Interpreting fundamental properties as powers of √2𝜋𝑐/𝛼
INTERPRETING WHY TRIPLE-ADJUSTED PLANCK UNIT OBSERVABLE FUNDAMENTAL PROPERTIES
ARE SIMPLE POWERS OF √𝟐𝝅𝒄/𝜶
MICHAEL LAWRENCE
Maldwyn Theoretical Physics, Cranfield Park, Burstall, Suffolk, IP8 3DT, United Kingdom
mike.lawrence@maldwynphysics.org
This paper follows on from earlier papers which eliminated four important constants of nature, Planck’s constant h, the Gravitational constant 𝐺,
Permeability 𝑢 and Boltsmann’s constant 𝑘𝐵 by showing, after adjusting misaligned S.I. units, that they are only dimensionless ratios. Shown here
is the interpretation of what it means that the relative values in any units of all of the observable set of TAPU parameters can be described simply as
powers of the ratio 𝜗 = √2𝜋𝑐/𝛼 , where c is the speed of light and 𝛼 the fine structure constant.
Keywords: Gravitational constant; Planck constant; Planck units; SI units; Dimensionality; Parameters; Unification.
PACS numbers: 13.40.Em, 06.20.Jr, 06.30.Ka, 12.20.Ds, 12.10.-g
1. Background
parameter formula.
[1,2]
This paper follows on from two previous ones
where
the realignment of SI units across mechanical and
electromagnetic properties enabled the relationship between
the observable set of triple-adjusted Planck unit values of
those properties to be described as powers of only one ratio
𝜗 = √2𝜋𝑐/𝛼 where 𝛼 is the fine structure constant and c
light speed.
The paper considers what it means to have those
properties, here also described as parameters, as ratios of 𝜗.
The starting point is to consider how each of the
parameters could be most simply described in terms of the
product the normal length, velocity and time parameters
1
−1
(LVT) and respectively 𝜗 (mass m) and 𝜗 (charge q)
parameters. This is done to understand better what the
electromagnetic properties represent when considered as
mechanical properties. This analysis is the reversal of the
way that the description of the properties was parameterised
into powers of 𝜗.
2. Comparisons
Tables 1 and 2 show the final tables from the last paper [2]
so that the comparison in Table 3 can be understood here.
The 𝑞𝑒∗ set is the observable set of TAPU parameters which
can be compared with the maximal 𝑞∗ TAPU set as
described in that last paper. Although the 𝑞∗ set is described
as maximal because it is based on all adjusted Planck unit
sizes, it does contain smaller values when 𝜗 takes positive
powers.
Note that the LvT groups used may not correspond to the
normally accepted set due to the inclusion of m or q in every
3. Foundations
It is clear from a comparison of Table 3 columns 1-3 and
4-6 that the same grouping of LvT parameters with mass m
and with the product qc can be described identically. The
two sets have the same powers of 𝜗 which should make the
properties the same. However it is not clear that, for
example, Shear Viscosity (𝜂_ ) and Electric Field(𝜉_ ) are
the same properties, or Acceleration(𝑎_ ) is equivalent to
Magnetic Inductance(𝐵_ ).
The alternative interpretation has the same LvT groups
with mass m and then with charge q only, comparing
columns 1-3 and 7-9 in Table 3. This misaligns the powers of
0
𝜗 and can be shown to be incorrect by considering the 𝜗
−2
constant mass parameter which aligns with 𝜗 conductance
in the electromagnetic parameters. It cannot be the case that
a constant in the mass set matches with a variable in the
electromagnetic set. So the only possible alignment between
mass and charge parameters sets is by comparing m with qc,
rather than m with q.
The accepted definitions of the electromagnetic
properties are therefore shown to be incorrect. They should
all be adjusted by the extra c factor.
One difficulty in considering the alignments across all
possible powers of 𝜗 is that there are gaps where no known
15
−8
properties exist for that power of 𝜗, at powers 𝜗 and 𝜗 .
These gaps are properties that we have not yet realised
actually exist. Doubtless they will be uncovered
experimentally in due course.
