mainstream approaches too blithely.

The assessment of modern physics theories is given a special twist by the way both quantum mechanics and General Relativity have core aspects that feel counterintuitive to most people. This is a context in which being really weird is often seen as a feature rather than a bug. Early quantum pioneer Niels Bohr said of one colleague’s ideas: “We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct. My own feeling is that it is not crazy enough.”

Among the various “possibly crazy enough” theories of unified physics out there, some go beyond just trying to unify the Standard Model and General Relativity, and propose more or less radical modifications of these core theories. This sort of theory tends to be frowned upon by the physics establishment as being “crazy in the wrong sort of way” — but I think it’s worth being more open-minded in this regard.

Often when looking at an out-of-the-mainstream theory, it’s not immediately evident how the theory can be made to deal with all the practical phenomena that the Standard Model now deals with. In this context, though, it’s worth remembering that a huge amount of work by a huge number of brilliant people has gone into various conceptual and mathematical hacks aimed at making the Standard Model coincide with empirical data and with pragmatic physics theories dealing with more limited scopes. It could be that with a much more modest amount of additional conceptual and mathematical work, some alternative theory could also be rendered more empirically sensible than it first appears.

*(RAMBLING SEMI-RELATED ASIDE: As an indirect analogy, I remember 15 years ago or so when some friends were struggling to raise money for their project applying deep neural nets to speech processing. Simpler statistical models were being pretty successful at speech-to-text and such at the time (e.g. the company Nuance was the 800 pound gorilla in the space), and so much money and effort was being plunged into these statistical approaches, that it seemed impossible in practice to catch up with their performance via deep neural nets, even though the latter were obviously a better technology. Merely millions of dollars tuning a better tech could not compete with billions of dollars tuning an inferior tech. Until eventually tens-to-hundreds of millions of dollars was put into tuning deep neural networks for speech processing, and the approach was proved superior — and started absorbing and earning billions of dollars, and the world never looked back. The point is, when a lot of resources are put into patching and accelerating a relatively lame approach, it can be hard for a better approach to catch up until it’s resourced at least to a moderate fraction of the level of the lame approach…. This often holds with theoretical work as well as with empirical and engineering work. One sees a similar dynamic in AGI today of course — so much money is now going into deep neural nets, which are now the new orthodoxy just as statistical speech processing was in its time, that it’s hard for superior methods like neural-symbolic and integrative cognitive architctures and complex-self-organizing-emergent-networks to prevail over deep neural nets simply because they are so under-resourced by comparison. But then in time eventually enough resources will be put into these superior approaches and they will eventually show their strength and the older lamer methods will be left in the dust of history….)*

Given all this prelude, what I’m going to do in this post is give some links to an out-of-the-mainstream physics theory that popped onto my radar recently, which I’ll refer to as World Crystal theory.

Actually my route to digging up World Crystal theory from the vast pattern mines of the modern Internet was even crazier than Niels Bohr, and had to do with my desire to find a connection between modern physics and psi phenomena. I was wondering if replacing complex number truth values with quaternion or octonion truth values could somehow play a role in making an enhanced quantum mechanics that would explain psi phenomena — and this led me to Marek Danielewski’s work on the World Crystal model, which turned out not to be a plain-vanilla “quantum mechanics on quaternions” theory bus something. much more ambitious, out-there and fascinating.

The complex of ideas I’m going to vaguely gesture about here goes a fair bit further-out than Danielewski does — but I’m taking the time to type it in because, for whatever my wild-ass intuition may be worth in this domain (where my expertise is frankly somewhere in the nether-region between expert and amateur), I feel like it could possibly the right sort of direction for both unifying physics and explaining psi.

# World Crystal Theory

The notion of “space itself” being filled with structure and energy is an old one — this sort of space used to be known as “the ether” — and also a new one, resurging in the quantum era in the guide of “zero point vacuum energy.” Another, fascinating modern incarnation of this concept is the “Planck-Kleinert crystal” — an abstract geometric/energetic structure viewed as tiling the 4D space in which we live.

This Plank-Kleinert “World Crystal” is hypothesized to function somewhat like a typical flexible material — a simple elastic substance, modelable by the classical Cauchy elasticity equations. But this classical mathematics can be interpreted in fascinating quantum-esque ways. Marek Danielewski takes a quaternionic formulation of 4D simple elasticity, and shows that the 4 quaternionic dimensions {1, i, j, k} can be viewed as a generalization of the 2 dimensions {1,i} of the ordinary quantum amplitude.

