Dedicated to Fernando Arrioja González 
The Planck Constants Based on the Fundamental Physical
Constants
By Charles William Johnson
"An environment in the scientific community
of open access and free exploration is critical for advancing
knowledge," says Onsrud, who chairs the U.S. national committee
of CODATA, a group interested in the sharing of scientific and
technical information worldwide among scientists. "We openly
publish our research results. We seek peer review, invite others
to critique our work, extract data from our work, retest hypotheses
and challenge each other so that knowledge progresses. If you
now need permission to take data from an electronic journal
article before you can use it in a critique or extend from it,
that has substantial potential for impeding the advancement
of science."" 
The 2006 CODATA recommendations for the fundamental
physical constants, as one may observe from the list below, are
often based upon specified symbolic formulae. The defining
Planck constant 6.62606896 together with two other constants have
no corresponding symbolic formulae listed in the CODATA. Many physicists
mention that Max Planck, who created the Planck constant in 1899,
never disclosed how he derived the numerical value of his constant.
For nearly 110 years now, physicists
appear to have uncritically accepted Planck's constant, originally
given a value of 6.885 by Planck in 1899, which he later changed
in 1900 to 6.55. Such an unquestioning acceptance of a thesis is
not common within the field of physics, but supposedly Planck's
values in experimentally measuring the energy in a relationship
of frequencywaves worked well, and therefore it was accepted. Evidently
it continues to be accepted, as the constant carries Planck's name,
even though over the decades the numerical value has changed, finally
resting at the current 6.62606896 fractal value.
Ultimately, it is impossible to question
the symbolic formula of all the Planck constants inasmuch as three
out of the ten constants provided in the CODATA have no symbolic
formula listed for them. Planck's constant, the first one listed
by the CODATA appears without an obvious theoretical basis, as it
lacks a symbolic formula. Its derivation is thus unknown, or at
least undisclosed. No one apparently knows how it was theoretically
derived but only that it works empirically.
Hence, I sought to understand how
Max Planck may have derived the numerical values of his constants.
Not sharing confidence, however, in the symbolic formulae given
for the rest of the Planck constants, I decided to seek a possible
derivation of the Planck constants as of the other fundamental physical
constants. One analytical purpose that I had in my mind was to avoid
any reference to the symbolic formulae that contain square roots.
Four of the ten Planck constants contain formulae with square root
expressions. For although they have their symbolic formulae expressed
to the power of 0.5 that essentially means employing the square
root procedure. Square roots produce two possible answers to every
resolution depending upon where the decimal place lies in the numerical
values of the terms involved in the computations. The fundamental
physical constants, even those with square root expressions, present
a single constant or answer as though that were the only possible
answer.
Now, to move along, consider the original
general values forwarded by Max Planck in his 1899 lecture in Berlin:
Further, Planck provided the following
specific data:
Notice that in general the CODATA
follow the sequential order listed by Max Planck in his published
lecture; first, the general Planck constants; then, secondly, the
specific ones.
From my studies, the order of the
Planck constants should be reversed. First the specific constant
measurements must be presented, followed by the general theoretical
constants. Such is the order presented in Table I of the
attached Earth/matriX Table of the Planck Constants Based on
the Fundamental Physical Constants. The reason for inverting
the order is computational. One must first derive the specified
numerical values, and then proceed from there in order to be able
to derive the generally posited matterenergy relationships. After
the specific constant values are derived it is then possible to
derive the general theoretical Planck constants; not before. The
requirements of this procedure become clear through the computations
on Table I.
As a methodological procedure, I began
my research by multiplying the CODATA numerical values for the Planck
constants by the elementary charge [1.602176487]. The results from
that computation were then compared against the numerical values
of the CODATA fundamental physical constants. It soon became clear
that for some of those results there were two fundamental physical
constants whose numerical values in relationship to one another
could produce that same numerical value resulting from the Planck
constants being divided by the elementary charge. By reverse engineering
the Planck constants' numerical values in this manner it is possible
to identify the three main fundamental physical constants that derive
some of the Planck constants.