Interpreting fundamental properties as powers of √2𝜋𝑐/𝛼
Table 1. Values of the 𝑞𝑒∗ set of parameters
Parameter (𝑋𝑒∗ )
Permeability(𝑢𝑒∗ )
Angular Momentum(ℎ)
Boltzmann (𝑘𝐵 )
Mass(𝑚𝑒∗ )
Magnetic Flux(𝜙𝑒∗ )
Charge-mass(𝑞𝑒∗ 𝑐)
Velocity(𝑣𝑒∗ )
Resistance(𝑅𝑒∗ )
Momentum(𝑚𝑒∗ 𝑣𝑒∗ )
Current(𝜄𝑒∗ )
Action(𝑚𝑒∗ /𝐿𝑒∗ )
Angular Frequency(𝑤𝑒∗ )
Frequency(𝑓𝑒∗ )
Energy(𝐸𝑒∗ )
Temperature (𝐾𝑒∗ )
Potential Difference(∨𝑒∗ )
Acceleration(𝑎𝑒∗ )
Magnetic Inductance(𝐵𝑒∗ )
Magnetic Field (𝐻𝑒∗ )
Force(𝐹𝑒∗ )
Electric Field(𝜉𝑒∗ )
Shear Viscosity (𝜂𝑒∗ )
Mass Density(𝜌𝑒∗ )
Current Density(𝐽𝑒∗ )
Power(𝑃𝑒∗ )
Pressure(𝑝𝑒∗ )
Energy Density(𝜖𝑒∗ )
Charge(𝑞𝑒∗ )
Conductance(𝜍𝑒∗ )
Moment(𝑚𝑒∗ 𝐿𝑒∗ )
Distance(𝐿𝑒∗ )
Inductance(ℒ 𝑒∗ )
Permittivity(𝜀𝑒∗ )
Time(𝑇𝑒∗ )
Area(𝐴𝑒∗ )
Volume(𝑉𝑒∗ )
Capacitance(𝐶𝑒∗ )
𝑞𝑒 DAPU set’s NSI Value
√6.67428 × 10−11
6.62606896 × 10−34
1
1.30781284 × 10−11
1.30781284 × 10−11
1.30781284 × 10−11
2.58128076 × 1011
2.58128076 × 1011
3.37583212 × 1000
6.66301034 × 1022
6.66301034 × 1022
1.31510410 × 1045
1.31510410 × 1045
8.71397049 × 1011
8.71397049 × 1011
1.71991004 × 1034
3.39465292 × 1056
3.39465292 × 1056
4.15521180 × 1061
4.43957068 × 1045
8.76255225 × 1067
8.76255225 × 1067
1.72949881 × 1090
1.72949881 × 1090
1.14597784 × 1057
1.15236684 × 10113
1.15236684 × 10113
5.06652691 × 10−23
3.87404585 × 10−12
2.56696950 × 10−45
1.96279576 × 10−34
1.96279576 × 10−34
1.83707675 × 10−18
7.60396075 × 10−46
3.85256718 × 10−68
7.56180251 × 10−102
2.94580926 × 10−57
4. Interpretation
What, for example, does it mean that the maximal value
of the Triple-Adjusted Planck Unit (TAPU) of observable
5
1
energy is 𝜗 whilst that of mass is 𝜗 ?
This tells us that regardless of the relative size of the
electronic charge in the 𝑞𝑒∗ set to its maximum value in the
𝑞∗ set, the relationship will always be the same, only the
actual measurable value in whatever units are used will
differ, dependent on the value of 𝛼.
It is also possible to infer that the root of the value of the
fine structure constant must be motional, because it is part of
the ratio 𝜗 = √2𝜋𝑐/𝛼. This would be more obvious if the
inverse 𝑏 = 1/𝛼 were used instead, because then the ratio
would be 𝜗 = √2𝜋𝑏𝑐 and 2𝜋𝑏 would simply be a
dimensionless ratio adjusting velocity c.
Beyond these two points, it is difficult to make much
more progress without an underlying theory of the structure
of matter. But the hints are that what we observe at the most
fundamental level is based on motion.