Different forms of quaternionic quantum mechanics have been explored before, inspired by the mathematical observation that the only algebras able to fulfill the basic conceptual axioms of probability theory are the real numbers, the complex numbers, the quaternions and the octonions. There is significant empirical evidence that quantum theory’s use of complex numbers to measure probability is necessary to account for how our universe works. But could the world perhaps make use of an even richer probability structure?

Just replacing complex numbers with quaternions in quantum mechanics leads to interesting and vexing results, as explored for instance in Adler’s work. Danielewski’s work is doing something different — his quaternions aren’t just probability values, they emerge from the structure of the hypothesized underlying World Crystal. The 4-dimensionality of spacetime leads directly to the 4-dimensions of quaternionic probability values. The standard complex Schrodinger equation emerges as an approximation to a quaternionic Schrodinger equation under appropriate simplifying assumptions.

The wave dynamics of the elastic World Crystal involve two sorts of waves, transverse and longitudinal — the former traveling at the speed of light, and the latter faster than light. These superluminal longitudinal waves can be seen as playing the role of the “pilot wave” in Bohm’s interpretation of quantum mechanics (years ago I explored how to integrate morphic resonance into the pilot wave theory, according to a more simplistic and straightforward approach than the World Crystal direction explored here.)

Gravity is then seen to emerge from defects in the World Crystal, via math showing that curvature in a 4D continuum is formally equivalent to a certain pattern of defects in the crystal approximating the continuum.

Now there are a lot of routes to the Schrodinger equation and to curvature of spacetime, and the mathematical magic Danielewski and others have performed is still fairly far from showing the World Crystal theory to be fully physically viable. But there seems quite a lot of promise here, certainly proportionally to the relatively small amount of work that’s going into exploring this direction.

There is a lot here that is counterintuitive to the mind accustomed to standard quantum mechanics — but this isn’t necessarily a bad thing.

For instance, Scott Aaronson, in his blog post on why quantum mechanics uses complex numbers, points out that real and quaternionic probabilities fail to satisfy the “principle of local tomography.” For instance, he observes that in the quaternionic case, if one has two distant entangled systems A and B with a combined (entangled) mixed state, then probing A and probing B separately could give statistical results that do not correspond to any possible state of the combined system {A,B}. Which cannot happen using complex number probabilities — in the complex-number case, the statistical properties of the combined system {A,B} correspond precisely to the properties that can be inferred by probing A and B separately and combining results. (And with real number probabilities, on the other hand, probing A and B underdetermines the combined system {A,B} leaving multiple possibilities for the combined state that are all consistent with the separate-probe observations.)

Aaronson views this failure of local tomography as a strong reason why quaternionic quantum mechanics is a Bad Thing and not so promising or sensible. But Danielewski views it as a feature rather than a bug. One might say: These inconsistent states of A and B are not actually possible according to the underlying wave dynamics. Instead the (superluminal?) back and forth between A and B will cause them to settle into states that are mutually consistent according to the algebra of quaternionic mixed states.

Finally, while the literature on the World Crystal is all about continuous math, it’s worth noting there is a separate literature presenting discrete lattice dynamics that approximate elasticity in continua. One could straightforwardly use this approach to create a discretized version of the World Crystal, thus fitting it into the tradition of Ed Fredkin, Ben Dribus, Stephen Wolfram and others pursuing discrete computation-ish infrastructures for the physical world.

If I were rich enough to fund random grad students to pursue various intellectually fascinating and potentially super-important research directions, I’d be sponsoring a few PhD scholarships to create and analyze simulation models of discretized World Crystal physics.

And to explore some yet weirder stuff —

# Multiversal World Crystals

Now I’m going to take things one or two steps wackier — because, why not… it’s that sort of blog post, right?

What if the elasticity tensors underlying the world crystal have a certain intelligence to them, in a crude sense? What if they adapt over time?

Amusingly, when I Googled a little for “adaptive elasticity”, what I came up with was a medical paper on elasticity in human bones as they heal and grow. Makes total sense, actually.

Suppose that stretching a little bit along a certain connection between two locations in the world crystal, makes that connection a little stretchier? This is basically an analogue of Hebbian learning on elasticity tensors, right?

Or what if it’s just the opposite — stretching a little bit along a certain connection makes that connection a little stiffer? This is an analogue of reverse-learning in neural networks , which is a technique for getting rid of parasitic memory attractors and unclogging a neural net whose memory has become overfull and opening it up to efficient new learning.

Physics-wise, Hebbian learning in the world crystal elasticity tensor is closely related to Smolin’s Precedence Principle — which is essentially a more socially-acceptable version of Sheldrake’s principle of morphic resonance.

Reverse learning in the world crystal elasticity tensor would relate to a notion of morphic anti-resonance — via when once a pattern has become established, its likelihood of occurrence in new instances decreases.

