GEOMETRICAL DIMENSIONAL ANALYSIS
5 JULY 2010
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.
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Map. Not a drawing, not a chart, not an illustration. A map.
To whatever scale and however far away from center one looks,
every point on a map is recognizable as the endpoint of all
possible 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 the resultant of all possible quantity calculus operations begun
from any other quantity on the map.
If you can find or produce better maps so that the foundation
science of physics can be as well explored as any other territory,
if you can find or produce a better archive of calculation results
for further pattern recognition and comparison,
if you can find or produce forms of numerical expression or symbol
use that better facilitate the use of the tools mentioned above, or
if you can disprove or improve anything on this site, publish it!
That is why this is all public domain.
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Tutorial Read the Article References
Values table Symbol key Template1 Template2
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Unit Definitions Project a Lattice of Logic
The International System of Units (or SI) is a consistent, coherent
set: mapping conventions can project its members as a vector space.
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A Periodic Table of physics
Color print GJN165C and GJN165D B & W print GJN165B and GJN165E
Fundamental constants portray atomic units and SI units as a 4D
map, a 4D logarithm table, and a 4D structured natural unit system.
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By NIST CODATA 2006 fundamental constants values, as "allascii.txt",
seen JULY 5 2010 at http://physics.nist.gov , verify these excerpts:
If AUN = atomic unit of,
1/[2af] = AUN time, [2af] = AUN frequency,
[a0]= AUN length = Bohr radius, [B0]= AUN Magnetic flux density,
[aa]= Fine structure constant, [c ]= Speed of light in vacuum,
[d ]= Magnetic constant, [i0]= AUN current,
[k ]= Electric constant, [Ke]= 1/([4Pi][k]),
[Me]= AUN mass = mass of electron, [Pf]= 1/[PT] = 1/(Planck time),
[PL]= Planck length [PM]= Planck Mass
[Q0]= AUN charge = electron charge, [RK]= von Klitzing constant,
[v0]= AUN velocity, and [w0]= Magnetic flux quantum,
then, as defined by the SI,
[Kilogram] = [Coulomb][Second][Tesla] :
mass is charge X time X magnetic flux density
as in [Me] = [B0][Q0]/[2af],
[Kilogram] = [Farad][Meter^2][Tesla^2] :
mass is capacitance X length squared X magnetic flux density squared
as in [Me] = ([B0]^2) x [Atomic unit of Polarizability],
[Kilogram] = [Weber^2][Farad]/[Meter^2] :
mass is magnetic flux squared X capacitance per length squared
as in [Me] = ([w0]^2)/{([Pi]^2)[Ke][a0]},
[Kilogram] = [Coulomb^2][Henry]/[Meter^2] :
mass is charge squared X inductance per length squared
as in [Me] = ([Q0]^2)[d]/{[4Pi][a0]([aa]^2)},
[Kilogram] = [Ampere^2][Ohm][Second^3]/[Meter^2] :
mass is current squared X resistance X time cubed per length squared
as in [Me] = ([i0]^2)[RK]/{[2af]([v0]^2)[2Pi]}, and
[Kilogram] = [Coulomb^2][Second^2]/([Farad][Meter^2]) :
mass is ((charge X time per length) squared) per capacitance
as in [Me] = ([Q0]^2)/[{[4Pi][k][a0]}{([aa][c])^2}].
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The Gravitational Constant Has the Value 6.6917625e-11 **
or see a PDF file
When all possible factoral combinations of the Planck unit values
are mapped, enabling calculation of them all, differing numerical
results for differing factoring procedures that yield the same
given quantity prove that the 2006 CODATA values for the set of
Planck mass, Planck length, and Planck time values cannot be valid.
Investigation into this discrepancy discloses compelling evidence
for both an exact value for the Newtonian gravitational constant and
an explanation for the inability to relate gravity to other forces:
the definition or use of the SI includes an impropriety.
** The CODATA 2006 adjustment of the fundamental constants
specifically states that both the Fixler et al results and the
Bernoldi et al results play no significant part in the officially
adopted value for Newtonian gravitational constant [G],
(Rev Mod Phys, Vol 80, No 2, Apr-Jun 2008, table XXVII and fig 2),
but dimensional analysis still requires a set of Planck mass, Planck
length, and Planck time values that correctly combine into all the
quantities and there still exists one distinctive, all-pervasive and
repeating pattern of numerical coincidences among the constants in
general if [G] has the same numerical value as the product of the
magnetic constant and the square of the fine structure constant.
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Map the SI and verify: the units of gravitational constant [G] are
(Meter^3)/[(Kilogram)(Second^2)] OR
(Farad)(Meter)(Volt^2)/(Kilogram^2) OR
(Meter)/[(Farad)(Second^2)(Tesla^2)] OR
(Farad)(Meter)(Ohm)(Watt)/(Kilogram^2) OR
(Meter)(Weber^2)/[(Henry)(Kilogram^2)] OR
(Coulomb^2)(Meter)/[(Farad)(Kilogram^2)] OR
(Ampere^2)(Weber^2)/[(Kilogram^2)(Newton)] OR
(Ohm)(Meter^3)/[(Kilogram)(Henry)(Second)] OR
(Coulomb)(Meter^3)(Tesla)/[(Kilogram^2)(Second)] OR
(Newton)(Meter^2)/(Kilogram^2).
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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.
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If it gets you to the moon, save me a seat.
John Aikman
grnjn066_AT_gmail.com