Assuming this to be the case, it might be possible to use a
NSI Units
𝑁𝐴−2
𝐽𝑠
̌ −1
𝐽𝐾
𝑘𝑔
̃
𝑊
𝐶̃ 𝗆𝑠 −1
𝗆𝑠 −1
̃
Ω
𝑘𝑔𝗆𝑠 −1
𝐴̃
𝑘𝑔𝗆−1
𝐻𝑧
𝐻𝑧
𝐽
̌
𝐾
𝑉̃
𝗆𝑠 −2
𝐴̃𝗆−1
𝐴̃𝗆−1
𝑁
𝑉̃ 𝗆−1
𝑃𝑎 𝑠
𝑘𝑔𝗆−3
𝐴̃𝗆−2
𝐽𝑠 −1
𝑁𝗆−2
𝐽𝗆−3
𝐶̃
̃ −1
Ω
𝑘𝑔𝗆
𝗆
̃
𝐻
𝐹 # 𝗆−1
𝑠
𝗆2
𝗆3
𝐹#
DAPU equivalent
𝑛𝑜𝑛𝑒
𝑘𝑔𝗆2 𝑠 −1
𝑛𝑜𝑛𝑒
𝑘𝑔
√𝑘𝑔𝗆𝗆𝑠 −1
√𝑘𝑔𝗆𝗆𝑠 −1
𝗆𝑠 −1
𝗆𝑠 −1
𝑘𝑔𝗆𝑠 −1
√𝑘𝑔𝗆𝑠 −1
𝑘𝑔𝗆−1
𝑠 −1
𝑠 −1
𝑘𝑔𝗆2 𝑠 −2
̌
𝐾
√𝑘𝑔𝗆𝗆𝑠 −2
𝗆𝑠 −2
𝗆𝑠 −2
𝗆𝑠 −2
𝑘𝑔𝗆𝑠 −2
√𝑘𝑔𝗆𝗆−2 𝑠 −2
𝑘𝑔𝗆−1 𝑠 −1
𝑘𝑔𝗆−3
√𝑘𝑔𝗆𝗆−2 𝑠 −1
𝑘𝑔𝗆2 𝑠 −3
𝑘𝑔𝗆−1 𝑠 −2
𝑘𝑔𝗆−1 𝑠 −2
√𝑘𝑔𝗆
𝗆−1 𝑠
𝑘𝑔𝗆
𝗆
√𝑘𝑔𝗆𝗆−1 𝑠 −1
𝗆−2 𝑠 2
𝑠
𝗆2
𝗆3
𝗆−1 𝑠 2
As Constants
√𝐺
ℎ
𝑛𝑜𝑛𝑒
𝑑 −1 √ℎ𝑐
𝑑 −1 √ℎ𝑐
𝑑 −1 √ℎ𝑐
𝑑 −2 𝑐
𝑑 −2 𝑐
𝑑 −3 𝑐√ℎ𝑐
𝑑 −4 𝑐 2
𝑑 −4 𝑐 2
𝑑 −5 𝑐 2 √𝑐/ℎ
𝑑 −5 𝑐 2 √𝑐/ℎ
𝑑 −5 𝑐 2 √ℎ𝑐
𝑑 −5 𝑐 2 √ℎ𝑐
𝑑 −6 𝑐 3
𝑑 −7 𝑐 3 √𝑐/ℎ
𝑑 −7 𝑐 3 √𝑐/ℎ
𝑑 −7 𝑐 3 √𝑐/ℎ𝐺
𝑑 −8 𝑐 4
𝑑 −9 𝑐 4 √𝑐/ℎ
𝑑 −9 𝑐 4 √𝑐/ℎ
𝑑 −10 𝑐 5 /ℎ
𝑑 −10 𝑐 5 /ℎ
𝑑 −10 𝑐 5
𝑑 −14 𝑐 7 /ℎ
𝑑 −14 𝑐 7 /ℎ
𝑑√ℎ/𝑐
𝑑 2 𝑐 −1
𝑑 2 ℎ/𝑐
𝑑 3 𝑐 −1 √ℎ/𝑐
𝑑 3 𝑐 −1 √ℎ/𝑐
𝑑 4 𝑐 −2 /√𝐺
𝑑 5 𝑐 −2 √ℎ/𝑐
𝑑 6 ℎ/𝑐 3
𝑑 9 ℎ√ℎ/𝑐/𝑐 4
𝑑 7 𝑐 −3 √ℎ/𝑐
metaphor based on length 𝐿 to infer a similar relationship
for 𝜗. We call 𝐿 a length, 𝐿2 an area and 𝐿3 volume, each
increase representing a different dimension based on length.