Morphic resonance has been posited by Sheldrake as a potential explanation for various psi phenomena (and see this page for some references helping explain why I take psi phenomena seriously, especially if you don’t). Morphic anti-resonance could similarly be a potential explanation for vexing phenomena such as “psi-missing” — in which some individuals guess wrong in psi experiments to a highly improbable degree — and “decline effects” in which many psi experimental protocols, after they have worked well for a while, suddenly stop working.

In some hypotheses, the human brain alternates between learning and reverse learning, perhaps aligned with waking and dreaming states. In a fundamental physics context, an alternate possibility is a multiverse of world crystals, each of which varies between learning and reverse learning across its spatial extent. Observations are then samples from this multiverse, including for each region some universes that are morphically resonant in that region and some that are anti-resonant.

The “intelligence” of the multiverse is then manifested, perhaps among other ways, in the presence of a decent density of component universes that are VERY morphically resonant, and a decent density of others that are VERY morphically anti-resonant … instead of say a Gaussian distribution in which essentially all universes have minimal resonance or anti-resonance. In this sort of situation, quantum probabilities (be they complex or quaternionic ones) sampled across possible worlds would sometimes end up dominated by contributions from clusters of morphically-resonant universes, or clusters of morphically-anti-resonant universes. When this happens as regards quantum-biological subystems of human brains, we get psi (or psi-missing) — maybe?

If pilot-wave type theories are an alternative to multiverse theories, what I’m suggesting here is sort of the best (or worst) of both aspects. The pilot wave in the World Crystal is an alternative to the quantum multiverse, for plain-vanilla quantum phenomena. But to get even weirder stuff like psi, we have a multiverse of pilot-wave-driven universes (which could be interpreted as a multiverse of multiverses), with varying degrees of learning/resonance and reverse-learning/anti-resonance.

It’s complex and weird, but is it really any more so than 11 or 26 dimensional vibrating strings giving rise to our universe via their resonance modes, and so forth? Modern physics is way beyond “is it too weird” or “does it make any intuitive sense”, what matters is “does it work?” …. And in that regard, the trans-multiversal jury is very definitely still out regarding the speculative notions in this blog post (and especially those in this section)! It would/will take an awful lot of technical work to flesh out these ideas to the extent they could be compared to experiment.

But yet, in some senses these ideas are a bit “elementary” compared to string theory and loop quantum gravity. Doing the work to flesh them out would be a lot of work, but seems like it would be well within the scope of modern math and computer simulation capability. Unfortunately I don’t have a lot of time for this, as trying to create AGI and running a blockchain project and co-raising 2 little kids seem to be occupying essentially all my waking hours (and then there’s Jam Galaxy Band, etc. etc.). But I’m hoping elaboration of the multiversal World Crystal doesn’t need to wait for super-AGI to solve it, and perhaps this post will excite the imagination of some eager young (or old) reader to take the next few steps of elaboration…

What is it about Ulf Klein's papers on the foundations that you don't agree with?

https://arxiv.org/pdf/1201.0150.pdf

https://link.springer.com/article/10.1007/s40509-019-00201-w

https://arxiv.org/abs/2202.13364

Best read in order. In short, the complex amplitudes are necessary due to the MATHEMATICAL coupling between an action describing dynamics on phase space and the probability density AND the desire for linearity. In PLAIN ENGLISH, the complex amplitudes are necessary because quantum theory is an predictively incomplete ensemble theory. Hey, this could be why the difficulty uniting QM with GR! Imagine that! It could be that such unification will not be possible until we have predictively complete quantum theory, something like David Hestenes' Maxwell-Dirac Theory extended to the Quantum Fields.

https://arxiv.org/pdf/1910.11085.pdf

See also Oliver Consa's works:

https://arxiv.org/abs/2110.02078

http://www.ptep-online.com/2018/PP-53-06.PDF

I'm not going to give you a heart for this one, no way, even though I like the superluminal thing. I checked my email and saw your post because I was reading about stigmergy and thought about sending Francis Heylighen a link to this 2013 paper I recently found:

https://bmcecol.biomedcentral.com/articles/10.1186/1472-6785-13-19

It's about telepathic communication in plants. Anyway, I also found the original guy from the Robert Anton Wilson book; his name was Cleve Backster and he was working for the CIA when he did the plant experiments. But this research was actually initiated by

https://en.wikipedia.org/wiki/Jagadish_Chandra_Bose

back in 1902!

This deep mystery is one of the reasons that I really, really want to live way past the current human maximum so I have a chance of seeing what develops.

Fascinating post, Ben. I've been wanting to catch up on the frontiers of thinking in physics and cosmology and this does a lot to help.