|
|
A paper, with the title "A methodology to define physical constants using mathematical constants" has been
published in the July/August 2011 IEEE Potentials.
©2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this
material for advertising or promotional purposes or for creating new collective works for resale or redistribution
to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the
IEEE.
Until the concepts in the cited paper were identified, it was not possible to establish a set of scientific units
of measure that were based upon fundamental physical law. Currently, various units of measure, such as the kilogram and the
meter, are used for both commercial and scientific purposes, and the size of these units were established to be convenient for everyday use.
The official definition for the duration of the second is based upon 9192631770 complete cycles of the output of a cesium-133 atom.
The duration of the earth second, in reality, is based upon the ephemeris second, a 1/86,400 division of one complete earth rotation. The number
of cesium-133 cycle counts were made to fit the duration of the ephemeris second.
The geometric process exploits
the known physical law relationship between wavelength and frequency, this without needing
to know any contemporary units of measure. A unit of length and a time duration are mutually defined. A primary product of the triangle pair
is a mathematically defined value for the velocity of light. The geometric process
readily allows a set of fundamental units, and related derivations, to be compared to contemporary SI
units. A unit of energy can be established that is based upon the mathematically defined value of the speed of light and its corresponding
mathematically defined frequency.
Fundamental physical constants are directly related to mathematical constants through a geometric structure defined by numeric values that
are equal to those of mathematical constants.
The characteristics of the methodology presented herein require readers to re-examine some of the ingrained assumptions which are
taught at all levels of mathematics and physics. It is not known who first made the statement, "fundamental constants in mathematics are
not the same thing as fundamental constants in physical law," and there are a variety of ways this is stated in various publications.
Essentially, everyone is taught that the two types of constants cannot be the same.
The methodology described blurs the distinction between physical constants and mathematical constants and
identifies a fundamentally different way to apply mathematics to physical law.
The mathematics used in the paper consist of basic geometry, simple algebra, and one equation with a trigonometric identity. One physical
law concept is used; the relationship between wavelength and frequency, which has been known for at least 200 years.
f = c / λ
λ = c / f
c = f *
λ
The symbol f is frequency, λ is wavelength, and c is the speed of light (SOL). Frequency is dimensioned in "cycles" per "unit time",
wavelength in "length", and the SOL in "length" per "unit time". The relationships shown in the equation set are purely algebraic, no angular
elements are involved. The constant of proportionality is the value of "c".
The algebraic equation giving the relationship between wavelength and frequency cannot accommodate angular relationships, which is a key
factor in the methodology, which uses a pair of right triangles.
The wavelength-frequency triangle pair presents a basic postulate:
When the numeric value of the leg of one triangle is multiplied by the hypotenuse of the second triangle, the resultant is the constant of
proportionality between the triangles. When each of the products are equal the two triangles are inversely related.
Maxwell tried to prevent the meter from being made a scientific unit of measure.
“If we wish to obtain standards of length, time and mass which shall be absolutely permanent, we must seek them not in the
dimensions or
the motion, or the mass of our planet, but in the wavelength, the period of vibration, and the absolute mass
of this imperishable and unalterable and perfectly similar molecules. ”
Maxwell stated the same thing at other times with slightly different wording. Maxwell was voicing
his objection to the meter being considered as a scientific unit of measure. Maxwell was considering the wavelength
of a spectral line produced by a particular element, sodium, but the "light" of the neutral hydrogen atom,
which illuminates the universe, would have been an acceptable wavelength if Maxwell had known of it.
James Clerk Maxwell, 1873
See NOTICE at bottom between Maxwell and Euclid images.
The postprint is available for personal use. "Methodology"
The changes in the published version were to comply to IEEE publication conventions, the technical content
was unchanged.
This paper appears in: IEEE Potentials (Available to all IEEE members without additional cost)
Issue Date: July-August 2011
Volume: 30 Issue: 4
On page(s): 39 - 43
ISSN: 0278-6648
Digital Object Identifier: 10.1109/MPOT.2011.940377
Date of Version: July 25 2011
IEEE Potentials July/August 2011
|
|
