GEOMETRICAL DIMENSIONAL ANALYSIS
30 September 2012
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, then,
using four of the seven base units of the International System,
a majority of the most important quantities and laws of physics
project in graphical formats that approach the goal of any map:
to look at the problem is to solve it.
To whatever scale and however far away from center one looks,
every point on a map is the endpoint of all the 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
is the resultant of all possible quantity calculus operations begun
from any other quantity on that map, and
every unit is defined in terms of the other units on that map.
Read the Article Values table Symbol key References Tutorial
Template1 Template2 Text template1 Text template2
Quantity calculus relationships among the atomic units and
current values of fundamental constants let laws of physics project
A Periodic Table of physics
Color print GJN165C and GJN165D B & W print GJN165B and GJN165E
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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 cosmological 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:
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 GDA quantity calculus
mappings based on values of the fundamental constants can be seen as
multiple dimension vector spaces composed of such extensions. So it
is that numerical patterns in use for centuries in 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 just knowing of the choice is not enough, if the sheer number of
coincidences, of and not of the pattern, is not convincing, if the
historical precedents by Bayles and Feynman say nothing, the very
nature of some coincidences says much. With each entry on the left
varying as [G] is adjusted and each on the right well established:
in Newton meters squared per kilogram squared,
a [G] value of 6.6917626-11 = 10^-10.1744595 numerically matches
adjustable to immutable
[G] to [4Pi]{[aa]^2}/[10^7] ,
[G] to [d]{[aa]^2}
= [aa][d][E0]/{[B0][c]}
= [Me][a0][4Pi]{[aa]^4}/{[Q0]^2} ,
[PM] to [c][PQ]/[aa] ,
{[PM]^2} to [Me][a0][k][c^4]/[aa]
= [hB][c]/({[z0]^2}{[aa]^2}[k])
= {[Q0]^2}[c^2]/([4Pi]{[aa]^3}) ,
{[PL]^2} to [hB][d]{[aa]^2}/[c^3]
= {[Me]^2}{[aa]^6}/{[hB][c][k]{[2af]^2}} ,
and {[PT]^2} to ({[aa]^2}{[hB]^2})/([c^6]{[PQ]^2})
= {[aa]^2}[hB]/{[c^7][k]}
= {[aa]^3}[Me][a0]/{[c^6][k]}
for
AUN = Atomic unit of [aa] = Fine structure constant
[Me] = AUN mass permeability:[d] = Magnetic constant
[a0] = AUN length permittivity:[k] = Electric constant
[hB] = AUN action [z0] = vacuum impedance
[Q0] = AUN charge [c] = Speed of light
[B0] = AUN Magnetic flux density [PL] = Planck length
[E0] = AUN electric field strength [PM] = Planck mass
[PT] = Planck time
and for [hB][c][k] = {[PQ]^2} , [PQ] = Planck charge
CODATA 2010 values of the fundamental constants
as of 30 September 2012
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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