

Nutshell2019
19^{th}^{} April 2020

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"Plato is my friend; Aristotle is my friend, but my greatest friend is truth."  Isaac Newton "Un homme heureux est trop content du présent pour trop se soucier de l'avenir. (A happy man is too satisfied with the present to dwell too much on the future.)"  Albert Einstein "We should consider the laws of Nature as continually changing with the epoch."  Paul Dirac "Is the purpose of theoretical physics to be no more than a cataloging of all the things that can happen when particles interact with each other and separate? Or is it to be an understanding at a deeper level in which there are things that are not directly observable (as the underlying quantized fields are) but in terms of which we shall have a more fundamental understanding? "  Julian S. Schwinger “In other words, the laws of Newton could be stated not in the form F=ma but in the form: the average kinetic energy less the average potential energy is as little as possible for the path of an object going from one point to another."  Richard P. Feynman "Reading book after book the whole world died, and none ever became learned! But understanding the root matter is what made them gain the knowledge! "  Kabir Granthavali, XXXIII.3, Translated by Charlotte Vaudeville ***

Earlier we met with Aku the Amoeba and his commute in the universe known as “Blip” and as it happened Blip was infested. There was this quantity which did not change as Bliponians zipped through various Möbius and Lorentz Transformations, a quantity which measured this magnificent infestation, called entropy. The actiongauge which was supposed to provide information about Blip, was also compromised with entropy. Which meant Bliponians, were traveling blissfully unaware on a timeline with only one way forward, straight into a blackhole. Now Bliponians were not only unaware of entropy but they also did not know that the entropy was continuously increasing with the progression of time. So if an electron in Blip, was shaken more than 137 times before it spat out a photon. Then few millions years down the timeline same electron needed to be shaken more than 138 times before a photon poppedout. It did not matter to Bliponians that their minute existence was progressively sterile. It did not matter if Bliponians could not count to 2. But it did matter to some. Questions were being asked. The questions which required straight answers, answers that did not come from Bliponian rote, but from the nature herself. And it was then, the timeline curved away, from its predetermined path to apportion. It was also then, Blip stopped being a foreverbloating corpse and became a force.The fundamental eγ interaction, represented the measurementtools the observers were using for their measurements in Blip. The entropy inherent in the system not only limited the effectiveness of these measurementtools, but also ensured that these measurementtools became useless with the progression of time. The situation was as follows: Do we need time in Blip? Whether the time could be slowed down, or a new timeline could be started, or better still if time could be completely eliminated, was not known yet. But the basic idea was that the underlying topological space by definition, must have no entropy and therefore it must be independent of time. Therefore the constants defining the fundamental eγ interaction, must be correlated with each other in a manner such that time did not exist. Dimensional analysis led to the topological constant:
,
which
essentially is the Planck mass. The estimated mass of
a BH was of the order of solar mass,
approximately 2 × 10^{30} kg. Yet in
the topological
space, this mass was equivalent to Planck
mass, 2.18 × 10^{8} kg. The difference was
truly extraordinary. We can also think of this as duality between the measurements made by Obs_{M} and Obs_{c}. So the question arose, what did the quantity known as mass really represent? Was the value of the measured mass an intrinsic property or was it observer dependent? For a given measurement in jspace, Planckmass m_{P}_{}, Zeroentropy Mass m_{ZE}, and in this case Solar Mass M_{BH} in KruskalSzekeres coordinates, were shown below: Blip existed in the RegionI, so did M_{BH}_{}. The solar mass M_{BH}_{} was measured by Obs_{M } in the RegionI. The Planck mass m_{P} was measured in the RegionII and it was measured by Obs_{c}. The zeroentropy mass m_{ZE}_{} corresponded to the mass measured by Obs_{i}. It was finite but unmeasurable by either Obs_{M}_{} or Obs_{c}. (The continuity was defined as the succession of zeroentropy measurements.) If the radius of Blip was estimated as 4.4×10^{26} meters, then the definition of the constant j_{ML}_{}_{} could be used to estimate the mass of the Blob underlying Blip as 10^{67} kg, an incomprehensibly small number. For comparison the mass of the electron, a Blip entity with no known internal structure, was 9.1×10^{31} kg. An ecosystem of δ_{j}functions: Consider the internal structure of Blip, without planets, stars, galaxies, BHs etc. In jspace there was no perfect vacuum as a perfect "null" could not be measured. For any arbitrary time instant, the fabric in jspace consisted of jpixels which were seamed together by the Lorentz Invariance i.e the neighbouring jpixels were bound by Lorentz Invariance. And since Lorentz Transformation and Möbius Transformation were equivalent to each other, at any given instant on Blip timeline, the structures measured in the neighbouring pixels could be transformed into each other using Möbius transformations. So how can Aku and his team, think about the fieldequation shown below, describing the spacetime fabric of Blip, in the topological space? 