Discontinuum Critical Signal/Noise Density Matrix

Computing Critical Signal/Noise Matrix Physics

While signal profiles with [1] give velocity aspects, PDP circuit mechanism [2] eventually give operational critical density systems signal/noise matrix originating super luminous vacuum quanta to particle transition. This will provide universal property characterization of fundamental energy generating processes that naturally evolves, shown as event emerging timeline.

Gravity originated after infinite extent nebular superluminous, however, dark energy like eternal multiverse probabilistically produced PDP circuit mechanism with monopoles-electron-positron-hod-Plenum clocking assemblages [2, 3]. One may surmise, based on these, gravity helped differentiating existence versus dark matter to form geodesics within stellar constellation astronomical matter systems. These universal systems within multiverse realistically promulgate, eventually sustaining ever changing inorganic versus organic varied life forms.

Gradient vortex modeling point fields provided progenitor partial differential equations of superluminous vacuum quanta [1]. Gage PDP circuit mechanism provided hod Plenum PDP assemblages creating energy matter particle real universe; these mechanisms have dissipative discontinuum physics characteristics, helping in configuring observables especially giving mesoscopic authenticity while validating these theoretical modeling protocol [3, 4, 5, 6].

Further matrix simulation physics computing programming algorithms experimental observational measurements will confirm validity of models towards grand unifying physical mathematical Sciences. We have order of magnitude evaluation of PDP circuit to be about 10-

26 m, that is correspondingly h*c metrics, that approximately estimates the discontinuum length to have values as well in that scale [2, 3, 7]. Critical values with signal/noise density matrix may then be computed from these theoretical models with programmed simulations alongside experimental measurements [7, 8, 9, 10]. They will then determine conditional criteria with superforces, coming into action at each level of interaction. Particularly, gravity that wasn’t possible to quantify with any of existing theoretical physics may become realistically computable with these ansatz breakthrough approaches!!

Signal/Noise (“ Γ ”] Explains Gravity Oscillations Biosciences Natural Processes

With the signal/noise rules derived elsewhere, it is possible to explain the action of gravity based on critical signal/noise density matrix principle or i-rule, exemplified by mesoscopic observables there [3, 4, 5, 6]. Additionally, one can think of a card of a card deck, having only one side marking visibly. However, one card typically will give higher "Γ" than "Γcr", i.e. (Γ > Γcr); hence per model i-rule, the card has tendency to combine to form a deck or so we will intuitively perform manually that operation. Much like the simple harmonic motion, for example, simple pendulum situations, such actions will lead to Γ dipping to less than Γcr, i.e. (Γ < Γcr), then combination will get distributed or multiplied, simply expressed like: Γij => ::= Γij(Γij), where => ::= logic symbol denoting reversible aspects, depending on whether Γ > or < Γcr. We can thus explain situations where oscillations will happen and there will then establish optimum Γ oscillations around Γcr. This will typically correspond to gravity oscillations within geodesics as well. We know that lattice vibrations, absolute zero spin oscillations, as well as "zitterbewegung" zero-point oscillations all have this feature in common [1, 2, 3]. Further, these oscillations may arise due to hod-Plenum-PDP circuit mechanism within super luminous vacuum quanta as a "perpetual motion machine", that undergoing vacuum friction manifests by creating matter "inertia" [3]. They are explainable with reminiscent property exhibited explainable by this signal/noise principle or model i-rule, eventually to validate by experimental observations measurements ongoing. One point clarifying signal/noise decimal fraction aspect. Simple arithmetic multiplication of decimal fractions will have value less than both the decimal fractions, and then vice versa. This will apply to "Γ" since magnitude of the density matrix signal/noise is between 0 and 1. It is high note to realize that oscillations of "Γ", such as "zitterbewegung" around "Γcr" will be "offset oscillations". This also will be true of zero-point fluctuations, specifically, this "offset oscillations" will mean like a "raised ground" or "Γcr" is shift or elevated level, due to "Γcr" of "Γ" oscillatory behaviors.

Analogous to above, one can explain biosciences natural processes such as cell divisions, that try to have dynamic balance of Γ versus Γcr, and thereby attendant oscillatory characteristics of cells multiplying and/or dividing to keep Γ in the range of optimum Γcr. We might extrapolate to say that will involve forming organs, skins, and connecting inorganic-organic forms via bone creations to evolve life forms. Many connected human actions, consciousness, experience, thought processes physics to metaphysics are eventually explainable with these argumentations. Presently, author will not further expand on these, except to say that it is quite applicable to expert bio scientist to explore possible genetic linkage with the signal/noise or "Γ" factor in the feedback loop mechanism, which seems to be true in the quantum, micro, mesoscopic, macro, as well as astrophysical levels of not only inorganic existentialism, but also organic existentialism.

