12 Q-Pair Proof for complex-number Universe

[Mathematical Proof]

12 Q-Pair Proof for complex-number Universe

David M. Salaman

12-2024 {n. 2014}

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e^i*pi= -1
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It all starts at the beginning:

1

Nobody thought about what it really was - they just started using it thinking they understood it.

Had they realised what it was, they would have been aware of its "hidden" counterpart that was always there in their mind whether they knew it or not. No surprise this is the role i plays in all of this.

Of course, I don't expect the ancient Greeks to have known this (well, maybe I do).

For them, developing 'Mathematics' was like digging up a dinosaur fossil - you find some small pieces of it (even something large seeming like Pythagoras theorem) and you still really have no idea what you are dealing with until the whole fossil is unearthed. Only then can you know everything about it.


Complex numbers is the whole thing for mathematics. Until you know that, all the other parts can't be understood properly.



Pythagoras, in this way of thinking, becomes trivial because the "hypotenuse" (don't call it that!) in complex thinking joins the e^0=1 component on the Argand diagram to the e^(i*pi/2) = i component [the x and y axes in classical thinking].

In this way it represents the difference or the 'distance' across the plane (more of a brane actually) between those two points.


Well, in that case, since the complex-vector e^i*θ = cosθ + isinθ, the separation, s, should be in the form:

s^d = [cosθ]^d - [isinθ]^d

where d is the dimension in which you are inspecting.


In other words, if it is the separation along a one dimensional line (axis) it's just the difference between the magnitudes of the complex-vector components but if it's the separation across the 2-dimensional brane-side you are inspecting then it turns itself into what we have been calling 'Pythagoras':


d = 2:

s^2 = cos^2(θ) + sin^2(θ)




Continuing through mathematics in this rigorous way reveals how complex numbers explain everything that we are both most familiar with and also deeply curious about, perfectly simply: +/-infinity, "dark energy/matter", etc.. as well as the 'mundane' (not to me) - "day / night", "full moon / new moon", "star / black hole", even a supernova going off somewhere. It's all like binary-type quantum physics as it turns out (all set in an unbelievably majestic relativistic playground). That's how I now see it all, anyway.


Before we get ahead of ourselves, let's remember what we are trying to fix - modern physics is stuck. No Grand Unified Theory [GUT] therefore no Theory of Everything.


As with the number "1" - you can't just go about doing things without checking you have understood the most fundamental thing of all - what is it we are looking at. Until then you might do all sorts of things but the one thing you will never be able to do is solve everything with that approach. Ironically (a quantum physics effect, as it turns out), we needed to not know how the Universe works since the Copernican Revolution to be able to get to where we are now.

Standing on the shoulders of giants was necessary, until the very last step - "midnight", when everything changes (without anything appearing to have changed at all).


So, if you want to know why a GUT eludes you, you have to check whether you are allowing all possible avenues of discovery, not just the ones you think you should allow.

Suppose for example, the explanation for why we are stuck (modern physics - unresolved QM/GR understanding) was somewhere that the "scientific method" was preventing you from looking.

Once you understand that this self-imposed prison is what was holding us back from piecing modern physics together then everything falls into place - in the most unexpected way possible (quantum physics strangeness in action).

The only thing that changes once you understand complex numbers (not hard - our instinct is the way complex numbers work) is your subjective experience - you now understand what you see in a way that works seamlessly with the Universe. Your objective experience, meanwhile remains completely unchanged (this combination is the quantum strangeness of the effect on you - subjectively).




And now, with the stage set, here is the derivation of the fundamental quantum mechanics / general relativity Universe:


Ingredients:


*quantum mechanics

*e, i, 1, pi

*general relativity



*and an Argand diagram




[this is the Mathematical Proof - no diagrams necessary but they might help if you are not familiar with Argand]


If you imagine the 4 quadrants on the Argand circle, then suppose you rotate the phase by pi/6 (from theta=0) then you have effectively halved the imaginary component, i (the real component is (3/4)^0.5).

Do it again, (add another pi/6) and now it is the real component, 1, that is halved and the imaginary one that is (3/4)^0.5.


Keep doing this and you have 12 points around the edge of the Argand circle.


In other words, the simplest rule in complex numbers (halving/doubling, or quantum pairing/unpairing) produces a 12 quantized unit pattern but in fact there are also the ghosts on the back of the Argand diagram (the 'imaginary' [complex-reflex] version) so it is specifically 12 pairs - "quantum pairs".

12 Q-Pairs

Since complex numbers are what solved quantum mechanics and general relativity it doesn't seem surprising to me that the Universe might work like complex numbers.



e^i*pi = -1

Fundamental 12 Q-Pair pattern found underlying all structures [at all fractal scales in {real|dark} complex-n Universe].

Key examples:

Standard Model of the atom:

12 particles (6 leptons, 6 quarks)
12 anti-particles (6 anti-leptons, 6 anti-quarks)

The photon is the "origin" of the Argand circle.



Musical scale:

12 intervals up (twelfth-root of 2 factor between each in frequency)
12 intervals down (twelfth-root of 2 divisor between each in frequency)

Tuning reference is "origin".



Earth Year:

12 Full Moon phases
12 New Moon phases

SUN is "origin".



Clock face:

12 ordinals AM
12 ordinals PM

Atomic clock reference (if you are lucky) is "origin".



Human Genome:

12 pairs of chromosomes [11 pairs of homologous chromosomes + 1 pair sex chromosomes] - M
12 pairs of chromosomes [11 pairs of homologous chromosomes + 1 pair sex chromosomes] - F

Mitochondrial DNA is "origin".












Q.E.D.