1
2
It may be possible to consider 𝜗 as mass, 𝜗 as 𝑚𝑎𝑠𝑠2 =
velocity etc where each different power is a different mass
dimension and a different property. The actual value of the
property along that dimension is what is observed.
This would suggest that there must be at least 16 + 9 + 1
= 26 dimensions existing to accommodate all the properties
that we currently observe, even if we do not have names for
either the mechanical or electromagnetic properties at some
values of powers of 𝜗.
Note that, other than for m and q parameters, the
formulae used to provide the appropriate powers of 𝜗 for
each parameter do not use the target parameter in the
formula, so velocity v does not have v in its formula, for
example.
5. Conclusions
This paper presents new ways of understanding the
relationships between parameters. It strongly infers that the
Interpreting fundamental properties as powers of √2𝜋𝑐/𝛼
underlying relationships and values of observable
parameters are based on motion. This in turn suggests that
there is structure underlying our current interpretation of the
building blocks of matter and that hypotheses based on
pre-quark frameworks should be given greater consideration
by both theoretical and experimental practitioners.
Table 2. Values of parameters in BNSI, ratios of c and d and powers of 𝜗
Parameter (𝑋_ )
Permeability(𝑢_ )
Angular Momentum(ℎ)
Boltzmann (𝑘𝐵 )
Mass(𝑚_ )
Magnetic Flux(𝜙_ )
Charge-mass(𝑞_ 𝑐)
Velocity(𝑣_ )
Resistance(𝑅_ )
Momentum(𝑚_ 𝑣_ )
Current(𝜄_ )
Action(𝑚_ /𝐿_ )
Angular Frequency(𝑤_ )
Frequency(𝑓_ )
Energy(𝐸_ )
Temperature (𝐾_ )
Potential Difference(∨_)
Acceleration(𝑎_ )
Magnetic Inductance(𝐵_ )
Magnetic Field (𝐻_ )
Force(𝐹_ )
Electric Field(𝜉_ )
Shear Viscosity (𝜂_ )
Mass Density(𝜌_ )