Signal/noise matrix can be configured by considering directional eigen "ket" matrix times distributed corresponding eigen "bra" matrix to compute density matrix [6, 8, 9, 10, 11]. Procedures algorithmically laid out elsewhere [6] have been applied here as well. Typical "ket" matrix for complex angular momentum with {off, on} switching modes, giving signal/noise "Γ" at any point "Γpoint" with [point] = {states and/or modes} Example here: Ψ' : component wave-function imaginary, Ψ∞ : component wave-function angular momentum, Ψoff & Ψon are component wave-functions of switches modes off & on, and Γioff, on, Ψ} variable gives following algorithm equation operationally [6]:

$$\begin{pmatrix} \psi_i \\ \psi_\omega \end{pmatrix} \begin{pmatrix} \psi_{off}, \psi_{on} \end{pmatrix} =>: \because \left[ \left( \Gamma_i, \text{off}, \text{on}, \omega \right) \right]$$

If Γioff, on, Ψ > Γcr then matrices will combine, like "quantum entanglement", for example quantifying following argumentation ongoing: {if Γioff, on, Ψ < Γcr then matrices will multiply with having "quantum decoherence"}, per critical signal/noise density matrix principle or i-rule, explained above earlier in this Section 3.

One can schematically construct absolute zero matrix trivially. We configure algorithmically null-nonabsolute matrix, inputting Γioff, on, Ψ = 0 in the Equation (1), quantifying mathematically complex density switches momentum matrix. We note that immediately they are forming magic square symmetry matrix [2, 3, 6] of 2×2, 3×3, and so on square matrices, with sum = 0!!, like Equation (2) shows.

Since these magic squares matrices aren't having proper symmetry, prime factorization occurs [2, 3], generating nonzero points with "Γioff, on, Ψ ≠ 0 like Equation (3) shows.

0 0 0 0 0 0

•    
•    
•  
•    
•  
•    
•    
•  

0 0 0 0 0 $$ \varGamma_ {\mathrm {i}, \mathrm {o f f}, \mathrm {o n}, \omega} $$

Inhomogeneous “

” shown per Equation (3) will make them to rearrange, having sum ≠ 0 magic square matrix with $$ \Gamma_ {\mathrm {i}, \mathrm {o f f}, \mathrm {o n}, \omega} > \Gamma_ {c r} $$ , as explained earlier about random fluctuations [1, 2, 3, 12, 13, 14, 15] out of the absolute genesis evolving onto zero point fluctuations or “zitterbewegung” oscillations [1, 2, 3, 4, 5, 6, 13, 14, 15, 16, 17]. Applying “i-rule”, like above describing decimal fractional matrix arithmetic operational basics, :: ( ) i j ij ij Γ ⇒⇐Π Γ , this condition will make matrices to combine, entangle, and/or eventually collapse to form blackhole, in general, dark matter. Consequently, with the blackhole and/or dark matter formation, dipping of the “ ” below cr Γ occur, causing decohered multiplication of matrices events, with “zitterbewegung” keeping the “Γ ” factor oscillating within the range of Γ cr harmonically dynamically. Resultant gage vacuum string metrics that originally author has derived elsewhere [2, 3, 6] are shown below summarily, having the Figures 1 and 2, depicting natural mechanism generating energy perpetually sustaining oscillations by Hod-Plenum-PDP assembly circuit model [3, 6]. Author elsewhere put together these situations theoretically in terms of zero gage string metrics schematically sketching monopole-particle entities popping with gage vacuum [6] and per Equation (3). This will dissipate discontinuum physically, creating patrons, quasi-particles, particles, atoms, as well as mesoscopic to astrophysical entities [1, 2, 3, 4, 5, 6, 7, 12, 13, 14, 15, 16, 17] with algorithmically repeating matrix simulation population pattern rules, Equations (1) through (8), incorporating gage dissipative discontinuum physics [3].

$$ \varGamma_ {\mathrm {i}, \mathrm {o f f}, \mathrm {o n}, \omega} $$

String metrics [3, 6, 15, 16] give gage absolute matrix. Physically, matrix sketch of quantum density monopoles, per PDP circuit assemblage enhanced modeling will look like, per Figures 1 & 2 schematics [6]:

