GEOMETRICAL DIMENSIONAL ANALYSIS 30 Dec 2013 The Outlaw Map of Physics True wherever and however written, the definitions and formulas of the physics you thought you knew erect a 4D concept and factor map. Physics means experiments and the measurement of quantities. With or without additional descriptions or elaborate mathematics, the International System of Units defines every quantity with a numerical value as a magnitude, as a count, multiplied by the product of seven base units of measurement, each of which is raised to zero or some numerical value as a power. If numerical values as counts and numerical values as powers are both expressed in the same way, as powers of ten, a number of base and/or derived units of the International System can serve as unit vectors to project quantities and laws of physics in vector space graphical formats that approach the goal of any map: to look at the problem is to solve it. Every point on a map is the endpoint of all paths to that point from any other place on the map and every quantity in an International System of Units map, every quantity in an atomic system of units map, every quantity in a Planck system of units map can be seen as defined in terms of the other units, as all possible combinations of potential factors, and as the resultant of all quantity calculus operations begun from any other quantity on the vector space map. Symbol key or bare list GJN165C+GJN165D or GJN165B+GJN165E Read the Article Values table References Tutorial Template1 Template2 Text template1 Text template2 A Periodic Table of Fundamental Constants : Using CODATA 2010 values of the fundamental physical constants, a vector space depiction of a system built on atomic units displays both numerical fit of model to reality and coherency of the system : the quantity interrelationships involve no numerical value except 1. ===+====-====+====-====+====-====++====-====+====-====+====-====+=== Imagine a place where every police chief, every fire chief, every military commander, all the professional experts say the same thing: "Maps? I ain't got no map. I don't need no schtinkin' map!" Then, put that region in the real world and call it physics. An analogy: On an island so remote there has never been contact with the rest of the world, the city of Foggobia is eternally fogbound: no one has ever seen farther than a block in any direction. Since no one has ever viewed the big picture and the very concept of a street map is unheard of, a large enough building can be approached from different directions on different days without being recognized as one place, taking a longer way around is as common as getting there directly, wherever anyone might be going, and getting lost in the fog is easy. Knowing street maps to be indispensible, we try to empower them with the tool, but to no avail: "...don't need no schtinkin' map." There are practical reasons for such a reaction. In this part of town, streets are named for flowers, in French, in that part of town streets are named for rivers, in Chinese, with ideograms on all the street signs, and downtown each street is identified by a unique way to pile rocks. Needing to establish the validity of this street map thing in a completely abstract way, due to the fog, it would be nice to show that everyone's statements of relationship concerning the locations around town can be represented by line segments which join together to form a coherent and useful whole in only one way, but in such a babel of nomenclature, journeys and distances are rarely even recorded, let alone organized into any kind of useful collection. Worse yet, it happens that in Foggobia all the numerical values are expressed, all the calculations are done using Roman numerals. Fortunately, there is more to the situation. Having never had an opportunity to see the mast of a ship recede below the horizon as it diminished in the distance, having never seen anything in the sky except fog, the Foggobians still think the world is flat. The form of numerical expression in use is outmoded, the lack of measurement records is laughable, the chaos of their various nomenclatures makes organization of knowledge virtually impossible, and we must inform that their cosmological model is flawed, but there is still this: numbers do not lie and physics is the rock hard science where reason and logic, based upon experiment, prevail. If measurement records ARE kept and organized, if calculations CAN be efficiently done, we can produce that "God's eye view", that map, to prove that there is an all-pervasive, universally scaling pattern of error to be found that perfectly matches the rate of curvature of an Earth-sized ball, to prove that they only think they know their own stomping grounds and do indeed need some graphical representations of their home. The analogy applies, and modern physics has nothing comparable to the indispensable, buy one or copy one, everybody knows how to use one street map because, as in Foggobia, there is a combination of obstacles precluding such a solution. First, on nomenclature, here is a paraphrase from a note by a high school physics teacher, Mr K. Bailey: In a year, students will have seen use of about 52 symbols (many in Greek) for 35 units having to do with some 60 quantities, some entities with more than one symbol, a symbol as a quantity here that may be a symbol for a unit there, they will see subscripts, and they may see emphasis in letters of whatever language using italics and bold print, sometimes with vector arrows above symbols, and all used on blackboards and whiteboards, paper, and electronic displays via multiple authors employing differing sets of symbols, and all of this in a physics that still uses more than one system of units! On the form of numerical expression, remember that the scientific notation demanded as standard by publishers and authorities is an approach that emphasizes what is the mantissa in logarithmic form (mantissa: from the Latin for useless), and was tailor made for use with those slide rules and logarithm tables that modern devices have made obsolete. Further, scientific notation is not only a multiple context in and of itself, with multiplication of powers visible as the addition of exponents (the characteristics in logarithmic form), customary multiplication of numerical values (the mantissas in the logarithmic form), and then, maybe or maybe not, yet more addition or subtraction to the characteristics from what might have carried over from the customary multiplication. Finally, above