1. Λ is invertible iff it is nonsingular. 2. More importantly Λ is always nonsingular in jspace. The argument is straight forward. Λ is singular iff Λ = [0]. However in jspace [0] is equivalent to [0j] which always has a finite value corresponding to the least energy surface and hence Λ is nonsingular and invertible both. 3. Thus the condition that any metric tensor in GR has to be invertible, derives from the requirements of the underlying topological space, and it also prohibits the existence of pure vacuum in jspace since Λ is always finite. However the condition of invertibility also prohibits the existence of a pure solid as well. It can be stated as that the condition of "totality" in either direction is prohibited in Blip, per the requirements of the topological space underlying Blip. 4. Furthermore since Λ is invertible and nonsingular, we can derive the condition for continuity as, B = Λ^{1}AΛ. Here A and B are also singleelement matrices and hence by definition represent zeroentropy measurements in jspace, and thus continuity i.e. B and A are seamlessly connected via Λ. (Note that Λ is derived from g_{μν} and it is not a scalar in the topological space. We are merely counting in the topological space using singleelement matrices and Λ.) 5. In exterior RegionI, Λ can be represented as e^{iH}, where H is a Hermitian matrix. Since Λ by definition is nonsingular, it is not a zerotrace matrix describing a convex surface. Whereas no such restriction is placed on H, which converges to a zerotrace matrix under the relativistic limits. Thus eventual metric corresponding to the topological structure is always finite, though it can be represented in terms of zerotrace matrices in a measurement space corresponding to a lower information content. 6. The element in single element matrix, is not a number or a scalar per say. The definition of the element is based on the zeroentropy requirement of the topological space. The element can be represented as following: Here the element is shown just as a blob
with undetermined characteristics, rather than a number. The
definition of the element is purely a discrete measurement construct.
It represents the limitation of the observer making the
measurements. The element itself can have its own eigenvalue spectrum corresponding to a higher information space, not accessible to either Obs_{c}_{} or Obs_{M}_{}.
Another important issue is the definition of the inverse of the element. The entities "1" and the operation of inversion, have very different meanings in the topological space, unlike the standard definitions used in exterior regionI of KS representation discussed earlier. More importantly we must understand, why do we need to perform the inversion operation on the blob, to begin with? What does this operation signify? Continuity in jspace: Finally, the concept of continuity exists only in the context of topological space, which actually seems like a "particle" property^{1}. Traveling on a straight timeline in the RegionI is more analogous to moving in circles but not continuity, and it seems like a "wave" property. However in the core of all this, is the issue of the "measurement" using a fundamental interaction. The "measurement" of the topological structure underlying Blip, by using the tools based on a manifold comprising of fundamental interactions such as eγ and others. We will discuss single element matrices and the corresponding structures later on. We have already defined the challenge for ourselves. We will be discussing the Theory of Special Relativity in the Information Space of an infinite source first. Then we need to understand the Theory of General Relativity and required Tensor structures. Penrose diagrams are quite important. Anharmonic coordinates along with the constructibility condition, represent a powerful tool to describe an interaction. However all said and done, we must describe the Bliping problem in sufficient details first. That is all in a Nutshell2019! *** 
Previous Blogs: Stitching the Measurement Space  III Stitching the Measurement Space  II Stitching the Measurement Space  I Mass Length & Topology Chiral Symmetry
Sigmaz and I Spin Matrices Rationale behind Irrational Numbers The Ubiquitous zAxis Majorana ZFC Axioms Set Theory Nutshell2014 Knots in jSpace Supercolliders Force Riemann Hypothesis Andromeda Nebula Infinite Fulcrum Cauchy and Gaussian Distributions bField & Lower Mass Bound Incompleteness II The Supersymmetry The Cat in Box The Initial State and Symmetries Incompleteness I Discrete Measurement Space The Frog in Well Visual Complex Analysis The Einstein Theory of Relativity *** 

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