Saturday, November 6, 2021

Black Hole evolution as Quantum Ontology is now proven by Nobel Physicist Gerard 't Hooft - aka noncommutative phase logic!

 

 The Taiji means Gerard 't Hooft:

To reproduce realistic quantum mechanical models, we need these periods to be considerably shorter in time than the inverse of the highest energy collision
processes that are relevant.

 

 The bottom line is that the positions of the out going particles are effected by the momenta of the in-going ones, and, because of quantum duality relating position to momentum, the same relation is found when going backwards in time: the momenta of the out-going particles are linked to the positions of the in-going ones.
These findings allow one to construct a unique expression for the black hole evolution matrix, only requiring very basic knowledge of the mathematics of GR and QM. 

Godel incomplete theorems The Man who broke Math . Every mathematical system will have some statements that can never be proven. His incompleteness theorems destroyed the search for a mathematical theory of everything. Nearly a century later, we’re still coming to grips with the consequences.
This is incorrect. What Godel proved was that any attempt to axiomatize mathematics would be inconsistent and incomplete, which proves that mathematics is not a system created by man, like English language is. Mathematics is actually tautology, and tautology is true by definition: 1 = 1, 1+1 = 1+1, etc. These aren't axioms, but tautology, hence Godels theorem does not apply.
 @Joe Physics Educator  the circular logic of tautology doesn't apply to noncommutative quantum algebra math as Roger Penrose points out, and Penrose emphasizes Godel's Incompleteness Theorem as well. A tautology assumes the closed symmetric logic but noncommutative phase disproves that as Alain Connes points out. So as Penrose reveals the "proto-consciousness" of the Universe is before the "collapse" of the quantum wavefunction. There are other examples of this proof - the "weak measurements" by Yakir Aharonov's group. We don't have to prove the truth of reality. Stuart Hameroff goes into details about this - in his article on free will and precognition. A proof makes several assumptions while logical inference based on noncommutative phase is not a closed symmetric proof. Math professor Louis Kauffman calls this "primordial time" - so to go back to your 1 plus 1 example - he explains that 1, minus 1, 1, minus 1 as a time iteration is inherently noncommutative due to the square root of negative one as the quantum measurement problem.

 @Voidisyinyang Voidisyinyang  That's a problem with the interpretation of QM, not of mathematics in and of itself. QM is itself not a definite science as it has many competing interpretations, so when it comes to QM there are no absolute statements about reality or mathematics to be made, given that QM has no definite ontology. Godels theorems apply to any axiomatic system, but mathematics in itself is tautology.
 @TheConsciousCat  an axiom is fundamentally different from a tautology. A tautology is self evident, 1 = 1, whereas an axiom does not contain its own proof and requires other things to prove it, which is why any axiomatic system becomes incomplete.
For examples: e^(i*pi) + 1 = 0 is a tautology. The Fourier Transforms are tautologies. e^(i*x) = cos(x) + i*sin(x) is a tautology. The FT and Eulers equation are central to thermodynamics and QM, but it's the interpretation of QM which is the problem given the many competing theories, however the underlying equations are tautologies. Thus, the correct interpretation has eluded us to now, but the correct interpretation will eventually be discovered as being self evident and tautologous, given that the underlying mathematics is.
 @Joe Physics Educator  saying math is a tautology as circular reasoning is an empty statement - it's just semantics. What you say about quantum mechanics is not true. The noncommutative phase math of quantum mechanics occurs in a "primordial time" before the wavefunction collapse such that the future and the past overlap. Yakir Aharonov explains this ontology well: Yakir Aharonov: "There is a non-local exchange that depends on the modular variable....I'm saying that I have now an intuitive picture to understand interference by saying that when a particle moves through two slits, it always goes through one slit or the other, but it knows which other slit, the slit through which it did not go, whether it is open or not, because there are nonlocal equations of motion." Finally making sense of the double-slit experiment (2017, Aharonov): The nonlocal equations of motion in the Heisenberg picture thus allow us to consider a particle going through only one of the slits, but it nevertheless has nonlocal information regarding the other slit.... The Heisenberg picture, however, offers a different explanation for the loss of interference that is not in the language of collapse: if one of the slits is closed by the experimenter, a nonlocal exchange of modular momentum with the particle occurs....Alternatively, in the Heisenberg picture, the particle has both a definite location and a nonlocal modular momentum that can “sense” the presence of the other slit and therefore, create interference." 
 
 So as Alain Connes explains the Ritz-Rydberg spectral equation is noncommtuative time-frequency. This is also easily explained by music theory as Connes details in his youtube talks. 
 
Or consider Nobel Physicist Gerard 't Hooft: Ontology in quantum mechanics Gerard ’t Hooft:
 "This must also hold for any Stern-Gerlach set-up or any of the other paradoxical contraptions that have been proposed over the years. Real state in = real state out. This was called the ‘law of ontology conservation’ [14]. At first sight it seems that a Stern-Gerlach experiment, after a rotation over an arbitrary angle, turns into a superposition of several real states. This is true in the mathematical sense. "

 Joe Physics Educator

 @Voidisyinyang Voidisyinyang  again, that is all based on prevailing interpretations of QM, which is thus not at all a definite statement given the competing interpretations. A tautology ends up being totally meaningful, and the axiomatic systems are meaningless and empty, as per Godel: any axiomatic system suffers from incompleteness, hence contain no absolute meaning, whereas tautology does not suffer from this hence contain meaning by virtue of not suffering from incompleteness.
 @Joe Physics Educator  "The tautologies are essentially generated from a single propositional formula by a natural action of the symmetric group Sn. " As I have explained to you a tautology assumes symmetric logic while noncommutative phase is asymmetric time-frequency energy. Alain Connes has a Fields Medal all based on noncommutative geometry or quantum algebra - it's hard to get than a Nobel Prize. So why not just study Alain Connes and learn something? haha.

 However, we also hit upon a more sobering difficulty, The region behind the
horizon has to be used to describe the time reverse of the region normally visible, otherwise the evolution matrix (actually a quantum evolution matrix) fails completely to be unitary.

 Indeed, we find that black holes may be telling us something about the origin
of quantum mechanics.

 Math professor Louis Kauffman.

 "By starting with a discrete time series of positions, one has immediately a non-commutativity of observations, since the measurement of velocity involves the tick of the clock and the measurement of position does not demand the tick of the clock....In this sense, i [square root of negative one] is identical in concept to a primordial time." 

Math professor Alain Connes.

"The amazing fact is that exactly time is emerging from the noncommutivity. You think that these variables do not commute, first of all it is that they don't commute so you can have the discrete variable that coexists with the continuous variable. What you find out after awhile is that the origin of time is probably quantum mechanical and its coming from the fact that thanks to noncommutativity ONLY that one can write the time evolution of a system, in temperature, in heat bath, the time evolution is really coming from the noncommutativity of the variables...." 

Math Professor Louis Kauffman.

 "ab = −ba. One can take a as the iterant corresponding to a period two oscillation, and b as the time shifting operator. Then their product ab is a square root of minus one in a non-commutative context....In this sense the square root of minus one is a clock and/or a clock/observer. " 

 "There are two iterant views: [+1, −1] and [−1, +1]. R(x) = −1/x. 1,R(1) = −1,R(R(1)) = +1,R(R(R(1))) = −1,+1,−1,+1,−1, · · · ." ηη = 1 and [a, b]η = η[b, a] and i = [1,−1]η time is seen to be a process, an observation and a magnitude all at once."

 

 

 

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