We offer a purely computational and combinatorial explanation for Coldea *et* *al*.’s 2010 report of having measured the golden mean in a quantum system. Our method employs the roots of projectors (in the discrete and finite geometric algebra G5,0) to capture both the dimensionality (*3+1*d) and the detailed structure of the electro-magnetic field, in-cluding Majorana fermions (with fresh details).

Read more in the TauQuinion paper here.

*This text is from a post comment I made on http://profmattstrassler.com/2012/10/15/why-the-higgs-and-gravity-are-unrelated/#comments*

Dear Prof. Strassler –

Like so many of your readers, I say many many thanks for this initiative. You certainly nailed me with this posting! I hope we all don’t wear you out with our tortured inquiries.

I’m a computer scientist, and look at “processes” from the point of view of an operating system: it does not, it *cannot*, matter what the various processes are doing – that’s their business. From the os point of view they all look the same. Just anonymous abstract discrete processes, doing what processes do: Wait and Signal to the outside, maintain stable (often concurrent) state inside.

These being *discrete* processes, one can imagine doing some combinatorics both along and across various event sequences, and hopefully find some structure. And that’s what we did, starting with processes with one bit of state, and building up from there. We report the results at TauQuernions.org.

This is where your post about the Higgs and gravity comes in. One would expect that a purely combinatorial approach like ours would produce results unbiased by any other criteria – prior knowledge, theoretical constructions, biases, what-have-you. One pattern that pops out is

H = (ab-cd) + (ac+bd) + (ad-bc) = Tx + Ty + Tz

which is nilpotent. In fact, the three pairs are isomorphic to the quaternions except that they are irreversible, and as well, each is an entanglement operator. Quaternions being the very definition of 3d space, we MAYBE made the mistake you describe, of confounding the Higgs, mass creation, and gravity.

But I don’t *think* so, because we stop at the point where we dot Tx+Ty+Tz with whatever X is to manifest in 3+1d tauquernion space. Ie. we simply punt, not knowing the necessary physics to take it any further. I agree that if this projection disagrees with well-established theory, then we’ve likely figured wrong. But it’s not obvious to me this will be so. Eg. our measure of heft is bits, which translate to energy, not to mass.

In addition, we found a number of patterns that I don’t really find echoed in the expert discussions. One wonders. Finally, we suggest that it follows that the mechanism underlying gravity is entanglement, and this seems to collide with your argument. Yet our approach, being purely combinatorial, is supposedly theory-neutral.

So, if our approach *is* truly flawed, I’d sure like to know just where it goes off the rails.

**Michael Manthey**

The papers below all precede the finding that tauquernions map to SO(4) and tauquinions to SU(3), whence it is assured that the model being presented here has the overall structure U(1) x SU(2) x SU(3) x SO(4), ie. the Standard Model of quantum mechanics augmented with relativistic 3+1d spacetime.

The term “tauquernion” derives from the mathematical term “quaternion”, in part to retain the mnemonic ring of “quaternion”, and as well because “tau” itself often designates a time variable. Both apply.

**Do you know what “quaternions” are?** [Full explanations are in the papers!]

They are a different phase-based way to describe the axes of 3-space, using outer-product vector multiplication . The unit quaternions are the three mutually perpendicular planes . MORE: Each of these squares mathematically to -1 : taking , so each is a representation of . ‘s powers cycle through the four quadrants, , exhibiting the sequence of phases that determine an entity’s coordinates. In the end, an coordinate is turned into , where are the powers of that determine which quadrant (4 in the plane, 8 in 3-space).

It follows that motions in the quaternion coordinate system are reversible, since each quaternion is a root of unity.

They are called quaternions, with the connotation of 4-ness, because their discoverer, Hamilton, saw that when combined with a (fourth, scalar) time coordinate, he had discovered a brand new way to look at 3d space and its relationship to time, namely that the two domains are perpendicular to each other, via : take space as “imaginary” and time as “real”. In this 4-d sense, quaternions are widely used in the theory of special relativity. In quantum mechanics, as here, the phase/wave aspect dominates and time t is confined to irreversible multiplications (= energy use and entropy creation).

So back to tauquernions. They are exactly like quaternions except that they are not reversible. That is, particulate motion in tauquernion space always costs energy. And basically, energy use = time’s tick. This is another way to describe the Higgs field – the creator of gravity, mass, space, time, and entropy – and that is what the following paper does:

The tauquernions are inhabitants of the geometric (Clifford) algebra Noting that is isomorphic to the Pauli algebra, tauquernions therefore fall outside of the Standard Model of quantum mechanics (a good thing here).

It turns out that the sum has exactly the properties of the Higgs boson. Simultaneously, are themselves ebits, ie. entangled EPR information, and so the **mechanism** underlying space, mass, gravity and entropy turns out to be **entanglement!** All this and more is described in the above paper. BTW, one referee report described the mathematics as “sound” and “of interest in its own right”, so just relax and enjoy!

The algebraic theory of computational processes applied in the preceding paper is described in:

This paper, aka. *SynchFont*, analyzes the computational concept of inter-process synchronization in the form of the two primitive operations *wait(event)* and *signal(event)*. It turns out that *wait*s correspond to bosons and *signals* to fermions. All very clean and completely in accord with quantum measurement theory. So this establishes a solid, and novel, bridge between computation and quantum physics.

The following is a lighter piece, but in preceding the TauQuernion paper by several years, the result that comes out of plugging our geometric algebra into the Riemann Hypothesis is clearly prescient in its characterization of distributed systems. The process-representation of SynchFont shows up in the context of wave-particle duality, among a number of other observations of interest to those interested in process-based (Heracletian) systems.

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