and beyond that, for the quantity calculus in the quantitatve science physics, the purely numerical procedure just done must be followed by another addition of exponents to acquire the resultant units of measurement. Further, if use of Roman numerals IS recognized as an impediment, how much of that point of view has to do with one form of numerical expression versus another, and how much has to do with being tied to any one form instead of having a sophistication that facilitates a choice of form most conducive to the investigation underway? Next, remembering that the existence and use of street maps is intertwined with street indices, address books, and mileage charts, and that use of language means dictionaries, thesauruses, and etc, ponder the vocabulary of physics, numbers. Even if every numerical value encountered in every step taken in every calculation ever done is added to an ever growing master list as a vocabulary of numerical values, allowing the identification of a value as the "destination" previously approached from a different "direction", how useful can such an "address book" be, how can it accommodate the importance of pattern recognition or unsuspected identification in any numerical science if it is organized by that accident of birth, its name, or by any scheme that is not mathematical? To complete comparison to the analogy and prove that there are forms of numerical expression, labels, and symbols which can enable indispensable "address book" listings of values and mappings of the "territory" called physics, consider the ongoing efforts to resolve the value of Newtonian gravitational constant [G] and its dependent Planck unit values. Even though any publication of values of the fundamental physical constants must now declare that there is no known relationship between [G] and any other constants, (therefore that some assumptions are uncertain) and though an experiment done on a planetary surface to study a celestial phenomena is overly optimistic, every year millions of dollars are spent to secure results no more definitive than that of Cavendish more than two centuries ago. Verify this claim with appropriate maps of physics: Periodic Tables of Fundamental Constants Exactly Determine G For four hundred years, numerical patterns visible in slide rule scales and logarithm tables have enabled extrapolation of unseen marks and unlisted values in those one dimensional progressions. As the alternative forms of numerical expression and nomenclature used in Geometrical Dimensional Analysis enable them to be possible, the more usefully organized numerical value listings are recognizable as extensions of those single dimension maps, and the quantity calculus mappings, the periodic tables of fundamental physical constants, can be seen as vector spaces composed of just such extensions. Those numerical patterns in use for centuries in only one dimension now combine, intersect, align in multiple dimensions to leave no doubt: either there is one value for [G] which is too elegant to be wrong, or, in abstract quantity calculus spaces naturally choreographed by exact values of fundamental constants into Dumond's interconsistency of results, there is a universal pattern of numerical coincidences based on some near miss to the value of the fine structure constant. If a Planck units vector space is modelled on the template given validity by atomic unit spaces, one thing projected is the fact that the coherency of the system is dependent on adjustment of [G] . The Newtonian gravitational constant [G] has a numerical value of 6.6917625 x 10^-11 = 10^-10.1744595 because only this value gives coherency to the Planck unit system: only this [G] value forces the quantity calculus vector mapped from permeability to the gravitational constant, and thus all identical vectors, to equal the square of the fine structure constant instead of that value multiplied by something only close to one, something only almost uniting a whole class of vectors with a coherent space, only this [G] value and its dependent Planck unit values bring a maximum of consistency to the calculation archive, the Gunter Table, only this value forces the many other near misses among quantitative numerical values into exact coincidences with dissimilar quantities: only this gravitational constant value is numerically equal to [4Pi] and [10^-7] , two factors important in defining the SI , multiplied by the square of the fine structure constant , [G] <=> [4Pi][10^-7]{[aa]^2} , only this gravitational constant value is numerically equal to the magnetic constant (= vacuum permeability) multiplied by the square of the fine structure constant , [G] <=> [d]{[aa]^2} , only this gravitational constant value is numerically equal to the square of the vacuum impedance multiplied by the electric constant (= vacuum permittivity) multiplied by the square of the fine structure constant , [G] <=> {[z0]^2}[k]{[aa]^2} , only this gravitational constant value is numerically equal to the ratio of vacuum impedance to the speed of light , multiplied by the square of the fine structure constant , [G] <=> {[z0]/[c]}{[aa]^2} , only this gravitational constant value is numerically equal to the square of the ratio of atomic unit of electric field strength to the atomic unit of magnetic field strength, multiplied by the electric constant (= vacuum permittivity) , [G] <=> ({[E0]/[H0]}^2)[k] , and etc. Finally, added significance of the proposed value is to be found in appearances, conceptually and numerically, in subject literature. As early as 2003, Bayles equated the constant of gravitation to the product of permeability and square of the fine structure constant, he has cited Feynman's mention of the units of the gravitational constant as an obstacle to renormalization, and internet search has found this numerical result for [G] calculated in work by Vujicic. More than two hundred years into performing experiments some call embarrassing, here is the claim that the true [G] value identifies itself if all the candidate values are looked at in the right way, here is the claim that mapping the territory of what is known can lead to knowing more. ===+====-====+====-====+====-====++====-====+====-====+====-====+=== Disprove it or improve it, as the author, I declare this hypertext material and the original copyrighted GDA article in the public domain. Though produced with care, they are supplied without warranty. If my work makes you money, save me some. If it gets you to the moon, save me a seat. John Aikman