Current Density(𝐽_ )
Power(𝑃_ )
Pressure(𝑝_ )
Energy Density(𝜖_ )
Charge(𝑞_ )
Conductance(𝜍_ )
Moment(𝑚_ 𝐿_)
Distance(𝐿_ )
Inductance(ℒ _ )
Permittivity(𝜀_ )
Time(𝑇_ )
Area(𝐴_ )
Volume(𝑉_ )
Capacitance(𝐶_ )
𝑋∗ TAPU set’s BNSI
Value
√6.67428 × 10−11
1
1
1.73145158 × 1004
1.73145158 × 1004
1.73145158 × 1004
2.99792458 × 1008
2.99792458 × 1008
5.19076126 × 1012
8.98755179 × 1016
8.98755179 × 1016
1.55615108 × 1021
1.55615108 × 1021
1.55615108 × 1021
1.55615108 × 1021
2.69440024 × 1025
4.66522356 × 1029
4.66522356 × 1029
5.71044889 × 1034
8.07760871 × 1033
1.39859884 × 1038
1.39859884 × 1038
2.42160617 × 1042
2.42160617 × 1042
2.42160617 × 1042
2.17643109 × 1059
2.17643109 × 1059
5.77550080 × 10−05
3.33564095 × 10−09
3.33564095 × 10−09
1.92649970 × 10−13
1.92649970 × 10−13
1.36193501 × 10−12
6.42611129 × 10−22
3.71140109 × 10−26
7.15001309 × 10−39
2.14352000 × 10−30
𝑋𝑒∗ TAPU set’s BNSI
Value
√6.67428 × 10−11
1
1
5.08063063 × 1005
5.08063063 × 1005
5.08063063 × 1005
2.58128076 × 1011
2.58128076 × 1011
1.31145341 × 1017
6.66301034 × 1022
6.66301034 × 1022
3.38522944 × 1028
3.38522944 × 1028
3.38522944 × 1028
3.38522944 × 1028
1.71991004 × 1034
8.73822761 × 1039
8.73822761 × 1039
1.06959938 × 1045
4.43957068 × 1045
2.25558188 × 1051
2.25558188 × 1051
1.14597784 × 1057
1.14597784 × 1057
1.14597784 × 1057
7.63566217 × 1079
7.63566217 × 1079
1.96825960 × 10−06
3.87404585 × 10−12
3.87404585 × 10−12
7.62512793 × 10−18
7.62512793 × 10−18
1.83707675 × 10−18
2.95400952 × 10−29
5.81425760 × 10−35
4.43344580 × 10−52
1.14439683 × 10−40
𝑋∗ as
Constants
√𝐺
𝑛𝑜𝑛𝑒
𝑛𝑜𝑛𝑒
√𝑐
√𝑐
√𝑐
𝑐
𝑐
𝑐 √𝑐
𝑐2
𝑐2
𝑐 2 √𝑐
𝑐 2 √𝑐
𝑐 2 √𝑐
𝑐 2 √𝑐
𝑐3
𝑐 3 √𝑐
𝑐 3 √𝑐
𝑐 3 √𝑐/𝐺
𝑐4
𝑐 4 √𝑐
𝑐 4 √𝑐
𝑐5
𝑐5
𝑐5
𝑐7
𝑐7
1/√𝑐
𝑐 −1
𝑐 −1
𝑐 −1 /√𝑐
𝑐 −1 /√𝑐
𝑐 −2 /√𝐺
𝑐 −2 /√𝑐