Essentially that is the information
presented in Table I. The three fundamental physical constants that
derive certain Planck constants are listed in the first, second
and fourth columns of the cited table. The third column of the table
contains eight Planck constants and two reduced Planck
constants. On the fifth and last column of the table are listed
the ten reduced Planck constants, repeating the two
that appear in column three. The two reduced Planck constants that
appear in column three are thus twice reduced by the time they appear
on the fifth column.
The theoretical concept of "reduction"
may not be the best of terms, but I have retained its use for now
in order to be able to compare the implied values that I have derived from the CODATA Planck constants against the
given CODATA values. The theoretical concept of "implied values"
is itself not the best of terms either, but it draws attention to
the fact that some of the fractal numerical values presented on
the table are derived from the standing CODATA values, meaning the
given CODATA values imply the existence of still other values. Simply
put, the CODATA numerical values imply a prior set of numerical
values; in fact, they require them. Essentially this is what I have
done, take the CODATA numerical values and work backwards from them
in order to see which numerical values of a particular fundamental
physical constant produce the CODATA values.
Enter Table I, the Earth/matriX
Table of the Planck Constants Based on the Fundamental Physical
Constants. The theoretical foundations of the Planck units are
presented in detail in Table I. Errors and omissions that
I consider to exist in the CODATA are presented in Table II.
The entire critical analysis of the CODATA may be examined in my
book, Errors and Omissions in the CODATA and, The Planck Constants
Based on the Fundamental Physical Constants [Earth/matriX
Editions, 2010].
A word of caution is required here.
The fractal values presented on the Earth/matriX tables of the Planck
constants and fundamental physical constants may vary distinctively
as of the baseline fractal values used; be they from the CODATA
or from other sources. Further, using the same fractal values of
two fundamental constants may produce different values in their
mantissas depending upon whether they are divided or multiplied
by one another. The first computation on the table that follows
employs multiplying the reciprocal of the speed of light in vacuo times the proton mass. A similar result could be obtained inversely
by dividing the proton mass by the speed of light in vacuo,
yet the numerical result would differ slightly. In this summary
and in my book the choice of employing either multiplication or
division lies at times with the needs of illustrating a particular
numerical value.
Moving along, there are five computational
steps in the derivation of each of the ten cited Planck constants.
One begins on the first row of Table I, by multiplying the reciprocal
of the speed of light by the proton's mass. This step derives the
first Planck constant fractal value, which is 5.5792652262332 and
which must be halved to fractal multiple 3.487040766395. This latter
value is considered to be Planck mass. The reason for this
lies within the initial analytical procedure where I multiplied
the Planck constants by the elementary charge: Planck mass 2.17644
times 1.602176487 equals fractal 3.4870409933662. Therefore,
in inverse order, after obtaining the 3.487040766395 numerical value
from the first computation on the table, this value is divided
by the elementary charge figure in order to derive the reduced
Planck mass: 2.1764398583356, which is referred to in the
CODATA as Planck mass. As shown, however, this is actually a reduced
form of mass since it obtains from the division by the elementary
charge.
The constant Planck mass, 3.487040766395 defines the five general Planck constants listed last on Table
I. Without this value it is impossible to derive the Planck
constant and the subsequent [reduced] Planck constants. On Table
II, where the five general Planck constants appear first, the
analytical dilemma becomes obvious in that there appears a similar
but distinct value of 3.387040993, whose origin is not only
unknown, but not recognized in the CODATA. Nonetheless, the 3.387040993
fractal value is implied in and required by the CODATA in order
to theoretically produce the Planck constant, 6.62606896. Table
I and II essentially points out the anomaly of 3.387040993
and its contradiction to the 3.487040993 value for Planck implied
mass. Briefly, Table II illustrates how there exist two different
implied numerical values for Planck implied mass in the CODATA.;
that is the only manner in which the set of CODATA Planck constant
numerical values can be produced.
Returning to Table I, on its second
row, the speed of light in vacuo is divided by the
first radiation constant in order to produce Planck energy,
1.956066112. This Planck energy value is in turn divided by the elementary charge in order to produce the reduced Planck
energy fractal value, 1.22088055. The Planck energy value,
1.956066112 represents a serious omission from the CODATA even though
it is implied and is mandatory in deriving the CODATA value of 1.220892
for Planck energy. Again, the CODATA Planck energy is in fact a
reduced value for energy. In other words, some of the constants
that the CODATA identifies as Planck constants are actually reduced
Planck constants.
