An Exact Source |
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18^{th} February 2017 |
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“Seeing there is nothing that is so troublesome to mathematical practice, nor that doth more molest and hinder calculators, than the multiplications, divisions, square and cubical extractions of great numbers... I began therefore to consider in my mind by what certain and ready art I might remove those hindrances."
- John Napier, Mirifici logarithmorum canonis descriptio (1614) Reference: e:The Story of a Number by Eli Maor "Topology is a qualitative subject where quantity is banned."
- Henry Poincarè Quoted in Introduction to Graph Theory by Richard J. Trudeau. "From the point of view of logic, my report on « Exclusion principle and quantum mechanics » has no conclusion. I believe that it will only be possible to write the conclusion if a theory will be established which will determine the value of the fine-structure constant and will thus explain the atomistic structure of electricity, which is such an essential quality of all atomic sources of electric fields actually occurring in Nature." - Wolfgang Pauli, "Exclusion Principle and Quantum Mechanics" Nobel Lecture 13 ^{th} December 1946."He believed in the primacy of doubt, not as blemish on our ability to know but as the essence of knowing." - James Gleick on Feynman Quoted in Feynman lectures on computation edited by Hey and Allen. |
Defining a source is a subtle business. Anything or any object can be a source. For example sun is a source of energy, but then so is an electron or a collection of electrons i.e battery. In real life a bank can be a source of finance. There is no specific definition of source except probably for a consensus that it just exists. A good source is one which lasts longer. Well then, what is an "exact" source? Can it be a source which exists for an infinite time? Is the existence
By doing this we have characterized the only entity we know of, that is the "observer" itself. We do not need to know the nature of the infinite-source, as long as we know the nature of the interaction and results obtained from the interaction. So the question now becomes what is this interaction telling us about the predicament we are in? To answer this question we must revert back to a fundamental problem posed by the great Pauli himself, that is to explain the significance of the fine-structure constant, characterizing the electron-photon coupling. We summarize previously reported results in the context of the present discussion as follows: a) The information measured at an infinitesimally-later instant (t = 0 ^{+}), is related to information contained within the initial state (t = 0) as,I(t = 0
^{+}) ∝ I(t = 0) × e^{-q}The exponential function is selected, because its derivative is equal to itself and its initial value for q = 0, is 1 (or δ-function). The variable q is allowed to take only the positive integer values. Therefore the information structures being measured correspond to q = 1, 2 , 3 ,....etc. These information structures are proportional to e ^{-1}, e^{-2}, e^{-3} and so on. This is how the concept of source is introduced mathematically. b) If I(t = 0) is a δ-function then I(t = 0 ^{+}) is likely to be a stable probability distribution.^{2} In other words, in j-space the progression of measurements with respect to time is, from δ-function ( ≡ complete information in one measurement) to a probability distribution ( ≡ complete information if and only if the measurements can be made up to the instant t = ∞).c) We note that both I(t = 0) and I(t = 0 ^{+}) are measured values. Does it mean that I(t = 0) represents the source? No, all we are saying is that I(t = 0) is the information content an observer could measure at the instant t = 0. The observer does not have capacity to measure even δi with complete precision, otherwise the entropy would not have kicked in for the observer leading to a deteriorating measurement metric in j-space to begin with. The source will remain indeterminate. The relationship between the source, i-space, j-space and corresponding observers is shown in the following diagram:The i-space contains only an infinitesimal amount of information from the source, which then is equivalent to an infinite information space for the observer Obs
_{M}.The definition of the source in context to an observer, must be independent of different theories from different observers, used to describe the entrails of Humpty Dumpty also known as universe. It is difficult to imagine that the universe, the perceived description of the physical reality for us, is a bloating carcass, and that the explanation of the universe based on our severely limited organic capacities, will provide an exact description of the source. Is it possible to visualize a source as a point or the origin? If that is the case, then how are the stable structures formed? To understand the formation of the stable structures we need a scheme for optimization, a scheme which is independent of the physical constants. ^{3} We can worry about the book-keeping of the resources within the measurement metric for q = 3 state, later._______________________ 1. Note that we have just introduced a logarithmic relationship, although we did not know the base value. The base value of 'e' is introduced in the section-(a). 2. A brief summary of stable distributions in j-space, is provided in the footnotes here. 3. Geometry or Topology only. |
Previous Blogs:
Chiral Symmetry
Sigma-z and I Spin Matrices Rationale behind Irrational Numbers The Ubiquitous z-Axis Majorana ZFC Axioms Set Theory Nutshell-2014 Knots in j-Space Supercolliders Force Riemann Hypothesis Andromeda Nebula Infinite Fulcrum Cauchy and Gaussian Distributions Discrete Space, b-Field & 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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