𝑐 −3
𝑐 −4 /√𝑐
𝑐 −3 /√𝑐
𝑋𝑒∗ as
Constants
√𝐺
𝑛𝑜𝑛𝑒
𝑛𝑜𝑛𝑒
𝑑 −1 √𝑐
𝑑 −1 √𝑐
𝑑 −1 √𝑐
𝑑 −2 𝑐
𝑑 −2 𝑐
𝑑 −3 𝑐√𝑐
𝑑 −4 𝑐 2
𝑑 −4 𝑐 2
𝑑 −5 𝑐 2 √𝑐
𝑑 −5 𝑐 2 √𝑐
𝑑 −5 𝑐 2 √𝑐
𝑑 −5 𝑐 2 √𝑐
𝑑 −6 𝑐 3
𝑑 −7 𝑐 3 √𝑐
𝑑 −7 𝑐 3 √𝑐
𝑑 −7 𝑐 3 √𝑐/𝐺
𝑑 −8 𝑐 4
𝑑 −9 𝑐 4 √𝑐
𝑑 −9 𝑐 4 √𝑐
𝑑 −10 𝑐 5
𝑑 −10 𝑐 5
𝑑 −10 𝑐 5
𝑑 −14 𝑐 7
𝑑 −14 𝑐 7
𝑑/√𝑐
𝑑 2 𝑐 −1
𝑑 2 𝑐 −1
𝑑 3 𝑐 −1 /√𝑐
𝑑 3 𝑐 −1 /√𝑐
𝑑 4 𝑐 −2 /√𝐺
𝑑 5 𝑐 −2 /√𝑐
𝑑 6 𝑐 −3
𝑑 9 𝑐 −4 /√𝑐
𝑑 7 𝑐 −3 /√𝑐
BNSI Units 𝑋𝑒∗ set as
(h-adjusted) powers of 𝜗
0
𝑛𝑜𝑛𝑒
𝜗
0
𝑛𝑜𝑛𝑒
𝜗
0
𝑛𝑜𝑛𝑒
𝜗
1
𝑘𝑔
𝜗
1
̃
𝑊
𝜗
1
−1
𝐶̃ 𝗆𝑠
𝜗
𝗆𝑠 −1
̃
Ω
𝑘𝑔𝗆𝑠 −1
𝐴̃
𝑘𝑔𝗆−1
𝐻𝑧
𝐻𝑧
𝐽
̌
𝐾
𝑉̃
𝗆𝑠 −2
𝐴̃𝗆−1
𝐴̃𝗆−1
𝑁
𝑉̃ 𝗆−1
𝑃𝑎 𝑠
𝑘𝑔𝗆−3
𝐴̃𝗆−2
𝐽𝑠 −1
𝑁𝗆−2
𝐽𝗆−3
𝐶̃
̃ −1
Ω
𝑘𝑔𝗆
𝗆
̃
𝐻
𝐹 # 𝗆−1
𝑠
𝗆2
𝗆3
𝐹#
2
𝜗
2
𝜗
3
𝜗
4
𝜗
4
𝜗
5
𝜗
5
𝜗
5
𝜗
5
𝜗
6
𝜗
7
𝜗
7
𝜗
7
𝜗 /√𝐺
8
𝜗
9
𝜗
9
𝜗
10
𝜗
10
𝜗
10
𝜗
14
𝜗
14
𝜗
−1
𝜗
−2
𝜗
−2
𝜗
−3
𝜗
−3
𝜗
−4
𝜗 /√𝐺
−5
𝜗
−6
𝜗
−9
𝜗
−7
𝜗
Interpreting fundamental properties as powers of √2𝜋𝑐/𝛼
Table 3. Comparison of the parameterisation of properties at each power of 𝜗
1
2
Mass Parameter
𝑋𝑒∗
(Accepted)
mass
set as
powers
of 𝜗
0 Angular Momentum(ℎ)
1 Mass(𝑚_ )
2 Velocity(𝑣_ )
3 Momentum(𝑚_ 𝑣_ )
4 Action(𝑚_ /𝐿_ )
5 Energy(𝐸_ )
6 7 Acceleration(𝑎_ )
7 Acceleration(𝑎_ )
8 Force(𝐹_ )
9 Shear Viscosity (𝜂_ )
10 Mass Density(𝜌_ )
11 Luminance
12 Kinetic viscosity
13 Intensity
14 Pressure(𝑝_ )
15 16 Radiance
−1 −2 Moment(𝑚_ 𝐿_)
−3 Distance(𝐿_ )
−4 −5
−6
−7
−8
−9
Time(𝑇_ )
Area(𝐴_ )
Volume(𝑉_ )
3
4
Mass
𝑋𝑒∗ qc
Formula set as
powers
of 𝜗
𝑚𝑣𝐿
𝑚
𝑚𝑇𝐿−2
𝑚𝑣
𝑚/𝐿
𝑚𝑣2
𝑚𝑣/𝐿
𝑚𝐿−2
𝑚𝐿−2
𝑚𝑣 2 /𝐿
𝑚𝑣𝐿−2
𝑚𝐿−3
𝑚𝑇−2
𝑚𝐿−3
𝑚𝑣𝑇−2
3
𝑚𝑣2 /𝐿
2
2
𝑚𝑣 /𝑇
−3
𝑚𝑇
𝑚/𝑣
𝑚𝐿
2
𝑚/𝑣
𝑚𝑇
𝑚𝐿2
𝑚𝑇/𝑣
𝑚𝑇𝐿
𝑚𝐿3
𝑚𝑇𝐿/𝑣
5
Charge Parameter
(Proposed)
6
Charge (qc)
Formula
0
1
2
3
4
5
6
7
7
8
9
10
11
12
13
14
15
16
−1
−2
−3
−4
Magnetic moment x2/c
Magnetic Flux(𝜙_ )
Resistance(𝑅_ )
Current(𝜄_ )
Energy(𝐸_ )
Potential Difference(∨_)