Click to enlarge

Author developed mathematically following algorithms [3, 5, 6]. Integrated Physics Model quantum cosmological algorithm vacuum gage fields equation is given by [3]:

$$ \left\| \left[ \mathrm {G g} \right] \mathrm {P g} \left[ \varepsilon_ {\mathrm {G R}} \right] ^ {- 1} \left(< \left[ \psi_ {\mathrm {E}} \left(t _ {\mathrm {g}}\right) \right] \left| \left[ \psi^ {\mathrm {M}} (\mathrm {t g}) \right] >\right)\left[ \varepsilon_ {\mathrm {G R}} \right] \right\| = \left\| \left[ \rho_ {\mathrm {p}} \left(t _ {\mathrm {g}}\right) \right] * \left[ \varepsilon_ {\mathrm {G R}} \right] \right\| = \Lambda_ {g v} $$ (4) Here in the Equation (4), $$ (< \Psi \mu (\mathrm {t g}) | \Psi \mu (\mathrm {t g}) >) = (< [ \Psi_ {\mathrm {E}} (\mathrm {t g}) ] | \Psi^ {\mathrm {M}} \left(\mathrm {t} _ {\mathrm {g}}\right) ] >) $$ is gage wave function inner product of the electric and magnetic tensor $$ \left[ \rho_ {\mathrm {p}} \left(t _ {\mathrm {g}}\right) \right] $$ fields; g g G P     is Plenum* gradient functional;

is gage Plenum* quantum density matrix, [↋GR] stands for the quantum gage fields, E g (t ) Ψ is the wave function of gage electric fields, M g (t ) Ψ is the wavefunction of gage magnetic fields, (tg) is gage time, and gv Λ is the gage vacuum energy density equivalent to cosmological constant [18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29].

Elsewhere further, author has shown algorithmically, configuring constitutively quantum density matrix to obtain detailed signal/noise density matrix [3, 6]; these are explained here too, listing equations showing sequences.

ε     Γ Γ Γ Γ     Γ Γ Γ Γ         Γ Γ Γ Γ         Γ Γ Γ Γ     Ó − − Ó τ t X Y Z ε ψ ψ ψ ψ ε $$ \left| \left(\psi_ {\Gamma_ {0} ^ {+}} \psi_ {\Gamma_ {g} ^ {-}} \psi_ {\Gamma_ {g} ^ {+}} \psi_ {\Gamma_ {0} ^ {-}}\right) = >:: < = \right| $$ ϑ ϑ + + x t X t Z (5) $$ \Gamma_ {0} ^ {\uparrow} \psi_ {\Gamma_ {0} ^ {\downarrow}} \psi_ {\Gamma_ {0} ^ {\uparrow}} \psi_ {\Gamma_ {0} ^ {\downarrow}} $$ ϑ ϑ + + Γ Γ Γ Γ Ó Ó y t X Y Z ε Ó − − Ó z t X Y Z or compactly, $$ \left[ \Gamma_ {\mathrm {X Y Z}} \right] = >: < = \left[ \Gamma_ {\mathrm {X Y Z}} \right] \left[ \Gamma_ {\mathrm {X} ^ {\prime} \mathrm {Y} ^ {\prime} \mathrm {Z} ^ {\prime}} \right] \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \d { } [ ] X'Y'Z, X"Y"Z" XYZ Γ Γ > Γ (6) since $$
\sum_ {i = 1} ^ {n} \sum_ {j = 1} ^ {m} \Gamma_ {i j} = 1
$$ i j i j (7) noting that: ↋ ≡ field, Ψ ≡ wave function, Γ ≡ signal/noise on XYZ coordinates, [ ρ ] ≡ density matrix., with details provided there [6].

Algebra gage physics discontinuum equation (AI.5) [3], with $r_{\text{discontinuum\_energy-fields}}(t) = r\text{DEF}(t) = n(t)$. DL + $r_g(t)$, with $n(t)$: number of discontinuum lengths, DL; $r_g(t)$: DL gap length, provided discontinuum physics [7] gage transform of detailed quantification in Appendix [3]:

$$g[r_{\text{ref}}(t)] = g[n(t).\text{DL}] + g[r_g(t)] = g[n(t).\text{DL}] + g[r_g(t)] = g[r_g(t)]$$

with DEF, the discontinuum energy field, defined elsewhere [7] links with DL, discontinuum length and the rg, gap length in evolving and/or in emerging time domain number line scalarwise.

Per gage physics [6], conjecture of gravity, with observable parameters quantum astrophysics, where $[\Gamma]$ matrix of signal/noise ratio determines existence of matter, while $[\rho]$: point density matrix pattern determines property of gravity. Magic square symmetry prime factorization [2, 3, 6] will eventually differentiate among inertial, charged, and neutral matter. If $[\rho_{\text{object}}] > [\rho_{\text{cr}}]$, then object will sink or fall in relational gravitational inertial environment. Otherwise, if $[\rho_{\text{object}}] < [\rho_{\text{cr}}]$, then object will levitate or float in that environment. These were explained having the proposition and observable physics with real measurable observations [3, 6].