The third row on the Earth/matriX
Table I proposes the unified atomic mass unit times the solar constant
in order to derive Planck temperature, 2.269956514994.
By dividing Planck temperature by the elementary charge,
one obtains the reduced Planck temperature fractal
value of 1.41679554868; again, incorrectly presented by the CODATA
as Planck temperature. The computational procedure is obvious and
the reduction fractal value is evident; I state this again for emphasis.
The fourth row on Table I treats the
inverse fine structure constant divided by the Bohr radius
thus deriving Planck length, 2.589605097395. Following
the same systematic procedure, that value is thus divided by the elementary constant and obtains the reduced Planck length fractal value, 1.6163045197. Once again, what the CODATA identifies
as Planck length is in fact reduced Planck length.
The final specific Planck constant
appears on the fifth row of Table I, and involves multiplying the reciprocal of the speed of light in vacuo by the Planck
length, in order to derive Planck time, 8.63799280718.
This fractal value is then divided by the elementary charge value
in order to obtain the reduced Planck time value,
5.39141154377. The CODATA's Planck time is in fact reduced Planck
time.
In summary, this first section of
Table I, regarding the specific Planck constants, demonstrates
that the CODATA Planck constants for mass, energy, temperature,
length and time are in fact reduced Planck constants.
This occurs because of the fact that the specific CODATA Planck
constants are derived by the division of the elementary charge,
thus effectively reducing their values.
It is important to emphasize that
the two fundamental physical constants in the first and second columns
produce the numerical values of the third column; meaning that these
latter values of the table's third column represent the Planck
constants. As far as I can tell so far, no two fundamental physical
constants produce the values of the fifth column with the exception
of the Planck constant, 6.62606896. Nine of the values in the fifth
column are produced by the combination of a Planck constant together
with the elementary charge, 2pi or the reciprocal of
the speed of light.
Now, the possibility that the Planck
constant, 6.62606896 can be produced as of the multiplication of
Planck energy and Planck mass requires critical analysis. This procedure
breaks with the remaining nine constants as to how they are produced.
In other words, one must critically consider not only whether this
is a theoretically possible procedure for producing the Planck constant,
but whether it is sound one. In my book, I treat this anomaly in
detail.
The second half of Table I contains the general theoretical Planck constants which do not reflect
specifically measured matterenergy events. Only after having derived
the specific numerical values of the measured matterenergy events
represented in the first five Planck constants discussed above,
is it possible to derive the next five general Planck constants.
On the sixth row of Table I,
the speed of light in vacuo is divided by the first
radiation constant thus deriving the Planck energy constant, 1.956066112, previously listed on the second computational
row of this same table. The Planck energy constant in then multiplied
by the Planck mass, 3.487040766395, listed above on the first
row of the table, thereby producing the Planck constant, 6.8208822743077.
This value is quite distinct from the CODATA value for the Planck
constant, 6.62606896. Yet, it is extremely close to Max Planck's
original 6.885 value for the Planck constant forwarded by
him in 1899.
As explained in detail in my book,
the CODATA Planck constant, 6.62606896, is erroneously based upon
the multiplication of fractal numerical values grossly relating
to ±1.956084456 and ±3.387040993, with
any number of possible variations. The significant point is to recognize
the devalued term, 3.387040993, which is similar but distinct from
the 3.487040766395 Planck mass fractal value presented in Table I. In Table II one may observe how the general
Planck constants are based upon and affected by the 3.387040993
value. The contradiction between the Planck mass value of 3.487040766395
as against the implied 3.387040993 value is brought out in Table
II. My book presents an extensive critique of the theory behind
the 6.62606896 fractal numerical value for the Planck constant;
its empirical measurement is discussed indirectly.
The seventh row for the generalized
Planck constants involves Planck energy times Planck mass, obtaining
the Planck constant, 6.8208822743077 fractal value
and through standard procedure dividing it by the elementary charge.
The numerical value for Planck constant in eV s, 4.257602516964,
obtains. [The CODATA value for the Planck constant in eV s is
4.13566733.]