Magnetic Inductance(𝐵_ )
Magnetic Field (𝐻_ )
Force(𝐹_ )
Electric Field(𝜉_ )
Current Density(𝐽_ )
-
−5
−6
−7
−8
−9
Time(𝑇_ )
Area(𝐴_ )
Capacitance(𝐶_ )
Volume(𝑉_ )
𝑞𝑐𝑣𝐿
𝑞𝑐
𝑞𝑐𝑇𝐿−2
𝑞𝑐𝑣
𝑞𝑐/𝐿
𝑞𝑐𝑣2
𝑞𝑐𝑣/𝐿
𝑞𝑐𝐿−2
𝑞𝑐𝐿−2 /√𝐺
𝑞𝑐𝑣 2 /𝐿
𝑞𝑐𝑣𝐿−2
𝑞𝑐𝐿−3
𝑞𝑐𝑇−2
𝑞𝑐𝐿−3
𝑞𝑐𝑣𝑇−2
3
𝑞𝑐𝑣2 /𝐿
2
2
𝑞𝑐𝑣 /𝑇
−3
𝑞𝑐𝑇
𝑞𝑐/𝑣
𝑞𝑐𝐿
2
𝑞𝑐/𝑣
𝑞𝑐𝑇 /√𝐺
𝑞𝑐𝐿2
𝑞𝑐𝑇/𝑣
𝑞𝑐𝑇𝐿
𝑞𝑐𝐿3
𝑞𝑐𝑇𝐿/𝑣
Charge mass(𝑞𝑐_ )
Conductance(𝜍_ )
Inductance(ℒ _ )
Permittivity(𝜀_ )
7
8
Charge Parameter
𝑋𝑒∗ q
(Implied by grouping
set as
powers without c, but incorrect)
of 𝜗
−2
−1
0
1
2
3
4
5
5
6
7
8
9
10
11
12
13
14
−3
−4
−5
−6
−7
−8
−9
−10
−11
Magnetic moment x2
Charge
Resistance(𝑅_ )
Current(𝜄_ )
Energy(𝐸_ )
Potential Difference(∨_)
Magnetic Inductance(𝐵_ )
Magnetic Field (𝐻_ )
Force(𝐹_ )
Electric Field(𝜉_ )
Current Density(𝐽_ )
Conductance(𝜍_ )
Inductance(ℒ _ )
Permittivity(𝜀_ )
Time(𝑇_ )
Area(𝐴_ )
Capacitance(𝐶_ )
Volume(𝑉_ )
9
Charge (q)
Formula
𝑞𝑣𝐿
𝑞
𝑞𝑇𝐿−2
𝑞𝑣
𝑞/𝐿
𝑞𝑣2
𝑞𝑣/𝐿
𝑞𝐿−2
𝑞𝐿−2 /√𝐺
𝑞𝑣 2 /𝐿
𝑞𝑣𝐿−2
𝑞𝐿−3
𝑞𝑇−2
𝑞𝐿−3
𝑞𝑣𝑇−2
3
𝑞𝑣2 /𝐿
2
2
𝑞𝑣 /𝑇
−3
𝑞𝑇
𝑞/𝑣
𝑞𝐿
2
𝑞/𝑣
𝑞𝑇/√𝐺
𝑞𝐿2
𝑞𝑇/𝑣
𝑞𝑇𝐿
𝑞𝐿3
𝑞𝑇𝐿/𝑣
Interpreting fundamental properties as powers of √2𝜋𝑐/𝛼
Appendix A. References
1. Lawrence, M. (2013) “Eliminating the Gravitational constant G
and improving SI units, using two new Planck unit frameworks
with all parameters as ratios of only h, c and √(α/2π)” in R.L.
Amoroso, L.H. Kauffman & P. Rowlands (eds.) The Physics of
Reality: Space, Time, Matter, Cosmos, Singapore: World Scientific
Publishers.
2. Lawrence, M (2013) “Eliminating Planck’s constant h and
finishing the improvement of S.I. units, using two new Planck unit
frameworks with all parameters as powers of only √𝑐 or
√2𝜋𝑐/𝛼 ” The General Science Journal ISSN: 1916-5382 on
http://gsjournal.net/Science-Journals/Essays/View/4766