On the eighth row, once more the same
procedure obtains, multiplying Planck energy times Planck mass in
order to obtain the Planck constant, 6.8208822743077,
but this time it is divided by 2pi, 6.283185307, thus deriving
the reduced Planck constant, with a fractal value
of 1.0855771302349. [The CODATA value for the reduced
Planck constant is 1.054571628.]
The ninth row of Table I divides the Planck constant by 2pi obtaining the cited reduced Planck
constant, 1.0855771302349 value, and then divides this fractal by the elementary charge, thus producing the reduced
Planck constant in eV s, 6.775640131054. [The CODATA value for the reduced Planck constant in eV s is 6.58211899.]
The final and tenth row of the table
involves the reduced Planck constant divided by the elementary charge
that yields the reduced Planck in eV s, 6.7756401302349,
which in turn is divided by the reciprocal of the speed of
light in order to obtain the reduced Planck constant in Me
V fm. [The CODATA value for the reduced Planck
constant in Me V fm is 1.97326963.]
The computational procedure followed
on the Earth/matriX Table of the Planck Constants Based on
the Fundamental Physical Constants provides an analytical
perspective devoid of any of the CODATA's questionable symbolic
formulae. The analytical procedure on Table I relies totally upon
equivalencies found within the numerical fractal values of the fundamental
physical constants. There is no need to square the speed of light in vacuo or raise any of the terms to higher powers, nor
is there a need to employ square roots. As shown on Table I,
the ten cited Planck constants may be derived solely based upon
basic math procedures involving the fractal numerical expressions
of the Planck constants and selected fundamental physical constants.
The results provided by the computational
procedure followed on the cited table are derived theoretically
from the implied numerical fractal values of the CODATA. Nonetheless,
it is significant to note once more that the 6.8208822743077 numerical value derived for the Planck constant in this manner is
close to the original 6.885 value forwarded by Max Planck in his
1899 lecture in Berlin. In my book I explore possible reasons why
Max Planck may have changed the 6.885 value of 1899 to the 6.55
value in 1900 [the 6.55 value still listed in a Lange Handbook
of Chemistry in 1944.]. Another significant point to note
here, is that the ratio between the CODATA 6.62606896 value and
Planck's 6.55 value is a fractal multiple near phi, ±1.618581731;
imagine if the 6.626+ value were derived by multiplying the 6.55
figure times phi. Given the fact that Max Planck did not
disclose his procedural computation to derive his constant, one
may in fact imagine anything as an analytical possibility.
In this case, however, the relational
numerical values as illustrated in Table I suggest an analytical
approach to the Planck constants and the fundamental physical constants
beyond the traditional symbolic formulae presented by Max Planck
or the CODATA international committee. By now, it has become apparent
that the numerical value of the gravitational constant [G] is not
present in the tables. By using the fundamental physical constants
in order to derive all of the Planck constants without the gravity
constant, G, is itself a most significant aspect of this analytical
procedure. This obtains due to the presence of G in the original
symbolic formulae forwarded by Max Planck, and its continued presence
in the CODATA symbolic formulae. Further, every textbook and science
writer whose work I have read about the Planck constants offer definition
of these constants as of c, G, and h. From the analytical procedure
followed in my book and on the tables presented here, the extent
to which the fundamental physical constants intervene in the Planck
constants is quite distinct from those traditional definitions.
One can argue that G lies within some of the fundamental constants
cited [as in the inverse fine structure constant], which is true.
But, the fact remains that the numerical value of G [6.67428]
does not appear directly by itself.
Given the apparent theoretical contradiction
and anomaly of the Planck constant value of 6.62606896, one can
consider the nature of quantum physics at this point. Surely counter
arguments may cite the measurements of the Planck constant that
supposedly derive its empirical value and confirmation. The CODATA
6.62606896 fractal value is a mean obtained from experimental measurements
through different methodologies.
Yet, as is so often emphasized in
quantum physics, one may query whether the fact that scientists
seek to confirm the 6.62606896 number might actually produce that
soughtafter number through their experimental search as observers.
By the stated rules of quantum mechanics today, one must consider
the possibility that by seeking the practical confirmation of the
theoretical value of 6.8208822743077 [ 6.82088 en bref ]
for the Planck constant that they may possibly not only find it
but produce it amongst their measured experiments. With the myriad
of measured values for the Planck constant over its 110 year history,
from 6.885, 6.55, 6.624, 6.6523, 6.626+, 6.62606896, etc., one can
only wonder about the relationship between the existence of spacetime/motion
events and their observation and measurement.
It is not for me to say that the current
scientific measurements that have produced similar fractal values
around the 6.626plus number for the Planck constant are incorrect;
that is far beyond my practical experience. But, as determined in
the Earth/matriX Table of the Planck Constants Based on the Fundamental
Physical Constants, it is possible to say that a significant
discrepancy exists between the CODATA value for the Planck constants
and those derived in the manner as shown in this brief summation
of my studies.
I do suspect that Max Planck was initially
correct with his 6.885 value, and that the 6.82088+ value derived
herein is theoretically correct. Whether it is practically correct
is another issue. It must be noted that these two values also reflect
numerous constants in specific forms of matterenergy that involve
a 1.36+ fractal numerical value. Consider doubling the 6.82088 value,
which derives 1.364176. Similarly, the Max Planck original value
of 6.885 doubles to 1.377 and is suggestive of the inverse fine
structure constant. Consult the list of 1.36+ related physical and
chemical constants on my website, www.earrthmatrix.com.
An additional observation: when one
compares the fractal numerical expressions of 6.626+ and 6.82088+
the fractal difference between them, 0.19488, appears to be enormous.
But, when one is reminded that such a comparison is essentially
at the subatomic particle level, then the difference may be perceived
otherwise. Remember the numbers, not just the fractal expressions,
as in the comparison:
0.000 000 000 000 000 000 000
000 000 000 000 6 662 606 896 
0.000 000 000 000 000 000 000
000 000 000 000 6 820 882 274 307 7 
Ultimately, there is nothing like
looking at the numbers and seeing how they behave. One of the main
problems touched upon in my research is the tendency in today's
science writing to depend totally upon symbolic formulae and equations
that supposedly represent numbers, but actually hide them and even
disregard or confuse them in many cases.
The Earth/matriX Table of Planck
Constants Based on the Fundamental Physical Constants represents
an effort to emphasize the numerical values of the constants and
thereby propose a revision of the symbolic formulae which are at
times not only misleading, but incorrect. With that purpose, I present
this summation of my book entitled, Errors and Omissions in
the CODATA and, The Planck Constants Based on the Fundamental Physical
Constants [Earth/matriX Editions, 2010].
REFERENCES:
 Improving LongRange Energy Modeling: A Plea for Historical Retrospectives.
Jonathan Koomey, Paul Craig, Ashok Gadgil and David Lorenzetti. click
 CODATA Task Group on Fundamental Constants. click
 A Constant’s Secrets. A Different Look at Planck’s Constant. by
Deanl L. Sinclair click
Table I.
The Earth/matriX Table of the Planck Constants Based on the Fundamental
Physical Constants
©2010 Copyrighted by Charles William Johnson. All rights reserved.
Reproduction prohibited.
Table II.
The Planck Constants Based on the CODATA Computational Error
of Two Different Values Impled by the Planck Mass, 3.387040993 
3.487040993, in Relation to the Fundamental Physical Constants
©2010 Copyrighted by Charles William Johnson. All rights reserved.
Reproduction prohibited.
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THE PLANCK CONSTANTS BASED ON THE FUNDAMENTAL PHYSICAL
CONSTANTS AND ERRORS AND OMISSIONS OF THE CODATA
The author derives the Planck constants as of the fundamental physical
constants, instead of as of the traditional symbolic formulae given in
the CODATA. The implied numerical values that are generally omitted in
the science literature and which serve as a basis for deriving the Planck
constants are identified in detail in their basic math. As of the analysis
of the implied Planck values, errors and omissions of the CODATA Planck
values are identified and treated extensively. The Planck constants are
reverse engineered in order to employ the fundamental physical constants
as their computational foundation. Various Earth/matriX Tables of the
Planck Constants Based on the Fundamental Physical Constants are presented
for the first time, illustrating how the fundamental physical constants
serve as the foundation to the Planck constants.
Purchase and download the complete ebook:
Errors and Omissions in the CODATA and The Planck Constants Based on
the Fundamental Physical Constants
PDF file 142 Pages
Earth/matriX Editions ISBN 1586164635
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